Research ArticleA Numerical Modelling Approach forTime-Dependent Deformation of Hot Forming Tools underthe Creep-Fatigue Regime

B Reggiani L Donati and L Tomesani

DIN Department University of Bologna Viale Risorgimento 2 40136 Bologna Italy

Correspondence should be addressed to B Reggiani barbarareggiani4uniboit

Received 31 January 2016 Accepted 10 July 2016

Academic Editor Jun Liu

Copyright copy 2016 B Reggiani et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The present study was aimed at predicting the time-dependent deformation of tools used in hot forming applications subjected tothe creep-fatigue regime An excessive accumulated plastic deformation is configured as one of the three main causes of prematurefailure of tools in these critical applications and it is accumulated cycle by cycle without evident marks leading to noncompliantproducts With the aim of predicting this accumulated deformation a novel procedure was developed presented and applied tothe extrusion process as an example A time-hardening primary creep law was used and novel regression equations for the lawrsquoscoefficients were developed to account not only for the induced stress-temperature state but also for the dwell-time value which isdetermined by the selected set of process parameters and die designThe procedure was validated against experimental data both ona small-scale extrusion die at different stress temperature load states and for different geometries and on an industrial extrusiondie which was discarded due to the excessive plastic deformation after 64 cycles A numerical-experimental good agreement wasachieved

1 Introduction

Forming processes like die-casting extrusion and forging areeconomical ways of producing large quantities of complextight tolerance parts in lightweight alloys such as aluminumand magnesium However these processes involve severethermomechanical cyclic loads and high operating temper-atures in a mixed creep and fatigue environment leading tocritical working conditions for molds and dies In particularthe fatigue phenomenon appears since each process strokerepresents a single working cycle while creep arises andcan become dominant with increasing temperatures andexposure times In addition the interaction of these yieldingphenomena that is phenomena that progressively increasethe level of accumulated plastic deformation in the com-ponent can be more detrimental to die life than the singleeffect [1 2] This translates into very strict demands on toolmaterials in terms of resistance against cyclic thermal andmechanical stresses creep and wear Hot-work tool steelsrepresent an optimal solution for manufacturing dies dueto the high strength also in hot conditions good ductility

and also toughness [3] However cracking and failures forhigh-temperature forming tools are frequently documentedin literature and in industrial practice For example adetailed analysis carried out on hot forging tools showeda strict correlation of failure modes with a various kindof influencing variables such as die material die design anddie manufacturing and forging operations [4] Kosec et aldivided the failure of dies for casting of aluminum into fourmain groups big cracks heat checking cracking in cornersand sharp edges and abrupt transitions and cracking due towear and erosion [5] Arif and Sheikh presented an accurateinvestigation on the die failure mechanisms in hot aluminumextrusion concluding that on an overall basis all types of diesconsidered together the failure modes were fracture (46)wear (26) detection (19) mixed mode (4) miscella-neous (2) and mandrel-related (3) [6ndash8] Fracture andwear can be kept in some way under control by means ofproper initial design and by reliable die heat treatment andorcoating [3] In addition both phenomena are marked byevident material discontinuities in terms of separation forfracture and displacement for wear Conversely an excessive

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2016 Article ID 1276596 13 pageshttpdxdoiorg10115520161276596

2 Advances in Materials Science and Engineering

inelastic deformation is a time-dependent progressive andirreversible phenomenon accumulated cycle by cycle that canlead to the going-out of the diersquos geometry and thus to its finaldiscard even without the appearance of cracks or other mate-rial discontinuities [1 9] A robust and reliable knowledgeof these pieces of information is therefore recommended atthe die design stage This would indeed support engineers inpredicting the maximum number of workable componentsin order to remain within the required tolerances and inestimating die durability

At present in industrial practice die design is still mainlybased on experience and a set of common shared rules [10 11]while numerical simulations are seldomused However thereare several disadvantages of this practice

In-service experimental monitoring of time-dependentdeformation and then of stresses requires complex setupsdue to the involved high temperatures and difficult toolsrsquoaccessibility Secondly it merely allows for an ex-post evalua-tion since when noncompliant products are detected expen-sive tools have been already manufactured and need to bediscarded [12]

Conversely numerical simulations have been alreadywidely proved to be adequate tools to obtain reliable informa-tion on the level of stress and straindeformation in the diesthus serving as ldquoa priorirdquo estimations for die design optimiza-tion and lifetime improvementsThis has been demonstratedas example in [13 14] for aluminum extrusion dies in [15]for die-casting dies and in [16] for the H11 tool steel widelyused for forming tools Indeed the level of the achieveddeformation is the first necessary input for evaluating thedamage and the related lifetime models [16 17] Nowadaysmanufacturing processes can be reliably analyzed in terms ofplasticity conditions (strain strain rates and temperatures)but also pressure maps and damage distributions bymeans offinite element (FE) simulations Moreover dedicated struc-tural codes allow more specific thermostructural analyses ofmolds and dies for the prediction of the stress and strain levelsand distributions by offering a greater flexibility in terms oftool-material behavior models [13] In this context the mostcomprehensive elastoviscoplasticmodel based on the internalstate variables has been developed by Chaboche within thecontinuum damage mechanism approach [18 19] Despite itsclaimed ability to correctly describemost of the effects experi-mentally observed under creep-fatigue regime the Chabochedeformation model is only partially available within themain commercial FE codes In addition no values of thecoefficients are usually reported in technical papers probablydue to the time-consuming experimental calibration phaseand to the best of authorsrsquo knowledge few validations ofsuch models have been presented in literature against casesof industrial interest only on special tool steels Indeed thewide set of phenomena considered by the Chaboche modelproduces consequently a very wide number of parameters tobe experimentally identified thus making the model almostinapplicable or extremely critical to be properly calibratedand implemented in FEM

Accounting for all these restrictions the authors pro-posed a simplified numerical modelling approach for pre-dicting the time-dependent deformation of hot forming tools

Specimen

Figure 1 Specimen in the Gleeble simulator

operating in the creep-fatigue regime with the main focuson time-dependent deformation of specimens rather thandamage (material discontinuities in form of cracks pores orvoids) mechanisms The starting point was the application ofa simple creep law for cyclic (fatigue) and cyclic with dwell-time (creep-fatigue) loads Novel regression equations weredeveloped for the creep coefficients to correlate with stressstate temperature and exposure time

With the aim of explaining in detail the procedure it isapplied to the specific case of extrusion dies The considereddie material is the H11 hot-work tool steel (X38CrMoV5-1)one of the most commonly used for forming applications [3]The procedure was tested against an industrial die discardeddue to an achieved excessive permanent deformation after64 extruded billets Experimental mandrel deflection wascompared to numerical prediction

2 Materials and Method

During metal forming (extrusion processing included) mul-tiple billets are sequentially processed placing the die in theregime of fatigue each billet representing a loading cycleAccounting for the billet-die contact time during a single ramstroke and for the high temperature developed during theprocess also the creep mechanism plays a significant role Sothat the die deformation mechanism is due to creep-fatigueinteraction [2 20]

An innovative physical experiment was proposed by theauthors reproducing the thermomechanical conditions of anextrusion die [21] the specimens resembled the mandrelof a porthole die on a small scale thus accounting forrealistic stress-strain distribution and surface conditions andwere made of H11 (X38CrMoV5-1) hot-work tool steel Theexperimental tests were performed on a Gleeble simulator byheating the specimen using Joulersquos effect and by applying afull compressive load to the specimen up to 61 hours or tillspecimen failure (Figure 1)

The experimental trials included four levels of temper-ature namely 380∘C 490∘C 540∘C and 580∘C and threelevels of average stresses of 400 600 and 800MPa in thebridges of the specimen A number of porthole dies were pre-liminary simulated to properly calibrate the load level inorder to generate in the specimenrsquos bridges the same averagestress as in the diesrsquo ones (Figure 2(h)) Also the testingtemperature was that of the bridges andmandrel as measuredby 15 thermocouples placed in the specimen during theexperiments [21]Three types of loadwere applied pure creep

Advances in Materials Science and Engineering 3

Load

Time

Creep

2kN

600

sec

1200

sec

T∘

Fatigue

Time

600

sec

1200

sec

Load

2kN

T∘

10 sec

9 sec (unload)

Creep-fatigue

Time

600

sec

1200

sec

Load

2kN

T∘

10 sec

3min

9 sec (unload)

2500

5000

7500

1000

012

500

1500

017

500

2000

022

500

2500

00

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

2500

5000

75000

1250

015

000

1750

020

000

2250

025

000

1000

0

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

2500

5000

75000

1250

015

000

1750

020

000

2250

025

000

1000

0

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

u displacement (mm)

u

2500

5000

7500

1000

012

500

1500

017

500

2000

022

500

2500

00

Time (sec)

Reference region for the definitionof the average stress 120590

(a) (b) (c)

(d) (e) (f)

(g) (h)Figure 2 (a b c) Waveform of the applied load and (d e f) output peak displacement over the testing time for the three loading conditionsat 600MPa and 490∘C (data not purged by the press deformation) (g) Schematic explanation of the results (h) Reference region for thedefinition of the average stress in the small-scale die specimen

(with the load held at a fixed value) fatigue (cyclic load)and creep-fatigue (cyclic load with 3 minutes of dwell time)(Figures 2(a) 2(b) and 2(c)) Creep-fatigue represents thetesting condition with a prescribed dwell or exposure timecreep and fatigue tests correspond to two extreme conditionsof simulating respectively an infinite and a zero dwell-timeIn case of extrusion the dwell time is a function of the billetlength ram speed and extrusion ratio and it increases withthe raising of the billet length and extrusion ratio and withthe decreasing of the ram speed As main output of the testthe displacement of the specimensrsquo mandrel (u) as caused bythe specific loading conditions (load type temperature andstress level) was recorded over the testing time (Figure 2(g))Specifically the pure creep load generated a continuous curve(Figure 2(d)) while the pure fatigue and the creep-fatigueloads generated a cyclic curve with the loading-unloadingdisplacementrsquos path corresponding to each cycle (Figures 2(e)and 2(f))

As observed for standard tests for the same steel [22] acomparable pattern of the mandrel displacement-time curvewas found for all the experimental conditions reproducingthe stages of softening typical of the strain evolution in astandard creep test In particular the specific ranges of inves-tigated temperatures and stresses pointed out a primary phasewithout saturation typical of the secondary creep Thus anexponential type law was chosen to predict the displacementof the mandrel over time accounting for the stress time andtemperature behavior dependency of thematerial response inthis region of deformation that is the time-hardening creeplaw [23] consider the following

120576 = 119862

1sdot 120590

1198622sdot 119879

1198623 (1)

in which 120576 is the strain rate 120590 and 119879 are the stress andtemperature levels and119862

11198622 and119862

3are material constants

4 Advances in Materials Science and Engineering

Table 1 The computed values of time-hardening law coefficients

119899 119898 119886

0

119862

1

119862

2

119862

3

119879

∘

= 450 350493 00675 10858E minus 12 7329E minus 14 35049 minus09325119879

∘

= 500 185103 0085 16965E minus 07 1442E minus 08 18510 minus09150119879

∘

= 550 14848 010625 4198E minus 06 4460E minus 07 14848 minus08938

However other primary creep equations could have beenselected also adding the contribution of the secondary phasein case of specimenrsquos softening saturation

For a better estimation initial values of the coefficientsfor (1) and the H11 tool steel were extracted from datataken in literature for pure creep tests at different stress andtemperature levels [24 25] according to the following proce-dure

(1) Time-hardening law expressed in terms of creepstrain

120576 = 119886

0120590

119899

119905

119898

(2)

where 120576 is the strain 120590 is the stress level 119905 is the timeof the load application and 119886

0 119899 and 119898 are material

constants(2) Passage to the logarithmic form

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905)

= 119886

1+ 119899 ln (120590) + 119898 ln (119905)

(3)

(3) For each level of temperature 119899 computed by averag-ing values for fixed times (ln(119905) constant) and variablestresses

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905) = 119886

2+ 119899 ln (120590) (4)

(4) For each level of temperature 119898 computed by aver-aging values for fixed stresses (ln(120590) constant) andvariable times

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905) = 119886

3+ 119898 ln (119905) (5)

(5) For each level of temperature 1198860computed by enter-

ing 119899 and119898 in (1) for fixed times and by averaging thevalues

ln (120576) minus 119899 ln (120590) minus 119898 ln (119905) = ln (1198860) (6)

(6) Computation of the coefficients in (1)

120576 =

119889120576

119889119905

= 119886

0sdot 119898 sdot 120590

119899

sdot 119905

119898minus1

= 119862

1sdot 120590

1198622sdot 119879

1198623

119862

1= 119886

0sdot 119898 119862

2= 119899 119862

3= 119898 minus 1

(7)

The resulting values of the coefficients are reported in Table 1based on the experimental data in [24 25]

By means of FE analyses the values reported in Table 1were optimized for the set of experimental tests performedon the small-scale mandrel specimens [21] The temperaturedistribution in the specimen was computed by performing athermal-electrical simulation [26]While the time-hardeninglaw in (1) is usually applied in case of creep results for whichcontinuous curves are generated (Figures 2(a) and 2(d)) itsapplication for the fatigue (Figures 2(b) and 2(e)) and creep-fatigue (Figures 2(c) and 2(f)) tests is a nonconventional usesince loading-unloading ramps of the cycles are not mod-elled So for these tests a continuous curve was extrapolatedby connecting the peak values of the displacement of eachcycle and applying the same approach as for the creep tests(Figure 3) In Table 2 the values of the optimized coefficients119862

1 1198622 and 119862

3are reported

Figure 4 graphically shows the numerical correlationsexpressed in Table 2

It emerges that 1198621is a function of the temperature level

and of the dwell time (type of applied load) while it isindependent of the stress level The coefficient 119862

3can be

considered to be dependent only on the selected temperaturelevel while 119862

2 also if not so marked is a function of all the

involved parameters that is the stress and temperature levelsand the dwell time indeed even very small variations of thisparameter were found to have a great influence on the outputresults in terms of predicted numerical displacement of thespecimen Novel empirical regressions were formulated inorder to correlate each coefficient of the time-hardening creeplaw to the stress-temperature-load state as follows

119862

1= (119862

1min sdot [(119862

1max119862

1minminus 1) sdot (

119879

119879max)

(1198701119879)

]) sdot 119876 sdot 119905

119877

dwell

119862

1min = 1198621 (119879mincreep-fatigue) 1198621max = 1198621 (119879maxcreep-fatigue) 1198701 119876 119877 = material costants

119862

2= (119864 sdot 120590

119865

sdot 119879

119866

) sdot 119873 sdot 119905

119880

dwell 119864 119865 119866119873119880 = material costants

119862

3= minus(

1003816

1003816

1003816

1003816

119862

3min1003816

1003816

1003816

1003816

sdot [1 + (

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119862

3max119862

3min

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

minus 1) sdot (

119879

119879max)

(1198703119879)

])

119862

3min = 1198623 (119879mincreep-fatigue) 1198623max = 1198623 (119879maxcreep-fatigue) 1198703 = material costants

(8)

Advances in Materials Science and Engineering 5

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00D

ispla

cem

ent (

mm

)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(a)

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(b)

Figure 3 (a) Original rough experimental cyclic creep-fatigue curve (loading-unloading path of each cycle is reported) and (b) theextrapolated continuous curve dots are example of the extracting points

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400

Creep-fatigue dwell time)min(3Creep (infinite dwell time)Fatigue (0 dwell time)

600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

00051015202530354045

C2

00051015202530354045

C2

00051015202530354045

C2

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

0 200 400 600 800Temperature (

∘C)

Figure 4 Coefficients of (1) (on y-axis) reported as function of the temperature (on x-axis) for each loading condition (in column) and stresslevel (different type of curves)

6 Advances in Materials Science and Engineering

Table 2 Optimized values of the coefficients in (1) on the basis ofexperimental data for creep fatigue and creep-fatigue conditions

(a)

Creep380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 700E minus 14 144E minus 08 446E minus 07 400E minus 06600 [MPa] 733E minus 14 144E minus 08 446E minus 07800 [MPa] 733E minus 14 144E minus 08119862

2

400 [MPa] 397 192 135 106600 [MPa] 370 182 140800 [MPa] 357 182119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(b)

Fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 600E minus 14 133E minus 8 400E minus 7 300E minus 06600 [MPa] 600E minus 14 133E minus 8 400E minus 7800 [MPa] 600E minus 14 133E minus 8119862

2

400 [MPa] 396 190 134 099600 [MPa] 374 177 127800 [MPa] 360 174119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(c)

Creep-fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 640E minus 14 142E minus 8 420E minus 7 380E minus 06600 [MPa] 640E minus 14 142E minus 8 420E minus 7800 [MPa] 640E minus 14 142E minus 8119862

2

400 [MPa] 397 192 135 105600 [MPa] 372 184 130800 [MPa] 362 183119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

In (8) 119905dwell is the time in which during a creep-fatigue testthe imposed load is kept constant and as previously observedfor the specific case of extrusion dies it is correlated to the

Table 3 Material constants used in (8) for the H11 tool steel

119862

1

119862

2

119862

3

119862

1max 38E minus 06 119864 130E + 08 119862

3max minus087119862

1min 64E minus 06 119865 minus011245 119862

3min minus09325119870

1

16650 119866 minus28021 119870

3

3000119876 10421 119873 100251119877 00124698 119880 0002025

billet length ram speed and extrusion ratio Instead 1198621max

119862

1min and1198623max1198623min represent the values of the coefficientsfound for the maximum and minimum temperatures in theselected range of experimental investigation in case of creep-fatigue load for the first and the third coefficients Parameters119870

1119876119877119864 119865119866119873119880 and119870

3arematerial constants For the

presented specific case ofH11 tool steel the coefficient and thematerial constants in (8) are summarized in Table 3

The selected equations among different ones tested werethose best fitting the set of experimental data A total of36 experimental tests were initially performed to verify thesensibility of the small-scale die specimen to the operationalconditions (4 levels of stress and temperature and threeloading schemes) and the results were used to calibrate themodel However the selected equations form allows reducingthe number for a perfect matching to 27 (three levels of stresstemperature and loading type) that for a rougher estimationcan be additionally reduced to 12 (two levels of stress temper-ature and three loading types)The contribution of the dwell-time parameters (119876 119877 119873 119880 and 119905dwell) was kept separatedin order to further limit the number of experimental tests tocalibrate the equationsrsquo coefficients for the cases in which afixed dwell time can be considered (9 for a perfect matchingand 4 for a rougher estimation)

The set of (8) was then implemented in a dedicatedAPDL subroutine in the ANSYS Inc code and run to getan element-by-element assessment of the coefficients as afunction of the specific (120590 119879) state and additionally of thespecific workpiece-die contact (dwell) time

In a first verification stage the proposed procedure wasvalidated against additional experimental data performedwith different specimen geometries not included in the opti-mization step of the coefficients After that the procedurewastested by comparing numerical predictions of the mandreldisplacement history with experimental data for an industrialextrusion die

3 Results and Discussion

Results of the calibration phase of the model are reported inFigure 5 for each level of tested stress and temperature for thecreep loading configuration For these conditions the dwelltime was imposed equal to 61 hours In Figure 6 a magnifi-cation of the typical comparison output that shows the peakmandrel displacement along the load direction is reportedas experimentally computed and numerically predicted overthe total testing time The average percentage error overall the simulated creep conditions was 127 correspondingto 006mm difference The applied methodology fits an

Advances in Materials Science and Engineering 7

ExperimentalNumerical

1 2 3 4 5 6 701 2 3 4 5 6 701 2 3 4 5 6 70

1 2 3 4 5 6 701 2 3 4 5 6 70

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus05minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 5 Experimental versus numerical displacement of the mandrel for each testing condition under the creep load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

minus050

minus045

minus040

minus035

minus030

minus025

minus020

minus015

minus010

000

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 6 Example of the comparison between experimental andnumerical results Experimental dots represent the data extrapolatedat the same time steps of the numerical predictions

average behavior since in a number of comparisons thenumerical data overestimate the experimental results whilein other cases the predicted displacement underestimates theexperimental oneThehigher discrepancywith the increasingtemperature was due to a premature failure of the specimenin the most critical conditions (ie 540∘C-800MPa 580∘C-600MPa and 580∘C-800MPa) that were not included inthe calibration phase of the coefficients As declared in theIntroduction the procedure is able to account for yielding

phenomena while damaging (material discontinuities) onesare neglected

The overall discrepancies can be considered acceptablealso accounting for possible small experimental uncertain-ties In Figure 7 the results for the different tested levelsof stress and temperature for the pure fatigue loading arereported As for the creep tests the testing configurationsthat led to a premature failure of the specimen during trialswere not included in the calibration step (540∘C-800MPa and580∘C-800MPa) The average percentage error was higherthan that for creep test and equal to 325 (0124mm) As canbe observed in Figure 7 the greatest experimental-numericaldiscrepancies are observed at highest temperature of 580∘Cthat for the specific investigated steel coincides with thetempering temperature thus leading to a fast deterioration ofthe mechanical properties not accounted for in the modelHowever process parameters are usually set in order to avoidthis level of temperatures in the tools or at least to get it inlimited portions of the material far from the yielding regionsIn addition at these conditions damage in the form ofmaterial discontinuities (cracks pores and voids) reasonablyappears and it is not modelled by the set of equations Thismade also the average error of 325 acceptable

A similar agreement between experimental and numeri-cal results as that found for the creep tests was determined incase of creep-fatigue loading condition with an average per-centage error of 143 all over the testing configurationscorresponding to 008mm (Figure 8)

As expected the peak percentage error was in each casefound for the combination higher temperature-higher stresslevel

8 Advances in Materials Science and Engineering

ExperimentalNumerical

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 7072 3 4 5 610

1 2 3 4 5 6 70 1 2 3 4 5 6 70

minus07minus06minus05minus04minus03minus02minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus16minus14minus12minus10minus08minus06minus04minus02

00

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 7 Experimental versus numerical displacement of the mandrel for each testing condition under the fatigue load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

380 (∘C) 490 (∘C) 540 (∘C) 580 (∘C)

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus08minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 701 2 3 4 5 6 70

72 3 4 5 610 1 2 3 4 5 6 70 1 2 3 4 5 6 70

1 2 3 4 5 6 70 1 2 3 4 5 6 70

Figure 8 Experimental versus numerical displacement of the mandrel for each testing condition under the creep-fatigue load (x-axis testingtime in hours y-axis specimen displacement in mm)

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

2 Advances in Materials Science and Engineering

inelastic deformation is a time-dependent progressive andirreversible phenomenon accumulated cycle by cycle that canlead to the going-out of the diersquos geometry and thus to its finaldiscard even without the appearance of cracks or other mate-rial discontinuities [1 9] A robust and reliable knowledgeof these pieces of information is therefore recommended atthe die design stage This would indeed support engineers inpredicting the maximum number of workable componentsin order to remain within the required tolerances and inestimating die durability

At present in industrial practice die design is still mainlybased on experience and a set of common shared rules [10 11]while numerical simulations are seldomused However thereare several disadvantages of this practice

In-service experimental monitoring of time-dependentdeformation and then of stresses requires complex setupsdue to the involved high temperatures and difficult toolsrsquoaccessibility Secondly it merely allows for an ex-post evalua-tion since when noncompliant products are detected expen-sive tools have been already manufactured and need to bediscarded [12]

Conversely numerical simulations have been alreadywidely proved to be adequate tools to obtain reliable informa-tion on the level of stress and straindeformation in the diesthus serving as ldquoa priorirdquo estimations for die design optimiza-tion and lifetime improvementsThis has been demonstratedas example in [13 14] for aluminum extrusion dies in [15]for die-casting dies and in [16] for the H11 tool steel widelyused for forming tools Indeed the level of the achieveddeformation is the first necessary input for evaluating thedamage and the related lifetime models [16 17] Nowadaysmanufacturing processes can be reliably analyzed in terms ofplasticity conditions (strain strain rates and temperatures)but also pressure maps and damage distributions bymeans offinite element (FE) simulations Moreover dedicated struc-tural codes allow more specific thermostructural analyses ofmolds and dies for the prediction of the stress and strain levelsand distributions by offering a greater flexibility in terms oftool-material behavior models [13] In this context the mostcomprehensive elastoviscoplasticmodel based on the internalstate variables has been developed by Chaboche within thecontinuum damage mechanism approach [18 19] Despite itsclaimed ability to correctly describemost of the effects experi-mentally observed under creep-fatigue regime the Chabochedeformation model is only partially available within themain commercial FE codes In addition no values of thecoefficients are usually reported in technical papers probablydue to the time-consuming experimental calibration phaseand to the best of authorsrsquo knowledge few validations ofsuch models have been presented in literature against casesof industrial interest only on special tool steels Indeed thewide set of phenomena considered by the Chaboche modelproduces consequently a very wide number of parameters tobe experimentally identified thus making the model almostinapplicable or extremely critical to be properly calibratedand implemented in FEM

Accounting for all these restrictions the authors pro-posed a simplified numerical modelling approach for pre-dicting the time-dependent deformation of hot forming tools

Specimen

Figure 1 Specimen in the Gleeble simulator

operating in the creep-fatigue regime with the main focuson time-dependent deformation of specimens rather thandamage (material discontinuities in form of cracks pores orvoids) mechanisms The starting point was the application ofa simple creep law for cyclic (fatigue) and cyclic with dwell-time (creep-fatigue) loads Novel regression equations weredeveloped for the creep coefficients to correlate with stressstate temperature and exposure time

With the aim of explaining in detail the procedure it isapplied to the specific case of extrusion dies The considereddie material is the H11 hot-work tool steel (X38CrMoV5-1)one of the most commonly used for forming applications [3]The procedure was tested against an industrial die discardeddue to an achieved excessive permanent deformation after64 extruded billets Experimental mandrel deflection wascompared to numerical prediction

2 Materials and Method

During metal forming (extrusion processing included) mul-tiple billets are sequentially processed placing the die in theregime of fatigue each billet representing a loading cycleAccounting for the billet-die contact time during a single ramstroke and for the high temperature developed during theprocess also the creep mechanism plays a significant role Sothat the die deformation mechanism is due to creep-fatigueinteraction [2 20]

An innovative physical experiment was proposed by theauthors reproducing the thermomechanical conditions of anextrusion die [21] the specimens resembled the mandrelof a porthole die on a small scale thus accounting forrealistic stress-strain distribution and surface conditions andwere made of H11 (X38CrMoV5-1) hot-work tool steel Theexperimental tests were performed on a Gleeble simulator byheating the specimen using Joulersquos effect and by applying afull compressive load to the specimen up to 61 hours or tillspecimen failure (Figure 1)

The experimental trials included four levels of temper-ature namely 380∘C 490∘C 540∘C and 580∘C and threelevels of average stresses of 400 600 and 800MPa in thebridges of the specimen A number of porthole dies were pre-liminary simulated to properly calibrate the load level inorder to generate in the specimenrsquos bridges the same averagestress as in the diesrsquo ones (Figure 2(h)) Also the testingtemperature was that of the bridges andmandrel as measuredby 15 thermocouples placed in the specimen during theexperiments [21]Three types of loadwere applied pure creep

Advances in Materials Science and Engineering 3

Load

Time

Creep

2kN

600

sec

1200

sec

T∘

Fatigue

Time

600

sec

1200

sec

Load

2kN

T∘

10 sec

9 sec (unload)

Creep-fatigue

Time

600

sec

1200

sec

Load

2kN

T∘

10 sec

3min

9 sec (unload)

2500

5000

7500

1000

012

500

1500

017

500

2000

022

500

2500

00

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

2500

5000

75000

1250

015

000

1750

020

000

2250

025

000

1000

0

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

2500

5000

75000

1250

015

000

1750

020

000

2250

025

000

1000

0

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

u displacement (mm)

u

2500

5000

7500

1000

012

500

1500

017

500

2000

022

500

2500

00

Time (sec)

Reference region for the definitionof the average stress 120590

(a) (b) (c)

(d) (e) (f)

(g) (h)Figure 2 (a b c) Waveform of the applied load and (d e f) output peak displacement over the testing time for the three loading conditionsat 600MPa and 490∘C (data not purged by the press deformation) (g) Schematic explanation of the results (h) Reference region for thedefinition of the average stress in the small-scale die specimen

(with the load held at a fixed value) fatigue (cyclic load)and creep-fatigue (cyclic load with 3 minutes of dwell time)(Figures 2(a) 2(b) and 2(c)) Creep-fatigue represents thetesting condition with a prescribed dwell or exposure timecreep and fatigue tests correspond to two extreme conditionsof simulating respectively an infinite and a zero dwell-timeIn case of extrusion the dwell time is a function of the billetlength ram speed and extrusion ratio and it increases withthe raising of the billet length and extrusion ratio and withthe decreasing of the ram speed As main output of the testthe displacement of the specimensrsquo mandrel (u) as caused bythe specific loading conditions (load type temperature andstress level) was recorded over the testing time (Figure 2(g))Specifically the pure creep load generated a continuous curve(Figure 2(d)) while the pure fatigue and the creep-fatigueloads generated a cyclic curve with the loading-unloadingdisplacementrsquos path corresponding to each cycle (Figures 2(e)and 2(f))

As observed for standard tests for the same steel [22] acomparable pattern of the mandrel displacement-time curvewas found for all the experimental conditions reproducingthe stages of softening typical of the strain evolution in astandard creep test In particular the specific ranges of inves-tigated temperatures and stresses pointed out a primary phasewithout saturation typical of the secondary creep Thus anexponential type law was chosen to predict the displacementof the mandrel over time accounting for the stress time andtemperature behavior dependency of thematerial response inthis region of deformation that is the time-hardening creeplaw [23] consider the following

120576 = 119862

1sdot 120590

1198622sdot 119879

1198623 (1)

in which 120576 is the strain rate 120590 and 119879 are the stress andtemperature levels and119862

11198622 and119862

3are material constants

4 Advances in Materials Science and Engineering

Table 1 The computed values of time-hardening law coefficients

119899 119898 119886

0

119862

1

119862

2

119862

3

119879

∘

= 450 350493 00675 10858E minus 12 7329E minus 14 35049 minus09325119879

∘

= 500 185103 0085 16965E minus 07 1442E minus 08 18510 minus09150119879

∘

= 550 14848 010625 4198E minus 06 4460E minus 07 14848 minus08938

However other primary creep equations could have beenselected also adding the contribution of the secondary phasein case of specimenrsquos softening saturation

For a better estimation initial values of the coefficientsfor (1) and the H11 tool steel were extracted from datataken in literature for pure creep tests at different stress andtemperature levels [24 25] according to the following proce-dure

(1) Time-hardening law expressed in terms of creepstrain

120576 = 119886

0120590

119899

119905

119898

(2)

where 120576 is the strain 120590 is the stress level 119905 is the timeof the load application and 119886

0 119899 and 119898 are material

constants(2) Passage to the logarithmic form

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905)

= 119886

1+ 119899 ln (120590) + 119898 ln (119905)

(3)

(3) For each level of temperature 119899 computed by averag-ing values for fixed times (ln(119905) constant) and variablestresses

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905) = 119886

2+ 119899 ln (120590) (4)

(4) For each level of temperature 119898 computed by aver-aging values for fixed stresses (ln(120590) constant) andvariable times

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905) = 119886

3+ 119898 ln (119905) (5)

(5) For each level of temperature 1198860computed by enter-

ing 119899 and119898 in (1) for fixed times and by averaging thevalues

ln (120576) minus 119899 ln (120590) minus 119898 ln (119905) = ln (1198860) (6)

(6) Computation of the coefficients in (1)

120576 =

119889120576

119889119905

= 119886

0sdot 119898 sdot 120590

119899

sdot 119905

119898minus1

= 119862

1sdot 120590

1198622sdot 119879

1198623

119862

1= 119886

0sdot 119898 119862

2= 119899 119862

3= 119898 minus 1

(7)

The resulting values of the coefficients are reported in Table 1based on the experimental data in [24 25]

By means of FE analyses the values reported in Table 1were optimized for the set of experimental tests performedon the small-scale mandrel specimens [21] The temperaturedistribution in the specimen was computed by performing athermal-electrical simulation [26]While the time-hardeninglaw in (1) is usually applied in case of creep results for whichcontinuous curves are generated (Figures 2(a) and 2(d)) itsapplication for the fatigue (Figures 2(b) and 2(e)) and creep-fatigue (Figures 2(c) and 2(f)) tests is a nonconventional usesince loading-unloading ramps of the cycles are not mod-elled So for these tests a continuous curve was extrapolatedby connecting the peak values of the displacement of eachcycle and applying the same approach as for the creep tests(Figure 3) In Table 2 the values of the optimized coefficients119862

1 1198622 and 119862

3are reported

Figure 4 graphically shows the numerical correlationsexpressed in Table 2

It emerges that 1198621is a function of the temperature level

and of the dwell time (type of applied load) while it isindependent of the stress level The coefficient 119862

3can be

considered to be dependent only on the selected temperaturelevel while 119862

2 also if not so marked is a function of all the

involved parameters that is the stress and temperature levelsand the dwell time indeed even very small variations of thisparameter were found to have a great influence on the outputresults in terms of predicted numerical displacement of thespecimen Novel empirical regressions were formulated inorder to correlate each coefficient of the time-hardening creeplaw to the stress-temperature-load state as follows

119862

1= (119862

1min sdot [(119862

1max119862

1minminus 1) sdot (

119879

119879max)

(1198701119879)

]) sdot 119876 sdot 119905

119877

dwell

119862

1min = 1198621 (119879mincreep-fatigue) 1198621max = 1198621 (119879maxcreep-fatigue) 1198701 119876 119877 = material costants

119862

2= (119864 sdot 120590

119865

sdot 119879

119866

) sdot 119873 sdot 119905

119880

dwell 119864 119865 119866119873119880 = material costants

119862

3= minus(

1003816

1003816

1003816

1003816

119862

3min1003816

1003816

1003816

1003816

sdot [1 + (

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119862

3max119862

3min

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

minus 1) sdot (

119879

119879max)

(1198703119879)

])

119862

3min = 1198623 (119879mincreep-fatigue) 1198623max = 1198623 (119879maxcreep-fatigue) 1198703 = material costants

(8)

Advances in Materials Science and Engineering 5

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00D

ispla

cem

ent (

mm

)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(a)

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(b)

Figure 3 (a) Original rough experimental cyclic creep-fatigue curve (loading-unloading path of each cycle is reported) and (b) theextrapolated continuous curve dots are example of the extracting points

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400

Creep-fatigue dwell time)min(3Creep (infinite dwell time)Fatigue (0 dwell time)

600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

00051015202530354045

C2

00051015202530354045

C2

00051015202530354045

C2

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

0 200 400 600 800Temperature (

∘C)

Figure 4 Coefficients of (1) (on y-axis) reported as function of the temperature (on x-axis) for each loading condition (in column) and stresslevel (different type of curves)

6 Advances in Materials Science and Engineering

Table 2 Optimized values of the coefficients in (1) on the basis ofexperimental data for creep fatigue and creep-fatigue conditions

(a)

Creep380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 700E minus 14 144E minus 08 446E minus 07 400E minus 06600 [MPa] 733E minus 14 144E minus 08 446E minus 07800 [MPa] 733E minus 14 144E minus 08119862

2

400 [MPa] 397 192 135 106600 [MPa] 370 182 140800 [MPa] 357 182119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(b)

Fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 600E minus 14 133E minus 8 400E minus 7 300E minus 06600 [MPa] 600E minus 14 133E minus 8 400E minus 7800 [MPa] 600E minus 14 133E minus 8119862

2

400 [MPa] 396 190 134 099600 [MPa] 374 177 127800 [MPa] 360 174119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(c)

Creep-fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 640E minus 14 142E minus 8 420E minus 7 380E minus 06600 [MPa] 640E minus 14 142E minus 8 420E minus 7800 [MPa] 640E minus 14 142E minus 8119862

2

400 [MPa] 397 192 135 105600 [MPa] 372 184 130800 [MPa] 362 183119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

In (8) 119905dwell is the time in which during a creep-fatigue testthe imposed load is kept constant and as previously observedfor the specific case of extrusion dies it is correlated to the

Table 3 Material constants used in (8) for the H11 tool steel

119862

1

119862

2

119862

3

119862

1max 38E minus 06 119864 130E + 08 119862

3max minus087119862

1min 64E minus 06 119865 minus011245 119862

3min minus09325119870

1

16650 119866 minus28021 119870

3

3000119876 10421 119873 100251119877 00124698 119880 0002025

billet length ram speed and extrusion ratio Instead 1198621max

119862

1min and1198623max1198623min represent the values of the coefficientsfound for the maximum and minimum temperatures in theselected range of experimental investigation in case of creep-fatigue load for the first and the third coefficients Parameters119870

1119876119877119864 119865119866119873119880 and119870

3arematerial constants For the

presented specific case ofH11 tool steel the coefficient and thematerial constants in (8) are summarized in Table 3

The selected equations among different ones tested werethose best fitting the set of experimental data A total of36 experimental tests were initially performed to verify thesensibility of the small-scale die specimen to the operationalconditions (4 levels of stress and temperature and threeloading schemes) and the results were used to calibrate themodel However the selected equations form allows reducingthe number for a perfect matching to 27 (three levels of stresstemperature and loading type) that for a rougher estimationcan be additionally reduced to 12 (two levels of stress temper-ature and three loading types)The contribution of the dwell-time parameters (119876 119877 119873 119880 and 119905dwell) was kept separatedin order to further limit the number of experimental tests tocalibrate the equationsrsquo coefficients for the cases in which afixed dwell time can be considered (9 for a perfect matchingand 4 for a rougher estimation)

The set of (8) was then implemented in a dedicatedAPDL subroutine in the ANSYS Inc code and run to getan element-by-element assessment of the coefficients as afunction of the specific (120590 119879) state and additionally of thespecific workpiece-die contact (dwell) time

In a first verification stage the proposed procedure wasvalidated against additional experimental data performedwith different specimen geometries not included in the opti-mization step of the coefficients After that the procedurewastested by comparing numerical predictions of the mandreldisplacement history with experimental data for an industrialextrusion die

3 Results and Discussion

Results of the calibration phase of the model are reported inFigure 5 for each level of tested stress and temperature for thecreep loading configuration For these conditions the dwelltime was imposed equal to 61 hours In Figure 6 a magnifi-cation of the typical comparison output that shows the peakmandrel displacement along the load direction is reportedas experimentally computed and numerically predicted overthe total testing time The average percentage error overall the simulated creep conditions was 127 correspondingto 006mm difference The applied methodology fits an

Advances in Materials Science and Engineering 7

ExperimentalNumerical

1 2 3 4 5 6 701 2 3 4 5 6 701 2 3 4 5 6 70

1 2 3 4 5 6 701 2 3 4 5 6 70

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus05minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 5 Experimental versus numerical displacement of the mandrel for each testing condition under the creep load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

minus050

minus045

minus040

minus035

minus030

minus025

minus020

minus015

minus010

000

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 6 Example of the comparison between experimental andnumerical results Experimental dots represent the data extrapolatedat the same time steps of the numerical predictions

average behavior since in a number of comparisons thenumerical data overestimate the experimental results whilein other cases the predicted displacement underestimates theexperimental oneThehigher discrepancywith the increasingtemperature was due to a premature failure of the specimenin the most critical conditions (ie 540∘C-800MPa 580∘C-600MPa and 580∘C-800MPa) that were not included inthe calibration phase of the coefficients As declared in theIntroduction the procedure is able to account for yielding

phenomena while damaging (material discontinuities) onesare neglected

The overall discrepancies can be considered acceptablealso accounting for possible small experimental uncertain-ties In Figure 7 the results for the different tested levelsof stress and temperature for the pure fatigue loading arereported As for the creep tests the testing configurationsthat led to a premature failure of the specimen during trialswere not included in the calibration step (540∘C-800MPa and580∘C-800MPa) The average percentage error was higherthan that for creep test and equal to 325 (0124mm) As canbe observed in Figure 7 the greatest experimental-numericaldiscrepancies are observed at highest temperature of 580∘Cthat for the specific investigated steel coincides with thetempering temperature thus leading to a fast deterioration ofthe mechanical properties not accounted for in the modelHowever process parameters are usually set in order to avoidthis level of temperatures in the tools or at least to get it inlimited portions of the material far from the yielding regionsIn addition at these conditions damage in the form ofmaterial discontinuities (cracks pores and voids) reasonablyappears and it is not modelled by the set of equations Thismade also the average error of 325 acceptable

A similar agreement between experimental and numeri-cal results as that found for the creep tests was determined incase of creep-fatigue loading condition with an average per-centage error of 143 all over the testing configurationscorresponding to 008mm (Figure 8)

As expected the peak percentage error was in each casefound for the combination higher temperature-higher stresslevel

8 Advances in Materials Science and Engineering

ExperimentalNumerical

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 7072 3 4 5 610

1 2 3 4 5 6 70 1 2 3 4 5 6 70

minus07minus06minus05minus04minus03minus02minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus16minus14minus12minus10minus08minus06minus04minus02

00

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 7 Experimental versus numerical displacement of the mandrel for each testing condition under the fatigue load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

380 (∘C) 490 (∘C) 540 (∘C) 580 (∘C)

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus08minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 701 2 3 4 5 6 70

72 3 4 5 610 1 2 3 4 5 6 70 1 2 3 4 5 6 70

1 2 3 4 5 6 70 1 2 3 4 5 6 70

Figure 8 Experimental versus numerical displacement of the mandrel for each testing condition under the creep-fatigue load (x-axis testingtime in hours y-axis specimen displacement in mm)

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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MaterialsJournal of

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Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 3

Load

Time

Creep

2kN

600

sec

1200

sec

T∘

Fatigue

Time

600

sec

1200

sec

Load

2kN

T∘

10 sec

9 sec (unload)

Creep-fatigue

Time

600

sec

1200

sec

Load

2kN

T∘

10 sec

3min

9 sec (unload)

2500

5000

7500

1000

012

500

1500

017

500

2000

022

500

2500

00

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

2500

5000

75000

1250

015

000

1750

020

000

2250

025

000

1000

0

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

2500

5000

75000

1250

015

000

1750

020

000

2250

025

000

1000

0

Time (sec)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

minus16

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

u displacement (mm)

u

2500

5000

7500

1000

012

500

1500

017

500

2000

022

500

2500

00

Time (sec)

Reference region for the definitionof the average stress 120590

(a) (b) (c)

(d) (e) (f)

(g) (h)Figure 2 (a b c) Waveform of the applied load and (d e f) output peak displacement over the testing time for the three loading conditionsat 600MPa and 490∘C (data not purged by the press deformation) (g) Schematic explanation of the results (h) Reference region for thedefinition of the average stress in the small-scale die specimen

(with the load held at a fixed value) fatigue (cyclic load)and creep-fatigue (cyclic load with 3 minutes of dwell time)(Figures 2(a) 2(b) and 2(c)) Creep-fatigue represents thetesting condition with a prescribed dwell or exposure timecreep and fatigue tests correspond to two extreme conditionsof simulating respectively an infinite and a zero dwell-timeIn case of extrusion the dwell time is a function of the billetlength ram speed and extrusion ratio and it increases withthe raising of the billet length and extrusion ratio and withthe decreasing of the ram speed As main output of the testthe displacement of the specimensrsquo mandrel (u) as caused bythe specific loading conditions (load type temperature andstress level) was recorded over the testing time (Figure 2(g))Specifically the pure creep load generated a continuous curve(Figure 2(d)) while the pure fatigue and the creep-fatigueloads generated a cyclic curve with the loading-unloadingdisplacementrsquos path corresponding to each cycle (Figures 2(e)and 2(f))

As observed for standard tests for the same steel [22] acomparable pattern of the mandrel displacement-time curvewas found for all the experimental conditions reproducingthe stages of softening typical of the strain evolution in astandard creep test In particular the specific ranges of inves-tigated temperatures and stresses pointed out a primary phasewithout saturation typical of the secondary creep Thus anexponential type law was chosen to predict the displacementof the mandrel over time accounting for the stress time andtemperature behavior dependency of thematerial response inthis region of deformation that is the time-hardening creeplaw [23] consider the following

120576 = 119862

1sdot 120590

1198622sdot 119879

1198623 (1)

in which 120576 is the strain rate 120590 and 119879 are the stress andtemperature levels and119862

11198622 and119862

3are material constants

4 Advances in Materials Science and Engineering

Table 1 The computed values of time-hardening law coefficients

119899 119898 119886

0

119862

1

119862

2

119862

3

119879

∘

= 450 350493 00675 10858E minus 12 7329E minus 14 35049 minus09325119879

∘

= 500 185103 0085 16965E minus 07 1442E minus 08 18510 minus09150119879

∘

= 550 14848 010625 4198E minus 06 4460E minus 07 14848 minus08938

However other primary creep equations could have beenselected also adding the contribution of the secondary phasein case of specimenrsquos softening saturation

For a better estimation initial values of the coefficientsfor (1) and the H11 tool steel were extracted from datataken in literature for pure creep tests at different stress andtemperature levels [24 25] according to the following proce-dure

(1) Time-hardening law expressed in terms of creepstrain

120576 = 119886

0120590

119899

119905

119898

(2)

where 120576 is the strain 120590 is the stress level 119905 is the timeof the load application and 119886

0 119899 and 119898 are material

constants(2) Passage to the logarithmic form

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905)

= 119886

1+ 119899 ln (120590) + 119898 ln (119905)

(3)

(3) For each level of temperature 119899 computed by averag-ing values for fixed times (ln(119905) constant) and variablestresses

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905) = 119886

2+ 119899 ln (120590) (4)

(4) For each level of temperature 119898 computed by aver-aging values for fixed stresses (ln(120590) constant) andvariable times

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905) = 119886

3+ 119898 ln (119905) (5)

(5) For each level of temperature 1198860computed by enter-

ing 119899 and119898 in (1) for fixed times and by averaging thevalues

ln (120576) minus 119899 ln (120590) minus 119898 ln (119905) = ln (1198860) (6)

(6) Computation of the coefficients in (1)

120576 =

119889120576

119889119905

= 119886

0sdot 119898 sdot 120590

119899

sdot 119905

119898minus1

= 119862

1sdot 120590

1198622sdot 119879

1198623

119862

1= 119886

0sdot 119898 119862

2= 119899 119862

3= 119898 minus 1

(7)

The resulting values of the coefficients are reported in Table 1based on the experimental data in [24 25]

By means of FE analyses the values reported in Table 1were optimized for the set of experimental tests performedon the small-scale mandrel specimens [21] The temperaturedistribution in the specimen was computed by performing athermal-electrical simulation [26]While the time-hardeninglaw in (1) is usually applied in case of creep results for whichcontinuous curves are generated (Figures 2(a) and 2(d)) itsapplication for the fatigue (Figures 2(b) and 2(e)) and creep-fatigue (Figures 2(c) and 2(f)) tests is a nonconventional usesince loading-unloading ramps of the cycles are not mod-elled So for these tests a continuous curve was extrapolatedby connecting the peak values of the displacement of eachcycle and applying the same approach as for the creep tests(Figure 3) In Table 2 the values of the optimized coefficients119862

1 1198622 and 119862

3are reported

Figure 4 graphically shows the numerical correlationsexpressed in Table 2

It emerges that 1198621is a function of the temperature level

and of the dwell time (type of applied load) while it isindependent of the stress level The coefficient 119862

3can be

considered to be dependent only on the selected temperaturelevel while 119862

2 also if not so marked is a function of all the

involved parameters that is the stress and temperature levelsand the dwell time indeed even very small variations of thisparameter were found to have a great influence on the outputresults in terms of predicted numerical displacement of thespecimen Novel empirical regressions were formulated inorder to correlate each coefficient of the time-hardening creeplaw to the stress-temperature-load state as follows

119862

1= (119862

1min sdot [(119862

1max119862

1minminus 1) sdot (

119879

119879max)

(1198701119879)

]) sdot 119876 sdot 119905

119877

dwell

119862

1min = 1198621 (119879mincreep-fatigue) 1198621max = 1198621 (119879maxcreep-fatigue) 1198701 119876 119877 = material costants

119862

2= (119864 sdot 120590

119865

sdot 119879

119866

) sdot 119873 sdot 119905

119880

dwell 119864 119865 119866119873119880 = material costants

119862

3= minus(

1003816

1003816

1003816

1003816

119862

3min1003816

1003816

1003816

1003816

sdot [1 + (

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119862

3max119862

3min

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

minus 1) sdot (

119879

119879max)

(1198703119879)

])

119862

3min = 1198623 (119879mincreep-fatigue) 1198623max = 1198623 (119879maxcreep-fatigue) 1198703 = material costants

(8)

Advances in Materials Science and Engineering 5

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00D

ispla

cem

ent (

mm

)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(a)

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(b)

Figure 3 (a) Original rough experimental cyclic creep-fatigue curve (loading-unloading path of each cycle is reported) and (b) theextrapolated continuous curve dots are example of the extracting points

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400

Creep-fatigue dwell time)min(3Creep (infinite dwell time)Fatigue (0 dwell time)

600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

00051015202530354045

C2

00051015202530354045

C2

00051015202530354045

C2

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

0 200 400 600 800Temperature (

∘C)

Figure 4 Coefficients of (1) (on y-axis) reported as function of the temperature (on x-axis) for each loading condition (in column) and stresslevel (different type of curves)

6 Advances in Materials Science and Engineering

Table 2 Optimized values of the coefficients in (1) on the basis ofexperimental data for creep fatigue and creep-fatigue conditions

(a)

Creep380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 700E minus 14 144E minus 08 446E minus 07 400E minus 06600 [MPa] 733E minus 14 144E minus 08 446E minus 07800 [MPa] 733E minus 14 144E minus 08119862

2

400 [MPa] 397 192 135 106600 [MPa] 370 182 140800 [MPa] 357 182119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(b)

Fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 600E minus 14 133E minus 8 400E minus 7 300E minus 06600 [MPa] 600E minus 14 133E minus 8 400E minus 7800 [MPa] 600E minus 14 133E minus 8119862

2

400 [MPa] 396 190 134 099600 [MPa] 374 177 127800 [MPa] 360 174119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(c)

Creep-fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 640E minus 14 142E minus 8 420E minus 7 380E minus 06600 [MPa] 640E minus 14 142E minus 8 420E minus 7800 [MPa] 640E minus 14 142E minus 8119862

2

400 [MPa] 397 192 135 105600 [MPa] 372 184 130800 [MPa] 362 183119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

In (8) 119905dwell is the time in which during a creep-fatigue testthe imposed load is kept constant and as previously observedfor the specific case of extrusion dies it is correlated to the

Table 3 Material constants used in (8) for the H11 tool steel

119862

1

119862

2

119862

3

119862

1max 38E minus 06 119864 130E + 08 119862

3max minus087119862

1min 64E minus 06 119865 minus011245 119862

3min minus09325119870

1

16650 119866 minus28021 119870

3

3000119876 10421 119873 100251119877 00124698 119880 0002025

billet length ram speed and extrusion ratio Instead 1198621max

119862

1min and1198623max1198623min represent the values of the coefficientsfound for the maximum and minimum temperatures in theselected range of experimental investigation in case of creep-fatigue load for the first and the third coefficients Parameters119870

1119876119877119864 119865119866119873119880 and119870

3arematerial constants For the

presented specific case ofH11 tool steel the coefficient and thematerial constants in (8) are summarized in Table 3

The selected equations among different ones tested werethose best fitting the set of experimental data A total of36 experimental tests were initially performed to verify thesensibility of the small-scale die specimen to the operationalconditions (4 levels of stress and temperature and threeloading schemes) and the results were used to calibrate themodel However the selected equations form allows reducingthe number for a perfect matching to 27 (three levels of stresstemperature and loading type) that for a rougher estimationcan be additionally reduced to 12 (two levels of stress temper-ature and three loading types)The contribution of the dwell-time parameters (119876 119877 119873 119880 and 119905dwell) was kept separatedin order to further limit the number of experimental tests tocalibrate the equationsrsquo coefficients for the cases in which afixed dwell time can be considered (9 for a perfect matchingand 4 for a rougher estimation)

The set of (8) was then implemented in a dedicatedAPDL subroutine in the ANSYS Inc code and run to getan element-by-element assessment of the coefficients as afunction of the specific (120590 119879) state and additionally of thespecific workpiece-die contact (dwell) time

In a first verification stage the proposed procedure wasvalidated against additional experimental data performedwith different specimen geometries not included in the opti-mization step of the coefficients After that the procedurewastested by comparing numerical predictions of the mandreldisplacement history with experimental data for an industrialextrusion die

3 Results and Discussion

Results of the calibration phase of the model are reported inFigure 5 for each level of tested stress and temperature for thecreep loading configuration For these conditions the dwelltime was imposed equal to 61 hours In Figure 6 a magnifi-cation of the typical comparison output that shows the peakmandrel displacement along the load direction is reportedas experimentally computed and numerically predicted overthe total testing time The average percentage error overall the simulated creep conditions was 127 correspondingto 006mm difference The applied methodology fits an

Advances in Materials Science and Engineering 7

ExperimentalNumerical

1 2 3 4 5 6 701 2 3 4 5 6 701 2 3 4 5 6 70

1 2 3 4 5 6 701 2 3 4 5 6 70

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus05minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 5 Experimental versus numerical displacement of the mandrel for each testing condition under the creep load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

minus050

minus045

minus040

minus035

minus030

minus025

minus020

minus015

minus010

000

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 6 Example of the comparison between experimental andnumerical results Experimental dots represent the data extrapolatedat the same time steps of the numerical predictions

average behavior since in a number of comparisons thenumerical data overestimate the experimental results whilein other cases the predicted displacement underestimates theexperimental oneThehigher discrepancywith the increasingtemperature was due to a premature failure of the specimenin the most critical conditions (ie 540∘C-800MPa 580∘C-600MPa and 580∘C-800MPa) that were not included inthe calibration phase of the coefficients As declared in theIntroduction the procedure is able to account for yielding

phenomena while damaging (material discontinuities) onesare neglected

The overall discrepancies can be considered acceptablealso accounting for possible small experimental uncertain-ties In Figure 7 the results for the different tested levelsof stress and temperature for the pure fatigue loading arereported As for the creep tests the testing configurationsthat led to a premature failure of the specimen during trialswere not included in the calibration step (540∘C-800MPa and580∘C-800MPa) The average percentage error was higherthan that for creep test and equal to 325 (0124mm) As canbe observed in Figure 7 the greatest experimental-numericaldiscrepancies are observed at highest temperature of 580∘Cthat for the specific investigated steel coincides with thetempering temperature thus leading to a fast deterioration ofthe mechanical properties not accounted for in the modelHowever process parameters are usually set in order to avoidthis level of temperatures in the tools or at least to get it inlimited portions of the material far from the yielding regionsIn addition at these conditions damage in the form ofmaterial discontinuities (cracks pores and voids) reasonablyappears and it is not modelled by the set of equations Thismade also the average error of 325 acceptable

A similar agreement between experimental and numeri-cal results as that found for the creep tests was determined incase of creep-fatigue loading condition with an average per-centage error of 143 all over the testing configurationscorresponding to 008mm (Figure 8)

As expected the peak percentage error was in each casefound for the combination higher temperature-higher stresslevel

8 Advances in Materials Science and Engineering

ExperimentalNumerical

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 7072 3 4 5 610

1 2 3 4 5 6 70 1 2 3 4 5 6 70

minus07minus06minus05minus04minus03minus02minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus16minus14minus12minus10minus08minus06minus04minus02

00

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 7 Experimental versus numerical displacement of the mandrel for each testing condition under the fatigue load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

380 (∘C) 490 (∘C) 540 (∘C) 580 (∘C)

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus08minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 701 2 3 4 5 6 70

72 3 4 5 610 1 2 3 4 5 6 70 1 2 3 4 5 6 70

1 2 3 4 5 6 70 1 2 3 4 5 6 70

Figure 8 Experimental versus numerical displacement of the mandrel for each testing condition under the creep-fatigue load (x-axis testingtime in hours y-axis specimen displacement in mm)

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

4 Advances in Materials Science and Engineering

Table 1 The computed values of time-hardening law coefficients

119899 119898 119886

0

119862

1

119862

2

119862

3

119879

∘

= 450 350493 00675 10858E minus 12 7329E minus 14 35049 minus09325119879

∘

= 500 185103 0085 16965E minus 07 1442E minus 08 18510 minus09150119879

∘

= 550 14848 010625 4198E minus 06 4460E minus 07 14848 minus08938

However other primary creep equations could have beenselected also adding the contribution of the secondary phasein case of specimenrsquos softening saturation

For a better estimation initial values of the coefficientsfor (1) and the H11 tool steel were extracted from datataken in literature for pure creep tests at different stress andtemperature levels [24 25] according to the following proce-dure

(1) Time-hardening law expressed in terms of creepstrain

120576 = 119886

0120590

119899

119905

119898

(2)

where 120576 is the strain 120590 is the stress level 119905 is the timeof the load application and 119886

0 119899 and 119898 are material

constants(2) Passage to the logarithmic form

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905)

= 119886

1+ 119899 ln (120590) + 119898 ln (119905)

(3)

(3) For each level of temperature 119899 computed by averag-ing values for fixed times (ln(119905) constant) and variablestresses

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905) = 119886

2+ 119899 ln (120590) (4)

(4) For each level of temperature 119898 computed by aver-aging values for fixed stresses (ln(120590) constant) andvariable times

ln (120576) = ln (1198860) + 119899 ln (120590) + 119898 ln (119905) = 119886

3+ 119898 ln (119905) (5)

(5) For each level of temperature 1198860computed by enter-

ing 119899 and119898 in (1) for fixed times and by averaging thevalues

ln (120576) minus 119899 ln (120590) minus 119898 ln (119905) = ln (1198860) (6)

(6) Computation of the coefficients in (1)

120576 =

119889120576

119889119905

= 119886

0sdot 119898 sdot 120590

119899

sdot 119905

119898minus1

= 119862

1sdot 120590

1198622sdot 119879

1198623

119862

1= 119886

0sdot 119898 119862

2= 119899 119862

3= 119898 minus 1

(7)

The resulting values of the coefficients are reported in Table 1based on the experimental data in [24 25]

By means of FE analyses the values reported in Table 1were optimized for the set of experimental tests performedon the small-scale mandrel specimens [21] The temperaturedistribution in the specimen was computed by performing athermal-electrical simulation [26]While the time-hardeninglaw in (1) is usually applied in case of creep results for whichcontinuous curves are generated (Figures 2(a) and 2(d)) itsapplication for the fatigue (Figures 2(b) and 2(e)) and creep-fatigue (Figures 2(c) and 2(f)) tests is a nonconventional usesince loading-unloading ramps of the cycles are not mod-elled So for these tests a continuous curve was extrapolatedby connecting the peak values of the displacement of eachcycle and applying the same approach as for the creep tests(Figure 3) In Table 2 the values of the optimized coefficients119862

1 1198622 and 119862

3are reported

Figure 4 graphically shows the numerical correlationsexpressed in Table 2

It emerges that 1198621is a function of the temperature level

and of the dwell time (type of applied load) while it isindependent of the stress level The coefficient 119862

3can be

considered to be dependent only on the selected temperaturelevel while 119862

2 also if not so marked is a function of all the

involved parameters that is the stress and temperature levelsand the dwell time indeed even very small variations of thisparameter were found to have a great influence on the outputresults in terms of predicted numerical displacement of thespecimen Novel empirical regressions were formulated inorder to correlate each coefficient of the time-hardening creeplaw to the stress-temperature-load state as follows

119862

1= (119862

1min sdot [(119862

1max119862

1minminus 1) sdot (

119879

119879max)

(1198701119879)

]) sdot 119876 sdot 119905

119877

dwell

119862

1min = 1198621 (119879mincreep-fatigue) 1198621max = 1198621 (119879maxcreep-fatigue) 1198701 119876 119877 = material costants

119862

2= (119864 sdot 120590

119865

sdot 119879

119866

) sdot 119873 sdot 119905

119880

dwell 119864 119865 119866119873119880 = material costants

119862

3= minus(

1003816

1003816

1003816

1003816

119862

3min1003816

1003816

1003816

1003816

sdot [1 + (

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119862

3max119862

3min

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

minus 1) sdot (

119879

119879max)

(1198703119879)

])

119862

3min = 1198623 (119879mincreep-fatigue) 1198623max = 1198623 (119879maxcreep-fatigue) 1198703 = material costants

(8)

Advances in Materials Science and Engineering 5

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00D

ispla

cem

ent (

mm

)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(a)

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(b)

Figure 3 (a) Original rough experimental cyclic creep-fatigue curve (loading-unloading path of each cycle is reported) and (b) theextrapolated continuous curve dots are example of the extracting points

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400

Creep-fatigue dwell time)min(3Creep (infinite dwell time)Fatigue (0 dwell time)

600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

00051015202530354045

C2

00051015202530354045

C2

00051015202530354045

C2

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

0 200 400 600 800Temperature (

∘C)

Figure 4 Coefficients of (1) (on y-axis) reported as function of the temperature (on x-axis) for each loading condition (in column) and stresslevel (different type of curves)

6 Advances in Materials Science and Engineering

Table 2 Optimized values of the coefficients in (1) on the basis ofexperimental data for creep fatigue and creep-fatigue conditions

(a)

Creep380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 700E minus 14 144E minus 08 446E minus 07 400E minus 06600 [MPa] 733E minus 14 144E minus 08 446E minus 07800 [MPa] 733E minus 14 144E minus 08119862

2

400 [MPa] 397 192 135 106600 [MPa] 370 182 140800 [MPa] 357 182119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(b)

Fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 600E minus 14 133E minus 8 400E minus 7 300E minus 06600 [MPa] 600E minus 14 133E minus 8 400E minus 7800 [MPa] 600E minus 14 133E minus 8119862

2

400 [MPa] 396 190 134 099600 [MPa] 374 177 127800 [MPa] 360 174119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(c)

Creep-fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 640E minus 14 142E minus 8 420E minus 7 380E minus 06600 [MPa] 640E minus 14 142E minus 8 420E minus 7800 [MPa] 640E minus 14 142E minus 8119862

2

400 [MPa] 397 192 135 105600 [MPa] 372 184 130800 [MPa] 362 183119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

In (8) 119905dwell is the time in which during a creep-fatigue testthe imposed load is kept constant and as previously observedfor the specific case of extrusion dies it is correlated to the

Table 3 Material constants used in (8) for the H11 tool steel

119862

1

119862

2

119862

3

119862

1max 38E minus 06 119864 130E + 08 119862

3max minus087119862

1min 64E minus 06 119865 minus011245 119862

3min minus09325119870

1

16650 119866 minus28021 119870

3

3000119876 10421 119873 100251119877 00124698 119880 0002025

billet length ram speed and extrusion ratio Instead 1198621max

119862

1min and1198623max1198623min represent the values of the coefficientsfound for the maximum and minimum temperatures in theselected range of experimental investigation in case of creep-fatigue load for the first and the third coefficients Parameters119870

1119876119877119864 119865119866119873119880 and119870

3arematerial constants For the

presented specific case ofH11 tool steel the coefficient and thematerial constants in (8) are summarized in Table 3

The selected equations among different ones tested werethose best fitting the set of experimental data A total of36 experimental tests were initially performed to verify thesensibility of the small-scale die specimen to the operationalconditions (4 levels of stress and temperature and threeloading schemes) and the results were used to calibrate themodel However the selected equations form allows reducingthe number for a perfect matching to 27 (three levels of stresstemperature and loading type) that for a rougher estimationcan be additionally reduced to 12 (two levels of stress temper-ature and three loading types)The contribution of the dwell-time parameters (119876 119877 119873 119880 and 119905dwell) was kept separatedin order to further limit the number of experimental tests tocalibrate the equationsrsquo coefficients for the cases in which afixed dwell time can be considered (9 for a perfect matchingand 4 for a rougher estimation)

The set of (8) was then implemented in a dedicatedAPDL subroutine in the ANSYS Inc code and run to getan element-by-element assessment of the coefficients as afunction of the specific (120590 119879) state and additionally of thespecific workpiece-die contact (dwell) time

In a first verification stage the proposed procedure wasvalidated against additional experimental data performedwith different specimen geometries not included in the opti-mization step of the coefficients After that the procedurewastested by comparing numerical predictions of the mandreldisplacement history with experimental data for an industrialextrusion die

3 Results and Discussion

Results of the calibration phase of the model are reported inFigure 5 for each level of tested stress and temperature for thecreep loading configuration For these conditions the dwelltime was imposed equal to 61 hours In Figure 6 a magnifi-cation of the typical comparison output that shows the peakmandrel displacement along the load direction is reportedas experimentally computed and numerically predicted overthe total testing time The average percentage error overall the simulated creep conditions was 127 correspondingto 006mm difference The applied methodology fits an

Advances in Materials Science and Engineering 7

ExperimentalNumerical

1 2 3 4 5 6 701 2 3 4 5 6 701 2 3 4 5 6 70

1 2 3 4 5 6 701 2 3 4 5 6 70

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus05minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 5 Experimental versus numerical displacement of the mandrel for each testing condition under the creep load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

minus050

minus045

minus040

minus035

minus030

minus025

minus020

minus015

minus010

000

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 6 Example of the comparison between experimental andnumerical results Experimental dots represent the data extrapolatedat the same time steps of the numerical predictions

average behavior since in a number of comparisons thenumerical data overestimate the experimental results whilein other cases the predicted displacement underestimates theexperimental oneThehigher discrepancywith the increasingtemperature was due to a premature failure of the specimenin the most critical conditions (ie 540∘C-800MPa 580∘C-600MPa and 580∘C-800MPa) that were not included inthe calibration phase of the coefficients As declared in theIntroduction the procedure is able to account for yielding

phenomena while damaging (material discontinuities) onesare neglected

The overall discrepancies can be considered acceptablealso accounting for possible small experimental uncertain-ties In Figure 7 the results for the different tested levelsof stress and temperature for the pure fatigue loading arereported As for the creep tests the testing configurationsthat led to a premature failure of the specimen during trialswere not included in the calibration step (540∘C-800MPa and580∘C-800MPa) The average percentage error was higherthan that for creep test and equal to 325 (0124mm) As canbe observed in Figure 7 the greatest experimental-numericaldiscrepancies are observed at highest temperature of 580∘Cthat for the specific investigated steel coincides with thetempering temperature thus leading to a fast deterioration ofthe mechanical properties not accounted for in the modelHowever process parameters are usually set in order to avoidthis level of temperatures in the tools or at least to get it inlimited portions of the material far from the yielding regionsIn addition at these conditions damage in the form ofmaterial discontinuities (cracks pores and voids) reasonablyappears and it is not modelled by the set of equations Thismade also the average error of 325 acceptable

A similar agreement between experimental and numeri-cal results as that found for the creep tests was determined incase of creep-fatigue loading condition with an average per-centage error of 143 all over the testing configurationscorresponding to 008mm (Figure 8)

As expected the peak percentage error was in each casefound for the combination higher temperature-higher stresslevel

8 Advances in Materials Science and Engineering

ExperimentalNumerical

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 7072 3 4 5 610

1 2 3 4 5 6 70 1 2 3 4 5 6 70

minus07minus06minus05minus04minus03minus02minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus16minus14minus12minus10minus08minus06minus04minus02

00

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 7 Experimental versus numerical displacement of the mandrel for each testing condition under the fatigue load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

380 (∘C) 490 (∘C) 540 (∘C) 580 (∘C)

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus08minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 701 2 3 4 5 6 70

72 3 4 5 610 1 2 3 4 5 6 70 1 2 3 4 5 6 70

1 2 3 4 5 6 70 1 2 3 4 5 6 70

Figure 8 Experimental versus numerical displacement of the mandrel for each testing condition under the creep-fatigue load (x-axis testingtime in hours y-axis specimen displacement in mm)

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 5

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00D

ispla

cem

ent (

mm

)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(a)

minus16

minus15

minus14

minus13

minus12

minus11

minus10

minus09

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

0

5000

7500

1000

0

1250

0

1500

0

1750

0

2000

0

2250

0

2500

0

2500

Time (sec)

(b)

Figure 3 (a) Original rough experimental cyclic creep-fatigue curve (loading-unloading path of each cycle is reported) and (b) theextrapolated continuous curve dots are example of the extracting points

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

400 (MPa)600 (MPa)800 (MPa)

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400

Creep-fatigue dwell time)min(3Creep (infinite dwell time)Fatigue (0 dwell time)

600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

Temperature (∘C)

0 400 600 800200Temperature (

∘C)

0 400 600 800200

00051015202530354045

C2

00051015202530354045

C2

00051015202530354045

C2

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus094minus093minus092minus091minus090minus089minus088minus087minus086

C3

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

minus50E minus 07

50E minus 07

15E minus 06

25E minus 06

35E minus 06

45E minus 06

C1

0 200 400 600 800Temperature (

∘C)

Figure 4 Coefficients of (1) (on y-axis) reported as function of the temperature (on x-axis) for each loading condition (in column) and stresslevel (different type of curves)

6 Advances in Materials Science and Engineering

Table 2 Optimized values of the coefficients in (1) on the basis ofexperimental data for creep fatigue and creep-fatigue conditions

(a)

Creep380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 700E minus 14 144E minus 08 446E minus 07 400E minus 06600 [MPa] 733E minus 14 144E minus 08 446E minus 07800 [MPa] 733E minus 14 144E minus 08119862

2

400 [MPa] 397 192 135 106600 [MPa] 370 182 140800 [MPa] 357 182119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(b)

Fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 600E minus 14 133E minus 8 400E minus 7 300E minus 06600 [MPa] 600E minus 14 133E minus 8 400E minus 7800 [MPa] 600E minus 14 133E minus 8119862

2

400 [MPa] 396 190 134 099600 [MPa] 374 177 127800 [MPa] 360 174119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(c)

Creep-fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 640E minus 14 142E minus 8 420E minus 7 380E minus 06600 [MPa] 640E minus 14 142E minus 8 420E minus 7800 [MPa] 640E minus 14 142E minus 8119862

2

400 [MPa] 397 192 135 105600 [MPa] 372 184 130800 [MPa] 362 183119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

In (8) 119905dwell is the time in which during a creep-fatigue testthe imposed load is kept constant and as previously observedfor the specific case of extrusion dies it is correlated to the

Table 3 Material constants used in (8) for the H11 tool steel

119862

1

119862

2

119862

3

119862

1max 38E minus 06 119864 130E + 08 119862

3max minus087119862

1min 64E minus 06 119865 minus011245 119862

3min minus09325119870

1

16650 119866 minus28021 119870

3

3000119876 10421 119873 100251119877 00124698 119880 0002025

billet length ram speed and extrusion ratio Instead 1198621max

119862

1min and1198623max1198623min represent the values of the coefficientsfound for the maximum and minimum temperatures in theselected range of experimental investigation in case of creep-fatigue load for the first and the third coefficients Parameters119870

1119876119877119864 119865119866119873119880 and119870

3arematerial constants For the

presented specific case ofH11 tool steel the coefficient and thematerial constants in (8) are summarized in Table 3

The selected equations among different ones tested werethose best fitting the set of experimental data A total of36 experimental tests were initially performed to verify thesensibility of the small-scale die specimen to the operationalconditions (4 levels of stress and temperature and threeloading schemes) and the results were used to calibrate themodel However the selected equations form allows reducingthe number for a perfect matching to 27 (three levels of stresstemperature and loading type) that for a rougher estimationcan be additionally reduced to 12 (two levels of stress temper-ature and three loading types)The contribution of the dwell-time parameters (119876 119877 119873 119880 and 119905dwell) was kept separatedin order to further limit the number of experimental tests tocalibrate the equationsrsquo coefficients for the cases in which afixed dwell time can be considered (9 for a perfect matchingand 4 for a rougher estimation)

The set of (8) was then implemented in a dedicatedAPDL subroutine in the ANSYS Inc code and run to getan element-by-element assessment of the coefficients as afunction of the specific (120590 119879) state and additionally of thespecific workpiece-die contact (dwell) time

In a first verification stage the proposed procedure wasvalidated against additional experimental data performedwith different specimen geometries not included in the opti-mization step of the coefficients After that the procedurewastested by comparing numerical predictions of the mandreldisplacement history with experimental data for an industrialextrusion die

3 Results and Discussion

Results of the calibration phase of the model are reported inFigure 5 for each level of tested stress and temperature for thecreep loading configuration For these conditions the dwelltime was imposed equal to 61 hours In Figure 6 a magnifi-cation of the typical comparison output that shows the peakmandrel displacement along the load direction is reportedas experimentally computed and numerically predicted overthe total testing time The average percentage error overall the simulated creep conditions was 127 correspondingto 006mm difference The applied methodology fits an

Advances in Materials Science and Engineering 7

ExperimentalNumerical

1 2 3 4 5 6 701 2 3 4 5 6 701 2 3 4 5 6 70

1 2 3 4 5 6 701 2 3 4 5 6 70

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus05minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 5 Experimental versus numerical displacement of the mandrel for each testing condition under the creep load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

minus050

minus045

minus040

minus035

minus030

minus025

minus020

minus015

minus010

000

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 6 Example of the comparison between experimental andnumerical results Experimental dots represent the data extrapolatedat the same time steps of the numerical predictions

average behavior since in a number of comparisons thenumerical data overestimate the experimental results whilein other cases the predicted displacement underestimates theexperimental oneThehigher discrepancywith the increasingtemperature was due to a premature failure of the specimenin the most critical conditions (ie 540∘C-800MPa 580∘C-600MPa and 580∘C-800MPa) that were not included inthe calibration phase of the coefficients As declared in theIntroduction the procedure is able to account for yielding

phenomena while damaging (material discontinuities) onesare neglected

The overall discrepancies can be considered acceptablealso accounting for possible small experimental uncertain-ties In Figure 7 the results for the different tested levelsof stress and temperature for the pure fatigue loading arereported As for the creep tests the testing configurationsthat led to a premature failure of the specimen during trialswere not included in the calibration step (540∘C-800MPa and580∘C-800MPa) The average percentage error was higherthan that for creep test and equal to 325 (0124mm) As canbe observed in Figure 7 the greatest experimental-numericaldiscrepancies are observed at highest temperature of 580∘Cthat for the specific investigated steel coincides with thetempering temperature thus leading to a fast deterioration ofthe mechanical properties not accounted for in the modelHowever process parameters are usually set in order to avoidthis level of temperatures in the tools or at least to get it inlimited portions of the material far from the yielding regionsIn addition at these conditions damage in the form ofmaterial discontinuities (cracks pores and voids) reasonablyappears and it is not modelled by the set of equations Thismade also the average error of 325 acceptable

A similar agreement between experimental and numeri-cal results as that found for the creep tests was determined incase of creep-fatigue loading condition with an average per-centage error of 143 all over the testing configurationscorresponding to 008mm (Figure 8)

As expected the peak percentage error was in each casefound for the combination higher temperature-higher stresslevel

8 Advances in Materials Science and Engineering

ExperimentalNumerical

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 7072 3 4 5 610

1 2 3 4 5 6 70 1 2 3 4 5 6 70

minus07minus06minus05minus04minus03minus02minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus16minus14minus12minus10minus08minus06minus04minus02

00

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 7 Experimental versus numerical displacement of the mandrel for each testing condition under the fatigue load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

380 (∘C) 490 (∘C) 540 (∘C) 580 (∘C)

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus08minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 701 2 3 4 5 6 70

72 3 4 5 610 1 2 3 4 5 6 70 1 2 3 4 5 6 70

1 2 3 4 5 6 70 1 2 3 4 5 6 70

Figure 8 Experimental versus numerical displacement of the mandrel for each testing condition under the creep-fatigue load (x-axis testingtime in hours y-axis specimen displacement in mm)

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

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TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Advances in

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MetallurgyJournal of

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BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 Advances in Materials Science and Engineering

Table 2 Optimized values of the coefficients in (1) on the basis ofexperimental data for creep fatigue and creep-fatigue conditions

(a)

Creep380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 700E minus 14 144E minus 08 446E minus 07 400E minus 06600 [MPa] 733E minus 14 144E minus 08 446E minus 07800 [MPa] 733E minus 14 144E minus 08119862

2

400 [MPa] 397 192 135 106600 [MPa] 370 182 140800 [MPa] 357 182119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(b)

Fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 600E minus 14 133E minus 8 400E minus 7 300E minus 06600 [MPa] 600E minus 14 133E minus 8 400E minus 7800 [MPa] 600E minus 14 133E minus 8119862

2

400 [MPa] 396 190 134 099600 [MPa] 374 177 127800 [MPa] 360 174119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

(c)

Creep-fatigue380 [∘C] 490 [∘C] 540 [∘C] 580 [∘C]

119862

1

400 [MPa] 640E minus 14 142E minus 8 420E minus 7 380E minus 06600 [MPa] 640E minus 14 142E minus 8 420E minus 7800 [MPa] 640E minus 14 142E minus 8119862

2

400 [MPa] 397 192 135 105600 [MPa] 372 184 130800 [MPa] 362 183119862

3

400 [MPa] minus09325 minus09150 minus08700 minus08700600 [MPa] minus09325 minus09150 minus08700800 [MPa] minus09325 minus09150

In (8) 119905dwell is the time in which during a creep-fatigue testthe imposed load is kept constant and as previously observedfor the specific case of extrusion dies it is correlated to the

Table 3 Material constants used in (8) for the H11 tool steel

119862

1

119862

2

119862

3

119862

1max 38E minus 06 119864 130E + 08 119862

3max minus087119862

1min 64E minus 06 119865 minus011245 119862

3min minus09325119870

1

16650 119866 minus28021 119870

3

3000119876 10421 119873 100251119877 00124698 119880 0002025

billet length ram speed and extrusion ratio Instead 1198621max

119862

1min and1198623max1198623min represent the values of the coefficientsfound for the maximum and minimum temperatures in theselected range of experimental investigation in case of creep-fatigue load for the first and the third coefficients Parameters119870

1119876119877119864 119865119866119873119880 and119870

3arematerial constants For the

presented specific case ofH11 tool steel the coefficient and thematerial constants in (8) are summarized in Table 3

The selected equations among different ones tested werethose best fitting the set of experimental data A total of36 experimental tests were initially performed to verify thesensibility of the small-scale die specimen to the operationalconditions (4 levels of stress and temperature and threeloading schemes) and the results were used to calibrate themodel However the selected equations form allows reducingthe number for a perfect matching to 27 (three levels of stresstemperature and loading type) that for a rougher estimationcan be additionally reduced to 12 (two levels of stress temper-ature and three loading types)The contribution of the dwell-time parameters (119876 119877 119873 119880 and 119905dwell) was kept separatedin order to further limit the number of experimental tests tocalibrate the equationsrsquo coefficients for the cases in which afixed dwell time can be considered (9 for a perfect matchingand 4 for a rougher estimation)

The set of (8) was then implemented in a dedicatedAPDL subroutine in the ANSYS Inc code and run to getan element-by-element assessment of the coefficients as afunction of the specific (120590 119879) state and additionally of thespecific workpiece-die contact (dwell) time

In a first verification stage the proposed procedure wasvalidated against additional experimental data performedwith different specimen geometries not included in the opti-mization step of the coefficients After that the procedurewastested by comparing numerical predictions of the mandreldisplacement history with experimental data for an industrialextrusion die

3 Results and Discussion

Results of the calibration phase of the model are reported inFigure 5 for each level of tested stress and temperature for thecreep loading configuration For these conditions the dwelltime was imposed equal to 61 hours In Figure 6 a magnifi-cation of the typical comparison output that shows the peakmandrel displacement along the load direction is reportedas experimentally computed and numerically predicted overthe total testing time The average percentage error overall the simulated creep conditions was 127 correspondingto 006mm difference The applied methodology fits an

Advances in Materials Science and Engineering 7

ExperimentalNumerical

1 2 3 4 5 6 701 2 3 4 5 6 701 2 3 4 5 6 70

1 2 3 4 5 6 701 2 3 4 5 6 70

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus05minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 5 Experimental versus numerical displacement of the mandrel for each testing condition under the creep load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

minus050

minus045

minus040

minus035

minus030

minus025

minus020

minus015

minus010

000

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 6 Example of the comparison between experimental andnumerical results Experimental dots represent the data extrapolatedat the same time steps of the numerical predictions

average behavior since in a number of comparisons thenumerical data overestimate the experimental results whilein other cases the predicted displacement underestimates theexperimental oneThehigher discrepancywith the increasingtemperature was due to a premature failure of the specimenin the most critical conditions (ie 540∘C-800MPa 580∘C-600MPa and 580∘C-800MPa) that were not included inthe calibration phase of the coefficients As declared in theIntroduction the procedure is able to account for yielding

phenomena while damaging (material discontinuities) onesare neglected

The overall discrepancies can be considered acceptablealso accounting for possible small experimental uncertain-ties In Figure 7 the results for the different tested levelsof stress and temperature for the pure fatigue loading arereported As for the creep tests the testing configurationsthat led to a premature failure of the specimen during trialswere not included in the calibration step (540∘C-800MPa and580∘C-800MPa) The average percentage error was higherthan that for creep test and equal to 325 (0124mm) As canbe observed in Figure 7 the greatest experimental-numericaldiscrepancies are observed at highest temperature of 580∘Cthat for the specific investigated steel coincides with thetempering temperature thus leading to a fast deterioration ofthe mechanical properties not accounted for in the modelHowever process parameters are usually set in order to avoidthis level of temperatures in the tools or at least to get it inlimited portions of the material far from the yielding regionsIn addition at these conditions damage in the form ofmaterial discontinuities (cracks pores and voids) reasonablyappears and it is not modelled by the set of equations Thismade also the average error of 325 acceptable

A similar agreement between experimental and numeri-cal results as that found for the creep tests was determined incase of creep-fatigue loading condition with an average per-centage error of 143 all over the testing configurationscorresponding to 008mm (Figure 8)

As expected the peak percentage error was in each casefound for the combination higher temperature-higher stresslevel

8 Advances in Materials Science and Engineering

ExperimentalNumerical

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 7072 3 4 5 610

1 2 3 4 5 6 70 1 2 3 4 5 6 70

minus07minus06minus05minus04minus03minus02minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus16minus14minus12minus10minus08minus06minus04minus02

00

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 7 Experimental versus numerical displacement of the mandrel for each testing condition under the fatigue load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

380 (∘C) 490 (∘C) 540 (∘C) 580 (∘C)

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus08minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 701 2 3 4 5 6 70

72 3 4 5 610 1 2 3 4 5 6 70 1 2 3 4 5 6 70

1 2 3 4 5 6 70 1 2 3 4 5 6 70

Figure 8 Experimental versus numerical displacement of the mandrel for each testing condition under the creep-fatigue load (x-axis testingtime in hours y-axis specimen displacement in mm)

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CeramicsJournal of

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CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Biomaterials

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NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 7

ExperimentalNumerical

1 2 3 4 5 6 701 2 3 4 5 6 701 2 3 4 5 6 70

1 2 3 4 5 6 701 2 3 4 5 6 70

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus05minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 5 Experimental versus numerical displacement of the mandrel for each testing condition under the creep load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

minus050

minus045

minus040

minus035

minus030

minus025

minus020

minus015

minus010

000

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 6 Example of the comparison between experimental andnumerical results Experimental dots represent the data extrapolatedat the same time steps of the numerical predictions

average behavior since in a number of comparisons thenumerical data overestimate the experimental results whilein other cases the predicted displacement underestimates theexperimental oneThehigher discrepancywith the increasingtemperature was due to a premature failure of the specimenin the most critical conditions (ie 540∘C-800MPa 580∘C-600MPa and 580∘C-800MPa) that were not included inthe calibration phase of the coefficients As declared in theIntroduction the procedure is able to account for yielding

phenomena while damaging (material discontinuities) onesare neglected

The overall discrepancies can be considered acceptablealso accounting for possible small experimental uncertain-ties In Figure 7 the results for the different tested levelsof stress and temperature for the pure fatigue loading arereported As for the creep tests the testing configurationsthat led to a premature failure of the specimen during trialswere not included in the calibration step (540∘C-800MPa and580∘C-800MPa) The average percentage error was higherthan that for creep test and equal to 325 (0124mm) As canbe observed in Figure 7 the greatest experimental-numericaldiscrepancies are observed at highest temperature of 580∘Cthat for the specific investigated steel coincides with thetempering temperature thus leading to a fast deterioration ofthe mechanical properties not accounted for in the modelHowever process parameters are usually set in order to avoidthis level of temperatures in the tools or at least to get it inlimited portions of the material far from the yielding regionsIn addition at these conditions damage in the form ofmaterial discontinuities (cracks pores and voids) reasonablyappears and it is not modelled by the set of equations Thismade also the average error of 325 acceptable

A similar agreement between experimental and numeri-cal results as that found for the creep tests was determined incase of creep-fatigue loading condition with an average per-centage error of 143 all over the testing configurationscorresponding to 008mm (Figure 8)

As expected the peak percentage error was in each casefound for the combination higher temperature-higher stresslevel

8 Advances in Materials Science and Engineering

ExperimentalNumerical

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 7072 3 4 5 610

1 2 3 4 5 6 70 1 2 3 4 5 6 70

minus07minus06minus05minus04minus03minus02minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus16minus14minus12minus10minus08minus06minus04minus02

00

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 7 Experimental versus numerical displacement of the mandrel for each testing condition under the fatigue load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

380 (∘C) 490 (∘C) 540 (∘C) 580 (∘C)

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus08minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 701 2 3 4 5 6 70

72 3 4 5 610 1 2 3 4 5 6 70 1 2 3 4 5 6 70

1 2 3 4 5 6 70 1 2 3 4 5 6 70

Figure 8 Experimental versus numerical displacement of the mandrel for each testing condition under the creep-fatigue load (x-axis testingtime in hours y-axis specimen displacement in mm)

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 Advances in Materials Science and Engineering

ExperimentalNumerical

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 7072 3 4 5 610

1 2 3 4 5 6 70 1 2 3 4 5 6 70

minus07minus06minus05minus04minus03minus02minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus16minus14minus12minus10minus08minus06minus04minus02

00

0 1 2 3 4 5 6 7580 (∘C)

0 1 2 3 4 5 6 7540 (∘C)

0 1 2 3 4 5 6 7490 (∘C)

0 1 2 3 4 5 6 7380 (∘C)

Figure 7 Experimental versus numerical displacement of the mandrel for each testing condition under the fatigue load (x-axis testing timein hours y-axis specimen displacement in mm)

ExperimentalNumerical

380 (∘C) 490 (∘C) 540 (∘C) 580 (∘C)

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

400

(MPa

)

minus06

minus05

minus04

minus03

minus02

minus01

00

600

(MPa

)

minus08minus07minus06minus05minus04minus03minus02minus01

00

800

(MPa

)

minus12

minus10

minus08

minus06

minus04

minus02

00

minus07minus06minus05minus04minus03minus02minus01

00

minus05minus04minus04minus03minus03minus02minus02minus01minus01

00

minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

minus10minus09minus08minus07minus06minus05minus04minus03minus02minus01

00

1 2 3 4 5 6 7072 3 4 5 6101 2 3 4 5 6 701 2 3 4 5 6 70

72 3 4 5 610 1 2 3 4 5 6 70 1 2 3 4 5 6 70

1 2 3 4 5 6 70 1 2 3 4 5 6 70

Figure 8 Experimental versus numerical displacement of the mandrel for each testing condition under the creep-fatigue load (x-axis testingtime in hours y-axis specimen displacement in mm)

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 9

R

0 0002 0003 0005 0007 0009 0010 0013 0015Creep strain

(a)

R

Von Mises stress (MPa)3 113 223 332 442 552 661 771 881

(b)

R

Displacement (mm)minus045 minus04 minus034 minus029 minus024 minus019 minus014 minus009 minus004

(c)

Figure 9 (a) Equivalent creep strain for the testing condition of 490∘C and 400MPa (b) VonMises stress distribution and (c) displacementalong the load direction

In Figure 9 as example some output results of the FEsimulation performed according to the developed procedureat 490∘C temperature and 400MPa as stress level in thelegs are reported Specimen is shown in the deformed finalconfiguration after 61 hoursThe peak equivalent creep strain(Figure 9(a)) was found in the region of the connecting radiuswhere both the highest temperature and stress level werelocated

31 Verification against Specimens The comparison betweenexperimental and numerical results was made for two differ-ent geometries of the specimennot included in the calibrationphase of the coefficients Specimens differed for the values ofthe mandrel-legs connecting radius (R Figure 9) the valuesof 2mm used for the calibration phase and 1mm (R1) and3mm (R3) used for the verification one A reduced experi-mental plan was investigated for the R1 and R3 configurationsboth tested at two stress levels 400 and 800MPa but at fixedtemperature (540∘C) and dwell time (3 minutes) Results arereported in Figure 10 The effect of the characteristic radiuson the output results was significant especially at the higheststress level (800MPa) the R3 configuration ended the testwithout premature failure while the R1 configuration with asharper radius failed after only two cycles

For the lowest stress level (400MPa) the effect of thenotch radius was less significant and for both the R3 andthe R1 specimens the test was completed (61 hours) A goodaverage agreement was found for these specimen geome-tries between experimental and numerical results Averagepercentage error was less than 13 with a peak value of284 for the R3 configuration at the last cycle of the testperformed at 800MPa The errors for the R1 configurationtested at 400MPa were of the same order of magnitude whileat 800MPa data are not reported due to premature failure ofthe specimen after a reduced number of cycles

32 Verification against an Industrial Extrusion Die As laststep of the work the proposed procedure was applied to anindustrial extrusion die whose process data were monitoredand acquired during a controlled extrusion The selecteddie had a standard geometry with a three-leg mandrelequispaced at 120∘ commonly adopted in industry to produceround tubesThe specific extruded hollow profile was a 5mmthick tube with a 60mm outer diameter (Figure 11)

The die was made of H11 steel After 64 extrusion cycles(billets) the die was discarded due to an excessive permanentmandrel deflection equal to 032mmThis valuewas recordedby a feeler gauge after the die was dismounted from the

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

10 Advances in Materials Science and Engineering

R1R3

400

(MPa

)80

0 (M

Pa)

minus08

minus07

minus06

minus05

minus04

minus03

minus02

minus01

00

minus06

minus05

minus04

minus03

minus02

minus01

00

Disp

lace

men

t (m

m)

Disp

lace

men

t (m

m)

minus14

minus12

minus10

minus08

minus06

minus04

minus02

00

Disp

lace

men

t (m

m)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

0 1 2 3 4 5 6 7Testing time (hr)

Figure 10 Experimental versus numerical mandrel peak displacement over the testing time for the test performed at 540∘C and 400MPa forthe R1 and R3 specimen configurations

Figure 11 Mandrel of the porthole die used in the experiment

press In order to predict the pressure map on the die facesa steady-state process simulation was performed by means ofthe FE code Altair HyperXtrude (HX) [27] and by imposingboundary conditions in terms of friction and heat exchangecoefficients previously verified [28ndash30] With the aim ofverifying the robustness of code computations experimentaland numerical results were compared in terms of extrusionload profiles exit velocity and die and profile temperaturesA good agreement was foundwith percentage errors less than5 for each prediction (Table 4)

An FE model of the die was then generated in a differentFE code specifically dedicated to structural analyses (ANSYS

Table 4 Experimental versus numerical predictions for the indus-trial extrusion die

Experimental Numerical errorPeak extrusion load [tons] 3158 3290 41Exit velocity [mms] 121 115 49Die temperature [∘C] 423 440 40Profile exit temperature [∘C] 560 564 07

V170 Inc) in which the subroutines for (8) were defined intheAPDL language and then implemented A single solid wasgenerated including die and mandrel thus avoiding contactgeneration and then significantly reducing the computationaltime However this did not alter the output results due tothe rigid die-mandrel constraints asmade with reference pins(Figure 11) The aluminum pressure map applied to the diefaces in contact with the billet was imported from the processsimulation code (peak value 340MPa) as well as the temper-ature distribution (Figure 12(a)) Displacement constraintswere applied accounting for experimental settings the diefaces in contact with the bolster were fixed in the extrusiondirection while the nodes in contact with the saddle loadon the press were fixed in the other directions From theexperiment an extrusion time of 300 seconds was computedand imposed as dwell time for the subroutine calculationsin the FE simulation (Figure 12(b)) The total simulation

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 11

583552521490459428397365334303(a)

0

50

100

150

200

250

Extr

usio

n pr

essu

re (b

ar)

250 300 350 400 450 500 550200Extrusion time (sec)

(b)

Figure 12 (a) Temperature distribution [∘C] in the die as output from the process simulation Within the dashed area is the yielding region(b) Experimental pressure-time diagram for a single extrusion

minus0005 002 006 009 012 016 019 022 026 029

(a)0810 009 018 027 036 045 054 063 072

(b)

Figure 13 Die deflection [mm] along the extrusion direction as predicted with a static analysis (a) and according to the proposed procedure(b)

time was fixed to 166 hours corresponding to around 200extrusion cycles even if experimentally the die failed after 64billets

The standard industrial calculations used as bases fordie design decisions are usually static structural analysesequivalent to a single forming cycle In order to comparethe level of accuracy of such type of calculations with thoseperformed by means of more sophisticated computationslike those offered by the proposed procedure the outputmandrel deflection of the die was computed after one cycle(static) and after 200 extrusion cycles a reasonable numberfor a standard extrusion die life As showed in Figure 13 themandrel deflection was 028mm in loaded condition for thestatic computation (a) while it was 081 mm for themulticyclesimulation (b) as got by applying the procedure Thus it isinteresting to note that if 028mm is used as value to estimatethe die lifetime after 200 working cycles an error up to 64is committed

More in detail Figure 14 shows the trend of the mandreldisplacement with increasing the number of extruded billetsas computed by means of the developed procedure Aspreviously stated while after a single billet (static load) themandrel was displaced by 028mm under loading after 55billets the total deflection was increased to 065mm reachinga value 081mm after 200 billets So this type of informationcan be successfully used to define the number of workable

components in order to remain within the required toler-ances If for example it is experimentally tested or estimatedfrom practical experience that the maximum experimentalallowed die displacement is 05mm from the computationit emerges that a maximum of 12 billets can be consecutivelyextruded with the selected set of process parameters and diedesign

Concerning the comparison with the experimental mea-surement after 64 billets (032mm in unloaded condition)the numerical procedure predicted a mandrel deflection of067mm that was purged of the elastic quote of 028mmachieved in the first cycle and equalled 039mm A goodagreement was then achieved between experimental andnumerical prediction with an absolute error less than 01mm(007mm)

4 Conclusions

In the present work a novel modelling approach is pre-sented for the prediction of the time-dependent deformationundergone by hot forming tools in the creep-fatigue regimeNovel regression equations were developed to express thedependencies of the coefficients on the stress-temperaturestate in each point and on the dwell-time value representingthe workpiece-tool contact time typical of the specific appli-cation The extrusion context and the H11 (X38CrMV-5) tool

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

12 Advances in Materials Science and Engineering

Extr

usio

n di

rect

ion

028 mm

081 mm

065 mm

00

01

02

03

04

05

06

07

08

09M

andr

el di

spla

cem

ent (

mm

)

50 100 150 2000Number of billets

Figure 14 Total mandrel displacement [mm] against number of consecutively extruded billets as computed by the proposed model Threeplots of the FE simulation of the mandrel are reported as example

steel were selected as examples to describe and validate theprocedure however it is of general applicability to differentforming tools and to a variety of tool materials

Physical experiments performed at different levels ofstress and temperature and under three loading types (creepfatigue and creep-fatigue) were used to calibrate the coef-ficients of the novel equations Comparison of numericalpredictionswith experimental data showed a good agreementfor creep and creep-fatigue conditions with average errorsof 127 (006mm) and 143 (008mm) respectively Thepure fatigue condition was less well fitted showing an averageerror of 325 However in each tested condition the greaterexperimental-numerical discrepancies were found for themost critical conditions that is higher stress and temperaturelevels in which damage (material discontinuities) reasonablyappeared

Then two additional specimen configurations were usedas experimental data to be compared with numerical predic-tions For three of the four tested conditions under creep-fatigue load and 540∘C the average percentage error was lessthan 13The configuration with a sharper radius failed afteronly two cycles at the higher stress level (800MPa) so thatcomparison with numerical data was not feasible

In the last part of the work a verification was performedon an industrial extrusion die A very good agreement interms of permanent displacement after 64 consecutive cycles(billets) was achieved with an experimental value of 032against 039 numerically predicted by the proposed set ofequations

This confirmed the capability of the novel approach toaccurately account for the induced stress and temperaturestates as well as for the specific dwell time characteristic ofthe set of process parameters and die design The proposedprocedure can be therefore regarded as a valid support fordie designer in the ldquoa priorirdquo estimation of time-dependentdeformation of hot forming tools working under the creep-fatigue regime

Competing Interests

The authors declare that they have no competing interests

References

[1] J Lemaitre and J L Chaboche Mechanics of Solid MaterialsCambridge University Press Cambridge UK 1990

[2] R Domagaoj Lifetime Prediction and Constitutive Modeling forCreep-Fatigue Interaction vol 13 ofMaterialkundlich-TechnischeReihe Gebruder Borntraeger Berlin Germany 1996

[3] M Deshpande A Groseclose and T Altan ldquoSelection of diematerials and surface treatments for increasing die life in hotand warm forgingrdquo in Proceedings of the FIATECH TechnologyConference amp Showcase Paper no 644-FIA April 2011

[4] R Ebara and K Kubota ldquoFailure analysis of hot forging dies forautomotive componentsrdquo Engineering Failure Analysis vol 15no 7 pp 881ndash893 2008

[5] B K Kosec L Kosec and J Kopac ldquoAnalysis of casting diefailuresrdquo Engineering Failure Analysis vol 8 no 4 pp 355ndash3592001

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Advances in Materials Science and Engineering 13

[6] A F M Arif A K Sheikh S Z Qamar and K M Al-FuhaidldquoModes of die failure and tool complexity in hot extrusion ofAl-6063rdquo in Proceedings of the 16th International Conference onProduction Research (ICPR rsquo01) Prague Czech Republic 2001

[7] A F M Arif A K Sheikh and S Z Qamar ldquoA study ofdie failure mechanisms in aluminum extrusionrdquo Journal ofMaterials Processing Technology vol 134 no 3 pp 318ndash3282003

[8] A K Sheikh A F M Arif and S Z Qamar ldquoA probabilisticstudy of failures of solid and hollowdies in hot aluminumextru-sionrdquo Journal of Materials Processing Technology vol 155-156no 1ndash3 pp 1740ndash1748 2004

[9] A Kocanda ldquoDie deformation and geometry of extruded com-ponentsrdquo in Proceedings of the 2nd International Conference onIndustrial Tools (ICIT rsquo99) pp 69ndash78 Rogaska Slatina SloveniaApril 1999

[10] M M Kostic and L G Reifschneider ldquoDesign of extrusiondiesrdquo in Encyclopedia of Chemical Processing S Lee Ed pp633ndash649 CRC Press New York NY USA 2007

[11] T Pinter and B Reggiani ldquoQuantitative evaluation of portholedies design practices by means of FE analysesrdquo in Proceedings ofthe Aluminum Two Thousand 8th World Congress Milan ItalyMay 2013

[12] D Pietzka N B Khalifa L Donati L Tomesani and A ETekkaya ldquoExtrusion benchmark 2009 experimental analysis ofdeflection in extrusion diesrdquo Key Engineering Materials vol424 pp 19ndash26 2010

[13] B Reggiani L Donati and L Tomesani ldquoEvaluation of differentFE simulation codes in the stress analysis of extrusion diesrdquoInternational Journal of Material Forming vol 3 no 1 pp 395ndash398 2010

[14] Z Ahmer V Velay G Bernhart and F Rezaı-Aria ldquoCyclicbehaviour simulation of X38CRMOV5-47HRC (AISI H11)-temperedmartensitic hot-work tool steelrdquo International Journalof Microstructure and Materials Properties vol 3 no 2-3 pp326ndash335 2008

[15] S T Wang R S Lee H Y Li and C H Chen ldquoOptimaldie design for three-dimensional porthole extrusion using theTaguchi methodrdquo Proceedings of the Institution of MechanicalEngineers Part B Journal of Engineering Manufacture vol 220no 6 pp 1005ndash1009 2006

[16] V Velay G Bernhart D Delagnes and L Penazzi ldquoA con-tinuum damage model applied to high-temperature fatiguelifetime prediction of a martensitic tool steelrdquo Fatigue andFracture of Engineering Materials and Structures vol 28 no 11pp 1009ndash1023 2005

[17] C Sommitsch R Sievert T Wlanis B Gunther and V WieserldquoModelling of creep-fatigue in containers during aluminiumand copper extrusionrdquoComputationalMaterials Science vol 39no 1 pp 55ndash64 2007

[18] J L Chaboche ldquoConstitutive equations for cyclic plasticity andcyclic viscoplasticityrdquo International Journal of Plasticity vol 5no 3 pp 247ndash302 1989

[19] J L Chaboche ldquoOn somemodifications of kinematic hardeningto improve the description of ratchetting effectsrdquo InternationalJournal of Plasticity vol 7 no 7 pp 661ndash678 1991

[20] VVelay G Bernhart and L Penazzi ldquoCyclic behaviormodelingof a tempered martensitic hot work tool steelrdquo InternationalJournal of Plasticity vol 22 no 3 pp 459ndash496 2006

[21] B Reggiani L Donati J Zhou and L Tomesani ldquoThe roleof creep and fatigue in determining the high-temperature

behaviour of AISI H11 tempered steel for aluminium extrusiondiesrdquo Journal of Materials Processing Technology vol 210 no 12pp 1613ndash1623 2010

[22] V Velay D Delagnes and G Bernhart ldquoAdvances in cyclicbehavior and lifetime modeling of tempered martensitic steelsbased on microstructural considerationsrdquo Key EngineeringMaterials vol 378-379 pp 81ndash100 2008

[23] R K Penny and D L MarriottDesign for Creep McGraw-HillMaidenhead UK 1971

[24] H Berns C Broeckmann and H F Hinz ldquoCreep of high speedsteels part I-experimental investigationsrdquo in Proceedings of thethe 6th International Tooling Conference pp 325ndash337 KarlstadUniversity Karlstad Sweden September 2002

[25] H Berns and F Pschenitzka ldquoDas Kriechverhalten von War-marbeitsstahlen mit 5 Chromrdquo Materialwissenschaft undWerkstofftechnik vol 11 no 7 pp 258ndash264 1980

[26] B Reggiani L Donati and L Tomesani ldquoThermal-electricsimulations for the temperature settings in a creep-fatigue testrdquoin Proceedings of the 27th Danubia Adria Symposium WrocławPoland September 2010

[27] HyperXtrude (version 120) Simulation software for Extru-sion Process Altair Engineering Inc USA httpwwwaltair-hyperworkscom

[28] B Reggiani A Segatori LDonati andL Tomesani ldquoPredictionof chargewelds in hollow profiles extrusion by FEM simulationsand experimental validationrdquo International Journal of AdvancedManufacturing Technology vol 69 no 5ndash8 pp 1855ndash1872 2013

[29] C Zhang G Zhao Z Chen H Chen and F Kou ldquoEffect ofextrusion stem speed on extrusion process for a hollow alu-minum profilerdquoMaterials Science and Engineering B Solid-StateMaterials for Advanced Technology vol 177 no 19 pp 1691ndash16972012

[30] M Reddy and L Mazzoni ldquoBenchmark resultsrdquo in Proceedingsof the 2nd International Conference on Extrusion and Bench-mark pp 99ndash102 Bologna Italy September 2007

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials