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Design Guide for Steels at Elevated Temperatures and High Strain Rates

4 MA TERIAL PROPERTY D A TA FOR STEELS UNDER HIGHSTRAIN-RATE LOA DING

4 .1 In t roduc t i onThis chapter provides information on materialproperty data that can be used in the design ofoffshore structures against explosions. Data isprovided to enable the engineer to use bothsimplified methods and advanced non-linearmethods.4.2 Methods o f m easur ingNumerous techniques are employed to determinethe strain-rate sensitivity of steels. The objectiveis to obtain material properties that areunaffected by the instrumentation used, theeffects of inertia, friction or by the method ofprocessing the results. Quasi-static machines,such as screwdriven Instrons andservo-hydraulic machines, normally generatedata for strain rates between and10' s-'. Formedium rates (10' to lo2 s-I), cam and wedgeplastometers and drop hammers are used. Asstructural components of offshore installationsunder hydrocarbon-based blast loadingexperience strain rates within the range tolo2 s-', only the quasi-static, cam and wedgeplastometer and drop hammer methods arediscussed.

strain-rate ef fect s

4. 2 . 1 Quas i -s ta tic methodsQuasi-static methods comprise hydraulic testingmachines used routinely at low strain rates for avariety of tests. They have in some cases beenused successfully at medium strain rates. Whenoperating in the medium strain rate region,however, it is necessary to consider carefullythe compliance of the testing machine,especially as this may change dramaticallydepending on the size of the specimen beingtested and whether the machine is operating intension or compression.4 . 2 . 2 Cam and wedge p las tometersThe cam plastometer incorporates alogarithmic-shaped cam to change the speed indirect proportion to the instantaneous length ofthe specimen. In this way, a constant strain rate

is maintained. The energy for the deformation isobtained from a rotating flywheel.The principal advantage of this machine is thati t can produce large plastic strains and that thereis no severe impact during the engagement ofthe cam and specimen. However, the maximumstrain rate obtainable with the cam plastometeris of the order lo2 s.' before friction or theinertia effects becomes significant.A wedge plastometer is activated by a linearcam as opposed to a logarithmic one. In this,compression testing is possible in multiplestages, under constant engineering or naturalstrain rate at any selected temperature.Essentially, the principles are similar to therotational cam plastometer, but the energysource is a hydraulic press instead of a flywheeland the cam is effectively a profiled wedge thatis pulled over the cam follower to produce thecompression.4 . 2 . 3 D ro p h am m e rThis is essentially a mass released from acertain height onto the specimen, which rests ona load cell. The top is guided by rails. Theimpact velocity of the mass is usually measuredby photo-diodes or a laser light beam and theinstantaneous height of the specimen ismeasured by a resistance slide wire, acapacitance transducer or by high-speedphotography. The load is measured from a loadcell placed between the specimen and a rigidanvil. The instantaneous force and displacementcurves are then cross-plotted by eliminating timeto give force - displacement and stress-strain atthat particular impact velocity. Drop forges havebeen used in the medium strain rate region.It is important to recognise that the strain rateduring a drop forging test, particularly if largestrains are involved, is not constant. Mostinvestigators who have used this device have,therefore, referred to a mean strain rate. It isnoted that deviation from this mean may be asmuch as two or three times. Clearly the strainrates obtainable with devices such as these can

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be greater than those obtained using the camplastometer.4.3 Structural Carbon SteelsAlthough information on the strain rate effectson carbon steels is extensive, it predominantlyrelates to steel behaviour either at low strainrate and high temperatures or at very high strainrates and at room temperature (at least an orderof magnitude greater than those encountered inhydrocarbon explosions).This is not surprising, due to the interest fromthe metal forming, power and defenceindustries.Though information is available on mild steels(yield strength 240-275 N/mm*), virtually noinformation is available on the medium and highstrength structural steels that are commonly usedtoday (yield strength 345-460 MPa). Suchtesting as has been done has had as its chiefobjective the characterisation of Charpy Vnotched properties. This is not surprising, sinceall standards for such steels (eg BS EN 10025)do not include dynamic requirements except forthe impact Charpy test.The work that was performed by British Gas aspart of the Blast and Fire Engineering Projectfor Topside S tructures in 1991('), attempted toextract experimental data from the literature onsteels nearest in composition to those used inoffshore structures. That review mainly focussedon BS 4360 Grade 50D steels. Since 1991,however, BS 4360 Specification fo r weldablesteels has been superseded by BS EN 10025 Hotrolled products of non-alloy structural steels andBS 7191 Steels for ogshore structures. With theintroduction of these new Standards, newmanufacturing processes (thermo-mechanicallyrolled and quenched and tempered steels) andnew higher strength steels (yield stress typically450MPa), i t is not possible to apply withconfidence the 1991 data to these new steels.Although analytical expressions of therelationships between the properties consideredand the rate and other parameters that influencethese properties exist, they cannot be usedgenerally for all carbon steels. This is becausethe relationships proposed are not definitive norvalid throughout the range of rates and because

noticeably different behaviour is experienced bysteels with different composition.The commonly used mechanical properties ofsteel that are obtained in quasi-static tests atabout per sec rate of straining, will bedifferent when tested at higher strain rates. Thesteel yield stress and ultimate strength willincrease and the strains corresponding to thesestresses, as well as the strain at the beginning ofthe strain hardening range, will either increaseor remain constant with increasing strain rate.However, the steel modulus of elasticity will notbe significantly influenced by the rate ofstraining. Figure 4.1 presents stress-strainprofiles up to fracture for low-carbon mild steelat different strain rates").

Strain ra te s .'A - 106B = 55c - 2D - 0.22A E = 0.001

lW t0 0.1 0.2 0.3 0.4 0. 5

Strain

Figure 4.1 EfSect of strain rates onbehaviour of mi ld steelResults from dynamic tensile tests on low-carbon steels have been recorded over a longperiod of time and have been collated bySymonds").Dynamic tests have revealed that steels withlower yield strength are relatively more sensitiveto strain rate variations than steels with higherstrength. Other factors, such as the chemicalproperties and the manufacturing process, alsoinfluence the strain rate effects. This is clearlyshown in Figure 4.2, where the dynamicincrease factor for yield strength versus strainrate is plotted for a mild steel (ASTM A36 steelwith static yield stress of 250 MPa) and for ahigh strength, quenched and tempered steel(ASTM A514 steel with yield stress approx 760MPa)"".

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4.4 Cowper-Symonds RelationshipRelationships have been developed whichattempt to model strain rate dependency in steelsand other materials. The relationship that wasput forward by Cowper-Symonds"" is the onethat is most commonly used to calculate theenhancement of stresses due to strain rateeffects. The relationship is expressed as follows:

where(J d is the dynamic stress at a particular

strain rateoS is the static stress& is the uniaxial plastic strain rateand D and q are constants which arespecific to the steel.

For engineering purposes, the values of theconstants usually quoted for mild steel are thosedetermined by Symonds'') with D= 40.4 s-' andq=5. These values were obtained from dynamicuniaxial tensile tests that produced strains up toonly a few percent. (24%). Thus, theseparticular values are valid for estimating thedynamic flow stresses in the neighbourhood ofthe yield stress and for relatively small plasticstrains.

To describe the strain sensitive behaviour ofmild steel at the ultimate tensile stress,Campbell and Cooper"*' have shown that valuesof D=6844 .' and q=3.91 are appropriate. Dueto the variety of values for coefficients D and qthat have been obtained from differentexperimental studies, it is clear that there is aneed to conduct dynamic tensile tests to obtainthe dynamic material properties for the specificmaterial involving large plastic strains.For other structural grades of carbon steel theInterim Guidance notes for the design andprotection of topside structures against explosionand fire('3' recommends that dynamic yieldstresses can be derived from the results for mildsteel using the following equation:

II \ -

odYnu , 2 5 + 2 1 0 [ % ) q

Alternatively, D=300 s- ' and q=2.5 could beused to describe the behaviour at 5 % strain.

1 7 I II I I

where q is the specified minimum yield stressof the steel (in MPa) and D and q are as formild steel.This relationship is useful primarily to obtaindata for steels with yield stress in the vicinity of355 MPa. The relationship, however, may notbe valid for higher strength steels such as BS7191:Grade 450 EM steels and BS EN 10025:S420 and S460 teels.

Figure 4.2 Dynamic increase factor for yield strength of mild and high strength steel versusstrain rate""30 FABIG Technical Note 6 - September 2001

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4.5 Stainless steels

0 . m

Parameters for the Cowper - Symondsrelationship have also been derived for stainlesssteel("). The values of D and q quoted for Grade304 stainless steel a re D = 100 s -' and q = 10.

2, T .- I

Recently experimental work was undertaken byUniversity of Liverpool for the SteelConstruction Institute'l4). Static and dynamictensile tests were performed on three stainlesssteels; Grade 1.4404 (316L), Grade 1.4362(SAF 2304) and Grade 1.4462 (2205) steels.Stainless steels have a strong strain-ratedependency; strengths are increased (particularlyin the region of the 0.2%proof strain) for highstrain rates and the rupture strain is reduced.Figure 4.3 shows a typical strain versus timecurve for a dynamic tensile test, illustrating howthe strain rate can be idealised as two discreteslopes representing the pre- and post- yieldstrain rates i., and E.,espectively.

0.03 r

may be enhanced to ad, , to take advantage ofthe improvement in strength due to the highstrain rates. o d y n is given by:

The enhancement of stresses as a result of highstrain rates can also be represented by theCowper - Symonds empirical relationship. (SeeSection 4.4.)The Cowper-Symonds constants D and q , for316L, SAF2304 and 2205 stainless steels, whichhave been obtained from least mean squaresfit"') a re given in Table 4.1.Table 4.2 and Table 4.3 give values of thestrain rate enhancement factor KSR or the 0.1 %,0.2%an d 1% proof strengths ( ( K S R ~ O, (KSR)O,and ( K S R ) I respectively) for a range of pre-yield strain rates k y Values of KSR for theultimate tensile strength ( (KsdUTs)or a range ofpost-yield strain rates i, are also givenalongside the rupture strain g f .

G I0.025t0.02' .0150.01 1

n m @ I

Figure 4.3 Typical strain-time curve for atensile test on stainless steelThe minimum specified values of 0.2% nd 1 %proof strength q0.2and f i . 0 ~ ) and the ultimatetensile strength Cr;) are given in EN 10088-2,based on 'static' tests to EN 10002-1. The strainrates for static tests defined in EN 10002-1 are:iy< 2.5 x l o 3 s-' f oZpand, where specified for fi.@iU< 8.0 x lo6 s-' for strengths at strainsgreater than 1.0% roof strainFor general design in stainless steel, the designstrength cry is taken as the minimum specified0 . 2 %proof strength fo p. However, when blastloading is being considered, the design strength

Design Guide for Steels at Elevated Temperatures and High S train R ates


Using the strain rate enhancement factors givenin Table 4.2 and Table 4.3 the typically usedstrengths at known proof strains, it is possible toconstruct a simplified linearized stress-straincurve for a particular strain rate. A family ofcurves can be generated for a range of strainrates thereby producing full enhanced stress-strain curves. These curves can then be used forassessments of the plastic deformation usingnon-linear finite element analysis (NLFEA).Figure 4.4 shows one linearized stress-straincurve for a particular strain rate.

Figure 4.4 Linearized stress-strain curveallowing for strain rate effects

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Design Guide for Steels at E levated Temperatures and High S train R ates

Table 4.1 Cowper - Symonds constants fo r stainless steelsMaterial Proof D 4 0 0strength d MPa

316L 0. 1% 471 5.76 2630. 2% 240 4.74 277SA F 2304 0. 1% 22.0 2. 51 516635 (ah) 4.04alt)0. 2% 3489 5. 77 5272205 (318) 0.1% 769 5. 13 5440. 2% 5958 6. 36 575

Table 4.2 Strain rate enhancement for 0.1%, 0.2% and I .O % proof strengths, fo r stainless steelsGrade % 0 0 . 1 (KSd0.I 0 . 2 (Ksdo.2 q . 0 ( ~ S d I . 0

(d) (N/mm2) (N/mIl12) (N/m2)1A04 1.38e-4 269 0.93 276 0.92 316 0.94(316L) 0.0017 287 0.99 296 0.99 332 0.990.0025 291 1 . oo 300 1 . oo 335 1 . oo0.0086 304 1.04 313 1.04 346 1.030.0178 311 1.07 321 1.07 352 1.05

0.0880 327 1.12 338 1. 13 366 1.097.4200 372 1.28 385 1.28 404 1.211.4362 1. 3844 525 0.97 548 0.96 615 0.97(2304) 9.9e-4 536 0.99 562 0.98 626 0.99OOO25 543 1.00 572 1. oo 634 1 . oo0.0055 549 1.01 581 1.02 641 1.010.01 1 555 1.02 588 1.03 647 1.020.10oo 572 1.05 613 1.07 666 1.055.3900 604 1 . 1 1 656 1.15 700 1.101,4462 1.38e-04 565 0.95 596 0.95 680 0.96(2205) 0.0024 591 1. oo 627 1. oo 705 1 . OO

0.0025 592 1.oo 627 1.oo 705 1. oo0.0055 60 1.02 638 1.02 715 1.010.0112 610 1.03 648 1.03 723 1.030.1230 639 1.08 682 1.09 751 1.076.4800 688 1.16 737 1.18 797 1. 13

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Design Guide for Steels at Elevated Temperatures and High Strain RatesTable 4.3 Strain rate enhancement fo r ultimate tensile strength, fo r stainless steels

Grade 6 " 0, ( K S d U T S &f( s - 9 ( N / I d ) GL =60-m(%)

1.4404 1.38e-04 597 0.97 58.72.50e-03 619 1.01 49.38.63e-03 628 1.02 50.31.78e-02 632 1.03 50.08.8Oe-02 644 1.05 51.07.42e +00 658 1.07 52.71.4362 1.38-04 739 0.98 36.02.5e-03 758 1.01 28.05.50e-03 766 1.02 26.01.1 le-02 769 1.02 29.71 Ooe-Ol 779 1.03 29.05.39e+00 790 1.05 30.71.4462 1.38e-04 813 0.97 34.3(2205) 2 . e - 0 3 84 1 1.oo -2.5Oe-03 847 1.01 29.05 S3e-0 3 862 1.03 29.31.12e-02 867 1.03 30.01.23e-01 887 1.05 30.06.48e +00 905 1.08 28.3

(316L) 1.69e-03 615 1.oo

(2304) 9.9Oe-04 754 1.oo

4.6 Strain rate testsThe Steel Construction Institute commissioned aseries of tests, on behalf of the HSE, on highstrength structural steel plate to ascertain thesensitivity of their mechanical properties tostrain rate. Strain rates used in the testing werein the range O.OOl/sec to 10 /sec. The resultshave been published as an OTO report (OTO200 1/020 (~)).The material grades tested were 355EMZ in thenormalised and thermo-mechanically rolledcondition and 450EMZ in the quench andtempered condition, both to BS 7191. Bothgrades were supplied by Corns.Material properties measured were the upperyield strength (UYS), the lower yield strength(LYS) and the ultimate tensile strength (UTS).Strengths at numerous proof strains were alsomeasured, to enable stress-strain profiles for arange of strain rates to be produced.Detailed analysis of the test results is presentedin Appendix B. This analysis shows that ahigher level of confidence is achieved in the

following analyses when plastic true strain(determined using deformed length) is usedrather than total strain and when true stress(determined using deformed cross-sectional area)is used rather than engineering stress. From thisit is clear that the properties are governed bytrue stress and plastic strain.The engineering proof stress (s) values wereconverted into true stress (a) as follows(Dieter''''):cr =s(1+e )where e is the conventional engineering proofstrain equal to the plastic extensiondivided by the original und eform edgauge length,

s is the engineering stress defined asthe load divided by original un-deformed cross sectional area, andis the true stress defined as the loaddivided by deformed cross sectionalarea


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The engineering strain values e were alsoconverted to true strain (E) as follows:E =Zn ( +e )True strain E is the plastic extension divided bythe deformed gauge length.Regression analysis of the log of the tensileproperties versus the log of the strain ratesenabled equations of the following form to bedeveloped:

An advantage of having a single expressionwhich deals with both strain rate and strainhardening (as in the above equation) is that thestress at any combination of strain rate andstrain can be calculated from a single value.Thus, the Dynamic Increase Factor which onlyincorporates strain rate has been replaced by theIncrease Factor which incorporates both strainrate and strain hardening . For the proof stressvalues Lncrease Factors relative to a strain rateof 0.001 per sec and a proof strain of 0.2%were calculated by dividing the calculated stressat a given strain rate and strain by the 0.2%proof stress at the strain rate of 0.001 per sec.4.6.1 Tests on 355EMZ steelTh e 355EMZ steel in the normalised condition(N ) was supplied in three plate thicknesses of 12mm, 30 mm and 60 mm, whilst the thermo-mechanically rolled steel (TMCR) was suppliedin one thickness only of 11.5 mm.

where jkCJ

n

is the elastic limit stress, MPais the stress MPa at a true strainof 1.0,is load divided by deformedcross sectional area (true stress)is the strain hardening exponent,E is the proof strain,d E

mis the plastic strain rate sec-',is the strain rate exponent.

-dt andThe addition of the j stress was necessary inorder to linearize the log/log relationships and toobtain a high correlation coefficient. For theLYS, UYS and UTS values the strain hardeningcomponent is not applicable and the expressionused becomes:

m~ = k ( $ ) + jStructural engineering calculations may use totalstrain rather than proof strain and engineeringrather than true stress. The total strain includeselastic strain which depends on the stress whichis being calculated. The expression for truestress is therefore modified to enableengineering stress values to be calculated for agiven total strain with the following recursiveequation:

o = k [ Z n ( l i e , -%)]"($)"j

For the LYS, UYS and UTS values the IncreaseFactor is the value at a given strain rate dividedby the value at 0.001 per sec. Table 4.4presents strain-rate enhancement factors forsimplified methods, while Table 4.5 givesregression coefficients to be used in conjunctionwith the expression for true stress above foranalysis; both are for grade 355 EMZ TMCRsteels.Table 4.6 presents strain-rate enhancementfactors for simplified methods, while Table 4.7gives regression coefficients to be used inconjunction with the expression for true stressabove for analysis; both are for grade 355EMZnormalised steels.

where e, is the total engineering strain

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Design Guide for Steels at E levated Temperatures and High Strain Rates

Table 4.4 Strain rate enhancement factors for Grade 355EMZ TMCR steels (source, OTO20011020)'y (KSR)UYS (KSR)LYS (KSR)vrS (KSR)0 .2 (KSR)O.S ( KSR ) t .O (KSR) j .O (KSR)S.O (KSR)lO.O (KSR)IJ.O

(S.9

0.001 1.00 1 OO 1 1.oo 1.oo 1.oo 1.oo 1.oo 1.oo 1.oo0.01 1.05 1.04 1.02 1.01 1.02 1.02 1.02 1.02 1.02 1.020.1 1.10 1.08 1.05 1.03 1.04 1.04 1.04 1.04 1.05 1.051 1.17 1.13 1.07 1.04 1.06 1.06 1.06 1.06 1.07 1.0710 1.25 1.18 1.10 1.06 1.07 1.09 1.09 1.11 1.09 1.09100 1.34 1.25 1.13 1.07 1.10 1.10 1.11 1.11 1.12 1.10

Table 4.5 Regression coefficients fo r Grade 355EMZ TMCR steels (source, OTO 20011020)0.2-15%Strainegression coefficients W S ULS UTS

i 300 300 300 100k 181 153 229 821m 0.07 0.059 0.025 0.012

Table 4.6 Strain rate enhancemenr factors for Grade 355EMZ Normalised steels (source, OTO20011020)" ( K S R ) W S (KSR)LYS (KSR)vrS ( K S R ) 0 . 2 (KSR)O.S (KSR)I.O ( K S R ) Z . O (KSR)S.O (KSR)IO.O (KSR)IS.O

(S.9

0.001 1OO 1OO 1 OO 1 OO 1 OO 1 .OO 1 oo 1 oo 1.oo 1OO0.01 1.06 1.04 1.03 1.02 1.02 1.03 1.03 1.03 1.03 1.030.1 1.12 1.09 1.06 1.03 1.04 1.05 1.05 1.06 1.06 1.061 1.21 1.15 1.09 1.05 1.06 1.07 1.08 1.09 1.08 1.0910 1.31 1.21 1.13 1.07 1.09 1.10 1.11 1.12 1.12 1.12100 1.43 1.29 1.16 1.08 1.11 1.12 1.14 1.15 1.15 1.16

Table 4.7 Regression coeflcients for Grade 355EMZ Normalised steels (source, OTO 20011020)0.2-15%Strainegression coefficients W S ULS UTS

i 300 300 300 100k 182 151 257 937m 0.087 0.069 0.029 0.015


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4.7 Tests on 450EMZ steel Details of the tests are presented in Appendix B .The results obtained for the 450EMZ steelspecimens were analysed in the same manner asthat described above for the 355 EMZ steels andthe same equations apply.

Table 4.8 presents -strain-rate enhancementfactors for simplified methods, while Table 4.9gives regression coefficients to be used inconjunction with the expression for true stressabove for analysis; both for grade 450 EMZquenched and tempered steels.

Table 4.8 Strain rate enhancement factors for Grade 450 EMZ Normalised steels (source, OTO2001 /020)% (KSR)UYS (KSR)LYS ( K s R ) ~ (KSR)O.Z (KSR)O.S (KSR)I.O (KSR)Z.O (KSR)S.O (KSR)IO.O (KSR)IS.O(S?

0.001 1 oo 1 oo 1 oo 1 OO 1 oo 1 OO 1 OO0.01 1.04 1.02 1.03 1.01 1.01 1.01 1.020.1 1.09 1.05 1.06 1.01 1.02 1.02 1.041 1.17 1.09 1.09 1.02 1.03 1.04 1.05

.oo 1OO 1.00.02 1.03 1.02

.04 1.06 1.06.07 1.09 1.0910 1.27 1.13 1.13 1.03 1.05 1.06 1.07 1.10 1.13 1.13100 1.42 1.19 1.17 1.03 1.06 1.07 1.10 1.10 1.17 1.17

Table 4.9 Regression coeflcients for Grade 45OEMZ Normalised steels (source, OTO 2001 /020)Regression coefficients U Y S ULS UTS 0.2-15%StrainJ 400 400 400 400

k 116 86 174 535rn 0.148 0.09 0.047 0.038

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