Materials Science and Engineering A 480 (2008) 209217

Predictive modeling of multi-tractee

att. LafLafa5 Ju

Abstract

Laser har ncludquenchant. T be uOne known henThis study f percombined w ch wedimensional modtests and the -tracparameters o widtdepths up to 2007 Elsevier B.V. All rights reserved.

Keywords: Laser hardening; Back tempering; Multi-track hardening; Phase transformation; Modeling

1. Introdu

In recenfor selectivdelivers a la short timrial beneatincident. Tthe bulk ofcooled quicirons are gotheir goodbenefits, inof distortio

Despitehas been liation. Thea waveleng

CorresponE-mail ad

0921-5093/$doi:10.1016/jction

t years, lasers have proved to be an effective toole surface hardening. In laser hardening, a laser beamarge amount of heat to the surface of the material ine. This heat is conducted into the bulk of the mate-h the point on the surface where the laser beam ishe surface is heated quickly and then quenched bythe material and air. If heated for long enough andkly enough, a hardened layer forms. Steels and castod candidates for simple laser hardening because of

hardenability [1]. Laser hardening has some inherentcluding no need of a quenchant and the minimizationns due to thermal stresses.these advantages, widespread use of laser hardeningmited by the low absorptivity of metals to laser radi-most widely used lasers have been CO2 lasers, withth of 10.6m, but the normal absorptivity of metals

ding author. Tel.: +1 765 494 9775/6900; fax: +1 765 494 0539.dress: shin@ecn.purdue.edu (Y.C. Shin).

at that wavelength is very low [2]. Recently, the introductionof high power lasers with different wavelengths, e.g., Nd:YAGor diode lasers, has made laser assisted hardening an attrac-tive candidate for surface hardening processes. Steels exhibit40% absorptivity for diode laser (0.8m) radiation. In addition,diode or Nd:YAG lasers are smaller in size and have better beamdelivery systems as compared to CO2 lasers. Rectangular beamprofiles are readily available with diode lasers, providing uni-form heat flux over a large area, thus making laser hardeningfaster and more uniform.

Many studies have been made to assist the design of laserhardening processes and to improve the understanding of theunderlying physics. Shercliff and Ashby [3] developed anapproximate heat flow model, based on Ashby and Easterlings[4] model for laser hardening, to determine critical values ofdimensionless parameters to predict the laser operating condi-tions for hardening and to determine the case depth. Yang et al.[5] and Yang and Na [6] developed process charts in terms ofdimensionless parameters comprising of laser beam size, scan-ning rate and power to define a relationship between powerdensity and interaction time for tool steels, and proposed anempirical relation to predict the case depth in laser hardening.

see front matter 2007 Elsevier B.V. All rights reserved..msea.2007.07.054of AISI 4140 sRitesh S. Lakhkar a, Yung C. Shin a,, M

a School of Mechanical Engineering, Purdue University, Wb School of Materials Engineering, Purdue University, W.

Received 30 March 2007; accepted

dening provides benefits over the conventional hardening processes, ihis process is also faster than conventional hardening processes and canproblem with laser hardening in steels, however, is back tempering w

ocused on the development of a numerical model to predict the back temith existing models of thermal behavior and phase change kinetics, whihardness profiles after multiple track laser hardening. The combinedn used to predict and optimize the laser hardened case depth in multiptimized to obtain maximum case depth with the least variation along2 mm were obtained with 5 mm overlapping of laser tracks.k laser hardeningl

hew John M. Krane bayette, IN 47907, United statesyette, IN 47907, United Statesly 2007

ing minimum distortion in the parts and the absence of ased for selective hardening of specific areas of components.a large area is hardened by multiple, overlapping passes.ing in multi-track laser hardening. A tempering model wasre developed earlier in the authors group, to predict three-el was first validated through multi-track laser hardening

k laser hardening of AISI 4140 steel. The predictions andh of the hardened zone were experimentally verified. Case

210 R.S. Lakhkar et al. / Materials Science and Engineering A 480 (2008) 209217

But these dimensionless parameters which were based on cir-cular Gaussian beam were not applicable to the diode laser setup with amade by Ghardeningperature dinumerical hbeam profilworkpiecetransfer anof the matethree-dime

Skvarenmodel, whicase depthdone by Aset al. [11]multidimenof steels. Sexperimenthardness odiameter wpower. Lasgroove on abeneath thedicted and

One of tlaser hardetracks in mare used, thtracks, lead[12]. Lin anlapped tracsteels similout by movwhich caushardening wCO2 laser w3.5 mm/turwith a peakformity ofconcludedof the matoped durinby Ehlers ewith operadepth.

Crackinlapping ofusing 038improves tsteel compresistanceof the steeprofiles wiback tempenot address

multi-track laser hardening in their research. They reported pres-ence of soft band zone in hardness between two overlapped scans

r beam. Yang et al. [5] calculated the residual stresses inpass laser hardening. They concluded that the residualstress is present on the hardened surface, if the distancen the adjacent laser passes is larger than the width of eachass.n though some studies of multi-track laser hardeningeen done, no numerical model has been developed to

t the case depth profile, hardness values and back tem-effects in multi-track laser hardening. While Skvareninains [9] model is helpful in determining the hardnessof a single laser hardened track, there is a need for a

ical model for back tempering to predict final hardnesss in multi-track laser hardening. Availability of such awill be useful in designing the laser overlapping patternserating conditions to achieve uniform hardness and caseThe model in this study is used for laser hardening of140, ubiquitous alloy steel. The integrated model consist-a three-dimensional transient temperature model and ahardeningtempering model is developed to predict the

epth,arde

erma

primg of plaseansfer frod raroun

surfphyo profor

latin

Frectangular top hat profiled beam. An attempt wasalantucci and Tricario [7] to use a diode laser in laserand develop a numerical model to predict the tem-stribution in the material. Tian et al. [8] developed aeat transfer model for laser heating with an arbitrarye to predict the temperature distribution in a finite flatby taking into account convection and radiation heatd temperature dependence of the thermal propertiesrial. This model was based on energy diffusion for

nsional transient conduction.ina and Shin [9] developed a two-dimensional kineticch addressed some of the issues such as prediction ofin two-dimensions. This model was based on the workhby and Easterling [4], Inoue et al. [10] and Ohmura. The latter two groups of researchers developedsional carbon diffusion models for laser hardeningkvarenina and Shin [9] successfully predicted andally achieved a case depth of 2.5 mm with uniformf 57 HRC in the AISI 1536 steel cylinder of 60 mmith 2.9 mm/s scanning speed and 1220 W diode laserer hardening of a complex feature, viz., a 2 mm deep

cylindrical workpiece, with a case depth of 1.5 mmgroove with uniform hardness of 55 HRC, was pre-

experimentally achieved by Skvarenina and Shin [9].he limiting factors that prevented the extensive use ofning in industry has been back tempering of hardenedulti-track laser hardening. When multiple laser trackse later track causes the back tempering of the previousing to non-uniform hardness profiles and case depthsd Ericsson [13] carried out studies on effects of over-ks on fatigue property of cylindrical workpieces ofar to AISI 4140. The hardening process was carrieding a round focusing spot of 5 mm along a spiral tracked an overlapping zone of about 2.1 mm. This laseras carried out using 1100 W to 1300 W power with aith a scan speed of 3.13.6 m/min and a feed rate of

n. A maximum case depth of 0.46 mm was obtainedhardness value of 750 HV. However, degree of uni-

hardness profile was not measured by them. Theythat overlapping of tracks increases the fatigue lifeerial due to the compressive surface stresses devel-g laser hardening. A 2 mm case depth was achievedt al. [14] with hardness near 750 HV in 4140 steel

ting conditions optimized to achieve maximum case

g and cavitation are dependent on the extent of over-laser-hardened tracks. Pantelis et al. [15] showed that% overlapping ratios in multi-track laser hardeninghe wear and corrosion resistance of CK60 structuralared to that with un-overlapped tracks. Corrosiondepends upon the hardness and the microstructurel. Lower overlapping ratios produced non-uniformth soft spots in the overlapped zones. The issue ofring involved in multiple track laser hardening wased. Li et al. [16] were among the first to incorporate

of lasemulti-tensilebetweelaser p

Evehave bpredicperingand Shprofilenumer

profilemodeland opdepth.AISI 4ing ofkineticcase dlaser h

2. Th

Theheatintion ofheat trtransfetive anthe surheatedthermoorder turationa transhardening and back tempering effects in multi-trackning of AISI 4140 steel.

l model

ary heat transfer phenomena that influence the laserrismatic parts of 4140 steel are (1) the partial absorp-

r beam irradiation on the metal surface; (2) convectiver from the heated spot to the air jet; (3) radiation heatm the heated surface to the surroundings; (4) convec-diation heat transfer from the nonheated surfaces todings; and (5) conduction of the heat away from theace into the bulk material. Temperature dependentsical property data are incorporated into the model invide improved conditions. The experimental config-laser hardening includes a stationary workpiece andg laser, as shown in Fig. 1, traveling along X direction

ig. 1. Set up for laser hardening of a prismatic part.

R.S. Lakhkar et al. / Materials Science and Engineering A 480 (2008) 209217 211

at a given Y location. The workpiece area is defined such that itis affected by heat conduction away from the heated region. Themodel for lsolved usinconduction

The prisconservatiotionh(T )

t=

where the tand the thrdiffusion inthermal con

The theature distriVarious opeabsorptivitof the mate

3. Kinetic

3.1. Harde

A numShin [9]a two-dimmicrostrucmicrostrucis dividedassociatedThe distanc

L = 2 tt1

where D iscolony, and

It is asserned by sois used toformed soleends at theaustenite otemperaturposes to foFicks 2ndC

t=

x

where C iand D is tof concentr

The detain various p

enization of austenite is explained by Skvarenina and Shin [9].The diffusion coefficients of carbon in austenite and ferrite are

y

= D( )

D0, Qnstanr any.05%ite hed toardeoun

ectiothenferr

Hm

is thdnes

166

C is

ack t

n are

be cd. Tcrosandsingcon

tribue temhe mZhas du

odel

beaiallye is mter tpericarbmpee phe thanessel [9tensiaser-assisted heating, developed by Tian et al. [8], isg an implicit finite difference method for transientand uses top hat rectangular beam shape.matic model for laser heating is based on the energyn equation for three-dimensional transient conduc-

x

(k(T )T

x

)+

y

(k(T )T

y

)+

z

(k(T )T

z

),

(1)erm on the left hand side represents energy storage,ee terms on the right hand side stand for thermalx, y and z directions, respectively. Specific heat andductivity are temperature dependent and isotropic.

rmal model predicts the three-dimensional temper-butions within the workpiece during laser heating.rating parameters, such as laser power, scanning rate,

y of the material, emissivity and thermal propertiesrial are defined by the user.

hardeningtempering model

ning model

erical model was developed by Skvarenina andto predict the hardness and hardened zone inensional plane in laser assisted hardening. Theture is modeled using a micrograph of the realture as the initial condition. The calculation domaininto cells and a phase, or combination of phases, iswith each phase (e.g., austenite, pearlite, martensite).e over which the carbon diffuses is given by

2D0 exp

( Q

RT (t))

dt, (2)

the diffusion coefficient, L the radius of the pearlite is the average plate spacing in the colony.

umed that the homogenization of austenite is gov-lute diffusion and hence Ficks 2nd law of diffusionmodel this transformation. This calculation is per-ly over the , and / interface cells and starts andeutectoid temperature [9]. The homogenization of

ccurs at temperature above AC3 and by the time AC3e is reached, all of cementite from pearlite decom-rm austenite. The diffusion of carbon is governed bylaw(

DC

x

)+

y

(D

C

y

), (3)

s the carbon concentration in phase (either or )he related diffusion coefficient, which is a functionation and temperature.iled procedure to calculate the carbon concentrationhases, the solution of Eq. (3) and degree of homog-

given b

D(T )

wherephasegas cocells othan 0austenassum

laser hare enc

a subsgrid) is(f) andH = f

Hfthe har

Hm =

where

3.2. B

If ahas tobe useand miperingaddres

Thethe disand thdata, ting bychangethis m

Thepartzon

grea Tem

- -- te

If thmor

hardmodmar0 expQ

RT. (4)

is the pre-exponential of the diffusion coefficient for the activation energy of phase , R the universalt, and T is the temperature in Kelvin. If the austeniteother boundary (multiple phase) cells contain morecarbon [4] after the thermal cycle and associated

omogenization has completed, then those cells aretransform to martensite. This assumption holds for

ning as cooling rates of the order greater than 104 C/stered in laser surface hardening [4]. The hardness ofn of the domain (defined by 100 cells of the kineticsassigned based upon the mass fractions of martensite

ite (1 f)+ (1 f )Hf (5)e hardness of ferrite, taken to be 150 HV [4], whiles of the martensite is found from

7C 926C2

f+ 150, (6)

the carbon content of the steel.

empering model

a of a width larger than the width of the laser beamovered, multiple tracks of the laser beam have to

here has been substantial research in the hardnesstructure prediction areas related to conventional tem-annealing processes [17,18] which proved useful inback tempering in laser hardening.sequence of the back tempering process depends ontion of microstructure present after the first laser passperature history in the tempering pass. Given theseodel used for conventional tempering and anneal-

ng et al. [18] can be adapted to predict the hardnessring the second laser pass. Some key assumptions ofare:

m that overlaps or passes near the first beam tracktempers the material, if the phase in the overlappedartensite and temperature point is less than AC1 and

han 100 C.ng may form two phases:ide is formed between 100 C and 250 C;red martensite is formed between 250 C and 727 C.ase fraction of martensite in the overlapped zone isn the non-martensitic phase fraction, the resultantis given by hardness calculated by the hardening

], otherwise hardness is determined by consideringte and tempered phase fractions.

212 R.S. Lakhkar et al. / Materials Science and Engineering A 480 (2008) 209217

The fraction of martensite that has transformed during tem-pering is modeled by the JohnsonMehlAvarami equation,which is gi

f = 1 exwhere

= kt = k

and Q is tderived conconditions,exhibits a fbe taken aclaser hardetransient te

ddt

= k +

which wasequationsin overlappmodel provlapped regi

A numedetermineis calculatethat are prmay be preferrite (f),retained aufraction ( 1400 K)

cific heat of AISI 4140 steel was obtained from4] and was divided into three temperature ranges:

.0 J/(kg K) (T 378 K).43E-08 T4 + 3.99E-0.0395 T2 + 16.844 T 2109 J/(kg K), 1250 K).0 J/(kg K). (T > 1250 K)

onstants used in the kinetic models are given in

zed parameters and experimental results

etics models developed for multi-track laser harden-sed in conjunction with temperature predictions tothe case depths and overlapping pattern for harden-I 4140 steel. The objectives of the multi-pass laser

ere (1) to achieve a case depth of 2 mm with a hard-higher than 50 HRC in laser hardened tracks in AISI

(2) to determine an optimum overlapping patterne laser hardened tracks without a significant loss ofe to back tempering, and (3) to experimentally vali-dicted results of multi-track laser hardening of AISI

R.S. Lakhkar et al. / Materials Science and Engineering A 480 (2008) 209217 213

Table 1Constants used in diffusion model [4,9,2023]Property Value

Pre-exponential (carbon in ferrite), D0 6 105 m2/sPre-exponential (carbon in austenite), D0 l 105 m2/sActivation energy (ferrite), Q 80 kJ/molActivation energy (austenite), Q 135 kJ/molUniversal gas constant, R 8.314 J/molKPearlite grain spacing, 0.5mDiameter of pearlite grain, L 8.85mAverage grain size, g 13.6mVolume fraction of pearlite, f 0.45Critical carboActivation EnPre-exponentK0Maximum haMaximum haMaximum haMaximum ha

4140 steel.the extent otracks. In oto maximizback tempe

In the fisimulated tdepth. Usintrack laserextent of odetermine tin Table 2.length of 0This laser hused with fto 1200 W,through 2 m76.2 mm for the simuened AISI 4of the as-rno large-scvolume fraA represention was redomain.

It is seenatures abovfor powers

Table 2Simulation matrix for determination of maximum case depth in laser hardeningof AISI 4140 steel

Testno.

Power(W)

Speed(mm/s)

Maximumtemperature underlaser spot (C)

Depth ofhardenedzone (mm)

Meltingyes/no

1 1200 2 1431 a Yes2 1200 1 1457 a Yes3 1200 0.5 1610 a Yes4 1100 1 1344 a Yes5 1100 0.5 1477 a Yes6 100

9595908585858080

ardene to m

of 0condossiwer

ghsitedept

0.4ter aer tak

gover hate, 1ooding.acksones created by them are uniform and there is minimumnce between the depths of the tracks. The entire hard-

Table 3Simulation m

Test no. P

1 82 83 84 8n content value, Cc 0.05%ergy (martensite for tempering) Q 196.888 kJ/molial, n 0.109

51.111 108 s1rdness of martensite, Hmartensite 700.00 HVrdness of -carbide, H-carbide 600.00 HVrdness of ferrite, Hferrite 150.00 HVrdness of cementite, Hcementite 400.00 HV

The main factor influencing the back tempering isf overlapping of the heated regions under the laser

rder to determine the optimum operating conditionse (at least obtain 2 mm) the case depth and reducering a two step approach was used.rst step, the multi-track laser hardening process waso find an operating condition to maximize the caseg these operating parameters for the laser, the multi-hardening process was simulated by varying the

verlapping of tracks. The simulation matrix used tohe laser parameters for maximum case depth is shownA Nuvonyx 4 KW ISL 4000-L diode laser of wave-.808m was used in laser hardening of 4140 steel.as a rectangular beam shape of 12 mm 8 mm when

ocusing lens. The laser power was varied from 800 Wwhile the scanning rate was varied from 0.3 mm/sm/s. The workpieces used had the dimensions of

50.8 mm 25.4 mm. The initial phase distributionslations were obtained from a micrograph of unhard-140 steel. After examining several such micrographs

789

1011121314

a No hb Clos

valueTheseto the plow pois enoumartena case

0.5 andare fas

Aftup andfor lasning rawere ghardenlaser trened zdiffereeceived metal, it was determined that there wereale variations in the microstructure, with uniformctions of ferrite and pearlite at roughly 0.5 each.tative micrograph was taken and its phase distribu-peated over the entire, much larger, computational

from Table 2 that the thermal model predicts temper-e the melting point of the AISI 4140 steel (1400 C)between 1000 W and 1200 W for an absorptivity

ened zonea uniforment degreesthe laser wing processsimulationThe overla6 mm (thethe directio

atrix to determine optimum overlapping condition

ower (W) Overlap (mm) Speed (mm/s) Maximum temperature under las50 6 0.5 133150 5 0.5 133150 4 0.5 133150 3 0.5 13310 1 1448 NOa Yes0 0.4 1361 1.91 No0 0.3 1389 1.91b Nob0 0.4 1354 1.89 No0 0.5 1331 1.91 No0 0.45 1344 1.9 No0 0.4 1351 1.86 No0 0.4 1245 1.7 No0 0.3 1203 1.8 No

ed zone possible.elting temperature.

.69 and very close to it for 950 W and 0.3 mm/s.itions are not appropriate for further study here dueble remelting of the alloy. Operating conditions withand high speed are advantageous, as long as there

heat input to trigger austenization and formation ofat the desired depth (>2 mm). Cases 711 all predicth of approximately 1.9 mm. Cases 10 and 11 (850 W,5 mm/s) are better choices than cases 7 and 8 as theynd use less power.ing into consideration limitations of the physical set-erning factors for selection of optimum parametersrdening, it was concluded that 850 W, 0.5 mm/s scan-2 mm 8 mm diode laser beam size, and steel = 0.69choices for parameters for modeling multi-track laserDuring multi-track laser hardening of a large area,should be overlapped in such a manner that the hard-produced by the multiple tracks ideally should havecase depth. In order to analyze the effects of differ-

of overlap, the optimum operating parameters forere used to simulate the multi-track laser harden-using the coupled hardening-tempering model. Theconditions used in this study are shown in Table 3.p of the laser tracks was varied from 3 mm through12 mm axis of the laser beam was perpendicular ton of laser travel, so half of the beam width was inci-

er spot (C) Depth of hardened zone (mm) Melting yes/no1.9 No1.9 No1.9 No1.9 No

214 R.S. Lakhkar et al. / Materials Science and Engineering A 480 (2008) 209217

Fig. 2. Compfor different o

dent on preused). Thehardened zconditions

It is seedrop in the(Table 4) wzone in betwup to 5 mmincreases uto drop in thpredicted hto the maxthat the opt5 mm.

The simwere used iwhile a threpeatabilit

Sandbla76.2 mm mounted omaneuvere

laser beamsteady statreached besecond lasedge of thethe specimfrom the stthe workpi3000 infrar

Table 4Experimentalof AISI 4140

Test #

123

hase

oundticast trhe hpre

respshowroximd awas

hardaxi. Th

ion og the ofith eobse

nsitiofthe

erlapof thingover

icalover

se deunhaser-harison of hardness profile along width of the laser hardened areaverlaps.

viously covered surface when a 6 mm overlap washardness variation over the entire width of the laserone at a depth of 0.25 mm was predicted using theshown in Table 3 and is shown in Fig. 3.n from Fig. 2 that the 5 mm overlap leads to the least

hardness of the material in the overlapped zone,hile track overlap of 3 mm produces an unhardenedeen the two tracks. As the extent of overlap increases

, the minimum hardness in the overlapped zone alsop to 470 HV, whereas overlapping above 5 mm leadse lowest hardness value in the overlapped region. Theardness varies from the bulk hardness of the materialimum value of 668 HV. Thus it can be concludedimum overlapping for multi-track laser hardening is

ulated conditions found in tests 2 and 4 (Table 3)n two experiments to check the validity of the model,ird experiment was performed for test 2 to checky.sted AISI 4140 steel workpieces of50.8 mm 25.4 mm dimensions were cut andn an insulative material. The diode laser was

d using a Panasonic VR-016 welding robot. Thewas turned on outside the workpiece area so that a

e of diode laser emission at designated power wasfore the hardening process. The start point of the

Fig. 3. P

was grand opthe firzone. T

Thethe corple isof appshowetrackslappedin the m0.2 mmformatculatinand sizwell wsplit isthe traportiontion ofthe ovprofilehardenof the

Opt2, thethe cain theThe laer track was approximately 5 mm away from the

workpiece. After making two overlapping tracks,en was cross-sectioned approximately 89 mm awayart point of the second laser track. Temperatures inece were measured using the FLIR ThermaCAM SCed camera. The cross-sectional area of the specimen

matrix for validation of predictions of multi-track laser hardeningsteel

Power Overlap Notes

850 5850 5 Repeatability test850 4 Change in laser overlap

tempered mFig. 4(d), i2, Fig. 4(c)between thclearly shomartensite

The prein Fig. 5. Hhardened zThe measuthe approxin Figs. 7are repeatatrack 1 neaplot of cross-section of laser hardened tracks of test 1 in Table 4.

and polished and etched with a 5% Nital solutionl micrographs were made of the microstructures inack, second track, overlapped zone and transitionardness of the samples was then measured.

dicted phase plot of test 1 is shown in Fig. 3, whileonding micrograph of the actual laser hardened sam-n in Fig. 4. It is seen from Fig. 3 that a case depthately 1.9 mm was predicted, while the experiment

depth of 2.0 mm. The width of the laser-hardenedapproximately 18 mm, while the width of the over-ened zone was approximately 2 mm. The difference

mum case depth of the two tracks was approximatelye transition zone in each track was disregarded asf transition zone was not modeled in [9] when cal-

e case depth. As seen in Figs. 3 and 4, the shapethe predicted and measured overlapped zones matchach other. In the predicted hardened zone profile, arved in the overlapped zone, which is present due to

on zone of the second track and re-hardening of thethe first track. It is observed in Fig. 3 that the por-first track in the overlapped zone is re-hardened byped second track and it confirms the prediction. Thee overlapped zone that was predicted by the kinetictempering model matched with the observed profilelapped zone.micrographs of the phases present in tracks 1 andlapped zone and the transition zone (at the edge ofpth) are also shown in Fig. 4. The microstructurerdened zone, Fig. 4(a), contains ferrite and pearlite.ardened track 2, Fig. 4(b), contains martensite, whileartensite is present in the back-tempered region,

n track 1 near track 2. The transition zone of track, contains bainite, ferrite and pearlite. The boundary

e tracks 1 and 2 in the overlapped zone, Fig. 4(e)ws newly formed martensite in track 2 and temperedin track 1.dicted hardness profile of the cross-section is shownardness was measured along the width of the laser-

one at the depth of 0.15 mm below the surface (Fig. 6).rements into the depth (away from the surface) atimate centers of first and second tracks are shownand 8, respectively, showing that the measurementsble. Hardness was also measured into the depth inr the edge of the track 2 (Fig. 9) and also along the

R.S. Lakhkar et al. / Materials Science and Engineering A 480 (2008) 209217 215

Fig. 4. Micro artensite, (c) transition zone, (d) tempered martensite and (e) martensiteand tempered

depth of thfigures shomeasureme

steeper gracase depth,in the kinet

The prelapped zonaway fromfrom the ssurface exptempered fHowever, tcase and de

Fig. 10in the overstructures in the hardened zone in test 1 of Table 4: (a) ferrite and pearlite, (b) mmartensite in overlapped zone.

e overlapped zone in track 2 (Fig. 10). All of these

w excellent agreement between the predictions andnts. The predicted hardness profiles tend to have adient in hardness than the measured ones beyond thebecause the transition zone has not been consideredic model.dicted hardness profile into the depth in the over-e of track 1 (Fig. 9), taken at approximately 1.5 mmthe right edge of track 2, shows an initial rise away

urface. This trend is expected as the material neareriences a higher temperature longer and hence gets

aster as compared to the material at the larger depths.he measured hardness values are more uniform in thiscrease more slowly than the predictions.shows the hardness measurements along the depthlapped zone in track 2 at approximately 1 mm away

Fig. 5. Hardness profile of the test 1 in Table 4.

Fig. 6. Hardness profile at 0.15 mm below surface in test 1 in Table 4.

Fig. 7. Comparison of hardness profile in track 1 in tests 1 and 2 in Table 4.

216 R.S. Lakhkar et al. / Materials Science and Engineering A 480 (2008) 209217

Fig. 8. Comparison of hardness profile in track 2 in tests 1 and 2 in Table 4.

Fig. 9. Hardnin Table 4.

from the edlocation is apredicted awith each o

Fig. 11face whenAs expectecase depthlarge droprial, at the iis not desir

Fig. 10. Hardin Table 4.

Fig. 11. H

6. Conclu

ouppedred zhe b

tensialuestrackthe ht wabear trat meess profile along the depth in overlapped zone in track 1 in test 1

A cdevelotempesteel. Tof marness v

multi-usingified. Iwith aof lasewithouge of track 2. The depth of overlapped zone at thispproximately 1.3 mm and it contains martensite. Thend measured hardness values are in good agreementther.

shows hardness along a line 0.25 mm below the sur-the overlap is decreased to 4 mm (test 3 in Table 3).d, no significant difference is noted in the maximumwith the change to a smaller overlap, but there is ain hardness, nearly to the bulk hardness of the mate-ntersection of the two tracks. Obviously, this featureable and the larger overlap is necessary.

ness profile along the depth in overlapped zone in track 2 in test 1

tempered zmaterial isvalues variin the martof the back(4855 HRcent trackscould be cotracks.

Acknowled

This resResearch adation (Gra

Reference

[1] K. SridhISBN 0-

[2] F. DausiAppl. 2 (

[3] H. Sherc(No. 10)

[4] M.F. As1948.

[5] L.J. Yan130.

[6] Y.S. Yan[7] L.M. Gaardness profile at 0.25 mm below surface in test 3 in Table 4.

sions

led heat transferhardeningtempering model wasto predict the hardness and phases in the back-ones during multi-track laser hardening of AISI 4140ack-tempering model can predict the volume fractionte that has been tempered and the corresponding hard-. The optimal overlap for uniform case depth duringlaser hardening of AISI 4140 steel was determinedardeningtempering model and experimentally ver-s found that 850 W of diode laser beam irradiationm shape of 12 mm 8 mm, with 5 mm overlappingcks can produce a hardened case depth of 1.92 mmlting and a minimum loss of hardness in the back-one. The maximum hardness achievable within theapproximately 668700 HV (58 HRC). The hardnessed between 480 HV (48 HRC) and 669 HV (58 HRC)ensitic regions of tracks 1 and 2. The major portion

tempered track was in the range of 480571 HVC). The difference in the case depths of the two adja-was approximately 0.2 mm. The variation in hardnessntrolled by changing the extent of overlapping of the

gement

earch was partially supported by the 21st Centurynd Technology Fund and the National Science Foun-nt No. IIP 0538786).s

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Predictive modeling of multi-track laser hardening of AISI 4140 steelIntroductionThermal modelKinetic hardening-tempering modelHardening modelBack tempering model

Property data of AISI 4140 steelOptimized parameters and experimental resultsConclusionsAcknowledgementReferences