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Materials Science and Engineering A 529 (2011) 246– 252

Contents lists available at SciVerse ScienceDirect

Materials Science and Engineering A

journa l h o me pa ge: www.elsev ier .com/ locate /msea

he effect of specimen dimension on residual stress relaxation of carburized anduenched steels

hongyuan Qiana,∗, Scott Chumbleya, Eric Johnsonb

Iowa State University, 206 Wilhelm, Ames, IA 50010, USAJohn Deere Technology Center, Moline, IL, USA

r t i c l e i n f o

rticle history:eceived 3 May 2011eceived in revised form 9 August 2011ccepted 8 September 2011vailable online 16 September 2011

a b s t r a c t

In this study X-ray diffraction was used to measure the redistribution of residual stress in carburized andheat treated AISI 8620 steel specimens of different sizes during successive sectioning. Finite-elementmodeling was used to simulate the stress relaxation. Comparing the results of modeling to experimentalresults of ring-shaped specimens shows that the residual stress relaxation associated with the size reduc-tion was almost negligible. However, significant stress relaxation occurs while reducing the thickness of

eywords:esidual stresselaxationize reductionears

the specimens. The results seen in ring-shaped test specimens were verified by sectioning actual gearsamples.

Published by Elsevier B.V.

inite-element analysis

. Introduction

Although diffraction techniques have proven to be reliable andfficient methods for determining residual stress [1–8], measure-ent of residual stress in carburized parts, especially in the case

f gears, is often difficult to accomplish. Ideally, one would like toetermine the stress distribution on the surface of gear teeth and inhe roots of the teeth. However, the shape of a typical gear routinelyrevents sampling of these areas using conventional X-ray diffrac-ometry due to other parts of the gear blocking the area of interest.his means conventional X-ray systems often require gears to beplit or teeth to be sectioned from the gear before measurementsan take place. A similar problem is that most laboratory-scalenstruments are not capable of handling extremely large, heavyears, again requiring sectioning of the part. In cases such as thesehere is always the question as to what effect sectioning of the sam-le has had on changing the stress state in the part, and residualtress relaxation and redistribution is expected [9]. While neutroniffraction has a much deeper penetration and is able to measuretress in large bulk samples, minimizing the necessity of section-ng, such measurements are limited by the number of neutron sites

vailable and the high usage demands on these sites.

Fatigue is the major cause of failure in cyclically loaded parts,e they structural parts under vibration or rotating gears. For this

∗ Corresponding author. Tel.: +1 515 451 6133; fax: +1 515 294 4291.E-mail address: zyqian@iastate.edu (Z. Qian).

921-5093/$ – see front matter. Published by Elsevier B.V.oi:10.1016/j.msea.2011.09.024

reason, gears are usually carburized, quenched and shot-peened toacquire a higher hardness. As a result, a large amount of compres-sive residual stress is introduced into the material [10–13]. Thisbeneficial compressive stress can extend the life of the part pri-marily by acting to offset the tensile loads that normally lead tofatigue [14,15].

The work we reported in this paper was to study the relaxationbehavior of residual stress during successive reduction in dimen-sion of samples by sectioning. In order to reduce the complexity ofthe analysis, simple ring-shaped samples were chosen to simulategear geometries. These specimens were consecutively cut and theresidual stress was measured before and after each cut. The resultsof these model experiments were then compared to finite-elementsimulations of the expected stress. Finally, as a test of the analy-sis, measurements were made on an actual carburized productiongear. The results of all these experiments are discussed below.

2. Experimental procedure

2.1. Material and specimens

Carburized AISI 8620 steel rings of three different sizes wereused in the experiments. The measured composition (wt.%) was0.20 C, 0.89 Mn, 0.60 Cr, 0.12 Si, 0.35 Ni, 0.22 Mo, balance Fe. Young’s

modulus E and Poisson’s ratio � of the material are 205 GPa and0.29, respectively. The ring-shaped specimens were first machinedand the dimensions studied are listed in Table 1. The carburiza-tion process used in production of the ring samples simulated the

Z. Qian et al. / Materials Science and Engineering A 529 (2011) 246– 252 247

Fig. 1. Size reduction of the standard ring sample. (a

Table 1Specimen dimensions of three different sizes (all units in mm).

Samples Inner diameter (ID) Outer diameter (OD) Thickness

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JDR1 20 55 12.5JDR2 27 73 17JDR3 40 110 25

anufacture of similar gear components and involved being heatednder a carbon-providing atmosphere to 1227 K (954 ◦C) for 4 hollowed by cooling to 1116 K (843 ◦C) for 1 h. Then samples wereuenched in oil then tempered at 450 K (177 ◦C) for 2 h.

.2. X-ray diffraction measurement

A Bruker D8 diffractometer equipped with a two-dimensionalrea detector and Cr tube was used to acquire experimental X-rayiffractograms. The (2 1 1) peak (2� = 156◦) was examined and eachcquisition was obtained using 30 kV, 50 mA, by the sin2 � method,n accordance with ASTM standard [16]. The sampling area is a.8 mm circle and the surface residual stress was measured.

.3. Sample sectioning

Both the initial circumferential and radial residual stress waseasured along a line from the inside diameter (ID) to the outside

iameter (OD), as shown in Fig. 1. Two different procedures for

eduction in dimension were conducted in this study. For theurposes of this paper, the first is called “size reduction”. Inhis procedure, the full ring was carefully sectioned through thehickness of the ring using a cut-off saw and the residual stress

ig. 2. Thickness reduction of an eighth section of the JDR3 sample. (a) Original thicknesn both side A and side B.

) Full size, (b) half, (c) quarter and (d) eighth.

was measured along the same line. The ring was initially sectionedin half (Fig. 1b) and the process was repeated for quarter (1/4)and eighth (1/8) sections of the same specimen, producing datarepresenting the stress state before and after each cut. The sameprocedure was carried out on all the specimens of different sizes.

A second sectioning procedure was applied to study the effectsof reduction in thickness, and will be referred to as “thicknessreduction”. The eighth sections from the largest ring sample JDR3were consecutively thinned, first by sectioning in half, using a cut-off saw, then by milling to one quarter of the original thickness. Theresidual stress was measured at each different thickness. Examplesof a quarter-thickness specimen after final milling are shown inFig. 2.

3. Experimental results

3.1. Reduction in size: standard ring samples

Results related to the stress measured in the parts as a func-tion of size reduction are shown in Fig. 3 for the three differentlysized ring specimens we examined. Stress was measured both inthe circumferential and radial direction.

The stress measurements clearly show that compressive resid-ual stress was introduced to the rings as a result of the carburizationheat treatment. Regarding the circumferential residual stress, JDR1and JDR2 (Fig. 3a and c) show relatively smoother distributions

than in JDR3, the compressive stress values recorded for thesetwo smaller samples being in the range of −150 MPa to −250 MPa.JDR3 shows a stress that varies considerably, from an average of−125 MPa to −175 MPa, on both exterior surfaces to −275 MPa on

s, (b) half thickness and (c) quarter thickness. The residual stresses were measured

248 Z. Qian et al. / Materials Science and Engineering A 529 (2011) 246– 252

0 5 10 15-250

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Distance From ID (mm)

Res

idua

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0 5 10 15 20-250

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0 10 20 30-300

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0f. JDR3 Radial

Full RingHalf RingQuarter RingEighth Ring

cessiv

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Fig. 3. Distribution of residual stress as a function of suc

he middle surfaces. Initial observation of the stress in the radialirection for the three samples examined suggests that the scatterf stress is greater here than for the circumferential direction. How-ver, considering the scales of the plots are considered it appearshat while scatter still exists, the variation of the measured values isomparable or somewhat less in the radial direction than for the cir-umferential direction for all sizes. It is also evident that the radialtress is lower in value than in the circumferential direction. Givenhe scatter seen in the measurements in both directions, thereppears to be no general trends indicative of a consistent stresselaxation occurring as a result of the successive size sectioning.

.2. Reduction in size: finite-element model

To simulate the residual stress, a 3-D finite-element model wasuilt by using a commercial FEA software, ANSYS 12 [17]. The first

e sectioning. Measurement errors are around ±19 MPa.

step in this analysis is to simulate the heat treatment in order todetermine the initial residual stress field. Since the simulation ofcarburization and quenching is not the primary concern of thisstudy, a simplified nonlinear thermo-mechanically-coupled modelwas used in this case. In the second step, consecutive sectioning issimulated by “removing” elements (setting the stiffness of the ele-ments infinitesimal) corresponding to the material removed duringthe sectioning experiments. In other words, after the initial simula-tion elements were “removed” to produce first one-half of the ring,then a quarter ring, and finally one-eighth of the ring. The simu-lated redistribution of residual stress in both the circumferentialand radial directions from inner to outer diameters (ID and OD,

respectively) on the surface is shown in Fig. 4.

The simulations predict that stress extrema were seen in themiddle of the rings. This corresponded to a maximum compres-sive stress of −90 MPa in the radial direction and a minimum in

Z. Qian et al. / Materials Science and En

0 5 10 15 20 25 30 35-150

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50

Distance From ID (mm)

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a. Size Reduction: Circumferen tial Residual Stress

0 5 10 15 20 25 30 35-100

-80

-60

-40

-20

0b. Size Red uction : Radial Residu al Stress

Whole RingHalf RingQuarter RingEighth Ring

Fig. 4. Simulated distribution of residual stresses in FE model. (a) Circumferentialdirection and (b) radial direction.

0 10 20 30-300

-250

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idua

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0 10 20 30-350

-300

-250

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-150

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0c. Side B - Circumferential

Original T

Half Thick

Quarter T

Fig. 5. Distribution of residual stress as a function of thickness of specimens. (a) CircumfeB and (d) radial stress on side B. Measurement errors are around ±19 MPa.

gineering A 529 (2011) 246– 252 249

the circumferential stress in the range −25 to 0 MPa. Sectioningof the ring first in half and then to one-quarter size only resultedin minor changes in the stress values of both directions. Signifi-cant changes were not seen until the size is reduced to one-eighthof the ring, where the stress distribution tended to start to levelout. In both cases, major changes occurred in the center of the ringsection, rather than the edges.

3.3. Reduction in thickness: standard ring samples

The effect of reduction in thickness was studied using sampleJDR3. For this experiment the 1/8 size reduction sample was used.This was chosen because (1) no significant reduction in compres-sive residual stress had been observed in the initial size reductionstudy and (2) the small 1/8 piece makes it much easier to sectionin order to reduce thickness.

Stress distributions were measured on both side A and side B asa function of thickness reduction. After the initial stress state wasmeasured, the specimen was sectioned in half via slow cutting usinga cut-off saw. Stress on both sides was again measured. The samplewas then thinned to one-quarter of its original thickness, using slow

milling since the piece was now too small to be cut. Residual stresson both sides A and B was again measured in the circumferentialand radial directions. The stress distributions obtained as a functionof thickness are shown in Fig. 5.

0 10 20 30-250

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0b. Side A - Radial

0 10 20 30-400

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0d. Side B - Radial

hickness

ness

hickness

rential stress on side A, (b) radial stress on side A, (c) circumferential stress on side

250 Z. Qian et al. / Materials Science and Engineering A 529 (2011) 246– 252

0 5 10 15 20 25 30 35-80

-60

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Distance From ID (mm)

Res

idua

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ss (M

Pa)

a. Reduction in Thickness: Circumferential Residual Stress

0 5 10 15 20 25 30 35-80

-60

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-20

0

b. Reduction in Thickness: Radial Residual Stress

Original ThicknessHalf ThicknessQuarter Thickness

Fc

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4

4

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0 5 10 150

10

20

30

Distance From ID (mm)Res

idua

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ss (M

Pa) a. JDR1 Standard Deviation

0 5 10 15 200

10

20

30b. JDR2 Standard Deviation

0 5 10 15 20 25 30 350

20

40

60c. JDR3 Standard Deviation

Circumferential Standard DeviationRadial Standard DeviationAverage Error

ig. 6. Simulated distribution of residual stress as a function of thickness. (a) Cir-umferential direction and (b) radial direction.

It is quite obvious that extensive stress relaxation happens wheneducing the thickness of the specimens. The largest relaxationccurs in the middle part of specimens where the residual stress foroth circumferential and radial directions drops to one half of itsriginal value or less. Little relaxation was observed at both edgesf the rings’ inner and outer diameters. This is not surprising sinceeing a free surface stress is expected to be less here than in theenter of the ring.

.4. Reduction in thickness: finite-element analysis

The effect on relaxation behavior when reducing the thickness ofpecimens was also simulated by removing elements layer by layer.n this case the starting condition was the stress state present in theectioned eighth ring, and the results are shown in Fig. 6. Relaxations expected to be greatest in the middle of the specimen, where theircumferential stress was relaxed to approximately one-half of itsriginal level. An even greater effect is seen in the radial directionhere the stress drops to approximately 1/5 the initial value. The

imulated residual stress tends not to change at the ends in bothirections. It is obvious that reduction in thickness causes a moreronounced relaxation of residual stress than reduction in size.

. Discussion

.1. Size reduction effects

As is typical for measurement of residual stress, a considerablemount of scatter is seen in the measured data. In order to eval-ate the significance of the dispersion in measured stress values,he standard deviation of measurements on the differently sized

egments (i.e. full, half, quarter, eighth) was calculated and com-ared to the average instrumental errors inherent in the diffractionxperiments. The results are plotted in Fig. 7. For example, at loca-ion x = 2 mm, the measured residual stress in the radial direction of

Fig. 7. Standard deviation compared with errors in the experimental measure-ments. (a) JDR1, (b) JDR2 and (c) JDR3.

sample JDR1 is −101.2 MPa, −83.5 MPa, −88.1 MPa, and −100 MPafor full, half, quarter and eighth ring specimens, respectively. Thisgives a calculated standard deviation of 8.8 MPa at this locationfor the same specimens examined in four different sizes of seg-ments, which is less than the expected average experimental errorof ±19 MPa.

Observation of Fig. 7 shows that for the spots chosen on eachring section 2/3 s of the measurements are within the expectedinstrumental error for all three samples. Greater variation in stressdispersion was observed near the inner diameter, which is reason-able since not only are the constraints less to begin with but whenreducing size the amount of material remaining at the inner diam-eter becomes extremely small once the ring has been sectioned toone eighth of the original size.

The implication of the data is that there is little or no statis-tical difference in the stress distributions for the three sectionedsamples from the original complete ring. This is very surprising;it was expected that sectioning through the ring would signif-icantly reduce the value of the measured stress due to releaseof the hoop stress. However, our experimental results show thatstress distribution is primarily a function of distance from the innerand outer diameters, rather than section size. This trend is consis-tent, even though samples of three different sizes were examined.None showed significant relaxation during size reduction. Thus, it

appears when considering carburized parts as simulated by the ringspecimens, the size of the original specimen can be predicted tohave little or no effect on stress relaxation behavior.

Z. Qian et al. / Materials Science and Engineering A 529 (2011) 246– 252 251

ear. (a

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Fig. 8. Residual stress measurement of a triple pinion g

It should be noted that the simulations did not do a great job ofredicting the actually measured stress distribution. The simulatedtress varies much more over the diameter of the rings, being clearlyifferent in the center of the rings as opposed to the edges. This doesot appear to be the case for either the as-measured circumferentialr radial stress, which in general exhibit no discernable trends. Thiss most likely due to the difficulty simply of simulating the stresstate using FEA in the samples. The simplified model used doesot consider the effect of phase transformations and the differentaterial properties through the carbon gradient. However, as men-

ioned before, the precise simulation of heat treatment to obtain thenitial residual stress distribution is not the major concern in thistudy. Instead, the relaxation behavior is of most interest. In gen-ral, residual stress relaxation trends in the model behave similaro the experimental results. That the simulations predict no sig-ificant difference in stress state as a function of size reduction toalf or quarter size is in agreement with the experimental results,nd only a slight reduction when sectioned to one-eighth size. Thisupports the hypothesis that the effect of size reduction is fairlyinor when compared to the variation in measurements that can

e expected simply due to instrumental factors.The above hypothesis was tested by examination of an actual

arburized and quenched gear used in agricultural machinery. Ariple pinion gear was examined, and the radial residual stress was

easured on several points on the back-side of the gear, as shownn Fig. 8. The gear was then sectioned into quarter and eighth sec-ions and residual stress measurements were carried out at thexact same locations. The results are shown in Table 2. Only minor

hanges were observed throughout this sectioning process.

The data of Table 2 shows that while sectioning has had littleffect on the stress level, a stress gradient existed along the scan

able 2esidual stress measured in the radial direction. Error associated with the measure-ent is around ±20 MPa.

Point Original gear Sectioned to 1/4 Sectioned to 1/8Stress (MPa) Stress (MPa) Stress (MPa)

1. (5 mm from ID) −521 −512 −5102. (10 mm from ID) −428 −423 −4033. (15 mm from ID) −361 −356 −368

) Full gear and (b) a quarter of the gear after sectioning.

line. In this case, the inner diameter (point 1) shows a higher com-pressive stress than the outer (point 3). This differs somewhat fromwhat was seen in the standard samples, where the compressivestress distribution was relatively constant across the ring, beingslightly higher near the outer diameter – as measured and pre-dicted by FEA. However, the triple pinion gear examined was alsothicker in the inner diameter than for the outer diameter, whichbrings into consideration the effect of thickness reduction.

4.2. Thickness reduction effects

Fig. 5 shows that extensive relaxation is measured experimen-tally in both the radial and circumferential directions as a result ofreduction in thickness. Since the carburization and quenching pro-cess introduced a compressive residual stress on the surface of thematerial, a corresponding core tensile component must be presentto balance the surface compression. While sectioning through thethickness of the ring to achieve size reduction seems to affectthis stress only slightly, removing thickness of the ring by cut-ting into this tensile region allows redistribution and relaxation ofthe compression/tension balance that exists due to carburization.Significant changes occur in both the radial and circumferentialdirections. The results were confirmed by repeating the measure-ments on both surfaces A and B of the specimens.

The shape of the simulated FEA residual stress profiles (Fig. 6)still do not adequately predict the actual measured stress distribu-tion in either the circumferential or radial directions. In both cases,the absolute values of simulated compressive stress are much toolow. This is due to the simplification made in the FE model, lead-ing to an overestimation of stress relaxation in the one-eighth ring.The situation is much better for the simulations of radial stress dis-tributions, where the general shape is much more accurate andreflects the measured trends adequately. However, considering thetrends that occur due to sectioning in both directions, the FE modelpredicts significant relaxation occurring due to a reduction in thick-ness. Thus, while absolute values cannot be predicted the expected

trends are still apparent, even when employing a simple FEA model.

The above discussion of size and thickness reduction can beextended to other shapes. Usually, carburized/quenched com-ponents have compressive stress in the exterior surfaces with

252 Z. Qian et al. / Materials Science and En

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ig. 9. The residual stress of an induction hardening bar to be measured is indicatedy the arrow. (a) Original bar, (b) section A–A and (c) section B–B.

alancing tensile stress in the interior. As long as the sectioninginimizes the exposure of the core tensile region, the relax-

tion of surface compressive residual stress should be minor. Onepplication of these results might be in the examination of annduction-hardened cylindrical bar as shown in Fig. 9. Suppose thenformation desired is the amount of residual stress that exists athe point indicated in Fig. 9a. According to the results of this study,ectioning as per Fig. 9b can be expected to result in a large amountf relaxation, whereas the cut in Fig. 9c should to a large extentreserve the true residual stress value.

. Conclusions

Reducing the size of carburized rings by sectioning into arc seg-ents appears to have little effect on the measured residual stress

istribution in the part that results due to carburization. The exper-mental results indicate that no significant relaxation, even whenhe rings were reduced to one-eighth of the original size. This is not

rue if the rings are sectioned perpendicular to their axes to pro-uce a change in thickness. In this case a large extent of relaxation

s observed. The general trends of stress relaxation predicted inhe simplified FEA model of this study are in good agreement with

[

gineering A 529 (2011) 246– 252

the experimental results, even though it gives poor simulations ofthe actual measured stress. The model accurately predicts little orno relaxation in the half- and quarter-sectioned rings during thesize reduction and also accurately predicts significant reductionsin residual stress as a function of reduction in thickness.

Experimental measurements of the residual stress in sectionsof an actual carburized gear as it was successively sectioned sup-ported the hypothesis that reduction in size produces only slightchanges in residual stress. Almost no relaxation was observed inthe gear specimen when it was sectioned into one-eighth, in agree-ment with the standard experiments. This conclusion may apply toother similar geometries with similar heat treatments.

The implications of this study are fairly clear. When determin-ing whether a small laboratory XRD instrument can be employedto determine residual stress, or whether a more involved neutrondiffraction experiment is necessary that allows examination of alarge part, simple FEA models maybe employed to quickly discernthe effect sectioning will have on the stress.

References

[1] M.T. Hutchings, P.J. Withers, T.M. Holden, T. Lorentzen, Introduction to theCharacterization of Residual Stress by Neutron Diffraction, Taylor& FrancisGroup, Boca Raton, FL, 2005.

[2] P.J. Withers, H.K.D.H. Bhadeshia, Materials Science and Technology 17 (2001)355–365.

[3] I.C. Noyan, J.B. Cohen, Residual Stress Measurement by Diffraction and Intepre-tation, Springer-Verlag, New York, 1987.

[4] SAE International: SAE HS-784, Warrendale, PA, 2003.[5] J. Lu, Handbook of Measurement of Residual Stresses, Society For Experimental

Mechanics, Lilburn, GA, 1996.[6] P.J. Webster, L.D. Oosterkamp, P.A. Browne, et al., Journal of Strain Analysis 35

(1) (2001) 61–70.[7] J.A. Francis, H.K.D.H. Bhadeshia, P.J. Withers, Material Science and Technology

23 (9) (2007) 1009–1020.[8] P.S. Prevey, Developments in Materials Characterization Technologies, ASM

International, Materials Park, OH, 1996, pp. 103–110.[9] M. Chiarelli, A. Lanciotti, M. Sacchi, International Journal of Fatigue 21 (10)

(1999) 1099–1110.10] R.C. McClung, Fatigue & Fracture of Engineering Materials & Structures 30

(2007) 173–205.11] R. John, K.V. Jata, K. Sadanada, International Journal of Fatigue 25 (2003)

939–948.12] G.A. Webster, A.N. Ezeilo, International Journal of Fatigue 23 (Suppl. 1) (2001)

375–383.13] C.D.M. Liljedahl, O. Zanellato, M.E. Fitzpatrick, J. Lin, L. Edwards, International

Journal of Fatigue 32 (2010) 735–743.14] D.P. Townsend, Improvement in surface fatigue life of hardened gears by high-

intensity shot peening, NASA Technical Memorandum 105678, 1992.15] M.A.S. Torres, H.J.C. Voorwald, International Journal of Fatigue 24 (2002)

tion Instrumentation for Residual Stress Measurement, ASTM International,West Conshohocken, PA, 2004.

17] ANSYS® Academic Research, Release 12.0, ANSYS, Inc., Canonsburg, PA.