Materials Science and Engineering Publications Materials Science and Engineering

7-2013

The Residual Stress Relaxation Behavior ofWeldments During Cyclic LoadingZhongyuan QianIowa State University

L. Scott ChumbleyIowa State University, chumbley@iastate.edu

Tugce Karakulaktugcek@iastate.edu

Eric JohnsonJohn Deere

Follow this and additional works at: http://lib.dr.iastate.edu/mse_pubs

Part of the Metallurgy Commons

The complete bibliographic information for this item can be found at http://lib.dr.iastate.edu/mse_pubs/140. For information on how to cite this item, please visit http://lib.dr.iastate.edu/howtocite.html.

This Article is brought to you for free and open access by the Materials Science and Engineering at Iowa State University Digital Repository. It has beenaccepted for inclusion in Materials Science and Engineering Publications by an authorized administrator of Iowa State University Digital Repository.For more information, please contact digirep@iastate.edu.

The Residual Stress Relaxation Behavior of Weldments During CyclicLoading

AbstractAccurate measurement of residual stress is necessary to obtain reliable predictions of fatigue lifetime andenable estimation of time-to-facture for any given stress level. In this article, relaxation of welding residualstresses as a function of cyclic loading was documented on three common steels: AISI 1008, ASTM A572, andAISI 4142. Welded specimens were subjected to cyclic bending (R = 0.1) at different applied stresses, and theresidual stress relaxation existing near the welds was measured as a function of cycles. The steels exhibitedvery different stress relaxation behaviors during cyclic loadings, which can be related to the differences in themicrostructures of the specimens. A phenomenological model, which treats dislocation motion during cyclicloading as being analogous to creep of dislocations, is proposed for estimation of the residual stress relaxation.

KeywordsSurfaces and Interfaces, Thin Films Nanotechnology

DisciplinesMetallurgy

CommentsThis article is from Metallurgical and Materials Transactions A 44 (2013): 3147-3156, doi: 10.1007/s11661-013-1688-9. Posted with permission.

RightsCopyright 2013 ASM International. This paper was published in Metallurgical and Materials Transactions A,Vol. 44, Issue 7, pp. 3147-3156 and is made available as an electronic reprint with the permission of ASMInternational. One print or electronic copy may be made for personal use only. Systematic or multiplereproduction, distribution to multiple locations via electronic or other means, duplications of any material inthis paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.

This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/mse_pubs/140

The Residual Stress Relaxation Behavior of Weldments DuringCyclic Loading

ZHONGYUAN QIAN, SCOTT CHUMBLEY, TUGCE KARAKULAK,and ERIC JOHNSON

Accurate measurement of residual stress is necessary to obtain reliable predictions of fatiguelifetime and enable estimation of time-to-facture for any given stress level. In this article,relaxation of welding residual stresses as a function of cyclic loading was documented on threecommon steels: AISI 1008, ASTM A572, and AISI 4142. Welded specimens were subjected tocyclic bending (R = 0.1) at different applied stresses, and the residual stress relaxation existingnear the welds was measured as a function of cycles. The steels exhibited very different stressrelaxation behaviors during cyclic loadings, which can be related to the differences in themicrostructures of the specimens. A phenomenological model, which treats dislocation motionduring cyclic loading as being analogous to creep of dislocations, is proposed for estimation ofthe residual stress relaxation.

DOI: 10.1007/s11661-013-1688-9� The Minerals, Metals & Materials Society and ASM International 2013

I. INTRODUCTION

RESIDUAL stresses introduced during the weldingprocess can have a significant influence on the fatiguestrength of welded components.[1–7] There are manyways to reduce potentially harmful residual stress toprolong service life, such as annealing,[8,9] pre-stretch-ing,[6] and shakedown.[10–12] For the purpose of accurateassessment of fatigue lifetime, not only the magnitude ofthe residual stresses, but also their stability factors andevolution during service are of great importance.[13]

Numerous researchers have reported significant relax-ation during cyclic loading,[7,14–24] with redistribution ofresidual stresses occurring after the first loading cyclefollowed by minimal further relaxation during subse-quent cycles.[8,25–27] By applying the principles of con-tinuum mechanics and fundamental physics, theevolution and redistribution of residual stresses suchas those caused by welding can be explained.[28] How-ever, an understanding of the complicated interactionsthat result between the applied stresses and those thatdevelop when a part is welded requires knowledge of afull 3D residual stress profile and detailed materialproperties, which is rarely possible in practice. As analternative, some empirical relaxation models[25,27,29–31]

based on experimental data obtained from studies of anumber of different combinations of material andloading have been proposed. For example, Valluri

et al.[32] suggested that residual stress relaxation is aphenomenon similar to creep. Several investiga-tions[8,27,33] have shown that the amount of relaxationis a function of applied cyclic stress. However, onecommon deficiency of the existing models is that theyare unable to separate variables related to the materialfrom those related to the applied stresses. Perhaps evenmore importantly, they are incapable of accounting forthe high amount of relaxation that occurs during thefirst cycle. These two aspects were emphasized in thecurrent study. In general, the proposed mechanisms forresidual stress relaxation due to cyclic loading can bedivided into three regimes according to the appliedcyclic stress amplitudes: (1) below the endurance limit,(2) above the macroscopic yield strength, and (3) inbetween these two extremes.[13]

In the current study, cyclic amplitudes were applied inall three regimes noted above on different weld speci-mens, including low carbon steel AISI 1008, low alloysteel ASTM A572 and AISI 4142. These steels wereselected for study because of their wide use in engineer-ing applications such as structural components, heavyconstruction equipment, and machinery parts andcomponents. The steels selected range from low-to-medium strength. The corresponding relaxation behav-iors of the residual stresses present in welded samplessubjected to cyclic loading were measured by X-raydiffraction method,[34–38] and the results obtained arepresented later. These results are related to the observedmicrostructures and are discussed in light of possibledislocation movement in the materials. A phenomeno-logical model analogous to the mechanism of disloca-tion creep, which correlates the amount of relaxationwith the applied stress, number of cycles, magnitude ofwelding stress, and several material variables, is pro-posed for the first time and compared with theexperimental results.

ZHONGYUAN QIAN, formerly Ph.D. Candidate with the IowaState University, Ames, IA 50011, is now Materials Consultant withthe Invetech Inc., Houston, TX. Contact e-mail: zqian@invetech.comSCOTT CHUMBLEY, Professor, and TUGCE KARAKULAK,Ph.D. Candidate, are with the Iowa State University. ERICJOHNSON, Staff Engineer, is with the John Deere Company, Moline,IL.

Manuscript submitted May 2, 2012.Article published online March 15, 2013

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JULY 2013—3147

II. EXPERIMENTS

A. Materials and Specimens

Materials chosen for the current study were lowcarbon steel AISI 1008 and low alloy steels ASTM A572and AISI 4142. These materials were selected becausethey are widely used in agriculture and constructionmachinery where the materials are often subjected torepeated loadings. The yield strength and ultimatetensile strength of the materials were measured and areshown in Table I.

The original stress state present in the as-received thinplate was first determined by averaging several mea-surements, and those values are also shown in Table I.Note that the rolling of the sheet plate used in thecurrent study results in an original compressive state ineach of the materials and the stresses in longitudinal andtransverse direction are almost equal.

Long plates (600 mm 9 100 mm, with slightly differ-ing thicknesses) of all three materials were metal-inert-gas (MIG) welded using welding robots at (1)21.7 V, 137.5 A, and welding speed 0.8 m/minute forAISI 1008 steel; and (2) 24 V, 248.5 A, and weldingspeed 0.7 m/minute for ASTMA572 and AISI 4142materials, to make single pass bead on plate weld. Thewelded plates were sectioned into 50 mm 9 100 mmspecimens for residual stress measurements. The dimen-sions of the specimens are shown in Table I andFigure 1, and a thin plate assumption was applied inthe current study.

B. Experimental Procedures

A Bruker D-8 X-ray diffractometer, operated at30 kV and 50 mA with a Cr tube, and with 0.5-mmcircular collimator and 2D area detector, was used tomeasure the residual stresses. The gauge volume isapproximately 1 9 10�4 mm3. The stresses were mea-sured by the W method and determined using the a-Fe(211) peak shift according to SAE E915 standard.[39]

The preliminary test shows the excellent reproducibilityof less than ±9 MPa error. The measurements weretaken as close to the weld root as possible (2 mm fromthe weld toe), in both transverse (perpendicular to theweld) and longitudinal (parallel to the weld) directions.On each specimen, three points (5 mm apart) weremeasured and averaged to reduce statistical errors, asshown in Figure 1.

First, the welding residual stresses were measuredafter welding process. Then, cyclic four point bendingwas applied to the specimens along the transversedirection using a MTS servo-hydraulic fatigue-testing

machine according to the ASTM E855 standards. Themeasurement points were under tensile loadings at aloading ratio R = 0.1. The applied flexural stress wascalculated by the following Eq. [1]:

rs ¼3Fa

wt2½1�

where F is the loading force, a is distance from thesupport to the load applicator, w is specimen width, andt is the specimen thickness.After the first cycle, each specimen was removed from

the fixture and taken for X-ray measurement. Aftermeasurement, the specimen was put back into thebending fixture for further loading. After ten cycles,each specimen was again taken for X-ray measurementat the exact same locations. Depending on the specificsample studied, this procedure was repeated at 100,1000, and/or 10000 loading cycles, as shown in Table II.Several levels of loading, also shown in Table II, wereapplied to each material based on percentages of theiryield strength. This insured that the three regimes ofinterest, namely (1) below the endurance limit, (2) abovethe yield strength, and (3) in between, were all covered.Each loading was repeated on at least three specimens,and the results were averaged to ensure statisticalsignificance. After these tests, a select number ofspecimens were subjected to further increased loadings,the details of which are also included in Table II. Thestress concentration factor (Kt) was calculated on thewelding geometries using finite-element models. Thevalue of Kt at the locations of the residual stressmeasurement is around 1.0 to 1.2.One great advantage of the non-destructive nature of

X-ray diffraction is that residual stress measurements

Table I. Properties of Test Materials

YieldStrength (MPa)

TensileStrength (MPa)

Original ResidualStress (MPa)

Length(mm)

Width(mm)

Thickness(mm)

Number ofSpecimens

AISI 1008 253 341 �73 100 50 3.88 22ASTM A572 (thin) 345 449 �51 100 50 4.0 6ASTM A572 (thick) 345 449 �98 100 50 6.0 6AISI 4142 768 947 �100 100 50 4.76 7

Fig. 1—MIG-welded plate specimen for residual stress measurement.

3148—VOLUME 44A, JULY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

could be repeated at the same locations on the samplesafter loading. As a result, any changes caused bydifferent loadings could be readily measured.

C. Experimental Results

1. Low carbon steel AISI 1008A typical redistribution of residual stress on AISI

1008 steel is shown in Figure 2. The specimen was first

subjected to a loading of 63 MPa, which is essentiallyequal to a quarter of the measured yield strength(0.25ry) of the material, up to 10000 cycles. The opensymbols show the results of three measured points (left,middle, and right as indicated in Figure 1) on thespecimen, which are 5 mm apart. The average value overthese three points, indicated by the diamond symbols,was used to represent the stress state in this specimen.After the initial loading and cycles, the stress was raisedto 167 MPa (0.66ry), and further cyclic loading wasapplied up to 1000 cycles. These results are included inFigure 2 at the right of the vertical dashed line. Notethat error bars are only shown on one set of data to keepthe plot from becoming too cluttered.Throughout the current study, the same procedures as

above were repeated for each loading on at least threespecimens, and the measured results were averaged toensure statistical significance, producing a series of plotsfor each material and stress level tested. Several studiesof weldments[40,41] reveal that in many cases fatiguecracks tends to open in a direction along the weld toe,which is caused by the superimposition of the appliedload and transverse residual stress. Therefore, the stressin the transverse direction of a weld is typically of moreconcern in practice.The results of relaxation under different loading

conditions for the AISI 1008 are summarized in Figure 3.In the transverse direction (Figure 3(a)), significantrelaxation was only observed after the first cycle. Nochange of the residual stress was seen with additionalcycles, even when the loadings were increased after10000 cycles, and linear fits of the data after the initialcycle showed only very slight slopes. The longitudinalstresses (Figure 3(b)) showed a slightly different behav-ior in that no initial drop was seen. Linear fitting againrevealed similar gentle slopes for all four applied loads,which indicated that only minor changes occurredthroughout the loading cycles, even when an increasein loading stresses was applied. Thus, the longitudinalresidual stress appears to remain at a constant magni-tude regardless of the amplitude or cycles.

2. Low alloy steel ASTM A572Similar experiments were performed on both 4- and

6-mm thicknesses of ASTM A572 steel specimens underthe applied stresses of 100 and 400 MPa, and the resultsare shown in Figure 4. In the transverse direction, alarge amount of relaxation was observed for boththicknesses after the first cycle for the 400 MPa loadings,

Table II. Cyclic Loading Applied to the Specimens

Material Load (MPa) Cycles (N) Further Load (MPa) Further Cycles (N)

AISI 1008 63 0,1,10,100,1000,10000 167 1,10,100,1000167 0,1,10,100,1000,10000 250 1,10,100,1000250 0,1,10,100,1000,10000 300 1,10,100,1000300 0,1,10,100,1000,10000

ASTM A572 100 0,1,10,100 400 1,10,100400 0,1,10,100

AISI 4142 150 0,1,10,100 600 1,10,100600 0,1,10,100

0 (weld) 1 10 100 1000 10000 further 1 10 100 10000

40

80

120

Number of Cycles (N)

Tra

nsve

rse

Res

idua

l Str

ess

(MP

a)

Transverse Residual Stress Redistribution

left middle right average

0 (weld) 1 10 100 1000 10000 further 1 10

(b)

(a)

100 10000

40

80

120

160

Number of Cycles (N)

Long

itudi

nal R

esid

ual S

tres

s (M

Pa)

Longitudinal Residual Stress Redistribution

left middle right average

Fig. 2—Typical residual stress redistribution of one AISI 1008 speci-men 2E, under 63 MPa cyclic loading. The specimen was subjectedto a further loading of 167 MPa. (a) Transverse stress. (b) Longitu-dinal stress.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JULY 2013—3149

followed by the stress remaining relatively constant.This differed greatly from the 100 MPa loadings, whichshowed no significant changes up to 100 cycles. At thispoint, the loading level was increased to 400 MPa, and aconsiderable amount of relaxation was seen after onecycle at this higher load. The amount of relaxation wason the same order of magnitude as occurred in the firstcycle for specimens that were directly loaded to400 MPa. Again, only a minor decrease was seen inthe longitudinal stresses when the specimens weresubjected to a stress amplitude that exceeded the yieldstrength.

Measurements showed that no relaxation occurredwhen the applied stress ra < ry, and a large relaxationwas observed when ra > ry. This relaxation behaviorhas been widely observed also in the literature.[13,25]

3. Low alloy steel AISI 4142The original AISI 4142 plate had a compressive

residual stress of�100 MPa.Figure 5 shows themeasured

transverse and longitudinal residual stresses as a func-tion of cyclic loading after welding. Measurements showan average stress of 600 MPa in the longitudinaldirection, which approximates the yield strength of thematerial.In Figure 5, there is no significant stress relaxation in

either transverse direction or longitudinal directionunder the 150 MPa load. A minor stress reductionwithin the range of measurement error did occur afterthe initial cycle for the 600 MPa load. An experimentwas attempted where after the 100th cycle, the loadingwas increased from 600 to 700 MPa for one specimen.Despite the specimen being below the bulk yieldstrength of 768 MPa, it failed right at the weld toeduring the first cycle, indicating that the local stress(where stress cannot be measured by x-ray because ofgeometrical constraints associated with the samplestage) is most likely even higher than the obtainedmeasurements.

0 (weld) 1 10 100 1000 10000 further 1 10

(a)

(b)

100 10000

20

40

60

80

100

Number of Cycles (N)

Tra

nsve

rse

Res

idua

l Str

ess

(MP

a)Transverse Residual Stress on AISI1008

63MPa

167MPa250MPa

300MPa

0 (weld) 1 10 100 1000 10000 further 1 10 100 10000

20

40

60

80

100

120

140

Number of Cycles (N)

Long

itudi

nal R

esid

ual S

tres

s (M

Pa)

Longitudinal Residual Stress on AISI1008

63MPa

167MPa250MPa

300MPa

Fig. 3—The residual stress redistribution under different loading lev-els on AISI 1008 steel. (a) Transverse stress. (b) Longitudinal stress.The experimental errors (±9 MPa) are not shown here for the sakeof clarity.

0 (weld) 1 10

(a)

(b)

100 further 1 10 100-10

0

10

20

30

40

50

60

Number of Cycles (N)

Tra

nsve

rse

Res

idua

l Str

ess

(MP

a)

Transverse Residual Stress in A572

100MPa (4mm)

400MPa (4mm)100MPa (6mm)

400MPa (6mm)

0 (weld) 1 10 1000

20

40

60

80

100

Number of Cycles (N)

Long

itudi

nal R

esid

ual S

tres

s (M

Pa)

Longitudinal Residual Stress in A572

400MPa (4mm)

400MPa (6mm)

Fig. 4—The residual stress redistribution on 4- and 6-mm-thickA572 steel. (a) Transverse stress. (b) Longitudinal stress. For thesake of clarity, the experimental errors (±7 MPa) are not shownhere.

3150—VOLUME 44A, JULY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

III. DISCUSSION

A. Determination of Residual Stress Relaxation

The experimental results for all three steels studiedshow that no obvious stress relaxation occurs in thelongitudinal direction for a load applied perpendicularto the weld, while residual stress relaxation did occur inthe direction transverse to the weld. These results arecomplementary to the earlier studies of Takanashi[25]

and Holzapfel,[8] who applied loads in the longitudinaldirection (i.e., parallel to the weld) and saw relaxation ofthe longitudinal stresses but not the transverse stresses.Measurable relaxation only occurred in the first fewcycles, and the largest amount of relaxation was alwaysobserved after the first cycle. Minor changes of residualstress occurred during subsequent cycles conductedusing the same loading, although their amounts weremuch smaller. This is consistent with results reported byseveral studies.[26,27]

Although the transverse residual stress of all threematerials showed relaxation, the manner by whichrelaxation was produced was very different, with eachshowing its own distinctive relaxation behavior. Forexample, for plain carbon steel AISI 1008, residual stressrelaxation occurred at every applied load, even for thevery low loading of only a quarter of yield strength. Thiswas not seen for the other steels studied. In order tocompare results between steels, one must first considerthe factors that contribute to the measured stress results.

The hot-rolledAISI 1008 steel plate showed an averagecompressive residual stress of �73 MPa. This is theoriginal plate stress before welding, while the weldingstress is themeasured stress after welding but before cyclicloading begins, ranging from 40 to 100 MPa. Eventhough welding is a continuous process, random fluctu-ations such as power input, chemical composition and/ortexture of the sample, local restraints. etc., will causevariations of the welding residual stress distributionthroughout the specimens. This was why a spread ofmeasurements was made, and an average value was usedin the plots displayed in Figures 3, 4, and 5.

The percentage of relaxation, S, was calculated usingthe following expression and is illustrated in Figure 6.

percentage of relaxation of Nth cyclesðSÞ

¼ welding stress� residual stress of Nth cycles

welding stress� plate stress� 100%

½2�

The plate stress is the stress measured as existing inthe as-received plate before welding. This value is usedas the lower limit because it is the dominant stressthroughout the specimen, and previous studies haveshown that the residual stress appears to relax towardthis value instead of zero.[42]

While using the percentage reduction facilitates com-parison of the obtained data, it does present a drawbackin that the relaxation as defined by Eq. [2] results inincreased error when the welding stress is close to theoriginal plate stress. For example, in the case of AISI

0 (weld) 1 10 100 further 1 10

(a)

(b)

100-80

-60

-40

-20

0

20

Tra

nsve

rse

Res

idua

l Str

ess

(MP

a)

Number of Cycles (N)

Transverse Residual Stress in AISI4142

150MPa

600MPa

0 (weld) 1 10 100 further 1 10 1000

100

200

300

400

500

600

700

Number of Cycles (N)

Long

itudi

nal R

esid

ual S

tres

s (M

Pa)

Longitudinal Residual Stress in AISI4142

150MPa

Fig. 5—The residual stress redistribution in AISI 4142 steel. (a)Transverse stress. (b) Longitudinal stress.

Fig. 6—Illustration of the amount of residual stress relaxation. Platestress is the original stress state of plate before welding. Weldingstress is the stress caused by welding before cyclic loading wasapplied.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JULY 2013—3151

4142 steel at 600 MPa loading (Figure 6(a)), the error inthe calculation can be as large as ±15 pct. This highamount of error precludes meaningful interpretation ofthe relaxation behavior. For this reason, the plot forAISI 4142 will not be included in the followingdiscussion.

1. AISI 1008Turning now to a consideration of the data, the

calculated amounts of percent relaxation for AISI 1008steel are plotted in Figure 7. Relaxation is seen at allloading levels, although the highest loading (300 MPa,1.2ry) resulted in the largest amount. Relaxation ofresidual stress at the lowest loading (63 MPa, 0.25ry) issurprising and has rarely been reported.[43]

Increasing loading after 10,000 cycles did not alter theresidual stress, which indicates that the stress has been(and can only be) relaxed during the first cycle. In otherwords, the amount of relaxation is solely dependent onthe applied stress level of the first cycle. Thus, a highstress applied at the early stages of service or a severepreloading will be most effective in relieving detrimentaltransverse residual stress in AISI 1008 weldments.

2. ASTM 572The ASTM A572 steel showed a more commonly

reported behavior. A high loading that exceeded theyield point caused a relaxation in the residual stress,while low applied loads did not result in any notablechanges. However, when specimens that initially had alow load applied were subjected to further loading,involvement of a higher stress relaxation was seen. Theamount of relaxation was calculated in the same way asfor the AISI 1008 steel and is shown in Figure 8. Theresidual stress values of the original plates are �51 and�98 MPa for 4- and 6-mm-thickness plates, respec-tively. It is worth noticing that the initial high loading(400 MPa) and low–high loading (100 MPa then400 MPa) produce a similar total amount of relaxationof residual stress. Both loading profiles resulted in�20 pct relaxation. These results indicate that only ahigh loading beyond the yield strength of the materialhas any effect on residual stress relaxation in thismaterial.

Similar experimental results were obtained for spec-imens of both 4- and 6-mm thickness. Relaxation seemsbe independent on the thickness of the material but onthe relationship of the applied stress to the yieldstrength. The high applied stresses cause plastic flowand change local constraints of the residual stress,resulting in a redistribution/relaxation. This phenome-non can be explained by the theory of continuummechanics.[28]

3. AISI 4142AISI 4142 steel exhibited a behavior opposite in

nature to that of AISI 1008 steel. No significantreduction of residual stress could be confirmed at anylevel of loading since the slight drop seen after one cyclefor the 600 MPa initial load was within experimentalerror. Increasing loading to 600 MPa after initial cyclesat 150 MPa further confirms this observation—the

small drop that may be seen in Figure 5 being againwell within experimental error. If one grants that slightdrops are seen after the initial cycle upon loading to600 MPa as shown in Figure 5(a), it is interesting tonote that in the transverse measurements where com-pressive stresses are found, the material does not relax toa value tending toward zero but become more compres-sive. Considering the compressive stress of the originalplate, the residual stress appears to be relaxing towardthe original state of �100 MPa (compression). Thelongitudinal stress showed almost no change for bothdirections, stay at a high value throughout the test.Again, the small change in value results in large errorswhen considering percentage relaxation so these valuesare not plotted.

B. Microstructures and Dislocations

Several studies[12,44] present evidence exists linkingresidual stress relaxation behavior to the microstruc-tures/dislocation density of the material. For example,

0 (weld) 1 10 100 1000 10000 further 1 10 100 10000

4

8

12

16

20

Number of Cycles (N)

Am

ount

of R

elax

atio

n (%

)

Amount of Stress Relaxation in AISI1008

63MPa

167MPa250MPa

300MPa

Fig. 7—The amount of relaxation in transverse stress on AISI 1008steel.

0 (weld) 1 10 100 further 1 10 100

-10

0

10

20

Number of Cycles (N)

Am

ount

of

Rel

axat

ion

(%)

Amount of Stress Relaxation in ASTM A572

100MPa (4mm)

400MPa (4mm)100MPa(6mm)

400MPa(6mm)

Fig. 8—The amount of relaxation in A572 steel.

3152—VOLUME 44A, JULY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

Walker et al.[12] found a correlation between evolutionof residual stress and dislocation density on cold-rolledmild steel EN3b. It is interesting and unusual that theresidual stress relaxation in AISI 1008 occurred at everyapplied load, even very low ones, while no significantchanges happened in the AISI 4142 steel. Moreover, afurther loading did not result in any changes for eithermaterial. It is believed that the observed differences instress relaxation behaviors are related to the micro-structures of the materials that result because ofwelding. Welding is an intense local heat treatment,producing severe thermal gradients resulting in non-uniform plastic deformation. As a result, thermal misfitsand local shrinkage/expansion can be the source of largeamounts of dislocations as the material cools. Themanner by which dislocation motion may be affectedbecause of the varying microstructures is discussedbelow.

The microstructures of the materials at the locationswhere the residual stress measurements were taken areshown in Figure 9. AISI 1008 has the microstructure ofalmost pure ferrite, with a large grain size of �10 to15 lm. The ASTM A572 is composed primarily offerrite with small amounts of pearlite, and the grain size

is less than 5 lm. AISI 4142 steel was primarily finepearlite and ferrite. A number of fine precipitatessmaller than 1 lm are also present.One hypothesis for the results seen in AISI 1008 is

that the large grains of essentially single-phase ferritehave little resistance to dislocation slip and/or climb.Dislocation movement at highly plastically deformedlocations caused by welding may be expected to becomeactivate, even under a very low stress, for a microstruc-ture such as this. This changes the local plastic con-straints and results in residual stress redistribution.Since the dislocations can move freely, the stressredistribution is completed within the first few cyclesand no further relaxation occurs even when increasingthe applied load. Other studies[13] have suggested someforms of stress concentration such as microscopicyielding at the grain boundaries occurs, resulting inmicroplastic deformation. While ASTM A572 has asimilar microstructure with AISI 1008 the presence ofpearlite and a smaller grain size act as barriers to stopdislocation movement. Consequently, ASTM A572shows no stress relaxation until these barriers areovercome by applying a loading that exceeds thematerial’s yield point.

Fig. 9—Microstructures taken at the locations of residual stress measurements. Etched by 2 pct nital. (a) AISI 1008. (b) ASTM A572. (c) AISI4142.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JULY 2013—3153

The 4142 steel has a very different microstructurefrom the others, consisting of fine pearlite particles andsmall precipitates, both of which can be expected to pinand tangle dislocations during cyclic loading, makingthe movement of dislocations extremely difficult. As aresult, residual stress redistribution/relaxation is difficultto achieve even when a load is applied near or at theyield stress. A higher applied loads might be able toactivate dislocation movements and result in stressrelaxation; however, when this was attempted thematerial failed. Two of the specimens were also exam-ined using transmission electron microscope (TEM), onein the as welded state and had never been loaded, whilethe other was subjected to 300 MPa loading up to10,000 cycles. The TEM samples were taken from themiddle of the testing piece, as close to the weld aspossible, in the vicinity of the point marked ‘‘middle’’shown in Figure 1. Unfortunately, no evidence ofdislocations was observed in either sample in this verylimited examination. This is not to say that dislocationsare not present in the original material. However, owingto the small size of the TEM specimen (3 mm indiameter), it is entirely possible that most of theconstrains were removed, and residual stress has beenrelaxed.[45] A more extensive and detailed analysis,outside the scope of the current study, would berequired to support the observations of References 12,44.

C. Residual Stress Relaxation Model

Phenomenological models were often used to studythe residual stress relaxation behaviors[27,29–31] since it isextremely difficult to apply the first principles in thiscase. As discussed above, residual stress relaxation isclosely related to dislocation movement. Valluri[32]

suggested the situation of stress relaxation is similar tocreep. Both cause the evolution of stress/strain over aperiod of time under external loading. The creepcontrolled by dislocation movement can be expressed by

d�

dt¼ Aðr� rthÞne�

QRT ½3�

where Q (activation energy for dislocation motion),R (universal constant), and T (temperature) are allconstants in the case of residual stress; and rth is aconstant dependent on material. Equation [3] can berewritten as

d�

dt¼ B

rrth� 1

� �n

½4�

In a manner analogous to Eq. [4], a phenomenologicalmodel to predict the amount of residual stress relaxation(S) is proposed:

dS

dfðNÞ ¼ gra

ry

� �¼ a

ra

ry

� �n

þb ½5�

where f(N), which is a function of number of cycles,controls the relaxation rate, while the term g() determines

the amplitude of relaxation. a, b, and n are all materialconstants. Both Eqs. [4] and [5] are rate-dependentmodels, i.e., Eq. [4] expresses strain rate, while Eq. [5]gives relaxation rate. The right-hand side of bothequations gives the dependence of the rate under con-sideration of existing stress conditions and materialparameters. This model was derived by combining thematerial constants with experimental data. For themathematical convenience, the expression f(N) is deter-mined to be in the form:

f Nð Þ ¼ ½logðNþ 1Þ�m ½6�

where m is a material constant, and N is the numberof loading cycles. Then Eq. [5] can be rewritten in thefollowing form:

S ¼ ara

ry

� �n

þb� �

½logðNþ 1Þ�m ½7�

In this expression, ra = applied stress and ry = yieldstress. The material constants a, b, m, and n aredetermined by nonlinear fitting according to the exper-imental data. The relaxation model reveals the depen-dency on applied stress and number of cycles. Theamount of relaxation was plotted as a function of cyclesin Figure 10. The proposed model and showed a verygood fitting for both the AISI 1008 and ASTM 572steels. The fitted value of the material constant, m, issimilar under all applied load amplitudes for bothmaterials (m � 0.1), which indicates that the amount ofrelaxation stabilizes at a high rate in all specimens.Figure 11 showed the effect of both applied stressamplitude and number of cycles on stress relaxation ofAISI 1008 steel. It is obvious that the higher the appliedstress, and the larger the number of cycles, the greaterthe amount of relaxation. The fitting parameters arelisted in Table III. The goodness of fitting (R2) is 0.93.In order to further test the relaxation model, it was

applied to A. Wick’s[14] residual stress relaxation data ofAISI 4140 plates. They measured the change of residualstress when applying the cyclic loading on shot-peenedAISI 4140 steels. The result is shown in Figure 12 andTable III, and the relaxation model again shows a verygood fit with a goodness of fit (R2) equal to 0.92.Based on the externally applied stress, the residual

stress relaxation behavior can be separated into threeregimes, as shown in Figure 13. These regimes might beconsidered analogous to the three stages seen in creep,which is not surprising since the model assumes relax-ation similar to that occurs in creep. Behavior in RegimeI is not clear since it was not studied, and no data exist.Presumably this might correspond to very low loadswhere any relaxation would only occur after an exces-sively large number of cycles.In Regime II, the stress amplitude is intermediate. The

amount of relaxation in this regime showed a weakcorrelation with the applied stress, although it is stilldetermined by Eq. [7]. Instead, the relaxation highlydepends on the material constant b, which is a ‘‘thresh-old value’’ similar to rth in Eq. [3] involving creepdislocation. It represents the ability of material to

3154—VOLUME 44A, JULY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

activate the stress relaxation. In the current study, AISI1008 steel has a higher value of constant b, whichindicates that it has more stress relaxation than the

ASTM A572 and A. Wick’s AISI 4140 material underthe intermediate loading. It appears the materials withlower yield strength are easier to activate stress relax-ation and thus have higher values of constant b. Thisconclusion is consistent with observation made byMorrow et al.[44] who found that decay of mean stressis more pronounced for softer materials when theyconducted a study on martensitic steels as a function ofheat treatment.In Regime III, where the applied load approximates

the yield point of the material, the stress relaxation isproportional to the applied stress and is dominated bythe power law (Eq. [7]). The largest amount of relaxa-tion is expected in this regime, although more experi-ments are needed to completely elucidate the exact

0 0.31

23

4

0.250.5

0.751

1.251.5

0

10

20

30

40

50

log(N+1)

Applied Stress (Normalized)

Am

ount

of

Str

ess

Rel

axat

ion

(%)

0

5

10

15

20

25

30

35

40

R2 = 0.93

Fig. 11—Effects of both applied stress amplitude and number of cy-cles on stress relaxation of AISI 1008 steel. The solid symbols areexperimental data, and the applied stress is normalized to yieldstrength.

Table III. Fitting Parameters for AISI 1008 steel and A

Wick’s[14] AISI 4140 steel

m n a b R2

AISI 1008 0.1 8.0 1.15 0.098 0.93AISI 4140 0.1 3.0 1.03 0.059 0.92

01

23

45

00.25

0.50.75

11.25

1.50

20

40

60

80

100

log(N+1)

Applied Stress (Normalized)

Am

ount

of

Str

ess

Rel

axat

ion

(%)

0

10

20

30

40

50

60

70

80

90

100

R2 = 0.92

Fig. 12—The application of the proposed relaxation model on datafrom Ref. [14] The solid symbols are experimental data.

Applied Stress

Am

ount

of S

tres

s R

elax

atio

n

Regime IIIntermediate Stress

b

Regime IIIPower Law

Regime ILow Stress

Fig. 13—Residual stress relaxation can be separated into threeregimes as a function of applied stress.

0 0.3 1 2 3

(a)

(b)

4 50

4

8

12

16

18

log(N+1)

Am

ount

of S

tress

Rel

axat

ion

(%)

AISI 1008

63MPa

167MPa250MPa

300MPa

g(0.25)=10.24g(1)=9.72

g(1.2)=15.07 g(0.67)=10.46

0 0.3 1 2 3 40

5

10

15

20

25

log(N+1)

Am

ou

nt

of

Str

ess

Re

laxa

tion

(%

)

ASTM A572

6mm 100MPa

4mm 400MPa

4mm further 400MPa6mm 400MPa

6mm further 400MPa

g(0.29)=7.1

g(1.16)=21.22

g(1.16)=20.11g(1.16)=18.51g(1.16)=18.82

Fig. 10—Effect of number of cycles. (a) AISI 1008. (b) ASTM A572.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JULY 2013—3155

nature of the relationship. A greater n value will result ina sharper curve between Regime II and Regime III,which means larger discrepancy between these tworegimes. It appears that the soft materials like AISI1008 have the greater n value, indicating faster decayunder high stresses.

IV. CONCLUSIONS

The residual stress relaxation behaviors of threematerials, AISI 1008, ASTM A572, and AISI 4142,subjected to the cyclic tensile stress at R = 0.1, weredocumented in the current study. Relaxation occurs ateach applied stress in AISI 1008 steel, while nosignificant relaxation happened in AISI 4142 steelregardless of the applied stress level. ASTM A572 steelshowed a conventional relaxation behavior where stressredistribution only starts when the applied stress on thematerial reaches its yield point. However, all threematerials shared some common features, namely that, ifstress relaxation was to occur, it was generally com-pleted during the first few loading cycles, and that nosignificant reduction occurred in the longitudinal stresswhich is perpendicular to the loading direction.

Stress relaxation is most readily activated in AISI 1008steel, presumably because of a microstructure consistingof large ferrite grains. The very fine pearlite microstruc-ture with small precipitates seen in AISI 4142 steel can beexpected to obstruct dislocation motion and appears tohinder residual stress relaxation. A model based on theprinciple of creep dislocation movement was proposed toestimate the relaxation of welding residual stress. Thismodel shows good agreement with the experimental dataand suggested three regimes based on the applied stresses.The stress relaxation has a weak correlation with inter-mediate applied loads (Regime II), while a power lawdependence exists when external stresses over the yieldlimit of material (Regime III) are applied.

ACKNOWLEDGMENTS

The research was carried out at Iowa State Univer-sity (ISU) with financial support granted by Deere andCompany. The author would like to thank JerryAmenson and Scott Schlorholtz of the Materials Anal-ysis and Research Laboratory of ISU, and DavidEisenmann of CNDE for their help and permittingaccess to equipment.

REFERENCES1. R.C. McClung: Fatigue Fract. Eng. Mater. Struct., 2007, vol. 30,

pp. 173–205.2. S. Berge and O.I. Eide: ASTM STP 776, 1982.3. R. John, K.V. Jata, and K. Sadananda: Int. J. Fatigue, 2003,

vol. 25, pp. 939–48.4. M. Chiarelli, A. Lanciotti, and M. Sacchi: Int. J. Fatigue, 1999,

vol. 21, pp. 1099–1110.5. F.V. Lawrence Jr., J.D. Burk, and J.Y Yung: ASTM STP 776,

1982, pp. 33–43.

6. G.A. Webster and A.N. Ezeilo: Int. J. Fatigue, 2001, vol. 23,pp. 375–83.

7. C.D.M. Liljedahl, O. Zanellato, M.E. Fitzpatrick, J. Lin, and L.Edwards: Int. J. Fatigue, 2010, vol. 32, pp. 735–43.

8. H. Holzapfel, V. Schulze, O. Vohringer, and E. Macherauch:Mater. Sci. Eng., A, 1998, vol. 248, pp. 9–18.

9. P. Hurrell, C.T. Watson, D. Everett, and S. Bate: Proceedings ofASME Pressure Vessels and Piping Conference, Vancouver, BC,Canada, 2006, pp. 801–812.

10. S. Aoki, T. Nishimura, and T. Hiroi: Nucl. Eng. Des., 2005,vol. 235, pp. 1441–45.

11. A.S.M.Y Munsi, A.J. Waddell, and C.A. Walker: J. Strain Anal.,2001, vol. 36 (5), pp. 453–64.

12. C.A. Walker, A.J. Waddell, and D.J. Johnston: Proc. Inst. Mech.Eng., 1995, vol. 209, pp. 51–58.

13. M.R. James: Advances in Surface Treatments: Technology, Appli-cations, and Effects, Pergamon Press, Oxford, 1987, pp. 349–65.

14. A. Wick, O. Vohringer, and V. Schulze: Mater. Sci. Eng. A, 2000,vol. 293, pp. 191–97.

15. M.A.S. Torres and H.J.C. Voorwald: Int. J. Fatigue, 2002, vol. 24,pp. 877–86.

16. T. Lorentzen, C.N. Tome, B. Clausen, and M.R. Daymond: ActaMater., 2002, vol. 50, pp. 1627–38.

17. G. Bruno andT.N. Pagel:Appl. Phys. A, 2002, vol. 74, pp. 1388–90.18. V. Dattoma, M. De Giorgi, and R. Nobile: J. Strain Anal., 2004,

vol. 39 (6), pp. 663–72.19. Z. Barsoum: Mater. Sci. Forum, 2006, vols. 524–525, pp. 323–30.20. M. Benedetti, V. Fontanari, and B.D. Monelli: J. Eng. Mater.

Technol., 2010, vol. 132 (1), p. 011012.21. M. De Giorgi: Int. J. Fatigue, 2011, vol. 33, pp. 507–12.22. Y. Li, J. Lu, and K. Xu: Mater. Sci. Forum, 2005, vols. 490–491,

pp. 396–403.23. J.R. Teodosio, M.C. Fonseca, and P.D. Pedrosa: Mater. Sci.

Forum, 2003, vols. 426–432, pp. 3981–88.24. M.E. Fox and P.J. Withers: Mater. Sci. Forum, 2006, vols. 524–

525, pp. 153–58.25. M. Takanashi, K. Kamata, and K. Iida: Weld. World, 2000,

vol. 44 (4), pp. 2–8.26. C. Lachmann, T.N. Pagel, and H. Wohlfahrt: Mater. Sci. Forum,

2000, vols. 347–349, pp. 374–81.27. W.Z. Zhuang and G.R. Halford: Int. J. Fatigue, 2001, vol. 23,

pp. 31–37.28. P.J. Withers: Rep. Prog. Phys., 2007, vol. 70, pp. 2211–64.29. J. Morrow and G.M. Sinclair: ASTM STP 237, 1959.30. H.R. Jhansale and T.H. Topper: ASTMSTP 519, 1973, pp. 246–70.31. S. Kodama: Proc. Int. Conf. Mech. Behav. Met., 1972, vol. II,

pp. 111–18.32. S.R. Valluri: Acta Metall., 1963, vol. 11, pp. 759–75.33. V.M. Radhakrishnan and CR Prasad: Eng. Fract. Mech., 1976,

vol. 8 (4), pp. 593–97.34. M.T. Hutchings, P.J. Withers, T.M. Holden, and T. Lorentzen:

Introduction to the Characterization of Residual Stress by NeutronDiffraction, Taylor& Francis Group, Boca Raton, FL, 2005.

35. I.C. Noyan and J.B. Cohen: Residual Stress: Measurement byDiffraction and Intepretation, Springer, New York, 1987.

36. J. Lu: Handbook of Measurement of Residual Stresses, Society forExperimental Mechanics, Lilburn, GA, 1996.

37. P.J. Webster and L.D. Oosterkamp: Analysis, 2001, vol. 35 (1),pp. 61–70.

38. P.S. Prevey: Developments in Materials Characterization Technol-ogies, ASM International, Materials Park, OH, 1996, pp. 103–10.

39. ASTMInternational:ASTME915,WestConshohocken, PA,USA.40. F.V. Lawrence, S.D. Dimitrackis, and W.H. Munse: Report No.

173, Fracture Control Program, University of Illinois at Urbana-Champaign, 1996.

41. S.D. Dimitrakis: PhD Thesis, University of Illinois at Urbana-Champaign, 1999.

42. Z. Qian, S. Chumbley, and E. Johnson: Unpublished research, 2011.43. E.J. Pattinson and D.S. Dugdale: Metallurgia, 1982, vol. 66,

pp. 228–30.44. J. Morrow, G.M. Sinclair, and A.S. Ross: SAE Trans., 1960,

vol. 68, pp. 40–48.45. Z. Qian, S. Chumbley, and E. Johnson: Mater. Sci. Eng., A, 2011,

vol. 529, pp. 246–52.

3156—VOLUME 44A, JULY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A