two-dimensional and three-dimensional finite element

Two-Dimensional and Three-Dimensional Finite Element Analysis

of Finite Contact Width on Fretting Fatigue

Heung Soo Kim1;*, Shankar Mall2 and Anindya Ghoshal3

1Department of Mechanical, Robotics and Energy Eng. Dongguk University-Seoul, 100-715 Korea2Department of Aeronautics and Astronautics, Air Force Institute of Technology, Wright-Patterson Air Force Base, OH 45433, USA3US Army Research Lab, APG, MD 21005, USA

Three-dimensional effects of finite contact width fretting fatigue were investigated using the combination of full three-dimensional finiteelement model and two-dimensional plane strain finite element model, named as a hybrid layer method. Free edge boundary effect in finitecontact width fretting fatigue problem required full three-dimensional finite element analysis to obtain accurate stress state and relativedisplacement in contact zone. To save the computational cost with sufficient accuracy, traction distributions obtained from coarse three-dimensional finite element analysis was applied to the two-dimensional plane strain finite element model. The key idea of this hybrid layermethod was that traction distributions converged faster than the stresses. The proposed hybrid layer method predicted the free edge boundaryeffects of finite contact width fretting fatigue less than eight percent error bound and reduce the execution time to 5 percent of three-dimensionalsubmodeling technique. [doi:10.2320/matertrans.M2010268]

(Received August 9, 2010; Accepted November 8, 2010; Published December 22, 2010)

Keywords: fretting fatigue, contact, stick-slip, finite element analysis, three-dimensional effects, traction distribution, hybrid layer method

1. Introduction

Fretting is referred to wear and sometimes corrosiondamage at or near interface of two bodies in contact subjectedto oscillatory loads or vibratory excitation. In contrast to ator near surface damage associated with large scale relativemotion from either rolling or sliding action, fretting damageis a product of microslip amplitude concentrated in regionsnear the edges of contact. As a result, cracks are initiatedin the contact zone and the unexpected and/or prematurefailures under the fretting condition have been observed inmany structural components at stress levels below the fatiguelimit of materials.1–11) One of the most common examples,where the mechanical failure is caused by fretting fatigue,is the dovetail joint of the blade and disk attachments in gasturbine engines.

In the last decade, a number of finite element analysesof fretting tests with various contact geometries (spherical,cylindrical and flat pad geometry) have been reported. Mostof them are two-dimensional analyses based on the planestrain assumption. For example, McVeigh and Farris eval-uated the influence of the bulk stress on the contact pressurefor fretting fatigue contact problems.12) Namjoshi et al. usedfour noded quadrilateral plane strain element to estimatefretting fatigue life.13,14) Tsai and Mall incorporated elasto-plastic isotropic hardening model with a von Mises yieldcriterion in order to obtain the evolution of stress and strainduring a fretting fatigue test.15) Szolwinski and Farrissuggested juxtaposing an accurate characterization of thenear surface contact stress field with a multiaxial fatigue lifemodel to predict fretting fatigue behavior.16) Cormier et al.developed aggressive submodeling techniques to predictaccurate stress concentrations near the edge of contactregion.17) Fadaga et al. also developed submodeling tech-nique to analyze crack growth behavior of titanium alloy

under fretting fatigue condition.18) These analyses exploit thegeneral assumption that for contact areas with aspect ratiomuch less than one, the contact can be modeled accurately asa plane strain line contact of a pad with infinite length incontact with a half or finite thickness space. For realisticfinite width contact, this plane strain approach will approx-imate most closely the conditions at and near the mid-planeof the contact region and cannot explain the three-dimen-sional effects of the finite width of fretting fatigue testconfiguration (i.e. specimen and pad).

Johnson has provided a concise summary of ‘‘roller endeffects’’ that arise due to the free edge boundaries of finitewidth fretting fatigue tests.19) The impact of these end effectsvaries with the geometric details of the free edge boundaries,i.e. from an out-of-plane bulging of two coincident sharpfaces generated by the Poisson’s effect to a broadening of thecontact area where the free faces are not perfectly matched.Szolwinski and Farris addressed these end effects of finitewidth fretting fatigue tests using three-dimensional finiteelement model and infrared imaging system.20) Tur et al.showed the influence of finite dimensions of the specimen incontact with a spherical pad and subjected to fretting using athree-dimensional finite element model and an h-adaptivemesh refinement process.21) Kim and Mall studied three-dimensional effects of finite contact width on fretting fatigueby full three-dimensional finite element model and submod-eling technique.22) Three-dimensional finite element analysesprovided clear roller end effects and were in good agreementwith their experimental counterparts. However, the three-dimensional modeling requires significant computationalcost to implement the fine meshes at the edge of contact.Therefore, the need arose to develop an efficient computationmethod, which can reduce computational cost with sufficientsolution accuracy of stress state at the edge of contact.

The present study focused on the computational efficiencyof three-dimensional stress analysis under finite contactwidth fretting fatigue condition. The specific objective of this*Corresponding author, E-mail: [email protected]

Materials Transactions, Vol. 52, No. 2 (2011) pp. 147 to 154#2011 The Japan Institute of Metals

http://dx.doi.org/10.2320/matertrans.M2010268

paper was therefore to develop a hybrid layer method, whichwas a combination of coarse three-dimensional finite elementanalysis and fine two-dimensional plane strain analysis.The hypothesis in the present study was that the tractiondistributions converged faster than the stresses. The hypoth-esis was evaluated in the paper and the proposed hybrid layermethod was used to investigate into the three-dimensionaleffects of finite width of the specimen subjected to frettingfatigue and in contact with pad having either cylindrical orflat with rounded edge configuration.

2. Model Development

2.1 Three-dimensional finite element modelFigure 1 shows the schematic of fretting test configuration

analyzed in this study, which consists of a flat specimen and apair of fretting pads.14) Two zones of contact were generatedon a flat specimen when pressed by a constant contact load, Pon the two fretting pads. A cyclic tangential load, Q andcyclic bulk stress, �axial were applied during a fretting testafter the application of contact load. All tests were conductedunder the partial slip condition where the tangential load Q isless than �P, and � is friction coefficient, so both slip andstick regions were present in the contact area. Two differentcontact configurations, cylinder-on-flat and flat with roundededges-on-flat were used to investigate three-dimensionaleffects on fretting fatigue behavior. Cylindrical pad had anend radius of 50.8mm. A specimen thickness of 1.90mm(along y-direction in Fig. 1) and width of 6.35mm (alongz-direction in Fig. 2) were used in the analyses, which werethe actual dimensions of specimens in the experiments.14)

The pad width was equal to the width of the specimen(6.35mm). The other pad geometry had a flat center sectionwith rounded edge. Flat pad configuration had edge radiusof 2.54mm and a flat center section of 13.97mm. Bothspecimen and pad were made of titanium alloy, Ti-6Al-4Vwhose elastic modulus was 127GPa and Poisson’s ratio was0.32. The coefficient of friction was assumed as 0.8 in thisanalysis which varied from 0.5 to 0.8 in experiments.23)

Since the contact zone is the most critical region of anyfretting problem, refinement of mesh is required to obtain the

accurate stress state, particularly, at the edge of contact,where the fretting fatigue cracks initiated in experiments.14)

Three-dimensional contact analysis requires extremely finemeshes for accuracy which requires enormous computermemory and computation time. Therefore, the submodelingtechnique is generally used.17) The basic concept of sub-modeling is to study a local portion of a model with a refinedmesh based on interpolation of a solution from an initial,relatively coarse, global model. Submodeling is a useful andpowerful tool when it is necessary to obtain an accurate,detailed solution in a local region and the detailed modelingof that local region has a negligible effect on the overallsolution, which is the case in contact problems. A submodel-ing analysis consists of: running a global model analysis andsaving the results in the vicinity of the submodel boundary;defining the total set of driven nodes in the submodel;defining the time variation of the driven variables in thesubmodel analysis by listing the actual nodes and degrees offreedom to be driven in each step; and running the submodelanalysis using the ‘‘driven variables’’ to obtain the solution.24)

There are two symmetry planes in the fretting fatigueconfiguration shown in Fig. 1, i.e. along the axial andtransverse direction of specimen. Therefore, one quarter ofactual specimen and one of the pads were modeled as shownin Fig. 2. The details of various submodeling geometries ofthe current fretting fatigue problem are also given in Fig. 2.The directions x, y, z represent the length, thickness andwidth directions of the specimen. A commercially availablefinite element code ABAQUS was used in the study.24) Eight-node, linear brick element with reduced integration (C3D8R)was used with the master-slave contact algorithm on thecontact surface between the fretting pad and specimen. Asmall sliding contact condition was used between the contactpair to transfer loads between the two bodies. For this, thesurface of the pad was defined as a master contact surface andthe surface of the specimen was defined as a slave contactsurface. Both surfaces were defined as a contact pair that

P

Q

PQ

σaxial

R=50.8mmR=2.54mm

13.97mm

pad geometry

x

y

Fig. 1 Schematic of fretting fatigue test, specimen and pad.

sub1

sub2

sub3

sub4/sub5

sub4/sub5 sub4/sub5

P

σaxial

Q

pad

specimenlateral spring

x

y

z

Fig. 2 Details of submodels.

148 H. S. Kim, S. Mall and A. Ghoshal

enabled ABAQUS to determine if the contact pair wastouching or separated. The surface in contact was defined as acontact region. The contact region consisted of stick and slipregions. The stick region did not have a relative movementbetween the top and bottom of contact surface (i.e. pad andspecimen). The slip region showed a small relative move-ment between the top and bottom contact surface (i.e. pad andspecimen) which is commonly observed in a fretting fatiguetest. The FEA model had three bodies, fretting specimen,fretting pad and lateral spring as shown in Fig. 2. The lateralspring with elastic modulus of 34KPa was attached to theleft side of the pad to prevent rigid body translation of pad.The submodeling with mesh refinement was continued untilan appropriate convergence of the stress state was achieved,i.e. when the maximum stress between subsequent meshrefinements was less than a specific amount. For this study, adifference of 5 percent between the two consecutive stepswas used as the convergence criterion.22) Table 1 shows finiteelement mesh size and peak stresses of each three-dimen-sional FEA model for cylindrical pad. The convergence ratesat the center of specimen of submodel 5 were 4.18, 0.82 and1.12 percents for �xx, �yy, and �xy, respectively. Those at theedge of specimen were 2.42, 0.88 and 0.37 percents for �xx,�yy, and �xy, respectively. The peak stresses converged withfive steps of submodeling. The original and final mesh sizesof cylindrical pad were 119 mm and 7.45 mm, respectively.

2.2 Hybrid layer methodSubmodeling convergence process took 31 CPU hours of

computation and additional post processing of each succes-sive model was required. Therefore, the computational costof full three-dimensional submodeling convergence processis quite expensive. In order to reduce the required run time ofthe contact problem and maintain the accuracy of 3D edgeof contact problem, a hybrid method of a global 3D FEAsolution and 2D plane strain FEA was developed. In ourgroup, 2D plane strain finite element model was developedto investigate fretting fatigue behavior.15) This model isbased on four node, plane strain quadrilateral element (CPE4)in ABAQUS. The convergence study of this plane strainmodel was performed by comparing the finite element resultswith the analytical solution by Nowell and Hill.25) The finalmesh size of the 2D plane strain model in cylindrical padconfiguration was 6:2� 6:2 mm, which is similar to 3D FEAmodel. Figure 3 shows 2D plane strain finite element meshconfiguration.

The 3D FEA model allows for the stress analysis ofboundary effects where 2D FEA model fails. The proposedhybrid layer method is developed to save the efforts ofcomputational time and post process keeping with 3Dboundary effect. The proposed method involves obtainingtraction distributions from a relatively coarse 3D FEA modelto use as an input loading in 2D plane strain FEA model. Theschematic of contact traction distribution along the axial lineat the contact surface is shown in Fig. 4. The hybrid layermethod assumes that the forces converge much more quicklythan the longitudinal normal stress peak occurring at the edgeof contact. The traction distributions at the local contact zoneare normal contact force and two shear forces along thespecimen length and width (x and z direction in Fig. 4).In this work, tangential shear stress along the specimenwidth (z direction in Fig. 4) is ignored. This is because thegeometry is symmetric along the width and the axial load andinduced shear stress are applied to the axial direction only.The resultant normal traction and shear traction from 3Dcoarse mesh are obtained as follows.

P ¼ t

Z�yydl

Q ¼ t

Z�xydl

ð1Þ

where t is width of the specimen and l is tangential lengthalong the contact surface. The specimen width, t, is used toget the exact dimension of traction distribution and an inputforce of 2D plane strain finite element model.

3. Results and Discussion

To study three-dimensional effects of finite width of thetwo contact geometries (cylinder and flat), the comparisonand differences of stress profiles and relative displacements

Table 1 Finite element mesh and stress convergence for cylindrical pad.

ElementPeak stresses at the Peak stresses at the edge

Meshsize

center of specimen of specimen

details(mm)

(MPa) (MPa)

�xx �yy �xy �xx �yy �xy

3D global 119 167 287 144 182 247 149

sub1 59.5 198 304 161 220 245 169

sub2 29.8 284 337 185 287 246 173

sub3 14.5 324 342 193 312 232 170

sub4 9.93 355 358 198 318 232 166

sub5 7.45 370 361 200 326 231 167

Lateral spring P

Q

Pad

Specimen

σaxial

Fig. 3 2D plane strain finite element mesh configuration.

xz

Q

P

contact surface

traction distribution

Fig. 4 Schematic of traction distributions at the contact surface.

Two-Dimensional and Three-Dimensional Finite Element Analysis of Finite Contact Width on Fretting Fatigue 149

along the contact surface at the center and edge of thespecimen were investigated in the following discussion.

3.1 Cylindrical pad geometryFor the cylindrical pad configuration, the contact force

and shear force of cylindrical pad are 1335N and 554N,respectively. The applied axial stress is 53MPa. These loadsare the representative values from fretting fatigue tests.14)

Three-dimensional boundary edge effects of finite widthfretting fatigue were investigated first. Figure 5 presentscontact pressure on fretting surface obtained from the three-dimensional FEA model and typical micrograph of scar onfretted specimen. The contact pressure dictates the size andshape of the fretting scar, which were constant over most ofthe specimen width except for the region near the free edge.Contact pressure decreased at the edge of contact due to freeedge boundary. The computed contour of contact pressure isin good agreement with the shape of fretting scar from theexperiment as shown in the figure. Figure 6 shows stressprofiles of normalized longitudinal normal stress (�xx=p0)obtained by 3D FEA model at center and edge of the

specimen. Stress component was normalized with the peakcontact pressure, p0, which was obtained during the firstloading step, i.e. after the application of contact load only.The corresponding peak contact pressure (p0) was 358MPa.Stress profile at center of the specimen is close to 2D planestrain counterpart, but the edge stress shows large deviationfrom the center stress. The magnitude of overall edge stressdecreased due to the decrease of the contact pressure. Peakstress at the leading edge of contact reduced 18 percentcompared to the counterpart of center stress. The peak oflongitudinal normal stress indicates edge of contact. There-fore, the contact zone also decreased due to the free edgeboundary effect. The change of contact zone is clearlyobserved in shear stress profile in Fig. 7. Zero shear stressesrepresent no contact occurred in the specimen. The overallshear stress at the edge of specimen decreased compared tothe counterpart at the center. Relative displacements (RD) incontact zone are also presented in Fig. 7. Stick zone at theedge of specimen decreased 54 percent and large partial slipis observed in the figure. This partial slip can increase thefretting fatigue. From the observations, stress analysis in

Edge of contact

Edge of specimen

Free edge affected region

Center of specimen

x

z

Typical micrograph of scar on fretted specimen in contact with

cylindrical pad

Edge of contact

Fig. 5 Contour plot of contact pressure and typical micrograph of scar on fretted specimen.

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5σ xx/p

0

x/a

centeredge

Fig. 6 Comparison of longitudinal normal stress (�xx=p0) at center and

edge of specimen.

0

0.002

0.004

0.006

0.008

0.01

0

0.2

0.4

0.6

0.8

1

-1.5 -0.5 0.5 1.5

rela

tive

dis

plac

emen

t (u

/a)

− σxy

/p0

x/a

shear at centershear at edgeRD at centerRD at edge

Fig. 7 Comparison of shear stress (�xy=p0) and relative displacement (RD,

u=a) at center and edge of specimen.


finite width fretting fatigue problem must consider free edgeboundary effect. 2D plane strain FEA model cannot explainthis free edge boundary effect.

To implement the proposed hybrid layer method, theconvergences of traction distributions are investigated next.Traction distributions obtained from 3D global mesh and firstsubmodeling at the center and edge of the specimen ispresented in Table 2. The mesh sizes of 3D global model andfirst submodeling are 119 mm and 59.5 mm, respectively. Thefinal mesh size of 3D model is 7.45 mm. Two steps satisfies 5percent convergence criterion, whereas submodeling of 3Dmodel took six steps for peak stress convergence. This provesour initial hypothesis that traction distributions convergedfaster than peak stresses. Contact traction at the center ofspecimen is converged to the original contact force. How-ever, contact traction at the edge of specimen is converged to80 percent of the original contact force. This is due to the freeedge boundary effect, which means the lack of out of planeconstraint. The differences of resulting contact pressure fromoriginal load at the center of specimen are 5.4 percent from3D global model and 1.3 percent from first submodel. Theshear force resultant at the center of specimen is convergedfrom the lower value. The differences of shear force resultantfrom original load at the center of specimen are 5.2 percentfrom 3D global model and 0.9 percent from first submodel.Shear force resultant at the edge of specimen is convergedfrom higher value to the original load. The differences ofshear force resultant at the edge of specimen are 1.3 percentfrom 3D global model and 0.7 percent from first submodel.The shear force resultant at the edge is higher than itscounterpart at the center. To conclude, at the edge ofspecimen, the contact pressure converged to 80 percent of itsoriginal load, but shear load converged to its original load. Itis also concluded that the forces are converged much fasterthan the tensile normal stresses in 3D submodeling FEA.

The resulting contact force and shear forces obtained fromthe 3D modeling is applied to the 2D plane strain finiteelement model. The corresponding longitudinal and trans-verse normal stresses, shear stresses, and relative displace-ments at the center of specimen are given in Fig. 8. Stressprofiles obtained from the 3D model and hybrid layermethods are very close to each other as shown in Fig. 8(a).The difference of maximum normal stresses between 3Dmodeling and hybrid layer method is 3.2 percent. The edge ofcontact is also close to each other. The edge of contact is alsoclose to each other. Transverse normal stress (�yy) shown inFig. 8(b) shows almost no difference between these twomodels. The shear stresses (�xy) and relative displacementsare also close to each other as shown in Fig. 8(c). The peakdifference of shear stresses between 3D modeling and hybridlayer method is 4.3 percent and stick zone obtained fromlayer method is 2.9 percent smaller than that obtained from

3D modeling. One can find that 2D plane strain finite elementmodel approximates most closely the conditions at the mid-plane of the contact specimen.

The corresponding stresses and relative displacements atthe edge of the specimen are shown in Fig. 9. The location ofmaximum normal stress (�xx) obtained from hybrid layermethod is shifted 7.7 percent from 3D stress at the edge ofspecimen and the peak value is 7.6 percent smaller than itscounterpart of 3D stress as shown in Fig. 9(a). Althoughthere is a little bit large deviation in the prediction of locationand magnitude of maximum peak stress at the edge ofcontact, transverse normal stress (�yy) obtained from thehybrid method can be approximate free edge boundary

Table 2 Traction distribution from 3D coarse model, cylindrical pad.

Mesh Center of specimen (N) Edge of specimen (N)

details P Q P Q

3D global 1263 525 1037 561

sub1 1317 549 1061 558

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5σ xx/

p0

x/a

3D stress at center

Hybrid stress at center

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-1.5 -1 -0.5 0 0.5 1 1.5

σ yy/p

0

x/a

3D stress at center


(a)

(b)

0

0.002

0.004

0.006

0.008

0.01

0

0.2

0.4

0.6

0.8

1

-1.5 -0.5 0.5 1.5

rela

tive

dis

plac

emen

t (u

/a)

− σxy

/p0

x/a

3D stress at centerhybrid stress at centerRD from 3D modelRD from hybrid model

(c)

Fig. 8 Comparison of stresses between 3D model and Hybrid layer method

at the center of specimen, cylindrical pad; (a) longitudinal normal stress

(�xx=p0) along the contact surface, (b) transverse normal stress (�yy=p0),

and (c) shear stress (�xy=p0) and relative displacement (RD), u=a.


effects as shown in Fig. 9(b). The peak of maximum shearstress (�xy) obtained from hybrid layer method is 8.6 percentlarger than its counterpart of 3D stress at the edge and the sizeof stick zone obtained from layer method is 2.8 percent largerthan that obtained from 3D FEA solution as shown inFig. 9(c). The edge of contact obtained from layer method is1.7 percent smaller than that obtained from 3D solution. It isobserved that the proposed hybrid layer method can predictaccurate stress profiles and relative displacements at thecenter of the fretting model. However, there are around 8percent differences in the prediction of stresses at the edgeboundary, but small differences in the prediction of relative

displacements and edge of contact. It is observed that thehybrid layer method provides the trend of free edge boundaryeffect. The total execution time of the proposed hybridmethod is less than 1.5 CPU hours and just 5 percent of 3Dsubmodeling analysis.

3.2 Flat pad geometryFor the flat pad configuration, the original contact pressure

and shear stress of flat pad are 4003N and 440N,respectively. The applied axial stress is 423MPa. Theseloads are also the representative values of the previousfretting fatigue tests.14) The force resultants obtained from 3Dglobal mesh and first submodeling at the center and edge ofthe specimen are presented in Table 3. Contact traction at thecenter of specimen is also converged quickly to the originalcontact force. However, contact traction of edgeline isconverged to 77 percent of the original contact force due tothe free edge boundary effect. The differences of resultingcontact pressure from original load at the center of specimenare 2.2 percent from 3D global model and 2.0 percent fromfirst submodel. Both of shear force resultants at the center andedge of the specimen are converged from the lower value.

The corresponding normal and shear stresses at the centerof specimen are given in Fig. 10. The stresses at the center ofspecimen show small shift in the contact zone. However, thedifference of maximum normal stresses between 3D model-ing and hybrid layer method is 0.02 percent. Stress profiles atthe middle of contact zone shows small deviation. The edgeof contact is exactly same in this case. The tangential shearstresses are shifted inside contact zone, but it can preciselypredict edge of contact. This is because the contact zone offlat pad configuration is larger than that of cylindrical padconfiguration. The corresponding stresses at the edge of thespecimen are shown in Fig. 11. The differences of maximumnormal stresses are 1 percent. Stress profiles of both normaland shear stresses are very close to each other. The totalexecution time of the proposed hybrid method is also lessthan 1.5 CPU hours and just 5 percent of 3D submodelinganalysis. In both cylindrical and flat pad geometries, 2D planestrain hybrid layer method can provide accurate prediction offree edge boundary effect using the force resultants from the3D coarse analysis with computational efficiency.

4. Conclusions

The combination of three-dimensional FEA model andtwo-dimensional plane strain FEA model were developedto investigate the effects of finite width on the contactcharacteristics and fretting fatigue behavior. Small slidingcondition at the contact interface and master-slave contactalgorithm in ABAQUS were used to model fretting fatigueconfiguration. Submodeling technique was adopted to obtain

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5σ xx/

p0

x/a

3D stress at edge

Hybrid stress at edge

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

-1.5 -1 -0.5 0 0.5 1 1.5

σ yy/

p0

x/a

3D stress at edge


(b)

(a)

0

0.002

0.004

0.006

0.008

0.01

0

0.2

0.4

0.6

0.8

1

-1.5 -1 -0.5 0 0.5 1 1.5

rela

tive

dis

plac

emen

t (u

/a)

− σxy

/p0

x/a

3D stress at edgehybrid stress at edgeRD from 3D model RD from hybrid model

(c)

Fig. 9 Comparison of stresses between 3D model and Hybrid layer method

at the edge of specimen, cylindrical pad; (a) longitudinal normal stress

(�xx=p0) along the contact surface, (b) transverse normal stress (�yy=p0),and (c) shear stress (�xy=p0) and relative displacement (RD), u=a.

Table 3 Traction distribution from 3D coarse model, flat pad.

Mesh Center of specimen (N) Edge of specimen (N)

details P Q P Q

3D global 4090 346 3759 436

sub1 4083 357 3695 445


an accurate stress and displacement states in the contactregion. Two quite different pad geometries were investigat-ed; cylinder and flat with rounded edge. Traction distribu-tions obtained from the coarse three-dimensional mesheswere used as input loadings for the two-dimensional finemesh finite element model to increase computational effi-ciency and named as a hybrid layer method. Followings areimportant observations made from the present investigation.(1) Free edge boundary effect in finite width fretting fatigue

problem was clearly observed, which resulted thatcontact pressure and overall stress distributions de-creased near the free edge boundary due to the lackof constraints. Full three-dimensional finite elementanalysis is required to obtain accurate stress profiles andrelative displacement.

(2) The convergences of traction distributions were muchfaster than the convergences of peak stresses, whichresulted that the hybrid layer method was possible. Theconverged traction distributions at the center of speci-men were almost same as the original external loads,whereas those at the edge of specimen were around 80percent of the original external loads due to the freeedge effect.

(3) Two-dimensional plane strain finite element analysisprovides the most of contact characteristics and frettingfatigue behavior as obtained from the three-dimensionalfinite element analysis at the center of the specimen forboth fretting configurations. Based on this two-dimen-sional plane strain finite element model, hybrid layermethod can predict the free edge boundary effects offinite width fretting fatigue less than eight percent errorbound and reduce the execution time to 5 percent ofthree-dimensional submodeling technique.

Acknowledgement

This work was supported by the Dongguk UniversityResearch Fund of 2010.

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two-dimensional and three-dimensional finite element

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