Wear 260 (2006) 1274–1284

The role of plastic anisotropy deformation in fretting wear predictions

Lu Feng a,∗, Jinquan Xu b

a Department of Mechanics, School of Mechanical Engineering, Tianjin University, Weijin Road,Nankai, Tianjin 300072, People’s Republic of China

b Department of Mechanics, School of Civil Engineering and Mechanics, Shanghai Jiaotong University,800 Dongchuan Road, Minhang, Shanghai 200240, PR China

Received 10 August 2004; received in revised form 28 July 2005; accepted 23 August 2005Available online 26 September 2005

Abstract

The deformation occurring under fretting conditions occurs over length scales of the same order as the grain size, so the plastic anisotropy playsa significant role in the very local region near the contact edge during fretting process. The present study first describes plastic anisotropy by unifiedanisotropy plastic model coupling with Archard’s wear law on the fretting behavior incorporating the effect of wear debris into such a quantitativemodel. The finite element method, utilizing this model, is used to analyze gross slip fretting conditions. The implementation of the wear simulationtttst©

K

1

aiimsitfoirim

n

0d

ool together with anisotropy cyclic plasticity analysis during fretting process is applied to the wear depth simulation. The present study validateshe experiment phenomena from numerical simulation that failure location of the specimens under the flat-on-flat configuration is very close to therailing edge. The scar at the trailing edge is much deeper than any other locations and the larger relative slip range resulted in considerably deeperurface damage. Another interesting discovery is that when material with different orientations the degree of wear also develops differently andhe quantitative prediction is given.

2005 Elsevier B.V. All rights reserved.

eywords: Fretting wear; The plastic anisotropy; The unified visoplasticity Chboche model; A modified Archard’s wear law; Finite element

. Introduction

The field of fretting fatigue is extremely important in manyreas of mechanical engineering, where two components aren contact and one or both of them are subjected to alternat-ng fatigue loads. Fretting, small amplitude, oscillatory, relative

otion between contacting components, creates surface andubsurface damage from which fatigue cracks nucleate and grown the presence of a fatigue load. Fretting causes dramatic reduc-ion in fatigue strength of a component, with strength reductionactors on the order of three commonly recorded and has becomene of the most important considerations in designing engineer-ng structures or machine components. Thus, the efficiency andeliability of the design and operation of a wide range of mechan-cal systems are related to the fretting phenomenon and are the

otivation for this study.The complexities of fretting action have been discussed by

umerous investigators, who have postulated the combination

∗ Corresponding author. Fax: +86 21 54747252.E-mail address: luf20001226@hotmail.com (L. Feng).

of many mechanical, chemical, thermal, and other phenom-ena that interact to produce fretting. A major research effortis underway in the experimental and analytical characteriza-tion of fretting fatigue. Extensive testing to characterize frettingbehavior being conducted has been reported in the literatures[1–3]. Recent work has examined the experimental measure-ment and analytical modeling of plasticity-induced fatigue crackclosure. Goh et al. [4] employed state-of-the-art computationalcrystal plasticity constitutive laws that account for discretenessof grains, crystallographic surface texture, and heterogeneousplastic deformation at the scale of grains. The cyclic deforma-tion response in the region experiencing fretting predicted by acrystal plasticity model is compared to prediction of an initiallyisotropic J2 cyclic plasticity theory with nonlinear kinematichardening [5].

Depending on different contact conditions, fretting damagecan be either crack nucleation and fretting wear (permanentmaterial loss). Wear may be defined as the undesired cumulativechange in dimensions brought about by the gradual removal ofdiscrete particles from contacting surfaces in motion, due pre-dominantly to mechanical action. The fretting map approach,

043-1648/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2005.08.003

L. Feng, J. Xu / Wear 260 (2006) 1274–1284 1275

established by Vingsbo and Soderberg [6] and Vincent et al.[7], has shown that fretting damage evolution depends stronglyon the fretting regime. Debris is also a critical factor influenc-ing fretting wear. Wear debris in the form of thin platelets isobserved in wear of sliding, rolling and eroding components.Fretting fatigue tests were conducted by Jin and Mall [8] usingcylindrical pad and flat pad to examine the fretting scars onthe specimen surface. Analytical techniques were developed byKorovchinsky [9], Galin and Korovchinsky [10], among others.McColl et al. [11] presented a finite element-based method forsimulating both the fretting wear and the evolution of frettingvariables in a cylinder-on-flat fretting configuration. Jin and Mall[12] investigated the role of relative slip on fretting behavior byconducting experiments and analyses.

Although fretting fatigue, fretting wear are potential fail-ure modes in a wide variety of mechanical systems, and muchresearch effort has been devoted to the understanding of thefretting process, there are very few quantitative design data avail-able, and no generally applicable design procedure has beenestablished for predicting failure under fretting considerations.However significant progress has been made in establishing anunderstanding of fretting and the variables of importance infretting process. It is suggested that in numerous cases, techni-cal facilities are subjected to alternating loads which can causeinelastic material response. With repetition of the cyclic loadprocesses, alternating plasticity cannot be excluded. Undoubt-ewpafinlrnuotteCiccdmtfio

kitesmi

provides the change of contact surface of specimen during thewear process. The geometrical updating is based on nodal weardepths computed using a modified version of Archard’s equa-tion for sliding wear developed by McColl et al. [11]. This studyemphasizes the influence of plastic anisotropy and the load con-dition on the fretting behavior examined with the flat-on-flatcontact configuration. It is focused on microstructural charac-terization and mechanism-based modeling of the limiting statesof damage associated with fretting fatigue failure in titaniumand nickel-base alloys for propulsion systems. The present studyfirst describes the plastic anisotropy by unified anisotropy plasticmodel coupling with Archard’s wear law on the fretting behaviorincorporating the effect of wear debris into such a quantitativemodel.

Fretting fatigue experiment simulations are conducted using2D plane strain meshes. Assignment of boundary conditions isconsistent with experiments. The Finite element (FE) simula-tions have explored the nature of subsurface cyclic plasticityand interface contact stress fields for realistic fretting fatiguegeometries for an applied bulk stress amplitude with a stressratio of R = −1, two normal fretting pad loads, and two tangentialload. Parametric studies of the plastic strain history are con-ducted since the study of subsurface plastic strain may improveunderstanding of fretting fatigue crack nucleation as well as thesubsequent crack propagation process.

A description of the notation used in the paper is as follows.TaA

C

2

2

et

mW

D

W

wp

∇σ

wip

D

dly, plastic deformation and cyclic deformation response,hich is an integral part of any fretting fatigue mechanism,lays a significant role in the region experienced fretting dam-ge. Moreover, plastic deformation will result in residual stresselds that can significantly alter the strain range experiencedear the contact surface. For many industrial applications, a highevel of accuracy is desired. This requires the use of good mate-ial models. One of the material properties which cannot beeglected is the plastic anisotropy. The deformation occurringnder fretting conditions occurs over length scales of the samerder as the grain size. Consequently, the plastic anisotropy inhe scale of grain size plays a significant role in the deforma-ion response especially in the very local region near the contactdge. In our previous work [13], a unified cyclic viscoplasticityhaboche model incorporating fully explicit contact analysis

s used to investigate the plastic strain history in fretting pro-ess. The characteristics of the fretting fatigue, including localyclic stress–strain and cumulative plastic strain are all betterescribed. An analysis of plastic anisotropy is discussed ele-entarily. But how the field of stress and strain evaluates with

he plastic anisotropy is not discussed. And also wear and pro-le revision is not considered there which is the main purposef this paper.

This volume presents a summary of the current state ofnowledge of fretting fatigue, with particular reference to thenfluence of mechanical variables, such as the applied forces,angential load, cumulated plastic strain, and wear profile. Finitelement analysis (FEA) is used to obtain a stress state, relativelip and cumulated plastic strain in specimens for the experi-ental conditions used during fretting fatigue tests. A program

s then developed to simulate the fretting wear profile, which

ensors and vectors will be denoted by bold-face letters (e.g. Fnd T). The following definitions for operation are used: AB =ikBkjei ⊗ ej , where ⊗ denotes the tensor product and ei aartesian basis, A:B = AijBij.

. Framework for analysis

.1. Macroscopic anisotropic plasticity model

For rate-dependent plastic deformation, unified constitutivequations have been developed in a general framework consis-ent with both classic plasticity and viscoplasticity.

With the assumption of a small elastic and finite plastic defor-ation, the rate of deformation D and the total continuum spinare decomposed as:

= De + Dp (1)

= We + Wp (2)

here the superscripts e and p denote the elastic and viscoplasticarts, and W is the spin. The elasticity relation is assumed to be:

= σ − Weσ + σWe = ξ : De = ξ : (D − Dp) (3)

here ξ is the elasticity moduli tensor. The viscoplastic flow laws obtained from the normality hypothesis with a viscoplasticotential Ω in the form:

pij = ∂Ω

∂σij

(4)

1276 L. Feng, J. Xu / Wear 260 (2006) 1274–1284

The viscoplastic potential Ω is expressed as [14]:

Ω = K∗

n + 1

⟨f

K∗

⟩m+1

(5)

where K∗ and m are two constants characterizing the viscousstate of material, and 〈 〉 is Macaulay’s bracket. The yield func-tion and yield criterion in Chboche’s isotropic model is gener-alized by introduced a fourth-order material anisotropy tensor,Mijkl, to describe the initial anisotropy and the possibility of thedeformation induced material anisotropy. The anisotropic vis-coplasticity model is developed in the material principle axis,i.e. crystallographic axes [1 0 0]–[0 1 0]–[0 0 1]. In this way, theyield function can be expressed as a generalised in the form[15]:

f =√

3

2

(σ∗′

ij − X∗′ij

)Mijkl

(σ∗′

kl − X∗′kl

) − R − k

= J − R − k ≤ 0 (6)

where σ∗′ij and X∗′

ij are the deviatoric components of stress andback stress tensor in the material principle axis, and can beobtained from:

σ∗ = RW × σ × RWT (7)

where RW is transformation matrix. The viscoplastic strain isthen obtained from the normality hypothesis, where

D

w

p

i

n[

X

where two additional anisotropic material tensors, Nijkl and Qijkl,are introduced by microstructural anisotropy.

Cyclic softening or hardening is described by introducing theisotropic hardening variable R. The variable law of R is describedin a conventional form ([15,16]) given by:

R = b(W − R)p (11)

where p is the total accumulated inelastic strain, and b and Ware the material constants.

The relation for plastic spin employed here is based on theconcept of noncoaxiality between the stress and plastic rate ofdeformation, i.e.

Wp = β(σDp − Dpσ), β = a

J(12)

where a is a plastic spin coefficient. The Eq. (12) was used byKuroda [18].

There are a total of 12 material constants in the model.Five constants, k, K*, n, W, b describe the time-dependentviscoplasticity behavior. a describes the evolution of plasticspin. The anisotropic behavior of the three anisotropic materialtensors Mij, Nij and Qij. The identification of the materialparameters is not trivial due to the complexity of the model.A coupled set of differential equations has to be solved Han etal. [19] have proposed a numerical procedure to determine themeteapdTc

mcatCa

[1 1 1

p = ∂Ω

∂σ∗ij

= p∂f

∂σ∗ij

= 32

⟨f

K

⟩n

× Mijkl(σ∗′kl − X∗′

kl)√3/2(σ∗′

mn − X∗′mn)Mmnuv(σ∗′

uv − X∗′uv)

(8)

ith

˙ =√

3

2D

pijM

−1ijklD

pkl =

⟨f

K

⟩m

(9)

s the total accumulated inelastic strain rate.The evolution of the kinematic hardening stress follows the

on-linear kinematic hardening rules developed by Han et al.15], Lu [16], Li [17]:

˙ ∗ij = 3

2N ijklD

pkl − QijklXklp (10)

Fig. 1. Stress and strain for Chaboche model for [0 0 1] and

aterial constants for this model based on a group of genericquations. In this paper, we adopt this procedure to determinehe material constants for this model. The monotonic uniaxialxperiments were conducted for total strain controlled testslong the [0 0 1] and [1 1 1] orientations, respectively [19]. Fig. 1lot the stress and strain curves for [0 0 1] and [1 1 1], under fourifferent strain rates, with εT = 0.00004, 0.0004, 0.004, 0.04.he material constants of this model are determined from thoseurves.

It had been demonstrated in the earlier studies [17,19] that theechanical deformation behavior of a range of nickel base single

rystal superalloys, such as SRR99, PWA1480, AM1, CMSX 2re very similar. Similar to the earlier work of Han et al. [19] weake this kind of single crystal superalloy as our research object.orrespondingly, the material constants for this model are givens follows:

S11 = 1.162 × 10−5 MPa−1, S12 = −4.51 × 10−6 MPa−1,

] orientations for uniaxial loading for different strain rates.

L. Feng, J. Xu / Wear 260 (2006) 1274–1284 1277

Fig. 2. Experimental set-up for fretting fatigue tests.

Fig. 3. Finite element mesh of experiment configuration.

S44 = 1.135 × 10−5 MPa−1

K∗ = 1700 MPa s−1, n = 3.6, k = 110 MPa,

W = 60 MPa b = 50

M11 − M12 = 1.0, M44 = 2.39,

N11 − N12 = 310000 MPa, N44 = 50564

Q11 − Q12 = 600, Q44 = 700

Fig. 5. The loading history, where P and Q denote the normal and the tangentialloads per unit length.

3. Finite element implementation

The schematic diagram of the fatigue test for the observationof fretting fatigue crack initiation and propagation is shown inFig. 2. A finite element model representing a symmetric cornerof the fretting pad and fatigue specimen is shown in Fig. 3. Thelower surface is the fatigue specimen, while the upper surfaceis a fretting pad. Eight-noded biquadratic quadrilateral 2D solidplane strain ABAQUS elements are used in the analysis. For theelements under the contact zone, the element size is 8 m asshown in Fig. 4(a). The materials of the pad and the specimenare the same. Frictional contact elements are introduced alongthe interface. The specimen is defined as the master surface andthe fretting pad is defined as the slave surface. The force P isapplied to attain the average contact pressure on the pad foot.After application of the normal load per unit length, P, the peaktangential load per unit length, Q, is first imposed to +Q in thex-direction and then subsequently cycled between ±Q (Fig. 5).A unified Chaboche model is used to describe cyclic plasticitybehavior under fretting fatigue.

4. Wear simulation method

Prediction of wear depth in an actual design application mustigbAt

Fig. 4. (a) The local element mesh of the contact edge and (b

n general be based on simulated service testing. Some investi-ators have suggested that estimates of fretting wear depth maye based on the classical adhesive or abrasive wear equations.ccording to the work of McColl et al. [11], it is assumed here

hat the removal of material follows Archard’s law that is nor-

) several node locations used in the following analyses.

1278 L. Feng, J. Xu / Wear 260 (2006) 1274–1284

mally expressed as [11]:

V

S= K

P

H(13)

where K is the dimensionless wear coefficient and H the hardness(MPa) of the material, V the total wear volume, P the appliednormal load and, for fretting wear, and S the total accumulateddisplacement. In order to simulate the evolution of the contactsurface profiles with wear cycles, it is necessary to determine thewear depth locally as a function of horizontal contact position,x, at each contact node of the finite element model. By applyingEq. (13), for an infinitesimally small apparent contact area, dA,the increment of wear depth, dh, associated with an incrementof sliding distance, dS, we have:

dV

dA dS= K

dP

H dA(14)

The dP/dA term is the local contact pressure, p(x), while dV/dAis the required increment of local wear depth, dh. Then we getthe following equation for the prediction of the increment oflocal wear depth:

dh

dS= k1p(x) (15)

where the quantity K/H is replaced here by k1, the local wearcoefficient. The implication of Eq. (15) is that the incrementalwli

mwtpufss

k

Detwm

k

wixadffi

coefficients for the cylindrical specimens remain almost con-stant with respect to normal load variation. In this simulation,we let k1 get the value of 5.E-8 MPa−1.

Before closing this section, it is essential to recognize thatthere continue to be gaps in the wear simulation method pre-sented here. The most important ones, in the opinion of theauthor, are: At present time, there appears to be no quantita-tive measured data on the wear coefficient k under the conditionthat plastic anisotropy is considered. Furthermore, when suchdata is available, it may suggest further modification to the wearsimulation method and fretting analysis.

5. Results

The finite element method, utilizing the model described pre-viously, along with modified Archard’s wear law, is used toanalyze gross slip fretting conditions. The implementation ofthe wear simulation tool together with anisotropy cyclic plastic-ity analysis during fretting process is applied to the wear depthsimulation. The use of a commercial code as frictional contactsolver part of the tool facilitates generalization more complexcomponents. At the same time, the anisotropy inelastic analysisfor the fretting process gives more insight to the failure mecha-nism of fretting fatigue.

5

tsaPspgthir

wooesftastnpafifs

ear depth at a given point on the contact is proportional to theocal wear coefficient, the local contact pressure and the localncrement of slip distance [11].

Similar to the work of McColl et al. [11], an automated, incre-ental, wear simulation tool has been developed based on theear prediction equation of the above section. The simulation

ool consists of an interaction between a special purpose Fortranrogram and ABAQUS. Once the element model of the initial,nworn geometry has been generated, the program can be runor any specified numbers of wear cycles to predict the corre-ponding worn surface profiles and the evolution of surface andub-surface contact variables.

From Eq. (13) the Archard wear coefficient is defined by:

1 = V

SP(16)

irect calculation of the desired wear coefficient requires knowl-dge of the local contact slips and local contact pressures. Ashese are not readily measurable a modified form of Eq. (16)as used to determine an averaged wear coefficient from theeasured wear profiles using [11]:

1 = Wbhm

4δNkp(17)

here W is the wear scar width, b the width of the flat spec-men and hm is the average wear scar depth, with respect to-coordinate. It should be noted that this wear coefficient is aver-ged across a range of contact pressures and slips. The detailedetermination of wear coefficient is given in literature [11]. It isound in their research that for the flat specimen, the wear coef-cient changes as the variation of the normal load, however, the

.1. Predicted wear profiles and anisotropy plasticity

When we consider the fretting this special issue which plas-ic accumulation occurs in very local region, plastic anisotropyhould be significant. Here, we give an analysis of plasticnisotropy in fretting problem. For this case, a normal pressure,(the corresponding average compress stress acted on the pad

urface) is 60 MPa, which is applied on the top surface of thead. The friction coefficient (COF) is 0.8. The maximum tan-ential stress is 150 MPa, with the stress ratio of R = −1. In ordero give insight of plastic development during the load services,ere we simulate 11 complete cycles to get thorough understand-ng of plastic deformation especially for the existence of plasticatcheting.

In order to investigate the influence of plastic anisotropy,e consider materials with three different crystalline latticerientations: [0 0 1] orientation, [1 1 1] orientation and [1 1 2]rientation. We first investigate the stress distribution along thentail contact region for these three cases. Fig. 6 shows the sheartress curve σxy and normal stress σx curve along the contact sur-ace for materials with three different orientations. It shows thathe stresses develop differently along the entail contact zonend the common variation trend for them is that the peak normaltress is located near the trailing edge of the contact zone, whilehe shear stress near the leading edge develops more than thatear the trailing edge. But owing to the influence of anisotropiclasticity, the shear stress and normal stress develop differentlylong the entail contact zone for these three orientations. We cannd that the global level of normal stress of materials with dif-erent orientations changes more exquisitely than that of sheartress.

L. Feng, J. Xu / Wear 260 (2006) 1274–1284 1279

Fig. 6. The shear stress curves and the normal stress curves along the contact surface and subsurface: tangential stress is 150 MPa, the normal stress is 100 MPa, andCOF is 0.8.

Fig. 7. Comparison of cumulative effective plastic strain distribution in the subsurface field for different orientations.

Important connections between loading parameters, plasticstrain mechanisms, and component lifetime require a greaterunderstanding of how plastic strains evolve in the contact zone.This is emphasized by the fact that failure due to cyclic load-ing in other scenarios has been shown to depend on the typeof plastic strain mechanism (e.g. Kapoor [20]). Fig. 7 gives thecontour of effective plastic ratcheting strain near the trailingedge after 11 cycles. The effective plastic ratcheting strain dis-tributions penetrate more deeply into the subsurface similar tothe experimental observation [21]. In the subsurface field belowcontact, the model calculations predict inhomogeneous plasticstrain distributions with deeper penetration of regions of local-ized plastic shear strain. From another view, it shows that owing

to the anisotropy of plasticity, there are a lot of differences in thedistribution of plastic strain in the trailing edge. In order to givemore quantitative illustration of the effect of anisotropy plastic-ity, Fig. 8 shows the response of the effective plastic strain attwo nodes for material with different orientations. The locationof nodes 548, 543, 1488 is shown in Fig. 4(b). The plastic strainof the same node develops differently for material with differ-ent lattice orientations. From these curves we can see that thenodes near the trailing edge with [0 0 1] orientation develop moreplastic strain, next is [1 1 2] orientation and the least is [1 1 1]orientation. It can be deduced from Fig. 9 that the response ofcyclic shear stress and shear strain of node 1503 for three orien-tations has another characteristics which when material lattice is

respon

Fig. 8. Plastic strain histories showing local se over time: (a) node 1488; (b) node 1503.

1280 L. Feng, J. Xu / Wear 260 (2006) 1274–1284

Fig. 9. The shear stress and strain response of node 1503 of material with three orientation.

along [0 0 1] orientation there develops more plastic ratchetingstrain, but along other orientations the plastic strain developsmixed combination of cyclic plasticity and plastic ratcheting. Itis clear that in the very local region of contact edge, the evolu-tion of stress and strain is very completed and there are manymechanisms cooperation.

In present study, the role of relative slip on fretting behav-ior is investigated by conducing analyses. Fig. 10 shows thecomparison of relative slip amplitude after 11 cycles for elasticviscoplasticity materials with three different orientations. It isclear that the relative slip varies with horizontal position alongthe contact interface, and its value in magnitude is lower at thecenter than the edges of contact. The relative slip amplitude ofthe material with [0 0 1] orientation is higher than that of mate-rials with [1 1 1] orientation and [1 1 2] orientation. It can beexplained by the anisotropy plasticity. This spatial variation of

Fc

relative slip gives rise to a corresponding variation of local weardepth with horizontal position, as described below.

In order to estimate how much material is removed from thespecimen, the topography of the surface is simulated as shownin Fig. 11. From curves we can see that failure location of thespecimens under the configuration considered here is very closeto the trailing edge. The scar at the trailing edge is much deeperthan any other locations and the larger relative slip range resultedin considerably deeper surface damage. It is pointed in [8] thatthe fretted surface profile was affected by the contact config-uration and for flat-on-flat contact configuration the materialremoval did not occur in the flat portion of the fretted region andwas concentrated at the edges. The simulation results here areconsistent with their experiment observation. Another interest-ing discovery is that when material with different orientationsthe degree of wear also develops differently. It shows that the

Ft

ig. 10. Comparison of relative slip amplitude after 11 cycles for elastic vis-oplasticity materials.

ig. 11. Predicted wear profiles for the materials with three different orienta-ions.

L. Feng, J. Xu / Wear 260 (2006) 1274–1284 1281

Fig. 12. Comparison of shear stress and normal stress with [1 1 1] material orientation under different load combinations.

material with [0 0 1] orientation experiences more fretting wear,next is [1 1 2] orientation. This wear phenomenon simulated herecorresponds to the variation trend of relative slip.

5.2. Evolution of contact variables

The main parameters affecting fretting wear are reported to benormal load, slip amplitude, frequency, contact geometry, sur-face roughness and material properties, and so on. The influencesof contact pressure and tangential load have been investigatedby a number of researchers for a range of pressures being con-sidered in the HCF program [11]. Both of parameters are thesignificant factors in fretting process. In present study, we inves-tigate the influence of the contact load and the tangential loadon the evolution of inelastic strain, the wear profile, stress dis-tribution along the whole contact region, at the mean time weexamine the effect of plastic anisotropy during this process.

Experiment results show that the failure location of the spec-imens tested under this contact configuration depends on thenormal force and the size of the slip zone is larger with thesmaller normal force than that with larger normal force [8].Fig. 12 shows the comparison of shear stress and normal stresswith [1 1 1] material orientation under different load combina-tions. It can be seen from these curves that under the other sameconditions with the increase of normal load, the magnitude oftsnagl

tcttTliinto

Fig. 13. Comparison of relative slip amplitude after 11 cycles with [1 1 1] mate-rial orientation under different load combinations.

along the contact surface. In addition, the microslip is concen-trated mostly at the edges but does not have much affect on theflat portion of the fretting scar.

The complete analysis of gross slip would require consid-eration of crack initiation and propagation as well as materialremoval. Fig. 14 shows the FE-predicted evolution of the contactsurface profiles under different load combinations. It is foundthat as fretting wear proceeds; a wear scar develops in the flatsurface while the shape of the flat surface is also modified. Thelower normal force on the fretting pad results in the deeper fret-ting scar in the fretted region.

Experiment research [8] showed that failure location ofthe specimens tested under flat-on-flat contact configuration

Fr

he shear stress near the trailing edge decreases while the bulktress has little varieties, but there exists large disperse in mag-itude of stress near the leading edge. It is clear that there issignificant variation of normal stress and shear stress at any

iven position along the contact width with different tangentiaload.

Further, one of the goals of this study is to compare the rela-ive slip and wear state in the contact region under different loadombinations. The simulation is performed at different appliedangential load but under the same normal force, and at the sameime at different normal load but under the same tangential load.he fact that contact slip decreases with the increase of normal

oad under the same applied tangential load has been schemat-cally demonstrated in Fig. 13, while the relative contact slipncreases with the increase of tangential load under same appliedormal load. The magnitude of relative slip between the pad andhe specimen depends upon the locations where it is measuredr computed, and it also varies from zero to a maximum value

ig. 14. Comparison of predicted wear profiles after 11 cycles with [1 1 1] mate-ial orientation under different load combinations.

1282 L. Feng, J. Xu / Wear 260 (2006) 1274–1284

Fig. 15. The shear stress curves and the normal stress curves along the contact surface and subsurface: tangential stress is 150 M Pa, the normal stress is 100 MPa,and COF is 0.8 with [0 0 1] orientation.

Fig. 16. Comparison of relative slip amplitude and Predicted wear profiles for elastic viscoplasticity materials: P = 100 MPa; Q = 150 MPa.

Fig. 17. The evolution of plastic strain of node 1503 with time under different load combinations for materials with: (a) [0 0 1] orientation; (b) [1 1 1] orientation.

depended on the normal force and the specimens failed veryclose to the trailing contact edge. It is apparent that the localcontact slip-based approach gives rather good volume predic-tions and at least the predicted trend correlate the experimentresults.

In order to give thorough investigate the influence of plasticanisotropy, Fig. 15 shows the shear stress curves and the normalstress curves along the contact surface and subsurface when tan-gential stress is 150 MPa, the normal stress is 100 MPa, and COFis 0.8. Comparing Fig. 15 with Fig. 6 it can be seen that with theincrease the normal load under other same conditions, the plasticanisotropy has less influence on the magnitude of stress alongthe contact zone. Fig. 16 shows the comparison of relative slipamplitude and predicted wear surface for elastic viscoplasticitymaterials: P = 100 MPa, Q = 150 MPa.

Fig. 17 shows the evolution of plastic strain of node 1503 withtime under different load combinations for the case of materialswith [0 0 1] orientation and materials with [1 1 1] orientation.The load condition has influence the evolution of the plasticdeformation of contact zone. The tangential load has larger influ-ence of the evolution of the plastic strain comparing with that ofnormal load. Second, the evolution of plastic strain depends onthe material orientation.

6. Discussion

The plastic strain predictions in the study of Ambrico andBegley [22] illustrated that for the cylindrical geometry undermoderate to high normal load, cyclic plasticity is more persistentthan ratcheting. There are very few studies on flat-on-flat contact

L. Feng, J. Xu / Wear 260 (2006) 1274–1284 1283

configuration [8]. One of the difficulties involving these geome-tries is the alignment of the flat portion of the pad on the flatspecimen. Misalignment might induce stress singularity at thetransition from the flat portion to the edge [23]. For the geome-try configuration simulated here, ratcheting strains may be moreimportant because they may persist to a larger number of cycles,since sharp discontinuities in the contact geometry require muchmore material movement before ratcheting is eliminated.

Experimental results such as contact scars provide someimplications of ratcheting phenomena during the fretting fatigueprocess. The material calculations are consistent with theseresults. The progressive cyclic ratcheting of the plastic shearstrain dominates the reversed cyclic plastic shear strain after sev-eral cycles. Owing to the rate dependent of the flow rule in theChaboche model, it admits progressive cycle-by-cycle viscousstrain (viscous ratcheting). This leads to a persistent source ofratchet strain accumulation in this model for a local cyclic notchroot problem such as fretting. The plastic strain region developsnear the trailing edge, and it increases with the increasing ofcyclic number, the region near the leading edge develops littleplastic strain comparing with the region of trailing edge. Thissimulation result is in agreement with experimental results [21].

In present literatures [4,5,22] on plastic analysis for frettingprocess, three complete tangential load cycles are sufficient tocapture steady state response for the cases considered there,because on that situation steady state was determined by exam-iBmtFpe

owsettis

whfimbnmrdItaf

to more complex components, for academic research purposes,to assess, for example, the interaction between fretting wear andcrack nucleation associated with changes in stress field. Frettingscars on the specimen surface are examined through the modeldeveloped here to identify the characteristics of fretting damage,the surface profile of specimen scar. In case of gross slipping, thesurface profile is different from the stick–slip condition becauseof fretting wear.

7. Conclusion

The most significant deformation characteristic of singlecrystal nickel-base superalloy observed in the experiments isthe strong influence of crystal orientation on the stress–strainresponse. In present study, we first investigate the effect of crys-tal orientation or the plastic anisotropy on the fretting behaviorof materials. A unified cyclic viscoplasticity Chaboche model atfinite deformations that incorporates fully explicit contact anal-ysis is used to investigate the plastic strain history in frettingprocess. A detailed finite element model, which simulates thefrictional contact behavior of a flat-on-flat fretting configuration,is described. The main purpose in using finite element analysesin the wear calculations is to compute the contact stresses andthe sliding distances in the contact zone. Then a method for fret-ting wear simulation based on a modified Archard equation hasb

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ning cyclic plastic strain, since ratcheting strains shake down.ut for the contact configuration studied here, ratcheting strainsay be more important, so three complete cycles are not enough

o give insight of plastic development during the load services.or limit computational expense, here we simulate 11 com-lete cycles to get thorough understanding of plastic deformationspecially for the existence of plastic ratcheting.

Wear debris in the form of thin platelets is observed in wearf sliding, rolling and eroding components. The mechanisms ofear are manifestations of plastic ratcheting of material in a thin

ub-surface layer. It is driven by: (i) stress concentration at thedges of the hard slider; (ii) roughness on the slider, which causeshe high contact pressure at the taller asperities to traverse all overhe surface; and (iii) erosion where instead of sliding contacts,mpacting erodent subjects the sub-surface layer to high contacttresses [12].

The present paper has considered gross slip situations only,hile the fretting fatigue behavior under partial slip conditionas been extensively investigated in several studies. The analysisor the gross slip condition requires elaborate analysis involv-ng consideration of material non-linearity but also removal of

aterial. In [11], McColl et al. used a kind of local contact slip-ased approach to give rather good wear volume prediction. Theumerically prediction worn surface profiles of the flat speci-en after 18,000 cycles has been compared with experimental

esults. The predicted values of scar with and maximum wearepth were fitted well with corresponding experimental results.n present work, we use the same method used by McColl et al.o cope with the wear volume loss during fretting process. Here,commercial finite element code (ABAQUS) is adopted as the

rictional contact solver part of the tool facilitates generalization

een applied to gross slip flat-on-flat tests.The present study validates the experiment phenomena from

he view of numerical simulation that failure location of the spec-mens under the flat-on-flat configuration is very close to therailing edge. The scar at the trailing edge is much deeper thanny other locations and the larger relative slip range resulted inonsiderably deeper surface damage. Another interesting dis-overy is that when material with different orientations theegree of wear also develops differently. It shows that the mate-ial with [0 0 1] orientation experiences more fretting wear, nexts [1 1 2] orientation. This spatial variation of slip gives rise to

corresponding variation of local wear depth with horizontalosition, as described above. The wear phenomenon simulatedere corresponds to the relative slip trend.

A number of researches have suggested that the contact loadnd the tangential load are the key variables, which determine therack nucleation process. The simulation results show that con-act slip decreases with increasing normal load under the samepplied tangential load, while the relative contact slip increasesith increasing tangential load under same applied normal load.he magnitude of relative slip between the pad and the specimenepends upon the locations where it is measured or computed.n addition, the microslip is concentrated mostly at the edges butoes not have much affect on the flat portion of the fretting scar.n addition, the larger relative slip range results in considerablyeeper surface damage.

cknowledgements

This research was initiated with the support from Nationalatural Science Foundation of China (10402022).

1284 L. Feng, J. Xu / Wear 260 (2006) 1274–1284

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