The effect of grain orientation on fretting fatigue plasticity and life prediction O.J. McCarthy a , J.P. McGarry b , S.B. Leen a,n a Mechanical Engineering, NUI Galway, Ireland b Biomedical Engineering, NUI Galway, Ireland article info Article history: Received 28 June 2013 Received in revised form 30 August 2013 Accepted 30 September 2013 Keywords: Fretting fatigue life Microstructure sensitive 316L stainless steel Cyclic plasticity abstract A study on crystal and J 2 plasticity prediction of fretting fatigue is presented, using a microstructure- sensitive fatigue parameter for crystal plasticity crack nucleation and a critical-plane (multiaxial) fatigue parameter for J 2 plasticity. A short crack propagation methodology is also implemented. The effect of grain orientation on nucleation life is shown to be significant for fretting fatigue. J 2 plasticity generally predicts conservative lives. Crystal plasticity is superior in terms of (i) accuracy of life prediction, (ii) ability to facilitate wear prediction and (iii) capturing the key effects of substrate fatigue stress and grain orientation on life. The crystal plasticity model facilitates new insight into interaction between grain orientation, fatigue stress amplitude and fretting surface damage vis-à-vis fretting fatigue life. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Contact fatigue and, more specifically, fretting fatigue (FF) are common problems in engineering contacts, particularly highly-loaded contacts, across a wide range of industrial and other engineering applications. Obvious examples include aeroengine dovetail joints and spline couplings [1], biomedical implants [2], shaft-hub connections [3] and fastener connections [4]. A key ongoing challenge in the design against FF is the development of reliable predictive methods for crack nucleation. Fretting cracks have been identified at length-scales competitive with the mate- rial micro-structure, suggesting the need for a micro-mechanical approach. Length-scales have been identified as a key aspect in the development of reliable life prediction methods for FF, to capture stress gradient effects associated with the contact size effect [5], for example. Araujo and Nowell [5] identified the need for volume- averaging of critical-plane fatigue indicator parameters (FIPs), in the context of classical elasticity (analytical) solutions for fretting stress distributions, to capture the contact size effect. The averaging dimension was shown to be broadly associated with the key micro-structural dimension of grain size. Sum et al. [6] subsequently demonstrated that mesh refinement techniques within a finite element (FE) based critical-plane FIP approach (Smith–Watson–Topper and Fatemi–Socie) could achieve the same result, i.e. capture the stress gradient and hence contact size effect. In other words, it was demonstrated that the FE mesh refinement process was equivalent to an averaging approach. Fretting can typically be categorised into three different sliding regimes, namely, partial, mixed and gross slip, primarily depen- dent on normal load (P), displacement amplitude and coefficient of friction (COF) [7]. Fig. 1(a) shows the relationship between normal load and displacement amplitude for the different slip regimes. Fig. 1(b) illustrates the material damage associated with each respective fretting regime. A similar fretting map has been presented by Vingsbo and Soderberg [8] (Fig. 2) where the effect of fretting regime is plotted in terms of number of cycles to failure and wear rate. Experimental data has been presented by Jin and Mall [9], for example, to corroborate the key effect of increasing fatigue life with increasing slip amplitude on transition from partial to gross slip. Madge et al. [10] have demonstrated that this effect can be predicted using a wear–fatigue approach. This work involved the explicit simulation of wear-induced material removal and simultaneous computation of fatigue damage via Miner's rule due to the wear-induced evolution of contact stress and strain distributions. Madge et al. [10] demonstrated the importance of contact stress re-distribution, and associated fatigue damage re-distribution, due to widening of the contact region vis-à-vis the competition between material removal and crack propagation. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/triboint Tribology International 0301-679X/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.triboint.2013.09.023 Abbreviations: FF, fretting fatigue; FIP, fatigue indicator parameter; FE, finite element; COF, coefficient of friction; CP, crystal plasticity; SS, stainless steel; NLKH, non linear kinematic hardening; UMAT, user material subroutine; FCI, fatigue crack initiation; SEM, scanning electron microscope; ESBD, electron back scatter diffraction; SWT, Smith Watson Topper; PF, plain fatigue; SCG, short crack growth; SIF, stress intensity factor; FFRF, fretting fatigue reduction factor; Stdev, standard deviation; CPFE, crystal plasticity finite element n Corresponding author. E-mail address: Sean.leen@nuigalway.ie (S.B. Leen). Please cite this article as: McCarthy OJ, et al. The effect of grain orientation on fretting fatigue plasticity and life prediction. Tribology International (2013), http://dx.doi.org/10.1016/j.triboint.2013.09.023i Tribology International ∎ (∎∎∎∎) ∎∎∎–∎∎∎