Issue 35

C. Gandiolle et alii, Frattura ed Integrità Strutturale, 35 (2016) 232-241; DOI: 10.3221/IGF-ESIS.35.27 237 W=8mm σ Q P x z 33 11 y 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0 25 50 75 100 Cumulated plastic strain fretting fatigue cycles Elastic shakedown Asymptotic evolution (a) (b) Figure 5 : (a) Abaqus model of the test. (b) Cumulative plastic strain evolution simulated at the contact border hot spot for a crack arrest condition using the monotonic elastic-plastic law for the study material (P, σ F,moy /σ y,flat =0.78, R F =0.85, Q*/P=0.30). Surface-to-surface discretization with small sliding was adopted for contact accommodation. The Lagrange multiplier was selected as the contact algorithm. The friction coefficient of the contact µ was determined experimentally using the variable displacement technique described by Voisin et al. [14], µ=1.0. The cylinder and fatigue plane sample behaviors were described by the monotonic plastic laws introduced in Fig. 1. The normal force with which the cylinder was applied to the plane was high enough to generate plasticity. The added fatigue loading contributed to extend the plastic state. For each simulation, the most highly strained integration point was monitored and its cumulative plastic strain evolution was plotted as a function of the fretting fatigue loading cycles (Fig. 5b). The level of activated plasticity decreased after each cycle, due partly to material hardening but mostly to plastic accommodation of the contact geometry. So the cumulative plastic strain increased until reaching an asymptotic evolution, i.e. a stable state corresponding to elastic shakedown. Numerical analysis showed that elastic shakedown was achieved after around 80 loading cycles for fretting fatigue. Fatigue analysis was therefore performed on the stable elastic shakedown state. Crack propagation rate identification A decoupled approach was used to predict the crack propagation. First the contact stress state was obtained by finite elements modeling (FEM), then the normal stressing along the expected crack path are extracted at the contact border for the maximum and minimum loading conditions as schematized in Fig. 6. x P Q σ 11 h t Figure 6 : Stress extraction along crack path for a fretting fatigue case. Then the mode I stress intensity factor (SIF) was calculated using Bueckner weight function approach [13]: