Numerical modelling of microstructure inhomogeneity to reproduce experimentally observed scatter in fretting fatigue lifetimes

Abstract

Experimental fretting fatigue lives exhibit large degree of scatter. One of the aspects behind this is the microstructural inhomogeneity which affects the stresses in the material. Variance in stress values can greatly impact crack initiation speed, leading to changes in fretting fatigue lifetimes, as well as the crack propagation behaviour. This research aims to study this issue in more detail and recreate the experimentally observed scatter using numerical modelling. In this work, Voronoi tessellation is used to simulate microstructural topologies of low carbon steel, where each grain is assigned elasto-plastic properties at random, from a predetermined range. In total, 60 finite element models are created and the effect of microstructural inhomogeneity on fretting fatigue lifetime dispersion is evaluated using a Continuum Damage Mechanics approach. Additionally, crack propagation is studied with XFEM combined with Smith-Watson-Topper fatigue parameter to determine crack path under multiaxial, non-proportional loading conditions. For both crack initiation and propagation investigation, the Theory of Critical Distances is applied to overcome the effect of high stress gradients. Simulation results show that microstructural inhomogeneity has significant impact on the contact stress distributions and subsurface stress and strain fields. Scatter observed in the predicted lifetimes matches well with that observed in practical experiments and is used to propose a design curve for the studied material. The applied crack path prediction approach captures the variance in crack paths originating from microstructural inhomogeneity and shows good correlation with reference experimental results at low bulk stress levels.