Two-Scale analysis of fretting fatigue crack initiation in heterogeneous materials using Continuum Damage Mechanics

The phenomenon of fretting fatigue damage is related to tribological behaviour and commonly occurs at the contact interface between two bodies that sustain oscillation loads. Based on the complicated mechanical situation, several methods have been developed to predict the crack initiation location and life. The Continuum Damage Mechanics (CDM) approach in conjunction with Finite Element Method (FEM) is used in this paper. The fretting fatigue lifetime includes two parts, crack initiation lifetime and crack propagation lifetime, and this paper focuses on the crack initiation phase. Homogeneous materials are usually studied in fretting fatigue problems, and the influence of defects is necessary to be considered. In this study, the authors proposed several models to consider the effect of heterogeneity on crack initiation location and lifetime. The numerical model is a 2D one with plane strain assumption. To get more accurate numerical results with low computational cost, a Two-Scale Analysis approach is developed in this paper. Two macroscopic models and three microscopic models are proposed, including a Macroscopic homogeneous model (Macro-HOMO), a Multiscale Homogenization model with Direct Numerical Simulation (MH-DNS), a Microscopic homogeneous model (Micro-HOMO), a Microscopic Model with equivalent material properties by using Mean Field Homogenization method (Micro-MFH), and a microscopic model with Direct Numerical Simulation (Micro-DNS). The results obtained by using the CDM approach with different microscopic models are compared, and show that the prediction accuracy of the Micro-DNS is the best. In addition, in terms of computational cost, the Micro-DNS model shows great advantages as well comparing to the Macro-DNS model.