A grain-scale model for high-cycle fatigue degradation in polycrystalline materials

Abstract

A grain-scale three-dimensional model for the analysis of fatigue intergranular degradation in polycrystalline materials is presented. The material microstructure is explicitly represented through Voronoi tessellations, of either convex or non-convex domains, and the mechanics of individual grains is modelled using a boundary integral formulation. The intergranular interfaces degrade under the action of cyclic loads and their behaviour is represented employing a cohesive zone model embodying a local irreversible damage parameter that evolves according to high-cycle continuum damage laws. The model is based on the use of a damage decomposition into static and cyclic contributions, an envelope load representation and a cycle jump strategy. The consistence between the cyclic damage and the action of the external loads, which contribute to the damage due to the redistribution of intergranular tractions between subsequent cycle jumps, is assessed at each solution step, so to capture the onset of macro-failure when the external actions cannot be equilibrated anymore by the critically damaged interfaces. Several numerical tests are reported to illustrate the potential of the developed method, which may find application in multiscale modelling of fatigue material degradation as well as in the design of micro-electro-mechanical devices (MEMS).