A Model for high-cycle fatigue in polycrystals

A grain-scale formulation for high-cycle fatigue inter-granular degradation in polycrystalline aggregates is presented. The aggregate is represented through Voronoi tessellations and the mechanics of individual bulk grains is modelled using a boundary integral formulation. The inter-granular interfaces degrade under the action of cyclic tractions and they are represented using cohesive laws embodying a local irreversible damage parameter that evolves according to high- cycle continuum damage laws. The consistence between cyclic and static damage, which plays an important role in the redistribution of inter-granular tractions upon cyclic degradation, is assessed at each fatigue solution jump, so to capture the onset of macro-failure. Few polycrystalline aggregates are tested using the developed technique, which may find application in multiscale modelling of engineering components as well as in the design of micro-electro-mechanical devices (MEMS).