A computational framework for low-cycle fatigue in polycrystalline materials

Abstract

A three-dimensional framework for low-cycle fatigue analysis of polycrystalline aggregates is proposed in this work. First, a cohesive law coupling plasticity and damage is developed for modelling cycle-by-cycle degradation of material interfaces up to complete de-cohesion and failure. The law may model both quasi-static degradation under increasing monotonic load and degradation under cyclic loading, through a coupled plasticity-damage model whose activation and flow rules are formulated in a thermodynamically consistent framework. The proposed interface laws have been then implemented and coupled with a multi-region boundary element formulation, with the aim of analysing low-cycle intergranular fatigue in polycrystalline aggregates. The boundary element formulation allows expressing the micro-mechanical problem in terms of grain-boundary displacements and tractions only, which are the quantities directly entering the cohesive laws, thus simplifying the coupling of the two tools. After assessing the response of an individual interface, to both quasi-static and cyclic loads, the coupled framework has been employed for the computational investigation of low-cycle degradation in fully-3D and pseudo-3D, or 2D columnar, polycrystalline aggregates, assuming that the degradation process remains confined in the intergranular regions. The discussed results show the potential of the developed formulation for multiscale materials modelling, which may find future application in the multiscale design of engineering structures subjected to complex loads and degradation processes, and for computational micromechanics, which may find direct application in the design and analysis of micro-electromechanical systems (MEMS).