A Model for Polycrystalline Thermo-Mechanical Homogenisation and Micro-Cracking

A grain scale framework for thermo-elastic and micro-cracking analysis of polycrystalline materials is proposed. The polycrys-talline morphology is represented through Voronoi tessellations, which retain the main statistical features of polycrystalline materials. The coupled thermo-mechanical response of the grains is modelled using an integral representation for anisotropic thermo-elasticity, which is the numerically addressed through a dual reciprocity boundary element method. The continuity of the aggregate is enforced through suitable intergranular thermo-elastic cohesive interfaces that represent the thermo-mechanical degradation through an irreversible damage parameter, which affects both the interface strength and thermal conductivity. Thanks to the features of the underlying formulation, the micro-mechanical thermo-elastic problem is expressed in terms of grain boundary variables only, which simplifies the meshing procedures and reduces the overall number of degrees of freedom and then the numerical cost of the analysis. Preliminary results about thermo-elastic homogenisation are discussed, while the results of micro-cracking simulations will be presented in a forthcoming study.