A controlled Poisson Voronoi tessellation for grain and cohesive boundary generation applied to crystal plasticity analysis

Abstract

A novel computational framework is presented for the representation of virtual polycrystalline grain structures with cohesive boundaries for large-scale crystal plasticity finite element (CPFE) analyses. This framework consists of a grain structure generation model and cohesive zone (CZ) representation and junction partitioning scheme. The controlled Poisson Voronoi tessellation (CPVT) model is employed to generate virtual grain structures that are statistically equivalent to metallographic measurements in terms of grain size distribution. In the CPVT model, physical parameters including the mean grain size, a small grain size, a large grain size and the percentage of grains within this range are used to determine the grain size distribution. To study inter-granular crack initiation and evolution using the cohesive zone model, a novel grain boundary representation scheme is proposed for producing cohesive interfaces for Voronoi tessellations and automatically partitioning multiple junctions. The proposed virtual grain structure generation model and cohesive boundary generation method is demonstrated in a crystal plasticity simulation of polycrystal tension. The features of inter-granular crack initiation and propagation are presented and the mechanical response is discussed.