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Brittle failure in polycrystalline RVEs by a grain-scale cohesive boundary element formulation


Polycrystalline materials are commonly employed in engineering structures. For modern applica- tions a deep understanding of materials degradation is of crucial relevance. It is nowadays widely recognized that the macroscopic material properties depend on the microstructure. The polycrystalline microstructure is characterized by the features of the grains and by the phys- ical and chemical properties of the intergranular interfaces, that have a direct influence on the evolution of the microstructural damage. The experimental investigation of failure mechanisms in 3D polycrystals still remains a challenging task. A viable alternative, or complement, to the experiments is Computational Micromechanics. The present-day availability of cheaper computational power is favoring the advancement of the sub- ject. A popular approach for polycrystalline fracture problems consists in the use of cohesive sur- faces embedded in a Finite Element (FE) representation of the microstructure, so that the evolution of microcracks stems as an outcome of the simulation, without any assumptions, see e.g. [4]. An alternative to the FEM is the Boundary Element Method (BEM). A 2D cohesive BE formula- tion for intergranular failure and a 3D BE formulation for polycrystalline materials homogeniza- tion have been recently proposed [1–3]. In this work, a novel 3D grain-level model for the study of polycrystalline intergranular degra- dation and failure is presented. The microstructures are generated as Voronoi tessellations, that mimic the main statistics of polycrystals. The formulation is based on a grain-boundary integral representation of the elastic problem for the crystals, seen as anisotropic domains with random crystallographic orientation in space. The integrity of the aggregate is restored by enforcing suit- able intergranular conditions. The evolution of intergranular damage is modeled using an extrinsic irreversible mixed-mode cohesive linear law. Upon interface failure, non-linear frictional con- tact analysis is used, to address separation, sliding or sticking between micro-crack surfaces. An incremental-iterative algorithm is used for tracking the micro-cracking evolution. Several numeri- cal tests have been performed and they demonstrated the capability of the formulation to track 3D micro-cracking, under either tensile or compressive loads.