Modelling intergranular and transgranular micro-cracking in polycrystalline materials

Abstract

In this work, a grain boundary formulation for intergranular and transgranular micro-cracking in three-dimensional polycrystalline aggregates is presented. The formulation is based on the displacement and stress boundary integral equations of solid mechanics and it has the advantage of expressing the polycrystalline problem in terms of grain boundary variables only. The individual grains within the polycrystalline morphology are modelled as generally anisotropic linear elastic domains with random spatial orientation. Transgranular micro-cracking is assumed to occur along specific cleavage planes, whose orientation in space within the grains depend upon the crystallographic lattice. Both intergranular and transgranular micro-cracking are modelled using suitably defined cohesive laws, whose parameters characterise the behaviour of the two mechanisms. The algorithm developed to track the inter/transgranular micro-cracking history is presented and discussed. Several numerical tests involving pseudo-3D and fully 3D morphologies are performed and analysed. The presented numerical results show that the developed formulation is capable of tracking the initiation and evolution of both intergranular and transgranular cracking as well as their competition, thus providing a useful tool for the study of damage micro-mechanics

Elucidating the Effect of Bimodal Grain Size Distribution on Plasticity and Fracture Behavior of Polycrystalline Materials

“…The methodology allows to study the microstructural evolution capturing the transition of individual interfaces from a pristine to a damaged and eventually cracked status. It has been successfully employed to model quasi-static micro-cracking [28,29,30], small-strains crystal plasticity [31], hydrogen embrittlement [32], high-cycle fatigue [33], micro-cracking of piezoelectric aggregates [34] and multi-scale modelling of polycrystalline components [35].…”

Preparation and Performance Analysis of Nb Matrix Composites Reinforced by Reactants of Nb and SiC

“…It can be seen from the figure that cracks existed only in the Nb 2 C and Nb 3 Si grains and ended at the grain boundary of Nbss, also known as crack arrest (CA). Cracks passed through the hard and brittle phases in the manner of transgranular fractures (TF) [15] and deflected when the cracks propagated. The Nbss phase is ductile.…”

A novel boundary element formulation for anisotropic fracture mechanics

“…Then, to retrieve the behaviour of the original domain, continuity/equilibrium interface conditions are enforced on the newly introduced boundaries, whereas traction-free boundary conditions are enforced over the crack surfaces. Advanced applications of such an approach, used in conjunction with cohesive zone modelling, have been developed for materials micro-mechanics [12,13,14,15,16]. However, multi-region formulations have the disadvantage of requiring a higher discretisation effort and introducing additional displacement and traction unknowns along the additional fictitious boundaries.…”