Multiscale modelling of short cracks in random polycrystalline aggregates

The identification and explanation of processes potentially responsible for the initiation and development of intergranular cracks are topics of wide concern. Especially the early phase of the development of cracks seems to be beyond the present state-of-the-art explanations. An effort was therefore made by the authors to construct a computational model of the crack growth kinetics at the grain-size scale. The main idea is to divide continuum (e.g., polycrystalline aggregate) into a set of subcontinua (grains). Random grain structure is modelled using Voronoi-Dirichlet tessellation. Each grain is assumed to be a monocrystal with random orientation of crystal lattice. Elastic behaviour of grains is assumed to be anisotropic. Crystal plasticity is used to describe (small to moderate) plastic deformation of monocrystal grains, caused mainly by the strains along the "incompatible" grain boundaries and at triple points. Finite element method is used to obtain numerical solutions of strain and stress fields. The analysis is currently limited to two-dimensional models. The paper focuses on the dependence of crack tip loading (J-integral) on the random orientation of neighbouring grains. The limited number of calculations indicate that the incompatibility strains, which develop along the boundaries of randomly oriented grains, influence the local stress fields (J-integrals) at crack tips significantly.