Multiscale Modeling of Crack Growth in Polycrystals

Abstract

Recent progress in macroscopic crack growth simulations allows us to attack arbitrary crack growth in complex three-dimensional structures [1]. One of the major deficiencies of the macroscopic description, however, is that it smears out the details of underlying polycrystalline material structure, which can play an important role in the fracture properties of metallic compounds. A polycrystalline metal is inherently inhomogeneous. In particular, the grain boundaries (GBs), which break the local crystalline order, are believed to be the favorable fracture paths in many engineering applications. We therefore need the ability to simulate intergranular crack grow in such a heterogeneous medium. Doing such simulations allow us to study the effects of texture (distribution of grain orientations) and grain geometry on the emerging macroscopic fracture properties. Because one of the key mechanisms at this length scale is the grain boundary (GB) decohesion, we expect the way GBs are modeled to be crucial. However, an accurate constitutive relation is hard to obtain from experimental measurements; this takes us to even lower scales, using atomistic simulations. One of our goals is to understand the effects of grain orientations and misorientations on the grain boundary properties at the atomic scale, and possibly the effects of different chemical compositions.

The above description involves three length scales (macroscopic, mesoscopic and atomic), where lower scale simulations provide information to upper scales, for example in the form of a constitutive relation: this is a typical scenario in multiscale modeling [2]. In this paper, we highlight several aspects of our developments toward the above-mentioned multiscale modeling of crack growth in polycrystals. At the mesoscale, we show how to model 2D and 3D grain geometry using Voronoi tessellation. We then perform a 2D intergranular crack growth subject to cyclic loading in the polycrystal sample, where the grain boundary decohesion is modeled using cohesive zone models. At the atomic scale, we show how to model decohesion of grain boundaries using atomistic simulations and to extract the key parameters from the simulations for the cohesive model used in mesoscale simulations.