A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II: Numerical examples

Numerical aspects of the grain level micromechanical model presented in part I are discussed in this study. They include, an examination of solution convergence in the context of cohesive elements used as an approach to model crack initiation and propagation; performance of parametric studies to assess the role of grain boundary strength and toughness, and their stochasticity, on damage initiation and evolution. Simulations of wave propagation experiments, performed on alumina, are used to illustrate the capabilities of the model in the framework of experimental measurements. The solution convergence studies show that when the length of the cohesive elements is smaller than the cohesive zone size and when the initial slope of the traction-separation cohesive law is properly chosen, the predictions concerning microcrack initiation and evolution are mesh independent. Other features examined in the simulations were the effect of initial stresses and defects resulting from the material manufacturing process. Also described are conditions on the selection of the representative volume element size, as a function of ceramic properties, to capture the proper distance between crack initiation sites. Crack branching is predicted in the case of strong ceramics and sufficient distance between nucleation sites. Rate effects in the extension of microcracks were studied in the context of damage kinetics and fragmentation patterns. The simulations show that crack speed can be significantly varied in the presence of rate effects and as a result crack diffusion by nucleation of multiple sites achieved. This paper illustrates the utilization of grain level models to predict material constitutive behavior in the presence, or absence, of initial defects resulting from material manufacturing. Likewise, these models can be employed in the design of novel heterogeneous materials with hierarchical microstructures, multi-phases and/or layers.