Crack growth in stochastic microstructures

Probabilistic models are employed to generate samples of a metal microstructure. The grain geometry is modeled using the Voronoi tessellation, while a vector random field model is used for crystal lattice orientation. Each of these models are calibrated to experimental data. These microstructural features were selected for modeling because it is thought that they may have significant impact on the behavior of short cracks. Concepts of;interface fracture mechanics are applied to intergranular fracture and a simplified mechanical model is introduced which relates the grain boundary (GB) fracture toughness to the misorientation between adjacent grains. The misorientation can be computed from the lattice orientations sampled from the random field model. Three criteria are introduced for determining the direction of intergranular crack propagation at a GB junction. Some example crack trajectories are presented.