Dynamic crack propagation in a heterogeneous ceramic microstructure, insights from a cohesive model

Silicon nitride is a widely used industrial ceramic, specifically for dynamic loading applications because of its special mechanical and material properties. The investigation of the underlying mechanisms which lead to these properties is experimentally challenging and the interpretations need to be numerically and analytically complemented. This research attempts to explore the influential parameters on dynamic crack propagation in silicon nitride microstructures through 2D tensile loading finite-element simulations. The dynamic macroscopic mechanical properties of toughness and strength, are evaluated as function of strain rate, microstructural and mechanical parameters. Voronoi tessellations are considered to model regular grains and these grains are merged to represent elongated ones. The model incorporates dynamic insertion of cohesive elements representing intergranular and transgranular cracking. The fracture modeling is enriched by using a parallel finite-element code for cohesive element insertion, which brings a significant increase in studied degrees of freedom. Diffuse crack networks are represented by a graph and its geometrical and mechanical properties are extracted with the help of graph properties. Simulation results reveal that material inertia causes strain rate strengthening. Moreover, elongated grains represent reinforcements in the specimen and contribute to the rate-hardening. Exploiting a parallel finite-element code for cohesive element insertion enables statistically-significant simulations of a main crack propagation and calibration of transgranular fracture properties with experimental data. The main crack deflection/penetration events at grain boundaries are compared with analytical static (Hutchinson and Suo, 1992) and dynamic (Xu et al., 2003) theories. It is seen that by neglecting the cases in which the crack tip jumps due to coalescence into a micro-daughter crack, the dynamic analytical criterion provides an accurate prediction for the crack path. Moreover, the main crack length and roughness are analyzed for different grain sizes and fracture properties of grains. It is observed that fine and coarse grains introduce local roughness and large deviations in the crack path respectively. A mutual competition of the crack length and transgranular fracture percentage specifies the material's toughness.