Stochastic Analyses of Dynamic Fracture in Composite Ceramic Microstructures
Variations in constituent properties, phase morphology, and phase distribution cause deformation and failure at the microstructural level to be inherently stochastic. This paper focuses on the stochasticity of fracture processes that arises as a result of measurement uncertainties in the properties of the constituents in the heterogeneous microstructures of an Al2O3/TiB2 ceramic composite system. A micromechanical cohesive finite element framework with explicit resolution of arbitrary fracture patterns and arbitrary microstructural morphologies is used. A deterministic analysis and a stochastic analysis are carried out simultaneously. The combination of determinism and stochasticity is achieved by integrating a perturbation analysis of the influence of stochastic property variations around their mean values and a deterministic analysis for the microstructure with the mean values of the constituent properties. Calculations are carried out for actual and idealized microstructures of the Al2O3/TiB2 material system. It is found that for the system analyzed the variations in the crack surface area generated and the variations in the energy release rate are of the same order as the variations in constituent properties.