”Research presented in this dissertation is focused on developing and validating a computational framework for study of crack propagation in polycrystalline composite ceramics capable of designing micro-architectures of phases to improve fracture toughness and damage tolerance of ZrB2-based ultra-high temperature ceramics (UHTCs). A quantitative phase-field model based on the regularized formulation of Griffith’s theory is presented for crack propagation in homogenous and heterogeneous brittle materials. This model utilizes correction parameters in the total free energy functional and mechanical equilibrium equation within the crack diffusive area to ensure that the maximum stress in front of the crack tip is equal to the stress predicted by classical fracture mechanics. Also, unlike other phase-field models, the effect of material strength on crack nucleation and propagation was considered. The accuracy of the model is benchmarked in different ways and the simulation results are validated against experimental results for concrete in the form of fracture of L-shaped plates and wedge splitting tests, and for ZrB2-based laminates and fibrous monolithic composites.

To study crack propagation in polycrystalline systems, a phase-field model for grain growth is coupled to the proposed model for crack propagation in multi-phase systems. Intergranular and transgranular crack propagation in ZrB2-bicrystal and polycrystalline systems in mode-I loading are studied.

The significant advantages of the proposed model are revealed in multi-phase systems with considerably different material properties for different phases in which the model enables accurate predication of the crack propagation path in composites consisting of materials with significantly different strengths”--Abstract, page iii.