Prediction of fracturess toughness of ceramic composites as function of microstructure: II. analytical model

Microstructure and constituent properties combine to determine the overall fracture toughness of particle-reinforced brittle composites through the activation of different fracture mechanisms. The toughening is through increases in energy dissipation when cracks are forced to follow tortuous paths. Based on the results of numerical simulations, a semi-empirical model is developed to predict the fracture toughness of brittle two-phase ceramic composites as a function of statistically defined morphological attributes of microstructure, constituent properties and interfacial bonding characteristics. The quantification of the fracture toughness is achieved by an assessment of the contributions of different fracture mechanisms including matrix fracture, interfacial debonding and particle cracking to the overall energy release rate. In particular, this assessment involves a statistical characterization of the competition between crack deflection and crack penetration at matrix/reinforcement interfaces using a modified version of the energy criterion of He and Hutchinson which accounts for the effects of finite reinforcement size, phase volume fractions, phase shape and phase distribution. The fracture toughness–microstructure relation obtained can be used to identify trends for materials design. Although the numerical quantification is specific to Al2O3/TiB2 ceramic composites, the approach and the model developed apply to brittle particle-reinforced composites in general.