Microstructural design is an important approach for enhancing material properties such as fracture toughness at the macroscopic scale. Tasks in this regard require systematic quantification of both microstructure and material response. We report the development of a multi-scale computational framework based on the cohesive finite element method (CFEM) for predicting fracture toughness of materials as a function of microstructure. The approach uses the J-integral to calculate the initiation/propagation fracture toughness, allowing explicit representation of realistic microstructures and fundamental fracture mechanisms. Calculations carried out concern both brittle and ductile materials and focus on the effects of constitute behavior, phase morphology, phase distribution, and size scale on fracture toughness. Based on the CFEM results, a semi-empirical model is developed to provide a quantitative relation between the propagation toughness and statistical measures of microstructure, fracture mechanisms, and constituent and interfacial properties. Both the CFEM calculations and model predictions show that microstructure and constituent properties can significantly influence the fracture behavior and combine to determine the overall fracture toughness through the activation of different fracture mechanisms. In particular, a combination of fine microstructure size scale, rounded reinforcement morphology, and appropriately balanced bonding strength and compliance can best promote desirable crack-reinforcement interactions and lead to enhanced propagation fracture toughness. The CFEM framework, phenomenological model and the relations obtained can be useful tools for the design of failure-resistant materials.

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