Estimating the lower-limit of fracture toughness from ideal-strength calculations

Fracture mechanics is a fundamental topic to materials science. Fracture toughness, in particular, is a material property of great technological importance for device design. The relatively low fracture toughness of many semiconductor materials, including electronic and energy materials, handicaps their use in applications involving large external stresses. Here, it is shown that quantum-mechanical density functional theory calculations of ideal strength, in conjunction with an integral stress-displacement method, can be used to estimate the fracture energy needed to calculate fracture toughness. Using the fracture energy associated with the weakest crystallographic direction provides an estimation for the lower-limit of the fracture toughness of a material. The lower-limit values are in good agreement with experimental single crystal measurements across several orders-of-magnitude of fracture toughness. Furthermore, the proposed methodology is useful for benchmarking experimental measurements of fracture toughness in polycrystalline materials and can serve as a starting point for the construction of more detailed fracture models and the computational design of new materials and devices.