Examining crack nucleation under spatially uniform stress states with a complete phase-field model for fracture

This work concerns crack nucleation problems in elastic brittle materials subjected to stress states that are spatially uniform or nearly so. Such conditions arise under a wide range of settings, including standard tests of material strength. This class of problems presents challenges from both modeling and computational standpoints, as the localization of fracture occurs as the strength is violated, and naturally represents a bifurcation from a state of uniform stress. In this work, these problems are examined using a complete phase-field model for fracture. In contrast to classical phase-field models, the complete model provides a formulation that can account for the elasticity, the strength, and the toughness of elastic brittle materials, whatever these material properties may be. We consider problems ranging from the fracture of thin films bonded to substrates to crack nucleation during thermal quenching. Where appropriate, we provide comparisons to both experimental observations and results provided by classical phase-field models for fracture. We also explore the introduction of stochastic aspects, using random field models for strength parameters. The material strength fields are represented either through a translation model with controlled correlation lengths, or with a simple random mosaic field (without spatial correlations). The results illustrate the utility of models employing arbitrary strength surfaces and spatial perturbation for simulations of fracture nucleation under near uniform stress states.