Novel framework for predicting constraint effects on fracture toughness using an elastic–plastic phase field model and modified boundary layer formulations

Fracture toughness is dependent on geometry according to a phenomenon known as the constraint effect on fracture toughness. In this paper, we propose a framework to predict constraint effects on fracture toughness using an elastic–plastic phase field model and modified boundary layer formulations. An elastic–plastic material was adopted because constraint effects are typically related to plastic deformation at the crack tip. Modified boundary layer formulations were used as loading methods to control phase field evolution at the crack tip. Numerical results indicate that fracture toughness increases with negative T-stress. The effects of yield stress and the linear hardening coefficient on constraint effects were also investigated. The results revealed that the variation in fracture toughness was greater in materials with low-strain hardening and yield stress compared to that in materials with high-strain hardening and yield stress. Finally, the variation in cleavage fracture toughness as predicted by our framework with a limited set of available experimental data was evaluated. The trend of the predicted results is consistent with that of the experimental results.