A phase-field model for mixed-mode fracture based on a unified tensile fracture criterion

Abstract

Different fracture patterns can be observed because of different material properties, even the geometry and loading are the same. However, most of the known phase-field fracture models have only considered the tensile failure and may not be directly applicable to the shear fracture. In this paper, a phase-field model for mixed-mode fracture is proposed based on a unified tensile fracture criterion. The proposed model is developed from the unified phase-field theory and the original unified phase-field model can be recovered as a particular case. General softening laws for cohesive zone models can also be considered. The unified tensile fracture criterion is embedded in the proposed mixed-mode phase-field model and different fracture patterns can be obtained in the simulation according to the material properties, including failures based on both maximum normal stress and maximum shear stress criteria. The crack propagation direction can be easily determined by the unified tensile fracture criterion. Compared with the classical phase-field model, two additional material parameters are needed, i.e., the failure tension strength and the ratio of the critical shear failure stress to the critical normal fracture stress. Numerical examples have shown that the proposed model has the ability to model mixed-mode fractures, and can also be applied to rock-like brittle materials under compression.