On the significance of diffuse crack width self-evolution in the phase-field model for residually stressed brittle materials

The Phase-Field method is an attractive numerical technique to simulate fracture propagation in materials relying on Finite Element Method. Its peculiar diffuse representation of cracks makes it suitable for a myriad of problems, especially those involving multiple physics and complex-shaped crack patterns. Recent literature provided linear relationships between the width of the diffuse crack and the material intrinsic fracture toughness, through a material characteristic length. However, lately, it was shown how the existence of a residual stress field can affect the represented crack width even for fully homogeneous materials, in terms of toughness. In this short note, the authors tried to shed some light on the factors influencing the width of the diffuse crack representation. By simulating crack propagation in several residually stressed brittle materials, it was shown how the width of the diffuse crack is affected by the ratio between the driving force - due to the externally applied load - and the driving force required to propagate the crack. In other words, the diffuse crack extent can be linked to the degree of crack propagation stability/instability. Monitoring the evolution of the studied quantity can be of great interest to rapidly assess crack instability circumstances, under displacement control.