A dialogue between Finite Fracture Mechanics and Phase Field approaches to fracture for predicting crack nucleation at the microscale

Unraveling the material behavior at the microscale is one of the challenges of this century, demanding progress in experimental and computational strategies. Among the latter, two approaches are commonly applied for predicting crack nucleation. The Coupled Criterion (CC) and the Phase Field (PF) model, both depending on a material length parameter. In brittle materials at the macroscale, this parameter is significantly smaller than the specimen size. However, when the scale decreases, this material length might approach the structural dimensions. In this context, a comprehensive comparison between the two models is conducted, changing the ratio between the material length parameter and the dimensions of the specimen. Results indicate that when this ratio is sufficiently small predictions from both models coincide, otherwise both the CC and the PF model predict different results. Despite their differences, an agreement with experiments reported in the literature have been observed.