Initiation of Regularized Cracks is Explained by the Coupled Criterion
Résumé
Matched asymptotic expansions and phase-field regularization are combined to propose an implementation of the coupled criterion that accounts for the presence of an initial process zone. The initial process zone is introduced by prescribing phase-field Dirichlet boundary conditions around the crack initiation location, which allows us to study either sharp or regularized crack initiation through an initial process zone. An increase in the initially prescribed phase-field value enlarges the effective process zone and progressively reduces the stress singularity at the V-notch tip, showing that even a partially developed process zone can mitigate singular stresses through non-uniform stiffness, without requiring plastic regularization. Furthermore the process zone tends to decrease the incremental energy release rate, thus resulting in a higher initiation generalized stress intensity factor than the one obtained without an initial process zone. The findings reveal that, unlike Griffith's singular formulation, the phase-field model remains intrinsically regularized -even in the vanishing-length limit -raising the fundamental question of whether truly sharp cracks can exist or if a finite process zone always emerges through local structural rearrangement. The proposed approach thus extends the coupled criterion to study crack initiation and propagation in quasi-brittle materials.