Understanding regularized crack initiation through the lens of finite fracture mechanics

As a remedy to pathological sharp crack configurations such as strong singularities or anti-plane shear cracks, where crack initiation is driven solely by energy, a regularized crack description can be adopted to study crack initiation. The nucleation of a regularized crack at a V-notch is studied using the coupled criterion through matched asymptotic expansions. The process zone around the crack is described by crack regularization usually employed in phase-field models. The effective crack length increases with increasing regularization length so that the incremental energy release rate decreases, which in turn increases the critical generalized stress intensity factor at initiation. Decreasing incremental energy release rate is also obtained with increasing Poisson's ratio. For a given material characteristic length, it is shown that the initiation crack length only depends on the V-notch angle and Poisson's ratio. For a given geometry and Poisson's ratio, the initiation length is proportional to the regularization length. The proposed description of regularized crack initiation shows good correspondence to the generalized stress intensity factor obtained by phase-field calculation, the only difference being in the description of the process zone prior to crack initiation.