Employing phase‐field descriptions of cohesive zone placements in cohesive fracture simulations

Cohesive zone models suffer from the fundamental problem that potential crack paths must be determined beforehand. Phase‐field models for (brittle) fracture, that have recently become immensely popular, are able to naturally handle essentially arbitrary crack patterns. However, due to their energetic nature, phase‐field approaches have difficulties to predict, for example, crack nucleation in consequence of their lack of strength criteria which are naturally incorporated in the cohesive zone model. In this contribution, an alternative approach is presented that allows the embedding of established (cyclic) cohesive laws into phase‐field modeling. Our work is conceptually in line with the ideas proposed by Verhoosel and de Borst in 2013. Since this novel approach to cohesive fracture is still in its infancy, many open challenges remain, of which the following are addressed in this article: (i) A strict separation between the description of the cohesive zone and the cohesive law itself is realized, (ii) the interplay between the different physical length‐scales inherent to the formulation is carefully investigated in order to quantify the parameters introduced in the phase‐field description, and (iii) an alternative finite element treatment is proposed, implemented, and tested that avoids spurious solutions for unstructured meshes. In this context, fatigue crack growth is simulated as a quantitative benchmark problem relevant to engineering applications.