Quasi-static crack front deformations in cohesive materials

When a crack interacts with material heterogeneities, its front distorts and adopts complex tortuous configurations that are reminiscent of the energy barriers encountered during propagation. As such, study deformations is key to rationalize effective failure properties micro-structured solids interfaces. Yet, impact localized dissipation in finite region behind front, called process zone, has often been overlooked. In this work, we derive equation ruling 3D coplanar propagation heterogeneous cohesive materials where opening resisted by some traction wake. We show presence zone results two competing effects on deformation fronts: (i) it makes more compliant small-wavelength perturbations, (ii) smooths out local fluctuations strength size, from which emerge heterogeneities fracture energy. Their respective influence shown strongly stability perturbed fronts, as well their stationary shapes when interacting arrays tough obstacles. Overall, our theory provides unified framework predict variety profiles observed experiments, even small-scale yielding hypothesis linear elastic mechanics breaks down.