A consistency assessment of coupled cohesive zone models for mixed-mode debonding problems

Due to their simplicity, cohesive zone models (CZMs) are very attractive to describe mixed-mode failure and debonding processes of materials and interfaces. Although a large number of coupled CZMs have been proposed, and despite the extensive related literature, little attention has been devoted to ensuring the consistency of these models for mixed-mode conditions, primarily in a thermodynamical sense. A lack of
consistency may affect the local or global response of a mechanical system. This contribution deals with the
consistency check for some widely used exponential and bilinear mixed-mode CZMs. The coupling effect on
stresses and energy dissipation is first investigated and the path-dependance of the mixed-mode debonding
work of separation is analitically evaluated. Analytical predictions are also compared with results from  numerical implementations, where the interface is described with zero-thickness contact elements. A node-to-segment strategy is here adopted, which incorporates decohesion and contact within a unified framework. A new thermodynamically consistent mixed-mode CZ model based on a reformulation of the Xu-Needleman model as modified by van den Bosch et al. is finally proposed and derived by applying the Coleman and Noll procedure in accordance with the second law of thermodynamics. The model holds monolithically for loading and unloading processes, as well as for decohesion and contact, and its performance is demonstrated through
suitable examples.