A multiscale based cohesive interface model for fatigue crack growth and frictional dilatancy

The initiation and propagation of cracks due to fatigue represents one of the critical mechanisms underlying the failure of many engineering structures. Accurate prediction of such phenomena remains a significant challenge for modeling and simulation. Fatigue-induced damage can result in unexpected failures, as the driving force for fatigue crack growth is often substantially lower than that required under monotonic loading conditions. This study proposes a cohesive zone-based fatigue crack growth model developed in the framework of a multiscale approach, and designed to accommodate arbitrary quasi-static cyclic loading histories. A cohesive interface law is formulated to capture the degradation of interface mechanical properties caused by alternating relative displacements that remain below the maximum previously attained displacement, such as during unloading–reloading cycles. The model incorporates the sub-critical growth of damage and the hysteretic local mechanical response. Notably, the model predicts the evolution of fatigue damage even in the elastic regime, prior to the local traction reaching the cohesive strength. Furthermore, the cohesive interface model is extended into a multiplane framework, where the representative volume element describing the interface response exhibits a micro-structured geometry in order to account in a clear mechanical way the dilatancy effect. The effectiveness of the proposed model is demonstrated through the analysis of mode I and mixed-mode cases, as well as by comparisons with numerical and experimental results available in the literature.