A path‐independent domain integral to characterize fatigue crack propagation by cyclic material forces

Abstract

A lot of structures undergoing cyclic loading fail at load values smaller than their ultimate design loads. In the framework of fracture mechanics, the crack propagation process can be separated into three different stages. In the first stage, micro‐cracks propagate and form together a macro‐crack. The macro‐crack propagates stably in the second stage, which is also known as the PARIS' regime. In the third stage, the crack propagates unstably leading to the failure of the structure. The pioneering law characterizing the stable crack growth is PARIS' law. The aforementioned law correlates the crack growth rate to the cyclic stress intensity factor. Unfortunately, the cyclic stress intensity factor is limited to cases where the theory of linear elastic fracture mechanics is applicable. To overcome the limitations of the cyclic stress intensity factor, domain‐integrals evaluated by configurational forces or material forces are used as a fatigue crack growth criterion. However, the aforementioned domain‐integrals are path‐dependent. The aim of the study at hand is to derive a path‐independent domain integral to characterize fatigue crack propagation in elastic‐plastic and linear viscoelastic solids at small strains. First of all, the cyclic material forces are derived using the cyclic free energy. Furthermore, the path‐independence of the cyclic material forces approach is illustrated by numerical examples. Finally, the cyclic material force approach is validated by comparing it to experimental results.