Assessment of the interaction between two collinear cracks in plates of arbitrary thickness using a plasticity-induced crack closure model

Fracture and fatigue assessment of structures weakened by multiple site damage, such as two or more interacting cracks, is currently a very challenging problem. The main objective of this paper is to develop a mathematical model and an approach to investigate fatigue crack closure behaviour of two through-the-thickness collinear cracks of equal length in a plate of arbitrary thickness under remote tensile cyclic loading. The developed mathematical model of the problem under consideration is based on the Dugdale strip yield model and plasticity-induced crack closure concept. The approach utilises the fundamental solution for an edge dislocation in a plate of finite thickness and the distributed dislocation technique to obtain an effective and accurate solution to the system of governing equations. The obtained results show a very good agreement with the previously published analytical solutions for limiting cases. In particular, the new results confirm that the crack closure behaviour and the opening stress variation in the case of two collinear cracks are significantly dependent on the separation gap between two cracks as well as the plate thickness.