Self-similar analysis of plasticity-induced closure of small fatigue cracks (Q5926707)

The authors consider the two-dimensional elasto-plastic problem of a center crack subjected to a uniform biaxial remote load. The major principal stress acts in a direction normal to the crack plane. The first objective is to establish a representation of plastic zone and plastic wake following fatigue crack growth from the initial crack length to the current length, with the crack occupying a line segment. The crack opening profile at the maximal applied stress can be analytically determined from Dugdale model. The effect of the plastic wake is simulated by a layer with thickness varying linearly with the distance from the center. An additional specific problem is to determine the residual stretch at the minimum in load cycle. The authors identify four zones on the crack line which are associated with specific boundary conditions in the configuration at the minimum load. The Muskhelishvili complex variable techniques together with complex potentials for anisotropic bodies are used to study the perturbation problem due to the crack. The problem is reformulated as a Riemann-Hilbert problem. Some numerical results are presented, and their relevance to predicting or correlating crack growth rates is also discussed. A particular feature of the model is that it can also be used under fully plastic conditions, with an appropriate implementation of model parameters.