A comparison of two and three-dimensional analyses of fatigue crack closure

Abstract

Plasticity-induced fatigue crack closure is an important mechanism in the reduction of the effective stress intensity factor range for a fatigue crack. A calculation of the level of reduction would allow more accurate predictions of fatigue crack growth rate. However, modelling plasticity-induced closure is not straightforward, particularly when the three-dimensional aspects of the problem are included. Some simplification is possible by reducing the problem to two dimensions, but it is not always clear how this can be achieved for practical crack geometries. In this work, two-dimensional plane stress and plane strain finite element analyses are used to predict crack opening in a centre-cracked plate. The results of these analyses are compared with those of a plane stress strip yield analysis and those of a three-dimensional finite element analysis. Results are obtained for different R-ratios and stress levels. Reasonable agreement is found between the plane stress finite element and strip yield results for higher levels of applied stress levels where an excessively high level of mesh refinement is not required. Plane stress finite element crack opening results agree with three-dimensional finite element results for the surface and plane strain finite element results agree with three-dimensional finite element results for the mid-thickness. The implications of the results for the behaviour of three-dimensional cracks are discussed.