A Method for determining the elastic-plastic response ahead of a notch tip

The stress distribution ahead of a notch tip is the prerequisite to calculating the driving force for cracks emanating from notches. This article first examines whether two commonly used engineering methods, which are often employed to determine the response at a notch tip, can be applied to evaluate the elastic-plastic response ahead of a notch tip. It is found that both methods would significantly underestimate the stress-strain distribution ahead of a notch tip. Based deformation theories of plasticity, an analytical method is then developed, taking into account of the effects of stress redistribution induced by notch plasticity and the in-plane and through-thickness constraints near the notch root. Predictions are shown to be in close correlation with finite element results.