When does a notch behave like a crack?

Abstract

The characteristic asymptotic fields at the tip of sharp, semi-infinite cracks and notches are first compared with corresponding features present in selected finite bodies (edge cracks and notches). This gives an explicit view of the gradual divergence of the semi-infinite and finite problem solutions as the observation point becomes remote from the tip. Hence, upper bounds for the local plastic zone to be characterized by the singular field are known. Asymptotic solutions for semi-infinite rounded features are introduced, whose remote fields may be matched to the sharp singular fields through the medium of the corresponding generalized stress intensity factor. Thus the semi-infinite sharp and rounded problems converge remotely but diverge as the apex of the feature is approached. This comparison sets a lower bound for loads at which the outer boundary of the plastic zone is characterized by the singular field. Thus, the range of loads for the plastic zones to be controlled by the singular solutions are derived. We then proceed to compare critically the nature of the semi-infinite sharp notch and semi-infinite crack states of stress, defining the circumstances in which these are alike.All these elements considered together enable the closeness of various notch plastic zones to that of the classical semi-infinite crack to be gauged.