CHAPTER 3 - NOTCH ANALYSIS OF FRACTURE

Abstract

Notch analysis of fracture is based on the assumption of a critical stress or strain which is required to initiate fracture. These conditions will be reached first in the immediate vicinity of stress concentrations. The elastic stress fields near such stress concentrations are presented in Neuber's comprehensive treatment of the subject and are reviewed here briefly. The theory also applies to sharp notches and cracks for which a dimensional material characteristic η, relating to the breakdown of continuum mechanics for steep stress gradients, is introduced. Some useful approximate solutions are given. Brittle fracture is governed by two material parameters, a critical fracture stress and η. The two parameters are related to the critical stress-intensity factor of sharp-crack fracture mechanics. Two approaches to fracture in the presence of plastic flow are presented: (1) modification of the elastic concept by plasticity corrections, and (2) notch analysis for materials showing nonlinear stress-strain relationships. The final portion of this chapter deals with two applications of notch analysis: (1) to the fracture of brittle inhomogeneous materials, and (2) to fatigue-crack propagation. Experimental data are presented to show the range of applicability of the analytical predictions.