A simple model to explain the geometry dependence of J−Δa-curves

Abstract

Very different patterns of geometry effects may occur if in a bend type specimen the ligament length is increased at constant specimen thickness. These geometry effects can be explained by a model of the total crack growth resistance R which is defined as the sum of the non-reversible energy which must be put into a body to produce an increment of crack area. The relationship between R and the commonly used J−Δa-curves is worked out. The model shows that a ‘wider-lower’ pattern, i.e. the case where an increase of the ligament length causes a flatter J−Δa-curve, appears for fracture under lefm conditions or for contained yielding where R is independent of the geometry. A ‘wider-no effect’ or a ‘wider-higher’ pattern may be observed if the crack extension occurs at the plastic limit load and if either plane strain or plane stress conditions prevail.