THE ELASTICALLY EQUIVALENT SOFTENING ZONE SIZE FOR AN ELASTIC-SOFTENING MATERIAL .2. A SIMPLE PIECE-WISE SOFTENING LAW

The paper determines the elastically equivalent softening zone size RE for an elastic-softening material when there is a semi-infinite crack in a remotely loaded infinite solid; the parameter R(E) plays a central role in size effect expressions that are used to correlate the maximum loads that can be sustained by solids having different dimensions. The stress (p) versus displacement (upsilon) softening law considered is that for which p = p(c) for o < upsilon < lambdadelta(c) and p = qp(c) = p* for lambdadelta(c) < upsilon < delta(c). Particular attention is focussed on the case where the parameters lambda and q are both small. Such a softening law simulates the softening behaviour of plain concrete, where there is an initially rapid softening to a low stress value at a small displacement, followed by a long tail that is associated with a low stress. The paper shows that the behaviour of a material with such a softening law can be conveniently analysed by assuming that there is a non-zero stress intensity (K(IC)) at the crack tip followed by a constant stress p* within the softening zone; K(IC) = square-root E0G(I) where E0 is the reduced modulus and G(I) = lambdap(c)delta(c) is the contribution to the specific fracture energy arising from the initially rapid softening region. Analysis of a specific model demonstrates the viability of this approach by showing that there is consistency with the proposed size effect expressions based on R(E).