THE ELASTICALLY EQUIVALENT SOFTENING ZONE SIZE FOR AN ELASTIC-SOFTENING MATERIAL .1. POWER-LAW SOFTENING BEHAVIOR

The paper is concerned with the determination of the elastically equivalent softening zone size (R(E)) associated with a semi-infinite crack in a remotely loaded infinite solid, with the material being of the elastic-softening variety. R(E) plays a prominent role in size effect expressions that are used to correlate the failure loads for solids having different dimensions. R(E) is determined for a range of softening behaviours, characterised by a power law variation, and a comparison is made with the value R(A): the actual softening zone size. The ratio R(E)/R(A) increases from a value 0.333 for the case where the stress is constant with the zone, to a value of unity for the other limiting case where G(F)/p(c)delta(c) --> 0; G(F) is the specific fracture energy, while p(c) and delta(c) are respectively the maximum stress and displacement within the softening zone.