On continuum models of ductile fracture

Several fracture criteria are reviewed with respect to ductile fracture. It is suggested that both critical crack-tip displacement, 2V _c ^*, and critical fracture strain,∃ ^*, criteria may describe the fracture of a ductile second phase rod in a ductile matrix. As a first approximation, this is experimentally verified by observations of ductile stainless steel fibres fracturing in an age-hardened aluminium matrix. For 0.05, 0.10 and 0.20 volume fraction composites, the average fracture strains are calculated to be 1.15 as compared to a measured average of 0.93 while the average critical crack-tip displacement is calculated to be 0.50 mm as compared to an “observed” average of 0.40 mm. The statistical variation in the fracture strain was not sufficiently small to allow any choice between these proposed criteria. In fact, both the experimental and theoretical evidence point to the equivalency of these criteria as given by 2V _c ^*=π/^*∃^* where /^* is the microstructural unit in front of the crack over which the strain is greater than or equal to∃ ^*.