On the distance criterion for failure at the tips of cracks, minimum fracture toughness, and non-dimensional toughness parameters

T he present paper describes a distance criterion for failure at the tips of cracks in materials showing plasticity which, for stress-controlled cleavage on the lower shelf of toughness, is based on consideration of plasticity local to individual crack-initiation sites rather than on the distance from the remote crack tip to a crack-initiation site. For the upper shelf, consideration is of conditions local to voids, but the thermodynamic balance determining the moment of failure is for the macrocrack rather than microcracks, and a criterion of strain is used rather than a criterion of stress. This new criterion of distance or critical distance leads to a good description of temperature-dependent changes in toughness, on the lower shelf where failure is caused by stress-controlled cleavage and on the upper shelf where fracture runs by a strain-controlled ductile mechanism as well as in the region of transition in between, and always on the basis that these changes are due to temperature-dependent changes in yield strength and Young's modulus. A non-dimensional toughness parameter is observed. The present work is in agreement with many accepted ideas about fracture. The significance of the self-similarity of the distributions of stress and strain at the tips of cracks and the over-riding importance of crack-opening displacement in the determination of conditions for propagation are emphasised.