Relationship between refined Griffith criterion and power laws for cracking

摘要

Rice [J. Mech. Phys. Solids 26 (1978) 61] proposes a refined Griffith criterion, (G - 2gamma)a greater than or equal to 0 at any local crack front, where G is the Irwin's energy release rate, gamma is the surface free energy and is the rate of crack advance. The refined version implies that the entropy production inequality should holds locally rather than globally from the thermodynamic point of view. Within the irreversible thermodynamic framework developed by Rice [J. Mech. Phys. Solids 19 (1971) 433; Constitutive Equations in Plasticity, 1975, p. 23], it is revealed in this paper that the entropy production inequality holds for each internal variable if its rate is a homogeneous function in its conjugate force. It is further shown that widely-used power laws for crack growth are just certain homogeneous kinetic rate laws, so it is concluded that the power laws directly lead to the refined Griffith criterion. (C) 2004 Elsevier Ltd. All rights reserved.