Relationship between refined Griffith criterion and power laws for cracking

Rice J. Mech. Phys. Solids 26 (1978) 61] proposes a refined Griffith criterion, at any local crack front, where G is the Irwin's energy release rate, γ 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.