Principle of Maximum Energy Dissipation Rate in Crack Dynamics

THE PRINCIPLE of maximum energy dissipation rate is introduced as an energy criterion for crack dynamics. That allows us to explain observed limiting crack speeds in brittle materials, and to complete the crack dynamics formulation. The upper limits of the crack speed in perfectly elastic and elastic-plastic bodies are obtained. It is found that the theoretical maximum crack speed in an isotropic elastic body (in the first mode of crack propagation) is approximately equal to half the shear wave speed. In the case of an elasticplastic body, the criterion is formulated as a maximum plastic strain work per unit time. The self-similar problem for the fracture mode III is solved (assuming the plastic zone to be narrow) and the crack speed limit is found as a function of the ratio of loading to yield limit : the plasticity decreases the crack speed limit and the latter tends to zero with the yield limit. The comparison of these theoretical results with some experimental data shows that under ordinary conditions crack propagation appears to conform to the “maximum dissipation rate” process.