Plastic Deformations Near a Rapidly Propagating Crack Tip

摘要

For rapid crack propagation in an elastic perfectly-plastic material, explicit expressions have been obtained for the dynamic strains on the crack line, from the moving crack tip to the moving elastic-plastic boundary. The method of solution uses power series in the distance to the crack line, with coefficients which depends on the distance to the crack tip. Substitution of the expansions in the equations of motion, the yield condition (Huber-Mises) and the stress-strain relation, yields a system of nonlinear ordinary different equations for the coefficients. These equations are exactly solvable for Mode-III, and they have been solved in an approximate manner for Mode-I plane stress. The crack-line fields have been matched to appropriate elastic fields at the elastic-plastic boundary. For both Mode-III and Mode-I plane stress, the plastic strains, which depend on the elastodynamic stress intensity factor and the crack-tip speed, have been used in conjunction with the crack growth criterion of critical plastic strain, to determine the relation between the far-field stress level and the crack-tip speed. (Author)