Effect of Inertia on Finite Near-Tip Deformation for Fast Mode-III Crack Growth

摘要

The combined effects of finite deformation and material inertia ave been analyzed for fast crack growth under anti-plane loading conditions. A steady-state dynamic solution has been obtained for the finite strain on the crackline, from the moving crack tip to the moving transition boundary with the z one of small strains. The crack propagates in a material with a response curve in uniform shear that is linear at small strains, and that remains constant once a critical strain has been exceeded. The corresponding quasi-static solution is given in the full zone of large deformation. For the dynamic formulation, an explicit expression for the crack-line strain has been obtained by expanding the displacement in a power series in the distance to the crackline, with coefficients which depend on the distance to the moving crack tip. Substitution in the equation of motion yields a nonlinear ordinary differential equation for the relevant coefficient, which can be solved rigorously. The finite deformation crack-line fields have been matched to appropriate small-strain fields at the transition boundary. The principal result is that the dynamic strain remains bounded at the crack tip, apparently due to the effect of material inertia.