Boundary layer phenomenon in the plastic zone near a rapidly propagating crack tip

Abstract

The steady-state dynamic fields near a rapidly propagating crack tip in an elastic perfectly-plastic material have been investigated for the case of Mode-III fracture. For arbitrary values of the dimensionless crack-tip speed (M) the inner solution consists of a central-fan field ahead of the crack tip and a uniform field in its wake. It is shown that the inner solution is valid in a “boundary layer” which shrinks on the crack tip in the limit of vanishing M. For small M the outer solution was found as a regular perturbation expansion in M, with the quasi-static solution as its first term. A uniform expansion over the polar angle θ measured from the plane of the crack was also obtained; its first term displays the connection between the inner and outer solutions. The expansion has also been used to obtain an exact solution for the shear strain in the plastic zone in the plane of the crack ahead of the crack tip.