The steadily propagating crack in an elastic/power-law material: Second order solutions

Abstract

We present second-order asymptotic solutions to the near-tip field for a crack propagating under steady-state, antiplane strain conditions in an elastic/power-law material. First-order solutions to this problem were originally given by Hui and Riedel. For values of the power-law exponent n < 3, the second-order solution is found to satisfy a linear, inhomogeneous equation. For n > 3, however, an eigenproblem results. In contrast to the first-order solution for n > 3, the second order solution contains an undetermined parameter whose value must be found from the remote boundary conditions.