Non-steady state solution of a moving crack in an anisotropic solid

Abstract

The non-steady state solution to a moving crack in an anisotropic material is derived using the complex potential theory and a moving coordinate system. An asymptotic analysis is used to obtain recurrence equations for determining the higher order solutions from lower order ones. For a moving crack in an isotropic solid, studied in a previous paper by Xu and keer (1992, Int. J. Fracture 58, 325), the displacement asymptotic field was separated into two parts, related respectively to two wave speeds, each of which satisfied its recurrence equation. For the case of an anisotropic solid, these two parts are, in general, coupled to each other through the recurrence formulae, and a special method has been developed to solve these equations. The calculations show that the non-steady state asymptotic field of a moving crack in an anisotropic material is determined by the time rate of change of the stress intensity factor, the crack tip acceleration and the rotation speed. Solutions are consistent with the related non-steady state solution in isotropic solids.