A Ray Theory for Elastodynamic Stress-Intensity Factors

Abstract

Elastodynamic stress-intensity factors generated by the interaction of wave motions with a crack are analyzed. It is shown that in an asymptotic approximation, which is valid for high frequencies, the stress-intensity factors at the edge of a crack are related to the fields of incident rays by a matrix of stress-intensity factor coefficients, which can be computed from canonical solutions. The canonical solutions are provided by the fields describing diffraction by a semi-infinite crack of plane body waves and plane surface waves, which are incident under an arbitrary angle with the edge of the crack. Several applications of the theory are presented. For cracks of finite length, the contributions due to the traveling back and forth of rays between the two crack tips is taken into account in a simple manner, to yield results which are in excellent agreement with numerical results obtained by other authors.