Elliptic arc crack subjected to anti-plane shear wave

Abstract

An elliptic arc crack subjected to an anti-plane shear wave is considered in this paper. The problem is first reduced to a set of simultaneous dual series equations by using the wave function expansion method. Then, a dislocation density function is introduced to transform these equations to a Hubert singular integral equation which is further converted to a Cauchy singular integral equation. The dynamic stress intensity factors (DSIFs) at crack tips are calculated by solving the integral equation numerically. The results show a low frequency resonance in the DSIF, especially for cracks of large angular width. The resonance frequency and the peak value of the DSIF depend on many factors, such as the ratio of long and short radii, the crack size and the incident angle of waves.