DIFFRACTION OF PLANE DILATATIONAL WAVES BY A FINITE CRACK

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Abstract
SUMMARY In this paper, the stress field around a finite closed crack in an elastic material is investigated when a plane dilatational wave is applied to the crack. Of particular interest is the stress concentration at the tips of the crack. Using the Wiener-Hopf technique, the problem is formulated as a system of coupled integral equations, representing the interaction between two half-plane problems. The dynamic stress intensity factors are obtained for the case of wave lengths small compared with the length of the crack. Solutions for short wave lengths are essential in obtaining the transient solution near the wave front. When the parameters of the incident dilatational wave are properly adjusted, the problem reduces to the case of oscillatory in-plane shear. Numerical results for the dynamic stress' intensity factors are calculated for a range of wave numbers as well as angles of incidence. The periodic nature of the dynamic stress intensity factors as functions of wave number can be understood as in-phase or out-of-phase interactions between the waves generated at the crack tips when the wave lengths are small.

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