Scattering of elastic waves by a rigid cylindrical inclusion partially debonded from its surrounding matrix .2. P and SV cases

This is Part II of a two-part paper which analyses the scattering of elastic waves by a rigid cylindrical inclusion partially debonded from its surrounding matrix. The scattering of SH waves was solved in Part I by the use of the wave function expansion method and singular integral equation technique. Here, in Part II, we consider the scattering of P and SV waves by using a similar approach. As in Part I, the debonds are modeled as interface cracks with noncontacting faces. Then the problems are reduced to a set of singular integral equations of the second type in terms of the dislocation density functions, which demonstrates the oscillatory behavior of the stresses near the crack tips. By representing the dislocation density functions with Jacobi polynomials, these equations are solved numerically. Two limiting situations are considered: the long wavelength limit with arbitrary debond sizes and the small debond limit with K(T0)r(0) = O(1) (where K-T0 is the shear wavenumber and r(0) the inclusion radius). The general solution simplifies in these two limiting cases and results, similar to those for SH case, are obtained. Finally, the numerical results for the dynamic stress intensity factors, rigid body motion of the inclusion, and scattering cross-sections are presented for both P and SV cases, and the low frequency resonance phenomenon, as in SH case, is explored. Copyright (C) 1996 Elsevier Science Ltd.