Scattering of elastic waves by a rigid cylindrical inclusion partially debonded from its surrounding matrix—I. SH case

Abstract

In Part I of this two-part paper, the scattering of SH waves by a rigid cylindrical inclusion partially debonded from its surrounding matrix is investigated by using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as multiple arc-shaped interface cracks with non-contacting faces. Expressing the scattered fields as the wave function expansions with unknown coefficients and considering the mixed boundary conditions, we reduce the problem to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations to a set of singular integral equations of the first type which can be easily solved numerically by using the quadrature method of Erdogan and Gupta [Int. J. Solids Structures7, 1089–1107 (1972)]. The solution is valid for arbitrary values of KT0r0 (where KT0 is the wave number and r0 the inclusion radius) and arbitrary numbers and sizes of the debonds. Explicit solutions are obtained in two limiting situations: (i) the long wavelength limit (KT0r0 ≪ 1). In this case, the solution reduces to the quasistatic solution; (ii) the small debond limit with KT0r0 = O(1). This means the wavelength greatly exceeds the debond size and the solution is identical to that of a flat interface crack between a rigid half space and an elastic one subjected to static loading at infinity. If the debond is small and KT0r0 ≪ 1, the solution will give the results of a flat interface crack subjected to an incident SH wave. Finally, the numerical results of the dynamic stress intensity factors, the rigid body translations of the inclusion and the scattering cross-sections are presented for an inclusion with one or two debonds. The phenomenon of low frequency resonance discovered by Yang and Norris [J. Mech. Phys. Solids39, 273–294 (1991)] for an elastic inclusion with one debond is shown and its dependence upon the various parameters is discussed. The solution of this problem is relevant to ultrasonic nondestructive detection of debonding and is expected to have applications to the question of how dynamic loading can lead to growth of debonds [Norris and Yang, Mech. Mater.11, 163–175 (1991)].