ABSTRACT
Developments on nondestructive laboratory detection of cracks in strategic defence material, ballistic missiles, aircraft etc., require the knowledge of three-dimensional scattering analysis. While detailed analytical results are available for scattering from penny-shaped cracks, such solutions for three-dimensional cracks are only available by the boundary integral method. In this Chapter, analytical method to study scattering from an elliptic crack both in the low frequency as well as mid frequency range is developed. The representation theorem is used to obtain the scattered displacement from an arbitrary incident field. The boundary conditions on the crack surface yield in isotropic cases two separate integro-differential equations, one for the normal loading and the other coupled integro-differential equations involving crack-opening displacement for the tangential components. In the first few sections the low frequency expansions of the crack opening displacements are discussed, and successive terms are obtained exactly solving the integro-differential equation by the polynomial method of solution for the elliptic crack described in Chapter 2. On knowing the crack-opening displacements for the low frequency case for both normal and shear loading various quantities of interest are obtained viz. scattering coefficients, stress intensity factors. In the next section for the mid-frequency range the resulting integral equation is reduced to an infinite system of Fredholm integral equations of the second kind. This is then solved using a new analytical cum numerical method by expanding the Fourier component of displacements in terms of Jacobi’s orthogonal polynomial. The last section includes a discussion of the attenuation coefficients, the wave speed and effective elastic moduli for a multitude of cracks.
