Ultrasonic Scattering in Composites Using Spatial Fourier Transform Techniques

Abstract

The heterogeneous nature of composite materials often makes their inspection using ultrasonics difficult unless the flaws are sufficiently large so that common B- or C- scans can be employed. Thus, flaw scattering models are essential in order to interpret the measured ultrasonic responses. However, even at low frequencies where the composite may be able to be replaced by an equivalent homogeneous, anisotropic material, conventional direct scattering methods such as the T-Matrix and Boundary Element techniques are not effective. This is because both methods rely on the superposition of exact solutions to the governing equations of elastodynamics and, except for very special anisotropics, such exact solutions are not available in closed form. One way around this difficulty is to pose the scattering problem in a spatial Fourier frequency domain where exact fundamental solutions for elastodynamics are available, even for general anisotropic materials (1). Employing these solutions in a conventional volume or surface integral equation for the scattering wavefields then yields a spatial frequency domain formulation to the direct scattering problem. Because the boundary conditions are given in the real spatial domain, it is necessary to iteratively satisfy these conditions via fast Fourier transforms (2). This approach is called the Spectral-Iteration Technique and has been applied successfully for a variety of electromagnetic scattering problems (3), (4). Here, we will obtain the equivalent elastic wave scattering formulations for cracks and volumetric flaws in a general anisotropic medium. Modifications of the standard Spectral-Iteration technique needed to ensure its convergence at low frequencies will also be discussed.