# Elastic Wave Propagation in Anisotropic Media. Application to Ultrasonic NDT

[Doktorsavhandling]

The subject of this thesis is elastic wave propagation in anisotropic materials with application to ultrasonic nondestructive testing (NDT).

The first part of the thesis is concerned with modeling of ultrasonic transducers and wave propagation in anisotropic materials in general. First, a scalar 2-D case is considered. The transducer is modeled by the traction beneath it and this traction is obtained by modifying the traction of a plane SH wave propagating in an infinite anisotropic material. The probe may be of any angle, frequency and width. A generalization of the 2-D model to 3-D is obtained by considering a plane wave incident upon the interface between an isotropic and an anisotropic half-space. The traction beneath the probe is obtained by modifying the traction at the interface when the plane wave is reflected/transmitted. This probe may be of any angle, type, size and frequency. A probe of phased array type is considered as well. This model consists of an arbitrary number of elements, each element being a probe in itself. The first two models are attached to anisotropic half-spaces and the phased array probe is attached to a layered anisotropic plate. The wave propagation problems are solved by means of Fourier transform techniques and the displacement fields are presented in contour plots.

The second part of the thesis is concerned with scattering of elastic waves and modeling of ultrasonic NDT situations. First, scattering of waves from the 2-D probe model by a strip-like crack located at the interface between two anisotropic materials is considered. The problem is formulated as an integral equation in the crack opening displacement (COD) and the integral equation is solved by means of Fourier expansions and projections. A complete test situation with a strip-like crack, a transmitting probe and a receiving probe is considered. The electrical signal from the receiver due to the crack when an electrical signal is incident upon the transmitter is calculated via an electromechanical reciprocity relation. Scattering of waves generated by the 3-D probe model by a strip-like crack is then considered. The scattering problem is solved via integral equations in the COD as in the 2-D case. A complete model is obtained by combining two probes and the crack. The electromechanical reciprocity relation is used to calculate the electrical signal from the receiver as before. Some numerical examples of the displacement field are given in contour plots for the 2-D model and examples of the electrical output are given for both models. Finally, scattering of plane waves by an anisotropic cylinder in an anisotropic material is considered. Both materials are transversely isotropic with symmetry axes parallel to the cylinder axis. The scattering problem is solved by means of separation-of-variables in cylindrical coordinates and potentials. Numerical examples of the displacement field are shown in contour plots.

**Nyckelord: **elastic waves, anisotropy, ultrasonics, nondestructive testing, transducers, scattering, cracks, cylinders, layered media, integral equations

Denna post skapades 2006-09-20. Senast ändrad 2013-09-25.

CPL Pubid: 1068