Background

One of the most important topics associated with the subject of stress wave propagation in solid materials is the wave reflection and refraction at an interface between two different media. (For more details, see Auld 1990; Graff 1991; Pilarski, Rose, and Balasubramaniam 1990; or Rose 1999.) The subject is important to the study of ultrasonic guided waves since oblique incidence via appropriate angles of incidence and frequency selection can be used to generate guided waves in a variety of different waveguides. Introductory topics and concepts are therefore presented in this chapter. If incident angles are selected properly, long enough wavelengths are used, and the material being inspected has a phase velocity larger than the dilatational velocity in the wedge material, then guided waves can be generated in the test material.

A general introduction to oblique incidence in ultrasonic wave analysis will be presented. The reflection (refraction) factor, or coefficient, is defined as the ratio of the amplitude of the reflected (refracted) wave to the amplitude of the incident wave. The factor depends on the angle of incidence, wave velocities, and possibly frequency, depending on the interface condition. In this chapter, we introduce a boundary condition approach for calculating these factors. We use this approach for the interface between two semi-infinite medium spaces: solid–solid, solid–liquid, and liquid–solid. If the reader would like to calculate reflection and refraction factors for a thin interface solid (and liquid) layer between two different media, it is recommended to follow guidelines established by Jiao and Rose (1991) and from a “spring” model (Pilarski and Rose 1998a,b; Pilarski et al. 1990). These cases are also discussed by Rose (1999).