Time-domain analysis of ultrasonic reflection from imperfect interfaces

Abstract

The specular reflection of ultrasound from defect covered bond planes is analyzed in the time-domain using the independent scattering model for incident plane waves. We hypothesize that the early-time asymptotics of the reflected wave are given exactly by the independent scattering model for waves that are normally incident on the bond plane. For non-normal incidence, a more restricted result is available for reflected longitudinal waves. We present theoretical arguments for the plausibility of the hypothesis. Experimental measurements made on two sets of model bond planes test and support the hypothesis. Our motivations are as follows. An effort is underway to develop nondestructive methods for estimating the integrity of metal-metal bonds. These methods primarily focus on the reflection of ultrasound in the long wavelength limit, where one can estimate an effective elastic constant. People have characterized the overall quality of the bond in terms of this elastic constant. However, one cannot in this way infer more detailed information such as the average size of the defects or their area fraction. Higher frequency probes, which do provide more detailed information, have been studied in the independent scattering model. Consequently, we have (1) extended the independent scattering model to the time-domain, and (2) shown that it is asymptotically correct for early-time reflections from a defect covered plane (the bond plane). We expect that time-domain methods, based on the analysis presented in this paper, will form the basis for a more rigorous technique for determining the area fraction and the average defect size.