Ultrasonic NDE of Adhesive Bonds: The Inverse Problem

Over the past quarter century, a wide variety of ultrasonic techniques have been developed to determine the phase velocity and thickness of elastic plates. Techniques to measure the phase velocity include toneburst [1–4], separable pulse methods [5–7], and spectroscopy [8–11]. These classical methods require that the specimen be thick enough such that two successive echoes from the front and the back faces of the specimen, respectively, be separable in the time domain. Kinra and Dayal [12], developed a through transmission technique which removes this particular limitation of the classical methods. This technique works satisfactorily for the measurement of the phase velocity for specimens whose thickness is greater than one-half of the wavelength; for thinner specimens, however, their numerical algorithm runs into convergence problems. Moreover, their numerical algorithm cannot be used to determine thickness at any wavelength. The reasons for their convergence problems are discussed in detail by Iyer, Hanneman and Kinra [13]. They demonstrated that a detailed sensitivity analysis is a necessary pre-requisite for the development of a robust inversion algorithm. Accordingly, a new inversion scheme based on the method of least squares was developed by Iyer and Kinra to determine thickness from the measurements of phase, magnitude and complex spectrum, respectively, [14–17]. In all of the above ultrasonic methods only one parameter can be determined i.e., an accurate knowledge of thickness is required to determine the wavespeed and vice versa. This defines the central objective of the present work: In this paper we present a technique for determining, simultaneously, the thickness and wavespeed of a thin layer