Nonlinear interaction of ultrasound with an unbounded rough interface

Abstract

Kissing bonds are one type of the defects in friction stir welds (FSWs), and often difficult to detect using linear ultrasound. Under the insonification of intensive ultrasound, they may show nonlinear behavior. This nonlinearity has been exploited to detect such deficient bonds. A kissing bond can be treated as an imperfect interface between rough surfaces in contact (an imperfect rough interface). Motivated by the practical problem, a theoretical model has been developed for calculating the nonlinear interaction of ultrasound with an imperfect planar rough interface. The model is established based on elastodynamic theory. It is a first-order differential equation governing the ultrasonic response of the interface (interface opening displacement). The model can be used for various planar interfaces like smooth interfaces, rough interfaces with either linear or nonlinear relation between contact force and interface opening, and rough interfaces with a hysteretic response to ultrasonic load. Analytical solutions are available for smooth interfaces, rough interfaces with linear relation between contact force and interface opening, and rough interfaces with piece-wise linear bistability (causing hysteresis). The model is applied to the prediction of experimental data from a single interface formed by compressing two copper cylinders together. The results show that the proposed model for rough surfaces may give a better prediction than Richardson's theory that is built for smooth interfaces and may give overestimation for rough interfaces.