On the emergence of the second harmonic shear horizontal wave in presence of tangential prestress

Abstract

Nonlinear ultrasonic techniques have significant advantages in characterizing incipient defects of materials. The classical nonlinear ultrasonic theory indicates that a primary longitudinal wave can generate a second harmonic longitudinal wave due to the material nonlinearity (MN) or contact acoustic nonlinearity (CAN). However, in both MN and CAN, a second harmonic shear horizontal (SH) component generated from a normally-incident SH wave has not been reported. In this work, a time domain spectral finite element method combined with the bi-potential contact theory is extended to simulate the CAN problems with prestresses. Numerical verifications are performed to show the robustness and accuracy of the developed method. After that, the nonlinear interactions between the SH wave and frictional interfaces under complex prestresses are investigated. It is found for the first time that when there are tangential prestresses at the frictional interfaces or crack surfaces, a primary SH wave of normal incidence can generate the second harmonic SH wave. A theoretical model is then proposed to interpret this new phenomenon. It is found that the even SH wave harmonics result from the asymmetric sliding of the frictional interface induced by the tangential prestresses. This asymmetric sliding mechanism can be compared with the breathing behavior of a crack caused by an incident longitudinal wave. The findings of this work could enrich the understanding of contact acoustic nonlinearity behavior of the SH wave and promote the development of related nondestructive evaluation techniques.