Finite difference method analysis of ultrasonic nonlinearity in partially degraded material

Abstract

In recent years, the fact that the nonlinear acoustic effect has a strong correlation to the microdeformation of materials has been considered to be useful for non-destructive evaluation (NDE) of material degradation. However, in the past, most research considered only the case in which the material degradation was distributed evenly along the path of the probing wave. In contrast, in this study, the nonlinear behavior of ultrasonic waves in a partially degraded material is considered. For this purpose, the finite difference method (FDM) model for the nonlinear wave equation is developed considering only 1-D longitudinal wave motion and the contribution of the partial degradation in the material to the measurable nonlinear parameter is analyzed quantitatively. In the simulation, three types of distribution of degradation are considered; single point, discrete distribution and continuous distribution. Simulation results reveal that the degradation level and the range of degradation have a strong correlation with the nonlinear parameter β which is estimated by measuring the harmonic generation. In order to verify the validity of this numerical analysis method, the simulation results in the case of continuous distribution of degradation are compared with the previous experimental results, and they are found to show a similar tendency.