Propagation characteristics and damage detection in metallic materials using nonlinear acoustic waves

The propagation properties of nonlinear acoustic waves are of paramount importance for detecting damage in metallic materials. Currently, the perturbation method, expanded with respect to the nonlinear coefficient, is a prevalent approach for solving the nonlinear acoustic wave equation in metals. However, this method falls short when dealing with strong nonlinearity, particularly in cases where the nonlinear coefficient significantly exceeds unity, as is often the case with steel. In such instances, the nonlinear coefficient cannot be regarded as a minor or micro-perturbation term. While the solution may be satisfactory for low-order harmonics or waves traveling over short distances, it lacks the necessary accuracy for high-order harmonics or waves propagating over extended distances. In our research, we opted to utilize the Mach number as the micro-perturbation term and expanded the nonlinear acoustic wave equation accordingly. By decomposing the equation into a linear component and a series of nonlinear terms, we were able to derive the harmonics of various orders. Based on the specific parameters of metallic materials, we obtained the propagation characteristics of the second- and third-order harmonic waves through a high-order solution. Our findings reveal that as the amplitude of the excitation source and the propagation distance increase, both the second- and third-order harmonics exhibit an initial rise, followed by a subsequent decline. This results in the presence of extreme points within their relationship curves. Notably, these extreme points occur earlier in materials with higher nonlinearity or in the presence of micro-damage. These results have been validated through corresponding experiments conducted on metallic materials, thereby establishing a theoretical foundation for the evaluation of material damage using nonlinear acoustics.