The acoustic nonlinearity measurement of ultrasonic waves are being extensively researched as a promising nondestructive evaluation element. In the condition of constant propagation distance and wave number, many researchers have measured the second-order relative acoustic nonlinear parameter, β′, that can be simply defined as the ratio of the amplitude of the second harmonic frequency component to the amplitude squared of the fundamental frequency component and compared them in order to identify the acoustic nonlinearity variation according to material degradation. In this study, we extended this concept to the third-order relative acoustic nonlinear parameter, γ′, by defining it as the ratio of the amplitude of the third harmonic frequency component to the amplitude cubed of the fundamental frequency component. To investigate its effectiveness as a nondestructive evaluation element for the material property degradation, both the second-order acoustic relative nonlinear parameter and the third-order relative acoustic nonlinear parameter were measured for the aluminum specimens processed by heat treatment for the different times and then contrasted each other. From the experimental results, the third-order acoustic relative nonlinear parameter was more sensitive than the second-order relative acoustic nonlinear parameter that has been widely used although the amplitude of the third harmonic frequency component was lower than the amplitude of the second harmonic frequency component.
