Numerical evaluation of the sideband peak count method for nonlinear ultrasonic damage detection

It is well established in the scientific literature that a material's nonlinear response is much more sensitive to increasing dislocation density, microcrack nucleation, and other types of early material degradation than its linear response. The nonlinear elastic behavior of materials can be studied using various nonlinear ultrasonic techniques (NLU). However, they are all significantly more complex than their linear counterparts; therefore, they are often limited to a laboratory environment, and their field of application in industry is very narrow. In recent years, numerous publications have proposed new techniques based on the so-called Sideband Peak Count (SPC) method that utilizes relatively simple ultrasonic measurements to evaluate the degree of nonlinearity in materials. In contrast to conventional NLU NDE techniques, such as harmonic generation or wave mixing, SPC currently lacks a rigorous theoretical basis. To fill this gap, this paper presents computational results obtained under the assumption of classical quadratic nonlinearity using the COMSOL Multiphysics finite element software package. Parametric studies of four relevant variables ‒ excitation level, material nonlinearity, localized nonlinearity caused by a defect, and linear scattering caused by a geometrical feature ‒ were conducted. All the results of this numerical parametric study indicate that the SPC method and the SPC damage parameter named SPC-Index (SPC-I) offer limited sensitivity to changes in the level of classical acoustic nonlinearity at typical excitation levels used in ultrasonic NDE.