Harmonic Scattering of SH Waves from a Localized Damage: Finite Element Studies

Abstract

Interaction of the monochromatic ultrasonic wave with the uniformly distributed micro-scale damages modeled as a weakly nonlinear solid generates higher harmonics. In practice, most of the metallic components under fatigue and fracture introduce highly localized early-stage damages like local plasticity and region of micro-cracks resulting in shear bands, etc. Theoretical studies by Tang (2012), Wang and Achenbach (2017), Kube (2018), and Wang et.al. (2019) on the interaction of the ultrasonic waves with localized material nonlinearities discuss the interesting effects of the scattered harmonic waves. Low amplitudes of the backscattered harmonic waves and the requirement of a specific set of wideband transducers make experimental studies hard. On the other hand, finite element studies presented in this paper demonstrate the interesting nature of harmonic scattering of the SH waves which will be helpful for the effective design of the laboratory experiments. Generation of backscattered Lamb waves by the interaction of SH wave with local damage due to monochromatic wave is verified with the analytical solution presented by Wang et.al. (2019). Only odd harmonics of the forward scattered SH waves are noted and only even harmonics of both backscattered and forward scattered Lamb waves are noted. Higher amplitudes of static components of Lamb waves are observed due to their cumulative nature similar to higher harmonics. The effect of harmonic scattering in nonlinear guided wave mixing is also studied by considering one-way and two-way two-wave mixing of SH waves. A greater number of sum and difference frequencies along with the odd and even harmonics of both the backscattered and forward scattered waves are noted in codirectional wave mixing, as the complete local damage region is covered by the mixing zone. In two-way mixing, the zero group velocity Lamb waves are generated at the local nonlinear material region. Both backscattered and forward scattered waves contain only Lamb waves with sum and difference frequencies and corresponding odd and even harmonics. To understand the effect of the intensity and size of the localized nonlinear material region various studies are carried out by scaling nonlinear material parameters and geometric size of the local damages (0-20 mm). Observed various characteristics of harmonically scattered waves show their potential in quantifying the intensity, size, and position of local damages by solving simple inverse problems.