One-dimensional harmonic scattering from a localized damage modeled as symmetric and asymmetric hysteretic nonlinearity

Abstract

A monochromatic ultrasonic wave propagating in damaged material modeled as quadratic, cubic, and hysteretic nonlinearities generates higher harmonics as reported in various theoretical, computational, and experimental studies. In metals under fatigue, certain grains get plastically deformed due to their preferentially oriented slip planes in certain regions and form localized damages like slip bands and micro-cracks. To capture the complex nature of the locally damaged material, local damage is modeled as symmetric and asymmetric hysteretic nonlinearity in this study. A one-dimensional domain is discretized as a long spring-mass chain with few spring-mass elements at the center of a domain modeled as hysteretic elements. Both the back and forward scattered waves from the symmetric hysteretic model contain only odd harmonics and in an asymmetric hysteretic model, both the odd and even harmonics observed. The amplitude of fundamental harmonics of the forward scattered wave decreases with an increase in local damage size and the amplitudes of higher harmonics increases due to an energy transfer from fundamental harmonics in both symmetric and asymmetric hysteretic models. Due to interference of backscatterd waves from two interfaces of local damage, backscattered higher harmonics amplitudes shows increasing and decreasing nature with an increase in local damage size.