Static displacement component and its significance in nonlinear ultrasonic measurements
10 Mar 2008-Vol. 975, Iss: 1, pp 1282-1289
TL;DR: In this paper, the authors present a numerical simulation of the propagation of an ultrasonic wave through a damaged material with focus on the generation of a static displacement component and suggest a simplified technique for measuring it.
Abstract: In the recent times nonlinear ultrasonics is being extensively studied to explore its viability to discern early material damage. The propagation of an ultrasonic wave through a damaged material leads to the generation of the harmonics of the original wave. The second harmonic generated quantifies the amount of nonlinearity present in the material and is related to the third order elastic constants of the material. However if the frequency spectrum of the transmitted wave is examined we find that there is an induced static displacement component due to the nonlinearities present in the material. This static displacement component is also related to the third order elastic constants of the material. The present paper presents a numerical simulation of propagation of an ultrasonic wave through a damaged material with focus on the generation of a static displacement component and suggests a simplified technique for measuring it. Demonstrating the fact that an asymmetry in the stress strain relationship of the material is required for the generation of a static displacement component, this paper explores its dependence on various parameters like the input amplitude, input frequency, propagation distance and the nonlinearity parameters of the material. The numerical simulations are validated against existing theories for generation of static displacement.
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TL;DR: It is shown that an eigenstrain is induced when a wave propagates through an elastic solid with quadratic nonlinearity, but the mean stress and the total mean strain are not.
Abstract: This letter demonstrates that an eigenstrain is induced when a wave propagates through an elastic solid with quadratic nonlinearity. It is shown that this eigenstrain is intrinsic to the material, but the mean stress and the total mean strain are not. Instead, the mean stress and total means strain also depend on the boundary conditions, so care must be taken when using the static deformation to measure the acoustic nonlinearity parameter of a solid.
26 citations
TL;DR: The symmetric zero-frequency mode induced by weak material nonlinearity during Lamb wave propagation is explored for the first time and it is theoretically confirmed that, unlike the second harmonic, phase-velocity matching is not required to generate the zero- frequency mode and its signal is stronger than those of the nonlinear harmonics conventionally used.
Abstract: The symmetric zero-frequency mode induced by weak material nonlinearity during Lamb wave propagation is explored for the first time. We theoretically confirm that, unlike the second harmonic, phase-velocity matching is not required to generate the zero-frequency mode and its signal is stronger than those of the nonlinear harmonics conventionally used, for example, the second harmonic. Experimental and numerical verifications of this theoretical analysis are conducted for the primary S0 mode wave propagating in an aluminum plate. The existence of a symmetric zero-frequency mode is of great significance, probably triggering a revolutionary progress in the field of non-destructive evaluation and structural health monitoring of the early-stage material nonlinearity based on the ultrasonic Lamb waves.
15 citations
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