Necessary and sufficient conditions for resonant mixing of plane waves in elastic solids with quadratic nonlinearity

Acoustic nonlinearity parameters in hyperelastic solids with quadratic nonlinearity

In general, the nonlinear behavior of an elastic wave in isotropic hyperelastic solids with quadratic nonlinearity depends on five independent elastic constants, namely, the three third-order elastic constants and two second-order elastic constants. In this article, we show that such nonlinear behavior can be described fully by only three independent non-dimensional parameters if the wave motion is two-dimensional. Furthermore, if the motion is a plane wave, only two independent non-dimensional parameters are needed to fully describe the nonlinear behavior of the wave. These results are useful for conducting numerical simulations and for interpreting experimental measurement data.

Phased array-based nonlinear wave mixing technique: Application to lack-of-fusion porosity characterization in additively manufactured metals

The objective of this research is to demonstrate the effectiveness of a phased array-based nonlinear wave mixing technique to characterize internal, localized microscale damage in an additively manufactured (AM) component. By using phased arrays for the generation of the incident waves, it is possible to produce a nonlinear wave mixing scanning technique without the need for immersion or changing coupling conditions. The phased arrays can be configured to generate incident waves in multiple directions that meet the resonance conditions required for nonlinear wave mixing at a variety of internal locations. This allows for the scanning of a specimen without the removal and re-coupling of the source transducers, leading to greater scanning speed and repeatability. To demonstrate the accuracy of this phased array wave mixing approach, measurements of acoustic nonlinearity in an AM component are first made with a bulk wave second harmonic generation through thickness measurement. Next, nonlinear wave mixing measurements are made with single element transducers to confirm the sensitivity of the proposed nonlinear wave mixing approach to lack-of-fusion porosity in AM metals. Finally, phased arrays are used to highlight the effectiveness of the proposed nonlinear wave mixing technique in these same AM components.

Numerical model of nonlinear elastic bulk wave propagation in solids for non-destructive evaluation

Nonlinear ultrasonic techniques can be difficult and non-intuitive to understand due to the range of wave mixing combinations available between similar or different wave modes. To overcome this, a numerical model that uses a Finite Difference Time Domain (FDTD) scheme, without a staggered grid system, to solve the nonlinear elastic bulk wave equations in two dimensions is proposed in this paper, with the purpose of better understanding nonlinear ultrasonic techniques. Both material and geometrical nonlinearities are considered and a stress-type boundary condition is used to model the excitation. The energy transfer between frequency bands is shown and the amplitude trend of the harmonics are validated against available theories. It is then used to simulate the nonlinear ultrasonic field generated by a finite-size element of an array in a solid to better understand its behaviour. An array-element directivity at the second harmonic frequency is shown. Since the FDTD model does not account for attenuation, a correction using a ray-based approach is applied to the simulated result for direct comparison against experimental measurements. The field obtained from a typical array used in non-destructive testing is then simulated to characterise its behaviour. Experimental comparison of the nonlinear displacement fields for different focal positions showed good agreement, further validating the FDTD model. This FDTD model opens opportunities to virtually experiment and design appropriate nonlinear ultrasonic array inspections whilst isolating and understanding contribution from material nonlinearity.

Envelope correction for shear-longitudinal collinear wave mixing to extract absolute nonlinear acoustic parameters

This paper addresses the effect of the excitation envelope on the generated nonlinear resonant signal (NRS) for collinear wave mixing of shear and longitudinal waves. The aim is to explore how the absolute material nonlinearity can be extracted accurately for any enveloped sinusoidal excitation signal. A finite difference time domain (FDTD) model was built to simulate the effect of input waveforms on the NRS. A change in the measured nonlinearity was seen as the input waveforms were changed from rectangular to Hanning windowed tone burst. The required waveform correction was derived theoretically and validated against the FDTD simulation. Experimental measurements were carried out for different waveforms at several input amplitudes, demonstrating its influence over the NRS. The theoretically derived correction factor, which is required to map the small NRS to the rectangular tone burst resonant amplitude, was validated experimentally. The correction was then used to extract one the fundamental Murnaghan constant (m). Comparatively, Hanning tone burst inputs showed lower variance in the extracted material property due to better control of the frequency bandwidth, relative to that of the transducers. This opens the opportunity to using Hanning windowed tone burst inputs reliably for the measurement of the absolute nonlinearity parameter and m through collinear shear-longitudinal wave mixing.

Interaction of elastic waves in solids with quadratic and cubic nonlinearity

This article investigates the interactions of two-plane waves in weakly nonlinear elastic solids containing quadratic and cubic nonlinearity. The analytical solutions for generated combined harmonic waves are derived using the Green's function approach applied to a generated system of quasi-linear equations of motion. Wave mixing solutions are obtained and include shape functions that permit closed-form solutions for a variety of interaction geometries. An explicit example is highlighted for a spherical interaction volume assuming isotropic elastic constants. Several parameters of the generated field after mixing are analyzed including resonant and nonresonant mixing, the role of interaction angle, and the frequencies of the two incident waves. Wave mixing offers the potential for sensing localized elastic nonlinearity and the present model can be used to help design experimental configurations.

Thermo-acoustoelastic effect of Rayleigh wave: Theory and experimental verification

Previous studies showed that the thermally-induced ultrasonic bulk wave velocity change could be used to measure acoustoelastic coefficients and third-order elastic constants of elastic materials. This method is naturally immune from the ambient temperature effect and has improved sensitivity and a simpler test setup than the conventional acoustoelastic test. However, Rayleigh wave is preferred for thick components or structures with only one accessible surface. In this work, the thermo-hyperelastic constitutive equation, along with acoustoelastic theory, is used to derive the expression of the thermo-acoustoelastic coefficient (TAEC) of Rayleigh wave. The numerical relationship between the TAEC of Rayleigh wave and Murnaghan constants (l, m and n) are given for common metals. The TAEC expressions for Rayleigh wave and shear wave are similar, and both are dominated by the constant m. The TAEC of Rayleigh wave was measured on an aluminum 6061 specimen using the thermal modulation experiment in a temperature range of 22 ∼35 °C. The measured TAEC shows good agreement with the theoretical calculation. Then the third-order elastic constants were calculated based on TAECs of bulk waves and Rayleigh wave.

One-way Lamb and SH mixing method in thin plates with quadratic nonlinearity: Numerical and experimental studies

This paper numerically and experimentally investigates the resonant behavior of one-way Lamb and SH (shear horizontal) mixing method in thin plates with quadratic nonlinearity. When the primary S₀-mode Lamb waves and SH₀ waves mix in the region with quadratic nonlinearity, both numerical and experimental results verify the generation of the resonant SH₀ waves if the resonance condition [Formula: see text] is satisfied. Meanwhile, we find that the acoustic nonlinear parameter (ANP) increases monotonously with material quadratic nonlinearity, the length of the damage region and the frequency of the resonant wave. Furthermore, the damage region can be located by the time-domain signal of the resonant wave based on one-way S₀-SH₀ mixing method. This study numerically and experimentally reveals that one-way Lamb and SH mixing method is feasible to quantitatively evaluate and locate the damage region of quadratic nonlinearity in thin plates.

Experimental and Numerical Investigation of the Micro-Crack Damage in Elastic Solids by Two-Way Collinear Mixing Method

This study experimentally and numerically investigated the nonlinear behavior of the resonant bulk waves generated by the two-way collinear mixing method in 5052 aluminum alloy with micro-crack damage. When the primary longitudinal and transverse waves mixed in the micro-crack damage region, numerical and experimental results both verified the generation of resonant waves if the resonant condition ωL/ωT=2κ/(κ−1) was satisfied. Meanwhile, we found that the acoustic nonlinearity parameter (ANP) increases monotonously with increases in micro-crack density, the size of the micro-crack region, the frequency of resonant waves and friction coefficient of micro-crack surfaces. Furthermore, the micro-crack damage in a specimen generated by low-temperature fatigue experiment was employed. It was found that the micro-crack damage region can be located by scanning the specimen based on the two-way collinear mixing method.