Determination of acoustic nonlinearity parameter (β) using nonlinear resonance ultrasound spectroscopy: Theory and experiment

Nonclassical nonlinear elasticity of crystalline structures

Hysteretic elastic nonlinearity has been shown to result in a dynamic nonlinear response which deviates from the known classical nonlinear response; hence this phenomenon was termed nonclassical nonlinearity. Metallic structures, which typically exhibit weak nonlinearity, are typically categorized as classical nonlinear materials. This article presents a material model which derives stress amplitude dependent nonlinearity and damping from the mesoscale dislocation pinning and breakaway to show that the lattice defects in crystalline structures can give rise to nonclassical nonlinearity. The dynamic nonlinearity arising from dislocations was evaluated using resonant frequency shift and higher order harmonic scaling. The results show that the model can capture the nonlinear dynamic response across the three stress ranges: linear, classical nonlinear, and nonclassical nonlinear. Additionally, the model also predicts that the amplitude dependent damping can introduce a softening-hardening nonlinear response. The present model can be generalized to accommodate a wide range of lattice defects to further explain nonclassical nonlinearity of crystalline structures.

Investigation of the relationship between classical and nonclassical ultrasound nonlinearity parameters and microstructural mechanisms in metals

This research studies two nonlinear ultrasound techniques: second harmonic generation and nonlinear resonant ultrasound spectroscopy, and the relationship to microstructural mechanisms in metals. The results show that there is a large change in both the classical, β, and nonclassical, α, ultrasound nonlinearity parameters in response to three specific microstructural mechanisms: precipitate growth in and along the grain boundaries, dislocations, and precipitate pinned dislocations. For example, both β and α increase with the growth of the precipitate radii (precipitate-pinned-dislocations). Additionally, both β and α increase when there is a growth of precipitates in and along the grain boundaries. As expected, β and α decrease when there is a removal of dislocations in the material. The relationship between β and α, and the microstructural mechanisms studied provide a quantitative understanding of the relationship between measured nonlinearity parameters and microstructural changes in metals, helping to demonstrate the possibility of using these two independent, but complementary, nonlinear ultrasound procedures to monitor microstructural damage.

Research on perturbation method for nonlinear elastic waves

This paper explores the propagation of nonlinear elastic waves in a two-dimensional isotropic medium. The analytical expressions of first-order potentials corresponding to second harmonic acoustic components are obtained and discussed by using the perturbation method. Based on the careful theoretical analysis, it is shown that the first-order P wave always has a resonant term, which is proportional to the propagation distance in the condition of simultaneous excitation of the P wave. On the contrary, the first-order SV wave does not have any cumulative effect. Moreover, the nonlinear interactions between the P wave and SV are also presented.

Steering the propagation direction of a non-linear acoustic wave in a solid material

In this research non-collinear wave mixing is used as a non-destructive testing method where the amplitude of the scattering wave contains information on the condition of a material. The practical implementation of non-collinear wave mixing as a non-destructive testing technique is limited by many factors such as the geometry and shape of the structure, the accessibility to the specimen's surfaces and the ultrasonic sensors available to perform measurements. A novel approach to steer the propagation direction of a generated wave from the mixing of two incident acoustic waves is proposed. The angle of the scattering wave is controlled by the frequencies of the two interaction waves, rather than by the angle between these waves. The scattering amplitude was analytically solved for the longitudinal plus shear interaction process. The analytical solution was validated with experiments. The model qualitatively agrees with the experiments. Furthermore, the possibility to use a wider range of excitation frequencies of the incident waves was found. This is a great advantage in applications where the space and access to the specimen under test is limited.

Multiscale model to study dislocation dynamics in nonlinear resonance spectroscopy of crystalline solids

This letter reports on a multi-scale model which captures the dislocation dynamics due to applied vibration stress and its influence on the bulk nonlinear response in a nonlinear resonance spectroscopy experiment. Due to dislocation dynamics, a sinusoidal variation in frequency shift could be observed at the low applied stress range, which was consistent with NRS experiments carried out on cold drawn steel. Using the model, NRS response to "Buck hook" phenomenon was also explored. The results showed that the frequency shift can exhibit three strain regions similar to non-classical nonlinear materials. Further discussions highlight the non-classical nonlinear nature of crystalline solids with lattice defects.

Linear Versus Nonlinear Acoustic Probing of Plasticity in Metals: A Quantitative Assessment

The relative dislocation density of aluminum and copper samples is quantitatively measured using linear Resonant Ultrasound Spectroscopy (RUS). For each metallic group, four samples were prepared with different thermomechanical treatments in order to induce changes in their dislocation densities. The RUS results are compared with Nonlinear Resonant Ultrasound Spectroscopy (NRUS) as well as Second Harmonic Generation (SHG) measurements. NRUS has a higher sensitivity by a factor of two to six and SHG by 14⁻62%. The latter technique is, however, faster and simpler. As a main result, we obtain a quantitative relation between the changes in the nonlinear parameters and the dislocation density variations, which in a first approximation is a linear relation between these differences. We also present a simple theoretical expression that explains the better sensitivity to dislocation content of the nonlinear parameters with respect to the linear ones. X-Ray diffraction measurements, although intrusive and less accurate, support the acoustics results.