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Elastic constants of components are usually determined by tensile tests in combination with ultrasonic
experiments. However, these properties may change due to e.g. mechanical treatments or service conditions during
their lifetime. Knowledge of the actual material parameters is key to the determination of quantities like residual
stresses present in the medium. In this work the acoustic nonlinearity parameter (ANP) for surface acoustic waves is
examined through the derivation of an evolution equation for the amplitude of the second harmonic. Given a certain
depth profile of the third-order elastic constants, the dependence of the ANP with respect to the input frequency is
determined and on the basis of these results, an appropriate inversion method is developed. This method is intended
for the extraction of the depth dependence of the third-order elastic constants of the material from second-harmonic
generation and guided wave mixing experiments, assuming that the change in the linear Rayleigh wave velocity is
small. The latter assumption is supported by a 3D-FEM model study of a medium with randomly distributed microcracks as well as theoretical works on this topic in the literature.

For an elastic medium containing a homogeneous distribution of micro-cracks, an effective one-dimensional stress-strain relation has been determined with finite element simulations. In addition to flat micro-cracks, voids were considered that contain a Hertzian contact, which represents an example for micro-cracks with internal structure. The orientation of both types of micro-cracks was fully aligned or, for flat micro-cracks, totally random. For micro-cracks with Hertzian contacts, the case of random orientation was treated in an approximate way. The two types of defects were found to give rise to different degrees of non-analytic behavior of the effective stress-strain relation, which governs the nonlinear propagation of symmetric (S0) Lamb waves in the long-wavelength limit. The presence of flat micro-cracks causes even harmonics to grow linearly with propagation distance with amplitudes proportional to the amplitude of the fundamental wave, and gives rise to a static strain. The presence of the second type of defects leads to a linear growth of all harmonics with amplitudes proportional to the power 3/2 of the fundamental amplitude, and to a strain-dependent velocity shift. Simple expressions are given for the growth rates of higher harmonics of S0 Lamb waves in terms of the parameters occurring in the effective stress-strain relation. They have partly been determined quantitatively with the help of the FEM results for different micro-crack concentrations.

Micro-cracks give rise to non-analytic behavior of the stress-strain relation. For the case of a homogeneous spatial distribution of aligned flat micro-cracks, the influence of this property of the stress-strain relation on harmonic generation is analyzed for Rayleigh waves and for acoustic wedge waves with the help of a simple micromechanical model adopted from the literature. For the efficiencies of harmonic generation of these guided waves, explicit expressions are derived in terms of the corresponding linear wave fields. The initial growth rates of the second harmonic, i.e., the acoustic nonlinearity parameter, has been evaluated numerically for steel as matrix material. The growth rate of the second harmonic of Rayleigh waves has also been determined for microcrack distributions with random orientation, using a model expression for the strain energy in terms of strain invariants known in a geophysical context.