Nonlinear effects of micro-cracks on acoustic surface and wedge waves
M. Rjelka1, P.D. Pupyrev2,3, B. Koehler1, and A.P. Mayer3
1Fraunhofer IKTS, D-01109 Dresden, Germany
2Prokhorov General Physics Institute of the Russian Academy of Sciences, Moscow 119991, Russia
3HS Offenburg, University of Applied Sciences, D-77723 Gengenbach, Germany
Received March 12, 2018
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 micro-mechanical 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 ma-trix material. The growth rate of the second harmonic of Rayleigh waves has also been determined for micro-crack distributions with random orientation, using a model expression for the strain energy in terms of strain in-variants known in a geophysical context.
PACS: 43.35.+d Ultrasonics, quantum acoustics, and physical effects of sound;
Key words: micro-cracks, surface acoustic waves, wedge waves, nonlinearity, harmonic generation.
Published online: May 28, 2018