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Characterizing micro-crack distributions with nonlinear acoustic surface and wedge waves

: Rjelka, Marek; Köhler, Bernd; Pupyrev, Pavel; Mayer, Andreas


Institute of Electrical and Electronics Engineers -IEEE-:
IEEE International Ultrasonics Symposium, IUS 2017 : 6-9 September 2017, Washington, DC, USA
Piscataway, NJ: IEEE, 2017
ISBN: 978-1-5386-3383-0
ISBN: 978-1-5386-3382-3
ISBN: 978-1-5386-3384-7
1 S.
International Ultrasonics Symposium (IUS) <2017, Washington/DC>
Fraunhofer IKTS ()
micro-crack; surface wave; wedge waves; Nonlinear ultrasound; nonlinearity; material characterization; third order elastic constant; second harmonic generation; stress-strain relation

Background, Motivation and Objective: Pre-fatigue damage can have drastic effects on the elastic nonlinearity of solid materials, offering the possibility of extracting spatially resolved information on the pre-fatigue state from nonlinear effects on guided waves, like harmonic generation. Of particular interest are surface and wedge acoustic waves. They are sensitive to surfaces and edges and are non-dispersive in homogeneous media, at planar surfaces and – in the case of wedge waves – perfect wedge tips on the scale of the wavelength. This favors nonlinear effects. Our current investigations focus on the nonlinearity generated by micro-cracks with the goal of extracting information about their spatial and orientational distribution from the efficiency of second harmonic generation and its dependence on amplitude and frequency of the input wave. The linear dispersion arising from a spatially inhomogeneous distribution of the micro-cracks is accounted for in the propagation of the second harmonic.
Statement of Contribution/Methods: Finite element simulations have been carried out for a model system of randomly oriented micro-cracks containing a Hertzian contact. Nonlinear stress-strain relations have been computed for this system and second-order and third-order elastic constants have been extracted. A simple micro-mechanical model has been fitted to the simulation results and allows for an extension to textured orientations of the micro-cracks. On the basis of the nonlinear stress-strain relations, the efficiency of second harmonic generation is calculated for Rayleigh waves and for wedge acoustic waves.
Results/Discussion: Results of calculations are presented and discussed for the acoustic nonlinearity parameter (ANP) of wedge acoustic waves in wedges with textured distributions of micro-cracks. An example is shown in the Figure. Consequences of non-analytical behavior (a kink or a kink of the derivative) of the stress-strain relations on second-harmonic generation of surface and wedge waves are analyzed in detail. An inversion method is introduced for the determination of the depth profile of the distribution of micro-cracks from the ANP of surface waves.