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Nonlinear effects of micro-cracks on long-wavelength symmetric Lamb waves

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


Ultrasonics 90 (2018), S.98-108
ISSN: 0041-624X
Deutsche Forschungsgemeinschaft DFG
MA 1074/11-3
Fraunhofer IKTS ()
micro-crack; effective material properties; FEM; penny-shaped crack; Hertzian contact; Nonlinear ultrasound; harmonic generation; perturbation theory; non-destructive evaluation; lamb wave

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. The orientation of the micro-cracks was either totally random or fully aligned. 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 only the odd harmonics with amplitudes proportional to the square 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.