Extraction of depth profiles of third-order elastic constants in cracked media

Rjelka, Marek; Koehler, Bernd; Mayer, Andreas

doi:10.1063/1.4974610

Cited by 4 publications

(5 citation statements)

References 16 publications

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“…In their study [ 6 ], a hyperelastic constitutive law was derived and implemented to simplify the micro-crack model. Rjelka et al [ 25 ] have determined the relationship between material properties (third-order elastic constants) and inhomogeneous distributions of micro-cracks. They then investigated the acoustic nonlinearity parameter for surface acoustic waves based on second harmonic generation.…”

Section: Introductionmentioning

confidence: 99%

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Generation Mechanism of Nonlinear Rayleigh Surface Waves for Randomly Distributed Surface Micro-Cracks

Ding

Zhao

et al. 2018

Materials

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This paper investigates the propagation of Rayleigh surface waves in structures with randomly distributed surface micro-cracks using numerical simulations. The results revealed a significant ultrasonic nonlinear effect caused by the surface micro-cracks, which is mainly represented by a second harmonic with even more distinct third/quadruple harmonics. Based on statistical analysis from the numerous results of random micro-crack models, it is clearly found that the acoustic nonlinear parameter increases linearly with micro-crack density, the proportion of surface cracks, the size of micro-crack zone, and the excitation frequency. This study theoretically reveals that nonlinear Rayleigh surface waves are feasible for use in quantitatively identifying the physical characteristics of surface micro-cracks in structures.

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Section: Introductionmentioning

confidence: 99%

“…In this work, and different from Oberhardt et al [ 6 ] and Rjelka et al [ 25 ], the simplified micro-crack model is not used. We employ a true contact model for modelling the micro-cracks.…”

Section: Introductionmentioning

confidence: 99%

Generation Mechanism of Nonlinear Rayleigh Surface Waves for Randomly Distributed Surface Micro-Cracks

Ding

Zhao

et al. 2018

Materials

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“…In the case of aligned micro-cracks, the initial growth rates are proportional to the parameter τ 1 in the nonanalytic stress-strain relation. This parameter can be quantified by finite-element simulations, which have been carried out for homogeneous distributions of aligned flat micro-cracks in the high-strength metallic alloy IN718 [13].…”

Section: Discussionmentioning

confidence: 99%

“…Kinks in this relation are known to be generated by flat micro-cracks of the "kissing bond" type [9] due to the difference of their elastic response to tensile and compressive stress. Non-analytic behavior of the stress-strain relation has also been found in finite element simulations of solids with micro-cracks that have an internal structure [13].…”

Section: Introductionmentioning

confidence: 90%

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Nonlinear effects of micro-cracks on acoustic surface and wedge waves

Rjelka

Pupyrev

Koehler

et al. 2018

Low Temperature Physics

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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.

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