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Cite this article as: P. Blanloeuil, A. Meziane, C. Bacon, 2D Finite Element modeling of the non-collinear mixing method for detection and characterization of closed cracks, NDT&E International, http://dx.doi.org/10.1016/j. ndteint. 2015.08.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractThe non-collinear mixing technique is applied for detection and characterization of closed cracks.The method is based on the nonlinear interaction of two shear waves generated with an oblique incidence, which leads to the scattering of a longitudinal wave. A Finite Element model is used to demonstrate its application to a closed crack. Contact acoustic nonlinearity is modeled using unilateral contact law with Coulomb's friction. The method is shown to be effective and promising when applied to a closed crack. Scattering of the longitudinal wave also enables us to image the crack, giving its position and size.

The nonlinear interaction of shear waves with a frictional interface are presented and modeled using simple Coulomb friction. Analytical and finite difference implementations are proposed with both in agreement and showing a unique trend in terms of the generated nonlinearity. A dimensionless parameter ξ is proposed to uniquely quantify the nonlinearity produced. The trends produced in the numerical study are then validated with good agreement experimentally. This is carried out loading an interface between two steel blocks and exciting this interface with different amplitude normal incidence shear waves. The experimental results are in good agreement with the numerical results, suggesting the simple friction model does a reasonable job of capturing the fundamental physics. The resulting approach offers a potential way to characterize a contacting interface; however, the difficulty in activating that interface may ultimately limit its applicability.

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.

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International audienceThe vibrations generated by friction are responsible for various noises such as squealing, squeaking and chatter. Although these phenomena have been studied for a long time, it is not well-understood. In this study, an experimental and numerical study of friction-induced vibrations of a system composed of two beams in contact is proposed. The experimental system exhibits periodic steady state vibrations of different types. To model and understand this experimental vibratory phenomenon, complex eigenvalue and dynamic transient analyses are performed. In the linear complex eigenvalue analysis, flutter instability occurs via the coalescence of two eigenmodes of the system. This linear study provides an accurate value of the experimental frequency of vibration. To understand what happens physically during friction-induced instability, a dynamic transient analysis that takes account of the non-linear aspect of a frictional contact is performed. In this analysis, friction-induced instability is characterized by self-sustained vibrations and by stick, slip and separation zones occurring at the surface of the contact. The results stemming from this analysis show that good correlation between numerical and experimental vibrations can be obtained (in time and frequency domains). Moreover, time domain simulations permit understanding the physical phenomena involved in two different vibratory behaviours observed experimentally. (C) 2010 Elsevier Ltd. All rights reserved

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