Numerical study of nonlinear interaction between a crack and elastic waves under an oblique incidence

Abstract A Finite Element (FE) model is proposed to study the interaction between in-plane elastic waves and a crack of different orientations. The crack is modeled by an interface of unilateral contact with Coulombs friction. These contact laws are modified to take into account a pre-stress σ 0 that closes the crack. Using the FE model, it is possible to obtain the contact stresses during wave propagation. These contact stresses provide a better understanding of the coupling between the normal and tangential behavior under oblique incidence, and explain the generation of higher harmonics. This new approach is used to analyze the evolution of the higher harmonics obtained as a function of the angle of incidence, and also as a function of the excitation level. The pre-stress condition is a governing parameter that directly changes the nonlinear phenomenon at work at the interface and therefore the harmonic generation. The diffracted fields obtained by the nonlinear and linear models are also compared.

[1]  K. E.-A. Van Den Abeele,et al.  Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS) , 2000 .

[2]  Koichiro Kawashima,et al.  Evaluation of Amorphous Diffusion Bonding by Nonlinear Ultrasonic Method , 2004 .

[3]  C. Pecorari.  Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact. , 2003, The Journal of the Acoustical Society of America.

[4]  Laurence J. Jacobs,et al.  Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves , 2006 .

[5]  Laurent Baillet,et al.  Mixed finite element methods for the Signorini problem with friction , 2006 .

[6]  Nonlinear acoustic scattering by a partially closed surface-breaking crack. , 2005, The Journal of the Acoustical Society of America.

[7]  Steven Delrue,et al.  Three-dimensional finite element simulation of closed delaminations in composite materials. , 2012, Ultrasonics.

[8]  D. Mendelsohn,et al.  Transient dynamic elastic frictional contact: A general 2D boundary element formulation with examples of SH motion , 1989 .

[9]  Ingolf Müller,et al.  Clapping in delaminated sandwich-beams due to forced oscillations , 2006 .

[10]  A Meziane,et al.  Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics. , 2011, The Journal of the Acoustical Society of America.

[11]  J. Achenbach,et al.  Higher harmonics in the far field due to dynamic crack‐face contacting , 1993 .

[12]  T J Ulrich,et al.  Interaction dynamics of elastic waves with a complex nonlinear scatterer through the use of a time reversal mirror. , 2007, Physical review letters.

[13]  K. Y. Dai,et al.  A Smoothed Finite Element Method for Mechanics Problems , 2007 .

[14]  Kyung-Young Jhang,et al.  Experimental investigation of nonlinear acoustic effect at crack , 2009 .

[15]  N. Ohno,et al.  Evaluation of interface wave velocity, reflection coefficients and interfacial stiffnesses of contacting surfaces. , 2005, Ultrasonics.

[16]  K. Y. Dai,et al.  Theoretical aspects of the smoothed finite element method (SFEM) , 2007 .

[17]  G. Busse,et al.  CAN: an example of nonclassical acoustic nonlinearity in solids. , 2002, Ultrasonics.

[18]  J. Akin.  The generation of elements with singularities , 1976 .

[19]  Siming Liu,et al.  Effects of experimental variables on the nonlinear harmonic generation technique , 2011, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[20]  Jin-Yeon Kim,et al.  Hysteretic linear and nonlinear acoustic responses from pressed interfaces , 2006 .

[21]  Kyung-Young Jhang,et al.  Nonlinear ultrasonic techniques for nondestructive assessment of micro damage in material: A review , 2009 .

[22]  P. R. Heyllger.  On conventional and quarter-point mixed elements in linear elastic fracture mechanics☆ , 1988 .

[23]  Simon A Neild,et al.  Measurement of the ultrasonic nonlinearity of kissing bonds in adhesive joints , 2009 .

[24]  Alexander Sutin,et al.  Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing , 2001 .

[25]  Michel Saint Jean,et al.  The non-smooth contact dynamics method , 1999 .

[26]  S. Hirose,et al.  2-D scattering by a crack with contact-boundary conditions , 1994 .

[27]  S. Biwa,et al.  Pressure-Dependent Stiffnesses and Nonlinear Ultrasonic Response of Contacting Surfaces , 2009 .

[28]  K. Pfleiderer,et al.  Nonlinear Acoustic NDE: Inherent Potential of Complete Nonclassical Spectra , 2006 .

[29]  R. Gr. Maev,et al.  Review / Sythèse Nonlinear acoustic applications for material characterization: A review , 1999 .

[30]  Hamouine Abdelmadjid,et al.  A state-of-the-art review of the X-FEM for computational fracture mechanics , 2009 .

[31]  Koen Van Den Abeele,et al.  Characterization and Imaging of Microdamage Using Nonlinear Resonance Ultrasound Spectroscopy (NRUS): An Analytical Model , 2006 .

[32]  Marc Duflot,et al.  Meshless methods: A review and computer implementation aspects , 2008, Math. Comput. Simul..