Abstract
Nonlinear reverberation spectroscopy (NRS) is a non destructive evaluation method exploiting the amplitude dependent change of the resonance frequency in samples made of a nonlinear elastic material. After a sample has been excited near resonance, the immediate vibration frequency of the decaying reverberation signal decays with the decreasing amplitude. The frequency-amplitude dependence can be used to quantify the nonlinearity of the material, typically caused by the damage level. This paper handles the possibilities and difficulties of using NRS to detect a single fatigue crack in specimens made of an linear material like a composite or steel. In this case, the nonlinearity is concentrated in a small zone which is not necessarily affected by the low frequency vibrations used for NRS. First, a proof of concept is given by testing composite beams with increasing levels of fatigue damage. Tests prove that the nonlinear frequency change is more efficient for quantifying early damage than its linear counterparts such as the damping coefficient, at least when the crack is located in a vibration antinode. The method is subsequently used to test steel industrial samples with a complex geometry, showing that efficient damage detection indeed depends on the used vibration mode.
Similar content being viewed by others
References
Antonets, V., Donskoy, D., Sutin, A.: Nonlinear vibro-diagnostics of flaws in multilayered structures. Mech. Compos. Mater. 15(5), 934–937 (1986)
Buck, O., Morris, W., Richardson, J.: Acoustic harmonic generation at unbonded interfaces and fatigue cracks. Appl. Phys. Lett. 33(5), 371–373 (1978)
Cantrell, J., Yost, W.: Acoustic harmonic generation from fatigue-induced dislocation dipoles. Philos. Mag. A 69(2), 315–326 (1994)
Donskoy, D., Sutin, A., Ekimov, A.: Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing. NDT & E Int. 34(4), 231–238 (2001)
Nagy, P.: Fatigue damage assessment by nonlinear ultrasonic materials characterization. Ultrasonics 36(1–5), 375–381 (1998)
Van Den Abeele, K., Carmeliet, J., TenCate, J., Johnson, P.: Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, Part II: Single-mode nonlinear resonance acoustic spectroscopy. Res. Nondestruct. Eval. 12(1), 31–42 (2000)
Delsanto, P.: Universality of Nonclassical Nonlinearity: Applications to Non-destructive Evaluations and Ultrasonics. Springer Verlag, New York (2007)
Johnson, P.: New wave in acoustic testing. Mater. World 7(9), 544–546 (1999)
Bruno, C., Gliozzi, A., Scalerandi, M., Antonaci, P.: Analysis of elastic nonlinearity using the scaling subtraction method. Phys. Rev. B 79(6), 064108 (2009)
Scalerandi, M., Gliozzi, A., Bruno, C., Van Den Abeele, K.: Nonlinear acoustic time reversal imaging using the scaling subtraction method. J. Phys. D 41, 215404 (2008)
Solodov, I., Busse, G.: Nonlinear air-coupled emission: The signature to reveal and image microdamage in solid materials. Appl. Phys. Lett. 91, 251910 (2007)
Van Den Abeele, K., Johnson, P., Sutin, A.: Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part I: nonlinear wave modulation spectroscopy (NWMS). Res. Nondestruct. Eval. 12(1), 17–30 (2000)
Ulrich, T., Johnson, P., Guyer, R.: Interaction dynamics of elastic waves with a complex nonlinear scatterer through the use of a time reversal mirror. Phys. Rev. Lett. 98(10), 104301 (2007)
Zagrai, A., Donskoy, D., Chudnovsky, A., Golovin, E.: Micro-and macroscale damage detection using the nonlinear acoustic vibro-modulation technique. Res. Nondestruct. Eval. 19(2), 104–128 (2008)
Johnson, P., Zinszner, B., Rasolofosaon, P.: Resonance and elastic nonlinear phenomena in rock. J. Geophys. Res. 101(B5), 11553–11564 (1996)
Van Den Abeele, K., Le Bas, P., Van Damme, B., Katkowski, T.: Quantification of material nonlinearity in relation to microdamage density using nonlinear reverberation spectroscopy: experimental and theoretical study. J. Acoust. Soc. Am. 126, 963 (2009)
Van den Abeele, K., Campos-Pozuelo, C., Juárez, G., Antonio, J., Windels, F., Bollen, B.: Analysis of the nonlinear reverberation of titanium alloys fatigued at high amplitude ultrasonic vibration. Proceedings Forum Acustica Sevilla, Sociedad Española de Acústica, Sevilla (2002)
Van Den Abeele, K., De Visscher, J.: Damage assessment in reinforced concrete using spectral and temporal nonlinear vibration techniques. Cem. Concr. Res. 30(9), 1453–1464 (2000)
Payan, C., Garnier, V., Moysan, J., Johnson, P.: Applying nonlinear resonant ultrasound spectroscopy to improving thermal damage assessment in concrete. J. Acoust. Soc. Am. 121, 125–130 (2007)
Van Den Abeele, K.: Multi-mode nonlinear resonance ultrasound spectroscopy for defect imaging: an analytical approach for the one-dimensional case. J. Acoust. Soc. Am. 122, 73 (2007)
Van Damme, B., Van Den Abeele, K.: Defect localization using the nonlinear impact modulation technique. Emerging Technologies in Non Destructive Testing 5, Ioannina (2011)
Géradin, M., Rixen, D.: Mechanical Vibrations: Theory and Application to Structural Dynamics. Wiley, New York (1994)
Rayleigh, B.: The Theory of Sound. Macmillan, London (1896)
Ten Cate, J., Shankland, T.: Slow dynamics in the nonlinear elastic response of Berea sandstone. Geophys. Res. Lett. 23(21), 3019–3022 (1996)
Johnson, P., Sutin, A.: Slow dynamics and anomalous nonlinear fast dynamics in diverse solids. J. Acoust. Soc. Am. 117, 124 (2005)
Bentahar, M., El Aqra, H., El Guerjouma, R., Griffa, M., Scalerandi, M.: Hysteretic elasticity in damaged concrete: quantitative analysis of slow and fast dynamics. Phys. Rev. B 73(1), 14116 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Van Damme, B., Van Den Abeele, K. The Application of Nonlinear Reverberation Spectroscopy for the Detection of Localized Fatigue Damage. J Nondestruct Eval 33, 263–268 (2014). https://doi.org/10.1007/s10921-014-0230-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10921-014-0230-3