Skip to main content
Log in

The Application of Nonlinear Reverberation Spectroscopy for the Detection of Localized Fatigue Damage

  • Published:
Journal of Nondestructive Evaluation Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Antonets, V., Donskoy, D., Sutin, A.: Nonlinear vibro-diagnostics of flaws in multilayered structures. Mech. Compos. Mater. 15(5), 934–937 (1986)

    Google Scholar 

  2. Buck, O., Morris, W., Richardson, J.: Acoustic harmonic generation at unbonded interfaces and fatigue cracks. Appl. Phys. Lett. 33(5), 371–373 (1978)

    Article  Google Scholar 

  3. Cantrell, J., Yost, W.: Acoustic harmonic generation from fatigue-induced dislocation dipoles. Philos. Mag. A 69(2), 315–326 (1994)

    Article  Google Scholar 

  4. 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)

    Article  Google Scholar 

  5. Nagy, P.: Fatigue damage assessment by nonlinear ultrasonic materials characterization. Ultrasonics 36(1–5), 375–381 (1998)

    Article  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. Delsanto, P.: Universality of Nonclassical Nonlinearity: Applications to Non-destructive Evaluations and Ultrasonics. Springer Verlag, New York (2007)

  8. Johnson, P.: New wave in acoustic testing. Mater. World 7(9), 544–546 (1999)

    Google Scholar 

  9. Bruno, C., Gliozzi, A., Scalerandi, M., Antonaci, P.: Analysis of elastic nonlinearity using the scaling subtraction method. Phys. Rev. B 79(6), 064108 (2009)

    Article  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. Solodov, I., Busse, G.: Nonlinear air-coupled emission: The signature to reveal and image microdamage in solid materials. Appl. Phys. Lett. 91, 251910 (2007)

    Article  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. 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)

    Article  Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. Johnson, P., Zinszner, B., Rasolofosaon, P.: Resonance and elastic nonlinear phenomena in rock. J. Geophys. Res. 101(B5), 11553–11564 (1996)

    Article  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. 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)

    Google Scholar 

  18. 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)

    Article  Google Scholar 

  19. 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)

    Article  Google Scholar 

  20. 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)

    Article  Google Scholar 

  21. Van Damme, B., Van Den Abeele, K.: Defect localization using the nonlinear impact modulation technique. Emerging Technologies in Non Destructive Testing 5, Ioannina (2011)

  22. Géradin, M., Rixen, D.: Mechanical Vibrations: Theory and Application to Structural Dynamics. Wiley, New York (1994)

    Google Scholar 

  23. Rayleigh, B.: The Theory of Sound. Macmillan, London (1896)

    MATH  Google Scholar 

  24. Ten Cate, J., Shankland, T.: Slow dynamics in the nonlinear elastic response of Berea sandstone. Geophys. Res. Lett. 23(21), 3019–3022 (1996)

    Article  Google Scholar 

  25. Johnson, P., Sutin, A.: Slow dynamics and anomalous nonlinear fast dynamics in diverse solids. J. Acoust. Soc. Am. 117, 124 (2005)

    Article  Google Scholar 

  26. 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)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bart Van Damme.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10921-014-0230-3

Keywords

Navigation