Advertisement

Acta Mechanica Solida Sinica

, Volume 32, Issue 6, pp 767–784 | Cite as

Numerical Analysis of the Nonlinear Interactions Between Lamb Waves and Microcracks in Plate

  • Hongtao Lv
  • Jingpin JiaoEmail author
  • Bin Wu
  • Cunfu HeEmail author
Article
First Online:
  • 95 Downloads

Abstract

In this paper, three-dimensional finite-element modeling is conducted to investigate the nonlinear interactions between Lamb waves and microcracks. The simulation research focuses on the influence of microcrack orientation on the propagation direction of generated sum-frequency Lamb waves. The simulation results show that the resonant conditions based on classical nonlinear theory are valid for such interactions, leading to the generation of transmitted and reflected sum-frequency S0 waves (SFSWs). Moreover, the propagation directions of these two SFSWs exhibit different trends with respect to the orientations of microcracks. The transmitted SFSW can be used to detect microcracks, whereas the reflected one can be used to measure their orientations.

Keywords

Nonlinear ultrasonic Lamb wave mixing Resonant condition Microcrack Finite-element method 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

This work was supported by the National Key Research and Development Program of China (Grant No. 2016YFF0203002) and National Natural Science Foundation of China (Grant Nos. 11572010, 11572011).

References

  1. 1.
    Lee YL. Fatigue testing and analysis: theory and practice. Oxford: Butterworth-Heinemann; 2005.Google Scholar
  2. 2.
    Song WT, Xu CG, Pan QX, Song JF. Nondestructive testing and characterization of residual stress field using an ultrasonic method. Chin J Mech Eng. 2016;29(2):365–71.Google Scholar
  3. 3.
    Liu ZH, Liu S, Wu B, Zhang YN, He CF. Propagation characteristics of high order longitudinal modes in steel strands and their applications. Acta Mech Solida Sin. 2008;21(6):573–9.Google Scholar
  4. 4.
    Chen JL, Li Z, Gong KZ. Nondestructive testing method based on Lamb waves for localization and extent of damage. Acta Mech Solida Sin. 2017;30(1):65–74.Google Scholar
  5. 5.
    Wang YK, Guan RQ, Lu Y. Nonlinear Lamb waves for fatigue damage identification in FRP-reinforced steel plates. Ultrasonics. 2017;80:87–95.Google Scholar
  6. 6.
    Li XD, Xie HM, Kang YL, Wu XP. A brief review and prospect of experimental solid mechanics in China. Acta Mech Solida Sin. 2010;23(6):498–548.Google Scholar
  7. 7.
    Xiang YX, Deng MX, Xuan FZ, Liu CJ. Cumulative second-harmonic analysis of ultrasonic Lamb waves for ageing behavior study of modified-HP austenite steel. Ultrasonics. 2011;51(8):974–81.Google Scholar
  8. 8.
    Nam T, Lee T, Kim C, Jhang KY, Kim N. Harmonic generation of an obliquely incident ultrasonic wave in solid-solid contact interfaces. Ultrasonics. 2012;52(6):778–83.Google Scholar
  9. 9.
    Croxford AJ, Wilcox PD, Drinkwater BW, Nagy PB. The use of non-collinear mixing for nonlinear ultrasonic detection of plasticity and fatigue. J Acoust Soc Am. 2009;126(5):EL117–22.Google Scholar
  10. 10.
    Jiao JP, Sun JJ, Li N, Song GR, Wu B, He CF. Micro-crack detection using a collinear wave mixing technique. NDT E Int. 2014;62:122–9.Google Scholar
  11. 11.
    Muller M, Sutin A, Guyer R, Talmant M, Laugier P, Johnson PA. Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone. J Acoust Soc Am. 2005;118(6):3946–52.Google Scholar
  12. 12.
    Novak A, Bentahar M, Tournat V, Guerjouma R, Simon L. Nonlinear acoustic characterization of micro-damaged materials through higher harmonic resonance analysis. NDT E Int. 2012;45(1):1–8.Google Scholar
  13. 13.
    Deng MX. Cumulative second-harmonic generation of Lamb-mode propagation in a solid plate. J Appl Phys. 1999;85(6):3051–8.Google Scholar
  14. 14.
    Deng MX. Analysis of second-harmonic generation of Lamb modes using a modal analysis approach. J Appl Phys. 2003;94(6):4152–9.Google Scholar
  15. 15.
    Lima WJ, Hamilton MF. Finite-amplitude waves in isotropic elastic plates. J Sound Vib. 2003;265(4):819–39.Google Scholar
  16. 16.
    Pruell C, Kim JY, Qu JM, Jacobs LJ. A nonlinear-guided wave technique for evaluating plasticity-driven material damage in a metal plate. NDT E Int. 2009;42(3):199–203.Google Scholar
  17. 17.
    Xiang YX, Deng MX, Xuan FZ, Liu CJ. Effect of precipitate-dislocation interactions on generation of nonlinear Lamb waves in creep-damaged metallic alloys. J Appl Phys. 2012;111(10):104905.Google Scholar
  18. 18.
    Hong M, Su ZQ, Lu Y, Sohn H, Qing XL. Locating fatigue damage using temporal signal features of nonlinear Lamb waves. Mech Syst Signal Process. 2015;60:182–97.Google Scholar
  19. 19.
    Rauter N, Lammering R, Kühnrich T. On the detection of fatigue damage in composites by use of second harmonic guided waves. Compos Struct. 2016;152:247–58.Google Scholar
  20. 20.
    Chrysochoidis NA, Assimakopoulou TT, Saravanos DA. Nonlinear wave structural health monitoring method using an active nonlinear piezoceramic sensor for matrix cracking detection in composites. J Intell Mater Syst Struct. 2015;26(15):2108–20.Google Scholar
  21. 21.
    Demčenko A, Akkerman R, Nagy PB, Loendersloot R. Non-collinear wave mixing for non-linear ultrasonic detection of physical ageing in PVC. NDT E Int. 2012;49:34–9.Google Scholar
  22. 22.
    Liu MH, Tang GX, Jacobs LJ, Qu JM. Measuring acoustic nonlinearity parameter using collinear wave mixing. J Appl Phys. 2012;112(2):024908.Google Scholar
  23. 23.
    Joglekar DM, Mitra M. Time domain analysis of nonlinear frequency mixing in a slender beam for localizing a breathing crack. Smart Mater Struct. 2016;26(2):025009.Google Scholar
  24. 24.
    Lv HT, Jiao JP, Wu B, He CF. Evaluation of fatigue crack orientation using non-collinear shear wave mixing method. J Nondestr Eval. 2018;37(4):74.Google Scholar
  25. 25.
    Lee DJ, Cho Y, Li W. A feasibility study for Lamb wave mixing nonlinear technique. AIP Conf Proc. 2014;1581(1):662–6.Google Scholar
  26. 26.
    Jiao JP, Meng XJ, He CF, Wu B. Nonlinear Lamb wave-mixing technique for micro-crack detection in plates. NDT E Int. 2017;85:63–71.Google Scholar
  27. 27.
    Jones GL, Kobett DR. Interaction of elastic waves in an isotropic solid. J Acoust Soc Am. 1963;35(1):5–10.MathSciNetGoogle Scholar
  28. 28.
    Taylor LH, Rollins FR Jr. Ultrasonic study of three-phonon interactions. I. Theory. Phys Rev. 1964;136(3A):A591.Google Scholar
  29. 29.
    Zarembo LK, Krasil’Nikov VA. Nonlinear phenomena in the propagation of elastic waves in solids. Sov Phys Uspekhi. 1971;13(6):778.Google Scholar
  30. 30.
    Korneev VA, Demčenko A. Possible second-order nonlinear interactions of plane waves in an elastic solid. J Acoust Soc Am. 2014;135(2):591–8.Google Scholar
  31. 31.
    Blanloeuil P, Meziane A, Bacon C. 2D finite element modeling of the non-collinear mixing method for detection and characterization of closed cracks. NDT E Int. 2015;76:43–51.Google Scholar
  32. 32.
    Jiao JP, Lv HT, He CF, Wu B. Fatigue crack evaluation using the non-collinear wave mixing technique. Smart Mater Struct. 2017;26(6):065005.Google Scholar
  33. 33.
    Deng MX, Liu ZQ. Generation of cumulative sum frequency acoustic waves of shear horizontal modes in a solid plate. Wave Motion. 2003;37(2):157–72.zbMATHGoogle Scholar
  34. 34.
    Krishna Chillara V, Lissenden CJ. Interaction of guided wave modes in isotropic weakly nonlinear elastic plates: higher harmonic generation. J Appl Phys. 2012;111(12):124909.Google Scholar
  35. 35.
    Furgason ES, Newhouse VL. Noncollinear three-phonon interactions in a multimode structure. J Appl Phys. 1974;45(5):1934–6.Google Scholar
  36. 36.
    Brower NG, Mayer WG. Noncollinear three-phonon interaction in an isotropic plate. J Appl Phys. 1978;49(5):2666–8.Google Scholar
  37. 37.
    Blanloeuil P, Meziane A, Norris AN, Baacon C. Analytical extension of finite element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack. Wave Motion. 2016;66:132–46. MathSciNetGoogle Scholar
  38. 38.
    Wooh SC, Shi Y. Optimum beam steering of linear phased arrays. Wave Motion. 1999;29(3):245–65.Google Scholar
  39. 39.
    Su Z, Ye L. Selective generation of Lamb wave modes and their propagation characteristics in defective composite laminates. J Mater: Des Appl. 2004;218(2):95–110.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Applied Electronics TechnologyBeijing University of TechnologyBeijingChina

Personalised recommendations

Cite article

Buy options