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Nonlinear Ultrasonic Techniques for Material Characterization

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Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation

Abstract

This chapter considers both the theoretical aspects of the nonlinear ultrasonic phenomena in elastic solids and their applications to materials characterization; it has been demonstrated that nonlinear ultrasound (NLU) measurements can provide quantitative inputs to determine the material state and measure damage in engineering components. It has recently been shown that NLU can be used to develop the framework for accurate life prediction of components under mechanical and thermo-mechanical loading. These NLU measurements are done at the material level, before the formation of macroscopic damage. The traditional NDE of damage of a material subject to, for example, fatigue starts from the time when a small crack initiates because there is no measurable macroscopic change in the material prior to the crack initiation. In most metallic materials, however, cracks of a measurable size appear late in the fatigue life (typically after 80%), while the material toughness and strength decreases gradually due to the microplasticity (dislocations) and associated change in the material’s microstructure. Starting from mechanics fundamentals, we first develop the theoretical equations of wave motion in an elastic solid with quadratic nonlinearity, covering bulk, surface, and guided waves. Various nonlinear acoustic phenomena occurring in the infinite and bounded elastic solids are described in a consistent mathematical framework. The next section considers measurement techniques for NLU, including examples of the assessment of fatigue and thermal damage in metals with NLU.

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References

  1. A. Norris, in Finite Amplitude Waves in Solids, ed. By M.F. Hamilton, D.T. Blackstock. Nonlinear Acoustics (Acoustical Society of America, New York, 2008)

    Google Scholar 

  2. L. Malvern, in Introduction to the Mechanics of a Continuous Medium. ed. By J.B. Reswick, W.M. Rohsenow. Prentice-Hall Series in Engineering of the Physical Sciences, (Prentice-Hall, Inc, Englewood, 1969)

    Google Scholar 

  3. D.O. Thompson, M.A. Breazeale, Ultrasonic waves of finite amplitude in solids. J. Acoust. Soc. Am. 35(11), 1884 (1963)

    Article  Google Scholar 

  4. J.H. Cantrell, Acoustic radiation stress in solids. IEEE Transac. Sonics Ultrason. 32(1), 100–100 (1985)

    MathSciNet  Google Scholar 

  5. J.D. Achenbach, Wave Propagation in Elastic Solids (North-Holland, Amsterdam, 1973)

    MATH  Google Scholar 

  6. G.L. Jones, D.R. Korbett, Interaction of elastic waves in an isotropic solid. J. Acoust. Soc. Am. 35(1), 5 (1963)

    Article  MathSciNet  Google Scholar 

  7. N. Kalyanasundaram, Non-linear surface acoustic-waves on an isotropic solid. Int. J. Eng. Sci. 19(2), 279–286 (1981)

    Article  Google Scholar 

  8. N. Kalyanasundaram, Non-linear mixing of surface acoustic-waves propagating in opposite directions. J. Acoust. Soc. Am. 73(6), 1956–1965 (1983)

    Article  Google Scholar 

  9. N. Kalyanasundaram, G.V. Anand, Surface acoustic-waves of finite-amplitude excited by a monochromatic line source. J. Acoust. Soc. Am. 68(2), 567–574 (1980)

    Article  MathSciNet  Google Scholar 

  10. N. Kalyanasundaram, G.V. Anand, Periodic rayleigh-waves of finite-amplitude on an isotropic solid. J. Acoust. Soc. Am. 72(5), 1518–1523 (1982)

    Article  MathSciNet  Google Scholar 

  11. N. Kalyanasundaram, D.F. Parker, E.A. David, The spreading of nonlinear elastic surface-waves. J. Elast. 24(1-3), 79–103 (1990)

    Article  Google Scholar 

  12. N. Kalyanasundaram, R. Ravindran, P. Prasad, Coupled amplitude theory of non-linear surface acoustic-waves. J. Acoust. Soc. Am. 72(2), 488–493 (1982)

    Article  Google Scholar 

  13. R.W. Lardner, Non-linear surface-waves on an elastic solid. Int. J. Eng. Sci. 21(11), 1331–1342 (1983)

    Article  Google Scholar 

  14. A.P. Mayer, Nonlinear surface acoustic waves: Theory. Ultrasonics 48(6-7), 478–481 (2008)

    Article  Google Scholar 

  15. A.P. Mayer, Surface acoustic-waves in nonlinear elastic media. Phys. Rep. Rev. Sect. Phys. Lett. 256(4-5), 237–366 (1995)

    Google Scholar 

  16. M.F. Hamilton, Y.A. Ilinskii, E.A. Zabolotskaya, in Nonlinear Surface Wave Propagation in Crystals, ed. By R.J. Wei. Nonlinear Acoustics in Perspective (Nanjing University Press, Nanjing, 1996), pp. 64–69

    Google Scholar 

  17. M.F. Hamilton, Y.A. Il'inskii, E.A. Zabolotskaya, Nonlinear Surface Acoustic Waves. ed. by W. Lauterborn, T. Kurz. Nonlinear Acoustics at the Turn of the Millennium (AIP, Melville, 2000), p. 55–64

    Google Scholar 

  18. M.F. Hamilton, Y.A. Il'inskii, E.A. Zabolotskaya, Nonlinear surface acoustic waves in crystals. J. Acoust. Soc. Am. 105(2), 639–651 (1999)

    Article  Google Scholar 

  19. M.F. Hamilton, Y.A. Ilinsky, E.A. Zabolotskaya, Local and nonlocal nonlinearity in rayleigh-waves. J. Acoust. Soc. Am. 97(2), 882–890 (1995)

    Article  Google Scholar 

  20. M.F. Hamilton, Y.A. Ilinsky, E.A. Zabolotskaya, Evolution-equations for nonlinear rayleigh-waves. J. Acoust. Soc. Am. 97(2), 891–897 (1995)

    Article  Google Scholar 

  21. M.F. Hamilton, Y.A. Ilinsky, E.A. Zabolotskaya, On the existence of stationary nonlinear rayleigh-waves. J. Acoust. Soc. Am. 93(6), 3089–3095 (1993)

    Article  Google Scholar 

  22. J. Herrmann, J.Y. Kim, L.J. Jacobs, J. Qu, J.W. Littles, M. Savage, Assessment of material damage in a Nickel-Base superalloy using nonlinear Rayleigh surface waves. J. Appl. Phys. 99, 124913 (2006)

    Article  Google Scholar 

  23. J.M. Qu, L.J. Jacobs, P.B. Nagy, On the acoustic-radiation-induced strain and stress in elastic solids with quadratic nonlinearity (L). J. Acoust. Soc. Am. 129(6), 3449–3452 (2011)

    Article  Google Scholar 

  24. J.D. Achenbach, Reciprocity in Elastodynamics (Cambridge University Press, London, 2004)

    Book  Google Scholar 

  25. B.A. Auld, Acoustic Fields and Waves in Solids, vol 2 (Wiley, New York, 1973)

    Google Scholar 

  26. W.J.N. de Lima, M.F. Hamilton, Finite-amplitude waves in isotropic elastic plates. J. Sound Vib. 265(4), 819–839 (2003)

    Article  Google Scholar 

  27. M.X. Deng, Analysis of second-harmonic generation of Lamb modes using a modal analysis approach. J. Appl. Phys. 94(6), 4152–4159 (2003)

    Article  Google Scholar 

  28. T.O. Mueller, J.Y. Kim, J. Qu, L.J. Jacobs, Nonlinear acoustic measurements and Rayleigh waves. 32nd Annual Review of Process in Quantitative Nondestructive Evaluation (American Institute of Physics, Brunswick, 2005)

    Google Scholar 

  29. A. Srivastava, F.L. di Scalea, On the existence of antisymmetric or symmetric Lamb waves at nonlinear higher harmonics. J. Sound Vib. 323(3-5), 932–943 (2009)

    Article  Google Scholar 

  30. M.F. Muller, J.Y. Kim, J.M. Qu, L.J. Jacobs, Characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates. J. Acoust. Soc. Am. 127(4), 2141–2152 (2010)

    Article  Google Scholar 

  31. C. Pruell, J.Y. Kim, J. Qu, L.J. Jacobs, Evaluation of plasticity driven material damage using Lamb waves. Appl. Phys. Lett. 91(23), 231911 (2007)

    Article  Google Scholar 

  32. K.H. Matlack, J.Y. Kim, L.J. Jacobs, J.M. Qu, Experimental characterization of efficient second harmonic generation of Lamb wave modes in a nonlinear elastic isotropic plate. J. Appl. Phys. 109(1), 014905 (2011)

    Article  Google Scholar 

  33. M.X. Deng, P. Wang, X.F. Lv, Experimental observation of cumulative second-harmonic generation of Lamb-wave propagation in an elastic plate. J Phys. D Appl. Phys. 38(2), 344–353 (2005)

    Article  Google Scholar 

  34. W.T. Yost, J.H. Cantrell, The Effects of Fatigue on Acoustic Nonlinearity in Aluminum Alloys (IEEE, Tucson, 1992)

    Book  Google Scholar 

  35. J.H. Cantrell, W.T. Yost, Nonlinear ultrasonic characterization of fatigue microstructures. Int. J. Fatigue 23(SUPPL 1), 487–490 (2001)

    Article  Google Scholar 

  36. J. Frouin, T.E. Matikas, J.K. Na, S. Sathish, In-situ monitoring of acoustic linear and nonlinear behavior of titanium alloys during cycling loading. in Proceedings of SPIE – The International Society for Optical Engineering, Vol. 3585, 1999, pp. 107–116

    Google Scholar 

  37. A. Moreau, Detection of acoustic 2nd-harmonics in solids using a heterodyne laser interferometer. J. Acoust. Soc. Am. 98(5), 2745–2752 (1995)

    Article  Google Scholar 

  38. D.C. Hurley, C.M. Fortunko, Determination of the nonlinear ultrasonic parameter beta using a Michelson interferometer. Meas. Sci. Technol. 8(6), 634–642 (1997)

    Article  Google Scholar 

  39. J.Y. Kim, L.J. Jacobs, J.M. Qu, J.W. Littles, Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves. J. Acoust. Soc. Am. 120(3), 1266–1273 (2006)

    Article  Google Scholar 

  40. G.E. Dace, R.B. Thompson, O. Buck, Measurement of the acoustic harmonic generation for materials characterization using contact transducers. Rev. Prog. Quant. Nondestr. Eval. 11, 2069–2076 (1992)

    Google Scholar 

  41. F.R. Rollins, Interaction of ultrasonic waves in solid media. Appl. Phys. Lett. 2(8), 147–148 (1963)

    Article  Google Scholar 

  42. F.R. Rollins, P.H. Todd, L.H. Taylor, Ultrasonic study of 3-phonon interactions .2. Experimental results. Phys. Rev. 136(3A), A597–A601 (1964)

    Article  Google Scholar 

  43. L.H. Taylor, F.R. Rollins, Ultrasonic study of 3-phonon interactions .I. Theory. Phys. Rev. 136(3A), A591–A596 (1964)

    Article  Google Scholar 

  44. A.J. Croxford, P.D. Wilcox, B.W. Drinkwater, P.B. Nagy, The use of non-collinear mixing for nonlinear ultrasonic detection of plasticity and fatigue. J. Acoust. Soc. Am. 126(5), El117–El122 (2009)

    Article  Google Scholar 

  45. Z.M. Chen, G.X. Tang, Y.X. Zhao, L.J. Jacobs, J.M. Qu, Mixing of collinear plane wave pulses in elastic solids with quadratic nonlinearity. J. Acoust. Soc. Am. 136(5), 2389–2404 (2014)

    Article  Google Scholar 

  46. M.H. Liu, G.X. Tang, L.J. Jacobs, J.M. Qu, Measuring acoustic nonlinearity parameter using collinear wave mixing. J. Appl. Phys. 112(2), 024908 (2012)

    Article  Google Scholar 

  47. G.X. Tang, M.H. Liu, L.J. Jacobs, J.M. Qu, Detecting localized plastic strain by a scanning collinear wave mixing method. J. Nondestruct. Eval. 33(2), 196–204 (2014)

    Article  Google Scholar 

  48. R.A. Dudley, P. Edwards, R.P. Ekins, D.J. Finney, I.G.M. McKenzie, G.M. Raab, D. Rodbard, R.P.C. Rodgers, Guidelines for immunoassay data processing. Clin. Chem. 31, 1264–1271 (1985)

    Google Scholar 

  49. D.J. Barnard, L.J.H. Brasche, D. Raulerson, A.D. Degtyar, Monitoring Fatigue Damage Accumulation with Rayleigh Wave Harmonic Generation Measurements. ed. By D.O. Thompson, D.E. Chimenti. Review of Progress in Quantitative Nondestructive Evaluation, Vols. 22a and 22b, Vol 20, (Springer, New York, 2003), pp. 1393–1400

    Google Scholar 

  50. J.L. Blackshire, S. Sathish, J. Na, J. Frouin, Nonlinear Laser Ultrasonic Measurements of Localized Fatigue Damage. ed. by D.O. Thompson, D.E. Chimenti. Review of Progress in Quantitative Nondestructive Evaluation, Vols 22a and 22b, Vol. 20 (American Institute of Physics, Melville, 2003), pp. 1479–1488

    Google Scholar 

  51. T. Stratoudaki et al., Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics. J. Acoustic. Soc. Am. 129(4), 1721–1728 (2011)

    Article  Google Scholar 

  52. A. Cobb et al., Nonlinear ultrasonic measurments with EMATs for detecting pre-cracking fatigue damage. Review of progress in quantitative nondestructive evaluation. AIP Conf. Proc. 1430, 299–306 (2012)

    Article  Google Scholar 

  53. C.B. Swacek. et al., Opical excitation of narrowband Rayleigh surface waves for secod harmonic generation. in Review of Progress in Quantitative Nondestructive Evaluation, AIP Conference Proceeding 1511 (2013), pp. 375–381

    Google Scholar 

  54. S. Thiele et al., Air-coupled detection of nonlinear Ryleigh surface waves to assess material nonlinearity. Ultrasonics 54, 1470–1475 (2014)

    Article  Google Scholar 

  55. D. Marino et al., Using nonlinear ultrasound to track microstructural changes due to thermal again in modifies 9% ferritic martenstic steel. NDT&E Int. 79, 46–52 (2016)

    Article  Google Scholar 

  56. C. Doerr et al., Evaluation of sensitization in stainless 304 and 304L using nonlinear Rayleigh waves. NDT&E Int. 88, 17–23 (2017)

    Article  Google Scholar 

  57. M.X. Deng, Cumulative second-harmonic generation of Lamb-mode propagation in a solid plate. J. Appl. Phys. 85(6), 3051–3058 (1999)

    Article  Google Scholar 

  58. C. Bermes, J.Y. Kim, J.M. Qu, L.J. Jacobs, Experimental characterization of material nonlinearity using Lamb waves. Appl. Phys. Lett. 90(2), 021901 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, USA

    J.-Y. Kim & L. Jacobs

  2. Tufts University, Medford, MA, USA

    J. Qu

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  1. J.-Y. Kim
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  2. L. Jacobs
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Correspondence to J. Qu .

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Editors and Affiliations

  1. Department of Civil Engineering and Engineering Mechanics, Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ, USA

    Tribikram Kundu

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Kim, JY., Jacobs, L., Qu, J. (2019). Nonlinear Ultrasonic Techniques for Material Characterization. In: Kundu, T. (eds) Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation. Springer, Cham. https://doi.org/10.1007/978-3-319-94476-0_6

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  • DOI: https://doi.org/10.1007/978-3-319-94476-0_6

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