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20 - Introduction to Guided Wave Nonlinear Methods

Published online by Cambridge University Press:  05 July 2014

Joseph L. Rose
Joseph L. Rose
Affiliation:
Pennsylvania State University
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Summary

Introduction

Up to this point we have described linear ultrasonics, that is, where the received signal is at the same frequency as the excitation. Now we consider nonlinear ultrasonics, where the received signal is not at the frequency of the excitation. The material is treated as weakly nonlinear elastic because the amplitude of the signal received at higher harmonics is very small relative to the excitation, which permits the use of a perturbation solution. The generation of higher harmonics in bulk solids has been studied for more than four decades, but the initial studies of higher harmonics in plates are much more recent. These studies are relevant because the amplitudes of higher harmonics have been shown to be sensitive to features of the microstructure of the material, whereas the primary harmonics are generally much less sensitive, or insensitive, to microstructural features such as dislocation density, precipitates, and cavities. This chapter introduces nonlinear methods for guided waves.

To maintain the best possible structural integrity of a component, it is highly desirable to detect damage at the smallest possible scale. Doing so with periodic nondestructive inspection or continuous structural health monitoring (SHM) enables tracking damage evolution over the service life of the structure, which can be used in conjunction with prognostics for condition-based maintenance and improved logistics. Nonlinear systems are known to be very good at indicating damage progression (e.g., Dace, Thompson, and Brashe 1991; Farrar et al. 2007; Worden et al. 2007). Generally speaking, linear ultrasonics with bulk waves can detect anomalies on the order of a wavelength. Ultrasonic guided waves can do significantly better in terms of wavelength, say λ/40 (e.g., Alleyne and Cawley 1992), but longer wavelengths are typically used to enable large penetration lengths. Nonlinear ultrasonics, where the received signal containing the information of interest is at a different frequency than the emitted signal, can provide sensitivity to microstructural changes.

Type
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Ultrasonic Guided Waves in Solid Media , pp. 378 - 401
Publisher: Cambridge University Press
Print publication year: 2014

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References

Alleyne, D. N., and Cawley, P. (1992). The interaction of Lamb waves with defects, IEEE Trans. Ultra. Ferro. Freq. Control 39: 381–97.CrossRefGoogle ScholarPubMed
Auld, B. A. (1973). Acoustic Fields and Waves in Solids. London: Wiley.Google Scholar
Bermes, C., Kim, J. Y., Qu, J., and Jacobs, L. J. (2007). Experimental characterization of material nonlinearity using Lamb waves, Appl. Phys. Letters 90: 021901.CrossRefGoogle Scholar
Cantrell, J. H. (2004). Fundamentals and applications of nonlinear ultrasonic nondestructive evaluation, in Ultrasonic Nondestructive Evaluation: Engineering and Biological Material Characterization, Kundu, T. (Ed.). Boca Raton, FL:CRC Press, 363–433.Google Scholar
Cantrell, J. H. (2009). Nondestructive evaluation of metal fatigue using nonlinear acoustics, in Review of Progress in Quantitative Nondestructive Evaluation, vol. 28, Thompson, D. O. and Chimenti, D. E. (Eds.). New York:Plenum Press, 19–32.Google Scholar
Cantrell, J. H., and Yost, W. T. (2001). Nonlinear ultrasonic characterization of fatigue microstructures, Int. J. Fatigue 23: S487–S490.CrossRefGoogle Scholar
Chillara, V. (2012). Higher harmonic guided waves in isotropic weakly non-linear elastic plates, MS thesis in engineering mechanics, University Park: Pennsylvania State University.
Chomette, S., Gentzbittel, J. M., and Viguier, B. (2010). Creep behavior of as received, aged and cold worked inconel 617 at 850 °C and 950 °C, J. Nuclear Materials 399: 266–74.CrossRefGoogle Scholar
Dace, G. E., Thompson, R. B., and Brashe, L. J. H. (1991). Nonlinear acoustics, a technique to determine microstructural changes in materials, in Review of Progress in Quantitative Nondestructive Evaluation, vol. 10B, Thompson, D. O. and Chimenti, D. E. (Eds.). New York:Plenum Press, 1685–92.CrossRefGoogle Scholar
Dace, G. E., Thompson, R. B., and Buck, O. (1992). Measurement of the acoustic harmonic generation for materials characterization using contact transducers, in Review of Progress in Quantitative Nondestructive Evaluation, vol. 11B, Thompson, D. O. and Chimenti, D. E. (Eds.). New York:Plenum Press, 2069–76.Google Scholar
de Lima, W. J. N., and Hamilton, M. F. (2003). Finite-amplitude waves in isotropic elastic plates, J. Sound Vibration 265: 819–39.CrossRefGoogle Scholar
Deng, M. (2000). Cumulative second-harmonic generation of generalized Lamb-wave propagation in a solid waveguide, J. Phys. D: Appl. Phys. 33: 207–15.CrossRefGoogle Scholar
Deng, M. (2003). Analysis of second-harmonic generation of Lamb modes using a modal analysis approach, J. Appl. Phys. 94: 4152–9.CrossRefGoogle Scholar
Deng, M., Wang, P., and Lv, X. (2005). Experimental observation of cumulative second-harmonic generation of Lamb-wave propagation in an elastic plate, J. Phys. D: Appl. Phys. 38: 344–53.CrossRefGoogle Scholar
Farrar, C. R., Worden, K., Todd, M. D., Park, G., Nichols, J., Adams, D. E., Bement, M. T., and Farinholt, K. (2007). Nonlinear System Identification for Damage Detection, LA-14353, Los Alamos National Laboratory.CrossRefGoogle Scholar
Gol’dberg, Z. A. (1960). Interaction of plane longitudinal and transverse elastic waves, Soviet Physics – Acoustics 6: 306–10.Google Scholar
Hikata, A., Chick, B. B., and Elbaum, C. (1965). Dislocation contribution to the second harmonic generation of ultrasonic waves, J. Appl. Phys. 36(1): 229–36.CrossRefGoogle Scholar
Jhang, K. Y. (2009). Nonlinear techniques for nondestructive assessment of micro damage in material: review, Int. J. Precision Engng. Manuf. 10(1): 123–35.CrossRefGoogle Scholar
Kim, J. Y., Jacobs, L. J., Qu, J., and Littles, J. W. (2006). Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves, J. Acoust. Soc. Am. 120(3): 1266–73.CrossRefGoogle Scholar
Landau, L. D., and Lifshitz, E. M. (1986). Theory of Elasticity. New York:Pergamon.Google Scholar
Lee, T. H., Choi, I. H., and Jhang, K. Y. (2008). The nonlinearity of guided wave in an elastic plate, Mod. Phys. Letters B 22(11): 1135–40.CrossRefGoogle Scholar
Liu, Y., Chillara, V., and Lissenden, C. J. (2013). On selection of fundamental modes for generation of strong internally resonant second harmonics in plate, J. Sound and Vibration 332(19): 4517–28.
Malvern, L. E. (1969). Introduction to the Mechanics of a Continuous Medium. Upper Saddle River, NJ: Prentice-Hall.Google Scholar
Matlack, K. H., Kim, J. Y., Jacobs, L. J., and Qu, J. (2011). Experimental characterization of efficient second harmonic generation of Lamb waves in a nonlinear elastic isotropic plate, J. Appl. Phys. 109: 014905.CrossRefGoogle Scholar
Matsuda, N., and Biwa, S. (2011). Phase and group velocity matching for cumulative harmonic generation in Lamb waves, J. Appl. Phys. 109: 094903.CrossRefGoogle Scholar
Müller, M. F., Kim, J. Y., Qu, J., and Jacobs, L. J. (2010). Characteristics of second harmonic generation of Lamb waves in nonlinear elastic plates, J. Acoust. Soc. Am. 127(4): 2141–52.CrossRefGoogle ScholarPubMed
Na, J. K., Cantrell, J. H., and Yost, W. T. (1996). Linear and nonlinear properties of fatigued 410Cb stainless steel, Rev. Prog. Quant. Nondestr. Eval. 15: 1479–88.Google Scholar
Norris, A. N. (1998). Finite-amplitude waves in solids, in Nonlinear Acoustics, Hamilton, M. F. and Blackstock, D. T. (Eds.). San Diego, CA:Academic Press, 263–77.Google Scholar
Nucera, C., and Lanza di Scalea, F. (2011a). Monitoring load levels in multi-wire strands by nonlinear ultrasonic waves, Structural Health Monitoring 10: 617–29.CrossRefGoogle Scholar
Nucera, C., and Lanza di Scalea, F. (2011b). Nonlinear guided waves: theoretical considerations and applications to thermal stress measurement in continuous welded rails, in Structural Health Monitoring 2011, Chang, F. K. (Ed.). Lancaster, PA:Destech Publications, 2521–8.Google Scholar
Pruell, C., Kim, J. Y., Qu, J., and Jacobs, L. J. (2007). Evaluation of plasticity driven material damage using Lamb waves, Appl. Phys. Letters 91: 231911.CrossRefGoogle Scholar
Pruell, C., Kim, J. Y., Qu, J., and Jacobs, L. J. (2009). A nonlinear-guided wave technique for evaluating plasticity-driven material damage in a metal plate, NDT&E Int. 42: 199–203.CrossRefGoogle Scholar
Srivastava, A., and Lanza di Scalea, F. (2009). On the existence of antisymmetric or symmetric Lamb waves at nonlinear higher harmonics, J. Sound Vibration 323: 932–43.CrossRefGoogle Scholar
Sun, L., Kulkarni, S. S., Achenbach, J. D., and Krishnaswamy, S. (2006). Technique to minimize couplant-effect in acoustic nonlinearity measurements, J. Acoust. Soc. Am. 120(5): 2500–5.CrossRefGoogle Scholar
Truell, R., Elbaum, C., and Chick, B. B. (1969). Ultrasonic Methods in Solid State Physics. New York:Academic Press.Google Scholar
Worden, K., Farrar, C. R., Manson, G., and Park, G. (2007). The fundamental axioms of structural health monitoring, Proc. R. Soc. A. 463: 1639–64.CrossRefGoogle Scholar

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