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Influence of Mesoscale and Macroscale Heterogeneities in Metals on Higher Harmonics Under Plastic Deformation

  • Negar Kamali
  • Niloofar Tehrani
  • Amir Mostavi
  • Sheng-Wei ChiEmail author
  • Didem Ozevin
  • J. Ernesto Indacochea
Article
  • 53 Downloads

Abstract

In nonlinear ultrasonic techniques, the material nonlinearity is observable in the ultrasonic signal through the generation of higher harmonics (HH). The HH generation, however, can be triggered by many sources. Any variation in the micro-, meso-, and macroscopic scales of the structure may collectively lead to HH generation. This paper presents a finite element approach with mesoscale heterogeneities explicitly modeled for the nonlinear wave propagation. The aim of this paper is to understand HH generation due to the non-mesoscale variation and non-uniform deformations introduced by the uniaxial tensile test. The study is divided into two parts: first, the effect of non-uniform plastic deformation resulted by geometrical variation of structures on HH is studied. The effect of non-uniformity due to mesoscale variations on HH is then analyzed. The numerical studies and predictions are crossly validated with nonlinear ultrasonic experiments and microscale imaging, including X-ray diffraction scanning. Numerical and experimental studies both indicate that non-uniform variations in different length scales affect the generation of both second- and third-harmonics and that both second- and third-harmonics acoustic nonlinearity parameters grow with the increase of plastic strain level. However, the third-harmonics acoustic nonlinearity coefficient is more sensitive when micro-, meso- and macrostructural variations exist.

Keywords

Non-linear ultrasonic testing Higher harmonics Acoustic nonlinearity parameter Multiscale modeling X-ray diffraction Non-uniform stress distribution 

Notes

Acknowledgements

This research is based upon work supported by the National Science Foundation (NSF) under Award Number CMMI 1463501 entitled “Assessing Microstructural Damage Using Nonlinear Ultrasonics and Multiscale Numerical Modeling”. Any opinions, findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF.

References

  1. 1.
    Abraham, S.T., et al.: Assessment of sensitization in AISI 304 stainless steel by nonlinear ultrasonic method. Acta Metall. Sin. 26(5), 545–552 (2013).  https://doi.org/10.1007/s40195-013-0168-y CrossRefGoogle Scholar
  2. 2.
    Cantrell, J.H., Yost, W.T.: Nonlinear ultrasonic characterization of fatigue microstructures. Int. J. Fatigue 23, 487–490 (2001).  https://doi.org/10.1016/S0142-1123(01)00162-1 CrossRefGoogle Scholar
  3. 3.
    Choi, G., et al.: Influence of localized microstructure evolution on second harmonic generation of guided waves. AIP Conf. Proc. 1581(33), 631–638 (2014).  https://doi.org/10.1063/1.4864879 CrossRefGoogle Scholar
  4. 4.
    Griffiths, J.R., Caceres, C.H.: Damage by the cracking of silicon particles in an Al-7Si-0.4 Mg casting alloy. Acta Metall. 44(1), 25–33 (1996)Google Scholar
  5. 5.
    Hong, M., et al.: Modeling nonlinearities of ultrasonic waves for fatigue damage characterization: theory, simulation, and experimental validation. Ultrasonics 54(3), 770–778 (2014).  https://doi.org/10.1016/j.ultras.2013.09.023 CrossRefGoogle Scholar
  6. 6.
    Kovács, I., Zsoldos, L.: Dislocations and Plastic Deformation. Akadémiai Kiadó International series of monographs in natural philosophy, vol. 60 (1973)CrossRefGoogle Scholar
  7. 7.
    Kumar, A., et al.: Nonlinear ultrasonics for in situ damage detection during high frequency fatigue. J. Appl. Phys. 106(2), 024904 (2009).  https://doi.org/10.1063/1.3169520 CrossRefGoogle Scholar
  8. 8.
    Landau, L.D.D., et al.: Theory of Elasticity. Pergamon Press, Oxford (1975)Google Scholar
  9. 9.
    Le, K.C.: Thermodynamic dislocation theory for non-uniform plastic deformations. J. Mech. Phys. Solids 111(2010), 157–169 (2018).  https://doi.org/10.1016/j.jmps.2017.10.022 MathSciNetCrossRefGoogle Scholar
  10. 10.
    Liu, Y., et al.: Third harmonic shear horizontal and Rayleigh Lamb waves in weakly nonlinear plates. J. Appl. Phys. 114(11), 114908 (2013).  https://doi.org/10.1063/1.4821252 CrossRefGoogle Scholar
  11. 11.
    Matlack, K.H., et al.: Review of second harmonic generation measurement techniques for material state determination in metals. J. Nondestr. Eval. 34(1), 273 (2015)CrossRefGoogle Scholar
  12. 12.
    Meo, M., Polimeno, U., Zumpano, G.: Detecting damage in composite material using nonlinear elastic wave spectroscopy methods. Appl. Compos. Mater. 15(3), 115–126 (2008).  https://doi.org/10.1007/s10443-008-9061-7 CrossRefGoogle Scholar
  13. 13.
    Mostavi, A., et al.: Wavelet based harmonics decomposition of ultrasonic signal in assessment of plastic strain in aluminum. Measurement 106, 66–78 (2017).  https://doi.org/10.1016/j.measurement.2017.04.013 CrossRefGoogle Scholar
  14. 14.
    Norris, A.: Finite amplitude waves in solids. Nonlinear Acoust. 9, 263–277 (1998)Google Scholar
  15. 15.
    Palit Sagar, S., et al.: Non-linear ultrasonic technique to assess fatigue damage in structural steel. Scripta Mater. 55(2), 199–202 (2006).  https://doi.org/10.1016/j.scriptamat.2006.03.037 CrossRefGoogle Scholar
  16. 16.
    Poole, W.J., Dowdle, E.J.: Experimental measurements of damage evolution in Al-Si eutectic alloys. Acta Metall. 39(9), 1281–1287 (1998)Google Scholar
  17. 17.
    Rauter, N., Lammering, R.: Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities. Smart Mater. Struct. 24(4), 045027 (2015).  https://doi.org/10.1088/0964-1726/24/4/045027 CrossRefGoogle Scholar
  18. 18.
    Sablik, M.J., Stegemann, D., Krys, A.: Modeling grain size and dislocation density effects on harmonics of the magnetic induction Modeling grain size and dislocation density effects on harmonics of the magnetic induction. J. Appl. Phys. 89(11), 7254–7256 (2001).  https://doi.org/10.1063/1.1355342 CrossRefGoogle Scholar
  19. 19.
    Shen, Y., Giurgiutiu, V.: Modeling of guided waves for detection of linear and nonlinear structural damage. Health Monit. Struct. Biol. Syst. 8695, 86951S (2013).  https://doi.org/10.1117/12.2009119 CrossRefGoogle Scholar
  20. 20.
    Silva, M., Gouyon, R., Lepoutre, F.: Hidden corrosion detection in aircraft aluminum structures using laser ultrasonics and wavelet transform signal analysis. Ultrasonics 41(4), 301–305 (2003)CrossRefGoogle Scholar
  21. 21.
    Sposito, G., et al.: A review of non-destructive techniques for the detection of creep damage in power plant steels. NDT E Int. 43(7), 555–567 (2010).  https://doi.org/10.1016/j.ndteint.2010.05.012 CrossRefGoogle Scholar
  22. 22.
    Su, H., Liu, Q., Li, J.: Boundary effects reduction in wavelet transform for time-frequency analysis. WSEAS Trans. Signal Process. 8(4), 169–179 (2012)Google Scholar
  23. 23.
    Taplidou, S.A., Hadjileontiadis, L.J.: Nonlinear analysis of wheezes using wavelet bicoherence. Comput. Biol. Med. 37(4), 563–570 (2007)CrossRefGoogle Scholar
  24. 24.
    Thurston, R.N.: Waves in Solids, Mechanics of Solids IV. Springer, Berlin (1974)Google Scholar
  25. 25.
    Xiang, Y.-X., et al.: Experimental and numerical studies of nonlinear ultrasonic responses on plastic deformation in weld joints. Chin. Phys. B 25(2), 024303 (2016).  https://doi.org/10.1088/1674-1056/25/2/024303 CrossRefGoogle Scholar
  26. 26.
    Zarembo, L., Krasil’nikov, V.: Nonlinear phenomena in the propagation of elastic waves in solids. Sov. Phys. Uspekhi 13(6), 778 (1971)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Negar Kamali
    • 1
  • Niloofar Tehrani
    • 1
  • Amir Mostavi
    • 1
  • Sheng-Wei Chi
    • 1
    Email author
  • Didem Ozevin
    • 1
  • J. Ernesto Indacochea
    • 1
  1. 1.Department of Civil and Material EngineeringUniversity of Illinois at Chicago ChicagoUSA

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