Journal of Nondestructive Evaluation

, Volume 33, Issue 2, pp 216–225 | Cite as

Dynamic Acousto-Elasticity in a Fatigue-Cracked Sample

  • J. RivièreEmail author
  • M. C. Remillieux
  • Y. Ohara
  • B. E. Anderson
  • S. Haupert
  • T. J. Ulrich
  • P. A. Johnson


Dynamic acousto-elasticity (DAE) provides a unique way to observe nonlinear elastic features over an entire dynamic stress cycle including hysteresis and memory effects, detailing the full nonlinear behavior under tension and compression. This supplemental information cannot be observed with conventional nonlinear ultrasonic methods such as wave frequency mixing or resonance measurements, since they measure average, bulk variations of modulus and attenuation versus strain level. Where prior studies have employed DAE in volumetrically nonlinear materials (e.g., rocks, bone with distributed micro-crack networks), here we report results of DAE on the application to a single localized nonlinear feature, a fatigue crack, to characterize the nonlinear elastic response in regions of the crack length, tip, and undamaged portions of an aluminum sample. Linear wave speed, linear attenuation and third order elastic moduli (i.e., nonlinear parameters) each indicate a sensitivity to the presence of the crack, though in unique manners. The localized nature of the DAE measurement and its potential for quantifying all of the third order elastic constants makes it a promising technique for both detecting cracks, as well as providing quantitative information on the effect of the cracks on the material integrity.


Nondestructive evaluation Nonlinear ultrasound Nonlinear acoustics Dynamic acousto-elasticity Fatigue crack 



This research was funded by the U.S. Dept. of Energy, Office of Basic Energy Science (Engineering and Geoscience) and Office of Nuclear Energy (Fuel Cycle R&D, Used Fuel Disposition Campaign).


  1. 1.
    Hughes, D.S., Kelly, J.L.: Second-order elastic deformation of solids. Phys. Rev. 92, 1145–1149 (1953)CrossRefzbMATHGoogle Scholar
  2. 2.
    Winkler, K.W., McGowan, L.: Nonlinear acoustoelastic constants of dry and saturated rocks. J. Geophys. Res. 109, B10204 (2004)Google Scholar
  3. 3.
    Landau, L.D., Lifshitz, E.M.: Theory of Elasticity, 3rd edn. (Theoretical Physics, vol. 7). Butterworth-Heinemann, (1986)Google Scholar
  4. 4.
    Renaud, G., Rivière, J., Haupert, S., Laugier, P.: Anisotropy of dynamic acoustoelasticity in limestone, influence of conditioning, and comparison with nonlinear resonance spectroscopy. J. Acoust. Soc. Am. 133, 3706–3718 (2013)CrossRefGoogle Scholar
  5. 5.
    Renaud, G., Le Bas, P.Y., Johnson, P.A.: Revealing highly complex elastic nonlinear (anelastic) behavior of earth materials applying a new probe: dynamic acoustoelastic testing. J. Geophys. Res. 117(B6), B06202 (2012)Google Scholar
  6. 6.
    Renaud, G., Rivière, J., Le Bas, P.Y., Johnson, P.A.: Hysteretic nonlinear elasticity of berea sandstone at low vibrational strain revealed by dynamic acousto-elastic testing. Geophys. Res. Lett. 40, 715–719 (2013)CrossRefGoogle Scholar
  7. 7.
    Guyer, R.A., Johnson, P.A.: Nonlinear Mesoscopic Elasticity: the Complex Behaviour of Rocks, Soil, Concrete. Wiley, New York (2009)CrossRefGoogle Scholar
  8. 8.
    TenCate, J.A.: Slow dynamics of earth materials: an experimental overview. Pure Appl. Geophys. 168(12), 2211–2219 (2011)CrossRefGoogle Scholar
  9. 9.
    Rivière, J., Renaud, G., Guyer, R.A., Johnson, P.A.: Pump and probe waves in dynamic acousto-elasticity: comprehensive description and comparison with nonlinear elastic theories. J. Appl. Phys. 114, 054905 (2013)CrossRefGoogle Scholar
  10. 10.
    Ingard, U., Pridmore-Brown, D.C.: Scattering of sound by sound. J. Acoust. Soc. Am. 28(3), 367–369 (1956)CrossRefGoogle Scholar
  11. 11.
    Westervelt, P.J.: Scattering of sound by sound. J. Acoust. Soc. Am. 29(8), 934–935 (1957)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Rollins Jr, F.R., Taylor, L.H., Todd Jr, P.H.: Ultrasonic study of three-phonon interactions. ii. Experimental results. Phys. Rev. 136(3A), A597 (1964)CrossRefGoogle Scholar
  13. 13.
    Taylor, L.H., Rollins Jr, F.R.: Ultrasonic study of three-phonon interactions. i. Theory. Phys. Rev. 136(3A), A591 (1964)CrossRefGoogle Scholar
  14. 14.
    Ohara, Y., Mihara, T., Yamanaka, K.: Effect of adhesion force between crack planes on subharmonic and dc responses in nonlinear ultrasound. Ultrasonics 44(2), 194–199 (2006)CrossRefGoogle Scholar
  15. 15.
    Ohara, Y., Mihara, T., Sasaki, R., Ogata, T., Yamamoto, S., Kishimoto, Y., Yamanaka, K.: Imaging of closed cracks using nonlinear response of elastic waves at subharmonic frequency. Appl. Phys. Lett. 90(1), 011902–011902 (2007)CrossRefGoogle Scholar
  16. 16.
    Ohara, Y., Endo, H., Hashimoto, M., Shintaku, Y., Yamanaka, K.: Monitoring growth of closed fatigue crack using subharmonic phased array. AIP Conf. Proc. 1211, 903 (2010)CrossRefGoogle Scholar
  17. 17.
    Ohara, Y., Endo, H., Mihara, T., Yamanaka, K.: Ultrasonic measurement of closed stress corrosion crack depth using subharmonic phased array. Jpn. J. Appl. Phys. 48(7), 07GD01-07GD01 (2009)Google Scholar
  18. 18.
    Renaud, G., Talmant, M., Callé, S., Defontaine, M., Laugier, P.: Nonlinear elastodynamics in micro-inhomogeneous solids observed by head-wave based dynamic acoustoelastic testing. J. Acoust. Soc. Am. 130(6), 3583–3589 (2011)CrossRefGoogle Scholar
  19. 19.
    Renaud, G., Callé, S., Defontaine, M.: Remote dynamic acoustoelastic testing: elastic and dissipative acoustic nonlinearities measured under hydrostatic tension and compression. Appl. Phys. Lett. 94, 011905 (2009)CrossRefGoogle Scholar
  20. 20.
    Renaud, G., Callé, S., Defontaine, M.: Dynamic acoustoelastic testing of weakly pre-loaded unconsolidated water-saturated glass beads. J. Acoust. Soc. Am. 128, 3344 (2010)CrossRefGoogle Scholar
  21. 21.
    Hamilton, M.F., Blackstock, D.T.: Nonlinear Acoustics. Academic Press, San Diego (1998)Google Scholar
  22. 22.
    Ulrich, T.J., Van Den Abeele, K., Le Bas, P.Y., Griffa, M., Anderson, B.E., Guyer, R.A.: Three component time reversal: focusing vector components using a scalar source. J. Appl. Phys. 106(11), 113504–113504 (2009)CrossRefGoogle Scholar
  23. 23.
    Sheriff, R.E.: Encyclopedic Dictionary of Exploration Geophysics. Society of Exploration Geophysicists, Tulsa, OK (1991)Google Scholar
  24. 24.
    Tao, H., Zavattieri, P.D., Hector Jr, L.G., Tong, W.: Mode i fracture at spot welds in dual-phase steel: an application of reverse digital image correlation. Exp. Mech. 50(8), 1199–1212 (2010)CrossRefGoogle Scholar
  25. 25.
    Solodov, IYu., Krohn, N., Busse, G.: Can: an example of nonclassical acoustic nonlinearity in solids. Ultrasonics 40(1), 621–625 (2002)CrossRefGoogle Scholar
  26. 26.
    Delrue, S., Van Den Abeele, K.: Three-dimensional finite element simulation of closed delaminations in composite materials. Ultrasonics 52(2), 315–324 (2012) Google Scholar
  27. 27.
    Biwa, S., Suzuki, A., Ohno, N.: Evaluation of interface wave velocity, reflection coefficients and interfacial stiffnesses of contacting surfaces. Ultrasonics 43(6), 495–502 (2005)CrossRefGoogle Scholar
  28. 28.
    Nagy, P.B.: Ultrasonic classification of imperfect interfaces. J. Nondestr. Eval. 11(3–4), 127–139 (1992)CrossRefGoogle Scholar
  29. 29.
    Ulrich, T.J., Johnson, P.A., Guyer, R.A.: Interaction dynamics of elastic waves with a complex nonlinear scatterer through the use of a time reversal mirror. Phys. Rev. Lett. 98, 104301 (2007)CrossRefGoogle Scholar
  30. 30.
    Ulrich, T.J., Sutin, A.M., Guyer, R.A., Johnson, P.A.: Time reversal and non-linear elastic wave spectroscopy (tr news) techniques. Int. J. Nonlinear Mech. 43, 209–216 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • J. Rivière
    • 1
    Email author
  • M. C. Remillieux
    • 1
  • Y. Ohara
    • 2
  • B. E. Anderson
    • 1
  • S. Haupert
    • 3
  • T. J. Ulrich
    • 1
  • P. A. Johnson
    • 1
  1. 1.Geophysics Group MS D446, Earth and Environmental SciencesLos Alamos National LaboratoryLos AlamosUSA
  2. 2.Department of Materials Processing, Graduate School of EngineeringTohoku UniversitySendai Japan
  3. 3.Laboratoire d’Imagerie ParametriqueUniversity of Paris VI, UPMC, CNRSParisFrance

Personalised recommendations