Advertisement

Modeling Scanned Acoustic Imaging of Defects at Solid Interfaces

  • John G. Harris
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 90)

Abstract

This is an expository summary of my and my collaborators work building mathematical models of scanned acoustic imaging of defects such as cracks or voids that break the surface of a solid or form along solid-solid interfaces. We construct explicit models both of a high frequency, scanned acoustic microscope operating in a reflection mode, and of a lower frequency, scanned confocal acoustic imaging system operating in a transmission mode. The acoustic microscope can operate from 100 megahertz to several gigahertz. One of its most interesting imaging modes is the detection of small surface- breaking cracks, whose traces at the surface of a solid are smaller than an acoustic wavelength, even at high megahertz frequencies. It does so by using a leaky Rayleigh wave as part of its imaging mechanism. The confocal imaging system operates in a neighborhood of 10 megahertz, a lower frequency. It is used to image complicated solid- solid interfaces comprised of scatterers at numerous length scales, many of which are less than a wavelength. For both cases, we explain how the sound scattered from the defects is mapped into the sound collected by the transducers and hence into the voltages they produce. The models are approximate, make use of reciprocity relations and depend upon asymptotic evaluations of Fourier integrals.

Keywords

Acoustic Signature Rayleigh Wave Crack Opening Displacement Acoustic Imaging Imperfect Interface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Achenbach, J.D., Kitahara, M., Mikata, Y. and Sotiropoulos, D.A. 1988. Reflection and transmission of plane waves by a layer of compact inhomogeneities. Pure Appl. Geophys. 128: 101–118.CrossRefGoogle Scholar
  2. Ahn, V.S., Harris, J.G. and Achenbach, J.D. 1992. Numerical analysis of the acoustic signature of a surface-breaking crack. IEEE Trans. Ultrason. Ferroelect. Freq. Cont. 39: 112–118.CrossRefGoogle Scholar
  3. Angel, Y.C. and Achenbach, J.D. 1984. Reflection and transmission of obliquely incident Rayleigh waves by a surface-breaking crack. J. Acoust. Soc. Am. 75: 313–319.MATHCrossRefGoogle Scholar
  4. Auld, B.A. 1979. General electromechanical reciprocity relations applied to the calculation of elastic wave scattering coefficients. Wave Motion 1: 3–10.CrossRefGoogle Scholar
  5. Baik, J.-M. and Thompson, R.B. 1979. Ultrasonic scattering from imperfect interfaces: a quasi-static model. J. Nondestr. Eval. 4: 177–196.CrossRefGoogle Scholar
  6. Brekhovskikh, L. M. and Godin, O.A. 1990. Acoustics of layered media I. New York: Springer. pp. 91–97 and pp. 105-112.CrossRefGoogle Scholar
  7. Briggs, G.A.D. 1992. Acoustic microscopy. New York: Oxford University Press.Google Scholar
  8. Chizhik, D., Davids, D.A. and Bertoni, H. L. 1992. A modified ray theory for predicting the V(x,z) response of a point-focus acoustic mocroscope in the presence of a crack. J. Acoust. Soc. Am. 91: 3265–3290.CrossRefGoogle Scholar
  9. Harris, J.G. 1987. Edge-diffraction of a compressional beam. J. Acoust. Soc. Am. 82: 635–646.CrossRefGoogle Scholar
  10. Harris, J.G. and Pott, J. 1985. Further studies of scattering of a Gaussian beam from a fluid-solid interface. J. Acoust. Soc. Am. 78: 1072–1080.MATHCrossRefGoogle Scholar
  11. Harris, J.G., Rebinsky, D.A. and Wickham, G.R. 1996. An integrated model of scattering from an imperfect interface. J. Acoust. Soc. Am. 99: 1315–1325.CrossRefGoogle Scholar
  12. Ilett, C., Somekh, M.G. and Briggs, G.A.D. 1984. Acoustic microscopy of elastic discontinuities. Proc. R. Soc. Lond. A 393: 171–183.CrossRefGoogle Scholar
  13. Kim, J.O., Achenbach, J.D., Mirkarimi, P.B., Shinn, M. and Barnett, S.A. 1992a. Elastic constants of single-crystal transition-metal nitride films measured by line-focus acoustic microscopy. J. Appl. Phys. 72: 1805–1811.CrossRefGoogle Scholar
  14. Kim, J.O., Achenbach, J.D., Shinn, M. and Barnett, S.A. 1992b. Effective elastic constants and acoustic properties of single-crystal TiN/NbN superlattices. J. Mater. Res. 7: 2248–2256.CrossRefGoogle Scholar
  15. Kushibiki, J. and Chubachi, N. 1985. Material characterization by line-focus beam acoustic microscope. IEEE Trans. Sonics Ultrason. 32: 189–212.CrossRefGoogle Scholar
  16. Lee, Y.C., Kim, J.O. and Achenbach, J.D. 1993. V(z) curves of layered anisotropic materials for the line-focus acoustic microscope. J. Acoust. Soc. Am. 94: 923–930.CrossRefGoogle Scholar
  17. Lemons, R.A. and Quate, C.F. 1979. Acoustic microscopy. In Physical acoustics, Vol. 14, ed. W.P. Mason and R.N. Thurston. pp. 1–92. New York: Academic.Google Scholar
  18. Liang, K.K., Kino, G. S. and Khuri-Yakub, B.T. 1985. Material characterization by inversion of V(z). IEEE Trans. Sonics Ultrason. 32: 213–224.CrossRefGoogle Scholar
  19. Li, Z.L., Achenbach, J.D. and Kim, J.O. 1991. Effect of surface discontinuities on V(z) and V(z,x) for the line-focus acoustic microscope. Wave Motion 14: 187–203.CrossRefGoogle Scholar
  20. Margetan, F.J., Thompson, R.B., Rose, J.H. and Gray, T.A. 1992. The interaction of ultrasound with imperfect interfaces: experimental studies of model structures. J. Nondestr. Eval. 11: 109–26.CrossRefGoogle Scholar
  21. Mikata, Y. 1993. Reflection and transmission by a periodic array of coplanar cracks: normal and oblique incidence. J.Appl. Mech. 60: 911–919.MATHCrossRefGoogle Scholar
  22. Mikata, Y. and Achenbach, J.D. 1988. Reflection and transmission by an infinite array of randomly orientated cracks. J. Acoust. Soc. Am. 83: 38–45.CrossRefGoogle Scholar
  23. Nikoonahad, M. 1984. Recent advances in high resolution acoustic microscopy. Con-temp. Phys. 25: 129–158.Google Scholar
  24. Pott, J. and Harris, J.G. 1984. Scattering of an acoustic Gaussian beam from a fluid-solid interface. J. Acoust. Soc. Am. 76: 1829–1838.MATHCrossRefGoogle Scholar
  25. Rebinsky, D.A. and Harris, J.G. 1992a. An asymptotic calculation of the acoustic signature of a cracked surface for the line focus scanning acoustic microscope. Proc. R. Soc. Lond. A 436: 251–265.MATHCrossRefGoogle Scholar
  26. Rebinsky, D.A. and Harris, J.G. 1992b. The acoustic signature for a surface-breaking crack produced by a point focus microscope. Proc. R. Soc. Lond. A 438: 47–65.CrossRefGoogle Scholar
  27. Saad, A., Bertoni, H.L. and Tamir, T. 1974. Beam scattering by nonuniform leaky-wave structures. Proc. IEEE 11: 1552–1561.CrossRefGoogle Scholar
  28. Shiloh, K., Bond, L.J. and Som, A.K. 1993. Detection limits for single small flaws and groups of flaws when using focused ultrasonic transducers. Ultrasonics 31: 395–404.CrossRefGoogle Scholar
  29. Somekh, M.G., Bertoni, H.L., Briggs, G.A.D. and Burton, N.J. 1985. A two-dimensional imaging theory of surface discontinuities with the scanning acoustic microscope. Proc. R. Soc. Lond. A 401: 29–51.CrossRefGoogle Scholar
  30. Somekh, M.G., Briggs, G.A.D. and Ilett, C. 1984. The effect of elastic anisotropy on contrast in the scanning acoustic microscope. Phil. Mag. A 49: 179–204.CrossRefGoogle Scholar
  31. Sotiropoulos, D.A. and Achenbach, J.D. 1988. Reflection of elastic waves by a distribution of coplanar cracks. J. Acoust. Soc. Am. 84: 752–759.CrossRefGoogle Scholar
  32. Stamnes, J.J. 1986. Waves in focal regions. Bristol: Adam Hilger. pp.243–281 and pp. 377-389.MATHGoogle Scholar
  33. Yogeswaren, E. and Harris, J.G. 1994. A model of a confocal ultrasonic inspection system for interfaces. J. Acoust. Soc. Am. 96: 3581–3592.CrossRefGoogle Scholar
  34. Wickham, G. 1992. A polarization theory for scattering of sound at imperfect interfaces. J. Nondestr. Eval. 11: 199–210.CrossRefGoogle Scholar
  35. Wickham, G. 1995. A general theory of scattering by thin interface layers, plates and shells. Preprint.Google Scholar
  36. Yamanaka, K. and Enomoto, Y. 1982. Observations of surface cracks with scanning acoustic microscope. J. Appl. Phys. 53: 846–850.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • John G. Harris
    • 1
  1. 1.Theoretical and Applied Mechanics, UIUC, 216 Talbot LaboratoryUrbanaUSA

Personalised recommendations