Skip to main content

Interface waves along an anisotropic imperfect interface between anisotropic solids

Abstract

First and second order asymptotic boundary conditions are introduced to model a thin anisotropic layer between two generally anisotropic solids. Such boundary conditions can be used to describe wave interaction with a solid-solid imperfect anisotropic interface. The wave solutions for the second order boundary conditions satisfy energy balance and give zero scattering from a homogeneous substrate/layer/substrate system. They couple the in-plane and out-of-plane stresses and displacements on the interface even for isotropic substrates. Interface imperfections are modeled by an interfacial multiphase orthotropic layer with effective elastic properties. This model determines the transfer matrix which includes interfacial stiffness and inertial and coupling terms. The present results are a generalization of previous work valid for either an isotropic viscoelastic layer or an orthotropic layer with a plane of symmetry coinciding with the wave incident plane. The problem of localization of interface waves is considered. It is shown that the conditions for the existence of such interface waves are less restrictive than those for Stoneley waves. The results are illustrated by calculation of the interface wave velocity as a function of normalized layer thickness and angle of propagation. The applicability of the asymptotic boundary conditions is analyzed by comparison with an exact solution for an interfacial anisotropic layer. It is shown that the asymptotic boundary conditions are applicable not only for small thickness-to-wavelength ratios, but for much broader frequency ranges than one might expect. The existence of symmetric and SH-type interface waves is also discussed.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    R. Stoneley, Elastic waves at the surface of separation of two solids,Proc. Roy. Soc. Lond. A 106416–428 (1924).

    Google Scholar 

  2. 2.

    K. Sezawa and K. Kanai, The range of possible existence of Stoneley waves, and some related problems,Bull. Earth Res. Inst. 171–8 (1939).

    Google Scholar 

  3. 3.

    J. G. Scholte, The range of existence of Rayleigh and Stoneley waves,Mont. Not. Roy. Astr. Soc. Geophys. Suppl. 5120–126 (1947).

    Google Scholar 

  4. 4.

    A. S. Ginzbarg and E. Strick, Stoneley wave velocities for a solid-state interface,Bull. Seismol. Soc. Am. 4851–63 (1958).

    Google Scholar 

  5. 5.

    W. L. Pilant, Complex roots of the Stoneley-wave equation,Bull. Seismol. Soc. Am. 62285–299 (1975).

    Google Scholar 

  6. 6.

    D. A. Lee and D. M. Corbly, Use of interface waves for nondestructive inspection,IEEE Trans. Sonics Ultras. SU 24 206–212 (1977).

    Google Scholar 

  7. 7.

    R. O. Claus and C. H. Palmer, Direct measurement of ultrasonic Stoneley waves,Appl. Phys. Lett. 31547–548 (1977).

    Google Scholar 

  8. 8.

    T. C. Lim and M. J. P. Musgrave, Stoneley waves in anisotropic media,Nature 225372 (1970).

    Google Scholar 

  9. 9.

    W. W. Johnson, The propagation of Stoneley and Rayleigh waves in anisotropic elastic media,Bull. Seismol. Soc. Am. 601105–1122 (1970).

    Google Scholar 

  10. 10.

    P. Chadwick and P. K. Currie, Stoneley waves at an interface between elastic crystals,Quart. J. Mech. Appl. Math. 27497–503 (1974).

    Google Scholar 

  11. 11.

    A. K. Morocha, T. D. Shermergor, and A. N. Yashina, Propagation of Stoneley waves along an interface between crystals of cubic symmetry,Soviet Phys. Acoust. 20524–527 (1975).

    Google Scholar 

  12. 12.

    A. R. Thölén, Stoneley waves at grain boundaries in copper,Acta. Metall. 32349–356 (1984).

    Google Scholar 

  13. 13.

    D. M. Barnett, J. Lothe, S. D. Gavazza, and M. J. P. Musgrave, Consideration of the existence of interfacial (Stoneley) waves in bonded anisotropic elastic half-spaces,Proc. Roy. Soc. Lond. A 402153–166 (1985).

    Google Scholar 

  14. 14.

    S. I. Rokhlin, M. Hefets, and M. Rosen, An elastic wave guided by a film between two solids,J. Appl. Phys. 513579–3582 (1980).

    Google Scholar 

  15. 15.

    S. I. Rokhlin, M. Hefets, and M. Rosen, An ultrasonic interface wave method for predicting the strength of adhesive bonds,J. Appl. Phys. 522847–2851 (1981).

    Google Scholar 

  16. 16.

    G. S. Murty, A theoretical model for the attenuation and dispersion of Stoneley waves at the loosely bonded interface of elastic halfspaces,Phys. Earth Planet. Inter. 1165–79 (1975).

    Google Scholar 

  17. 17.

    J. M. Baik and R. B. Thompson, Ultrasonic scattering from imperfect interfaces; A quasi-static model,J. Nondestr. Eval. 4177–196 (1984).

    Google Scholar 

  18. 18.

    S. I. Rokhlin and D. Marom, Study of adhesive bonds using low-frequency obliquely incident ultrasonic waves,J. Acoust. Soc. 80585–590 (1986).

    Google Scholar 

  19. 19.

    F. J. Margetan, R. B. Thompson, and T. A. Gray, Interfacial spring model for ultrasonic interaction with imperfect interfaces: Theory of oblique incidence and application to diffusion bonded butt joints,J. Nondestr. Eval. 7131–151 (1988).

    Google Scholar 

  20. 20.

    A. Pilarski and J. L. Rose, A transverse wave ultrasonic oblique-incident technique for interface weakness detection in adhesive bonds,J. Appl. Phys. 63300–307 (1988).

    Google Scholar 

  21. 21.

    A. K. Mal, Guided waves in layered solids with interface zones,Int. J. Eng. Sci. 26873–881 (1988).

    Google Scholar 

  22. 22.

    P. C. Xu and S. K. Datta, Guided waves in a bonded plate: Parametric study,J. Appl. Phys. 676779–6786 (1990).

    Google Scholar 

  23. 23.

    P. B. Nagy and L. Adler, New ultrasonic techniques to evaluate interfaces, inElastic Waves and Ultrasonic Nondestructive Evaluation, A. K. Datta, J. D. Achenbach, and Y. J. Rajapaske, eds. (North-Holland, New York, 1990), pp. 229–239.

    Google Scholar 

  24. 24.

    S. I. Rokhlin and Y. J. Wang, Analysis of ultrasonic wave interaction with imperfect interface between solids, inReview of Progress in Quantitative Nondestructive Evaluation (Vol. 10A), D. O. Thompson and D. E. Chimenti, eds. (Plenum Press, New York, 1991), pp. 185–192.

    Google Scholar 

  25. 25.

    S. I. Rokhlin and Y. J. Wang, Analysis of boundary conditions for elastic wave interaction with an interface between two solids,J. Acoust. Soc. Am. 89503–515 (1991).

    Google Scholar 

  26. 26.

    S. I. Rokhlin and Y. J. Wang, Equivalent boundary conditions for thin orthotropic layer between two solids. Reflection, refraction, and interface waves,J. Acoust. Soc. Am. 911875–1887 (1992).

    Google Scholar 

  27. 27.

    S. I. Rokhlin and W. Huang, Ultrasonic wave interaction with a thin anisotropic interfacial layer between two anisotropic solids: Exact and asymptotic-boundary-condition methods,J. Acoust. Soc. Am. 921729–1742 (1992).

    Google Scholar 

  28. 28.

    S. I. Rokhlin and W. Huang, Generalized boundary conditions for imperfect interface between two anisotropic media, inReview of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti, eds. (Plenum Press, New York, 1992), pp. 169–176.

    Google Scholar 

  29. 29.

    S. I. Rokhlin and W. Huang, Second order Asymptotic boundary conditions for modeling of imperfect interfaces, inReview of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti, eds. (Plenum Press, New York, 1993).

    Google Scholar 

  30. 30.

    A. Boström, P. Bövik, and P. Olsson, Exact first order vs. spring boundary conditions for scattering from thin layers,J. Nondestr. Eval. 11 (1992).

  31. 31.

    G. Wickham, A Polarization theory for the scattering of sound at imperfect interfaces,J. Nondestr. Eval. 11 (1992).

  32. 32.

    A. N. Stroh, Steady state problems in anisotropic elasticity,J. Math. Phys. 4177–103 (1962).

    Google Scholar 

  33. 33.

    K. A. Ingebrigsten and A. Tonning, Elastic surface waves in crystals,Phys. Rev. 184(3):942–951 (1969).

    Google Scholar 

  34. 34.

    A. H. Fahmy and E. L. Adler, Propagation of acoustic waves in multilayers: A matrix description,Appl. Phys. Lett. 22495–497 (1973).

    Google Scholar 

  35. 35.

    E. L. Adler, Matrix methods applied to acoustic waves in multilayers,IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 37485–490 (1990).

    Google Scholar 

  36. 36.

    S. I. Rokhlin, T. K. Bolland, and L. Adler, Reflection and refraction of clastic waves on a plane interface between two generally anisotropic media,J. Acoust. Soc. Am. 79906–918 (1986).

    Google Scholar 

  37. 37.

    O. L. Anderson, inPhysical Acoutics, W. P. Mason, ed. (Academic Press, New York, 1965), pp. 43–95.

    Google Scholar 

  38. 38.

    R. M. Christensen,Mechanics of Composite Materials (2nd Ed., Chap. 3) (Krieger, Malabar, Florida, 1991).

    Google Scholar 

  39. 39.

    P. B. Nagy and L. Adler,Physical Acoustics, O. Leroy and M. A. Breazeale, eds. (Plenum Press, New York, 1991), pp. 529–535.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Huang, W., Rokhlin, S.I. Interface waves along an anisotropic imperfect interface between anisotropic solids. J Nondestruct Eval 11, 185–198 (1992). https://doi.org/10.1007/BF00566409

Download citation

Key words

  • Ultrasonic interface waves
  • boundary conditions
  • imperfect interface
  • anisotropy