Skip to main content

Abstract

When a beam of ultrasound interacts with a flaw in a material, additional scattered waves are generated by the flaw; these waves travel in all directions. The distribution of scattered waves of course, depends strongly on the geometric and material properties of the flaw. In this chapter we characterize scattering responses of flaws in terms of their far-field scattering amplitudes, and we describe both exact and approximate methods of calculating scattering amplitudes. The scattering amplitude is a quantity of fundamental interest, since as shown later this quantity completely characterizes the flaw response in an LTI model of an ultrasonic system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. H. Tan, J. Acoust. Soc. Am. 61 (1977) 928.

    Article  MATH  Google Scholar 

  2. G. S. Kino, Acoustic Waves: Devices, Imaging, and Analog Signal Processing (Prentice-Hall, Englewood Cliffs, NJ, 1987).

    Google Scholar 

  3. J. E. Gubematis, E. Domany, J. A. Krumhansl, and M. Hubermann, J. Appl. Phys. 48 (1977) 2812.

    Article  Google Scholar 

  4. C. F. Ying and R. Truell, J. Appl. Phys. 27 (1956) 1086.

    Article  MathSciNet  MATH  Google Scholar 

  5. Y. H. Pao and C. C. Mow, J. Appl. Phys. 34 (1963) 493.

    Article  MathSciNet  MATH  Google Scholar 

  6. V. V. Varadan, Y. Ma, Y. K. Varadan, and A. Lakhtakia, Scattering of waves by spheres and cylinders in, Field Representations and Introduction to Scattering, Chap. 5 (V. V. Varadan, A. Lakhtakia, and V. K. Varadan, eds.) (Elsevier Science, Amsterdam, 1991).

    Google Scholar 

  7. Y. H. Pao and C. C. Mow, Diffraction of Elastic Waves and Dynamic Stress Concentrations (Crane, Russak, and Co., New York, 1973).

    Google Scholar 

  8. N. Einspruch, E. Witterholt, and R. Truell, J. Appl. Phys. 31 (1960) 806.

    Article  MathSciNet  MATH  Google Scholar 

  9. R. J. McBride and D. W. Kraft, J. Appl. Phys. 43 (1972) 4853.

    Article  Google Scholar 

  10. L. Knopoff, Geophysics 24 (1959) 209.

    Article  MathSciNet  Google Scholar 

  11. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, parts I and II (McGraw-Hill, New York, 1953).

    MATH  Google Scholar 

  12. A. Sedov and L. W. Schmerr, SIAM J. App. Math. 47 (1987) 1201.

    Article  MathSciNet  MATH  Google Scholar 

  13. G. T. Schuster, J. Acoust. Soc. Am. 77 (1985) 865.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Dominguez, Boundary Elements in Dynamics (Elsevier, Amsterdam, 1994).

    Google Scholar 

  15. M. Kitahara, Boundary Integral Equation Methods in Eigenvalue Problems in Elastodynamics and Thin Plates, Studies in Applied Mechanics, vol. 10 (Elsevier, Amsterdam, 1985).

    MATH  Google Scholar 

  16. L. J. Bond, M. Punjani, and N. Safari, Ultrasonic wave propagation and scattering using explicit finite difference methods, in Mathematical Modelling in Nondestructive Testing (M. Blakemore and G. A. Georgiou, eds.) (Clarendon, Oxford, UK, 1988).

    Google Scholar 

  17. R. Ludwig and W. Lord, IEEE Trans. Ultrasonics, Ferroelectrics, and Frequency Control UFFC-35 (1988) 809.

    Article  Google Scholar 

  18. J. L. Opsal and W. M. Visscher, J. Appl. Phys. 58 (1985) 1102.

    Article  Google Scholar 

  19. V. K. Varadan and V. V. Varadan, eds., Acoustic, Electromagnetic, and Elastic Wave Scattering—Focus on the T-matrix Method (Pergamon, New York, 1980).

    Google Scholar 

  20. P. Fellinger and K. J. Langenberg. Numerical techniques for elastic wave propagation and scattering, in Elastic Waves Ultrasonic Nondestructive Evaluation (S. K. Datta, J. D. Achenbach, and Y. S. Rajapakse, eds.) (North Holland, Amsterdam, 1990).

    Google Scholar 

  21. J. J. Bowman, T. B. A. Senior, and P. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes (North Holland, New York, 1969).

    Google Scholar 

  22. P. M. Morse and K. Uno Ingard, Theoretical Acoustics (Princeton Univ. Press, Princeton, NJ, 1968).

    Google Scholar 

Suggested Reading

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media New York

About this chapter

Cite this chapter

Schmerr, L.W. (1998). Flaw Scattering. In: Fundamentals of Ultrasonic Nondestructive Evaluation. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0142-2_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4899-0142-2_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-0144-6

  • Online ISBN: 978-1-4899-0142-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics