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Determination of Grain-Size Distributions from Ultrasonic Attenuation

  • Aran Anderson
  • Denise Nicoletti

Abstract

The overall research goal of this project is the nondestructive measurement of grain-size distribution parameters using ultrasonic attenuation. Ultrasonic attenuation α is dependent upon the sound wavelength (λ), the size of the grains (D), and in many cases elastic constants and sound velocities of the material. Assuming that multiple scattering can be ignored, the expression for the wavelength dependence of the attenuation is
$$ \alpha (\lambda ) = \int\limits_0^\infty {N(D)\,\alpha (\lambda, D)\,} \,dD $$
(1)
where N(D) is the grain-size distribution. In previous work [1] the sizes were assumed to be distributed following a power-law with exponent γ:
$$ N(D) = K{D^{ - \gamma }},0 < D < \infty $$
(2)
Different justifications for this assumption have been provided [1]. After substituting the power-law expression for the grain-size distribution, the attenuation was shown to be a power-law:
$$ \alpha (\lambda ) = K'\,{\lambda^{ - \gamma }} $$
(3)

Keywords

Inverse Fourier Transform Wavelength Dependence Ultrasonic Attenuation Worcester Polytechnic Institute Nondestructive Measurement 
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.

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References

  1. 1.
    D. W. Nicoletti, “Scaling Properties of Ultrasonic Attenuation and Grain Size in Metals,” Ph.D. Thesis, Drexel University, 1991.Google Scholar
  2. 2.
    D. W. Nicoletti, N. Bilgutay, B. Onaral, JASA 91, 3278 (1992).Google Scholar
  3. 3.
    D. Nicoletti, A. Anderson, IEEE UFFC Symp. Proc. 2 701 (1993).Google Scholar
  4. 4.
    A. Anderson, “A Study of the Relationships Between Ultrasonic Attenuation and Grain-Size Distributions in Polycrystalline Materials,” M.S. Thesis, Worcester Polytechnic Institute, 1995.Google Scholar
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    A. J. Jerri, Introduction to Integral Equations with Applications (Marcel Decker, New York, 1985).MATHGoogle Scholar
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    E. P. Papadakis, Methods of Experimental Physics. ed. P. D. Edmonds, (Academic Press, New York, 1981) 19, Chap. 5.Google Scholar
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    D. W. Nicoletti, D. Kasper. IEEE Trans UFFC 41 144 (1994).Google Scholar
  8. 8.
    Roney, R. K., “The Influence of Metal Grain Size on the Attenuation of an Ultrasonic Wave,” Ph.D. thesis, California Institute of Technology, 1950.Google Scholar

Copyright information

© Plenum Press, New York 1996

Authors and Affiliations

  • Aran Anderson
    • 1
  • Denise Nicoletti
    • 1
  1. 1.Electrical and Computer Engineering DepartmentWorcester Polytechnic InstituteWorcesterUSA

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