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The Inverse Problem in Materials Characterization through Ultrasonic Attenuation and Velocity Measurements

  • Emmanuel P. Papadakis

Abstract

The inverse problem in materials characterization is most often skipped over in favor of a correlation because the inverse problem is so difficult and the correlation is only tedious, not hard. In this talk the basic difficulty in the inverse problem field will be illustrated by two examples: finding grain size in metals when ultrasonic attenuation is measured, and finding graphite shape in cast iron when ultrasonic velocity is measured.

The basic difficulty arises because the measured quantity, attenuation or velocity, is a function of several variables. Thus, any single variable among the latter cannot be written as a single-valued function of the measured quantity.

For instance, attenuation α, caused by grain scattering, is a function of frequency f, grain diameter D, grain substructure μ, grain size distribution “GSD”, and the ratio of the grain diameter to the ultrasonic wavelength D/λ. The total attenuation “ATT” is also a function of geometrical beam spreading “BS” (which depends on sample anisotropy) as well as on physical absorption mechanisms “ABS” which in turn are functions of frequency and other parameters.

We have
$$ ATT = \alpha + ABS + BS $$
(1)
The portion BS can be calculated and subtracted out immediately as long as the macroscopic sample anisotropy is known. The portion ABS may then be separable by multi-frequency measurements or by changing other environmental parameters (temperature, magnetic field) which may influence it, or by calculating it in the simplest cases like thermoelastic losses. The remainder, a, is frequently numerically the largest of the three terms. The term a is written symbolically as
$$ \alpha = \alpha (D,{\kern 1pt} GSD,{\kern 1pt} \mu ,{\kern 1pt} D/\lambda ,{\kern 1pt} f) $$
(2)
The variables combine in such a way that there is a function F of D, GSD, and D/λ; another function n of D/λ; a coefficient A which is a function of n; and the term μ2. The result is
$$ \alpha = AF{\kern 1pt} {\mu ^{2}}{\kern 1pt} {f^{n}} $$
(3)
The multiple factors discussed above make it obvious that the simplistic hope of finding
$$ \bar{D} = \bar{D}{\kern 1pt} (\alpha ) $$
(4)
will not be fulfilled in engineering materials, and that many factors must be taken into account.

The talk will present further clarifications of these challenging research opportunities using ultrasonic attenuation and velocity.

Keywords

Inverse Problem Grain Size Distribution Physical Acoustics Ultrasonic Velocity Ductile Iron 
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.
    ARPA/AFML Program on Quantitative NDE: Various reports issued by WADC/WPAFB, Ohio, 1969 — date.Google Scholar
  2. 2.
    Papadakis, E. P., “Ultrasonic Attenuation Caused by Scattering in Polycrystalline Media,” in Physical Acoustics; Principles and Methods, Vol. IV Part B, W. P. Mason, editor, Academic Press, New York, 1968, pp. 269–328.Google Scholar
  3. 3.
    Papadakis, E. P., “Scattering in Polycrystalline Media,” in Methods of Experimental Physics — Ultrasonics, P. D. Edmonds, editor, Academic Press, New York, 1981, pp. 237–298.Google Scholar
  4. 4.
    Papadakis, E. P. “Physical Acoustics and the Microstructure of Iron Alloys,” Internat. Metals Rev. (to be published).Google Scholar
  5. 5.
    Papadakis, E. P., “Ultrasonic Attenuation by Spectrum Analysis of Pulses in Buffer Rods: Method and Diffraction Corrections,” J. Acoust. Soc. Amer. 53, 1336–1343 (1973).CrossRefGoogle Scholar
  6. 6.
    Papadakis, E. P., “Ultrasonic Diffraction Loss and Phase Change in Anisotropic Materials,” J. Acoust. Soc. Amer. 40, 863–876 (1966).CrossRefGoogle Scholar
  7. 7.
    Mansour, T. M., “Evaluation of Ultrasonic Transducers by Cross-Sectional Mapping of the Near Field Using A Point Reflector,” Mater. Eval. 37 (7), 50–54 (June 1979).Google Scholar
  8. 8.
    Zener, C., Elasticity and Anelasticity of Metals, U. of Chicago Press, Chicago, Ill., 1948.Google Scholar
  9. 9.
    Lucke, K., “Ultrasonic Attenuation Caused by Thermoelastic Heat Flow,” J. Appl. Phys. 27, 1433–1438 (1956).CrossRefGoogle Scholar
  10. 10.
    Granato, A. and Lucke, K., “Theory of Mechanical Damping Due to Dislocations,” J. Appl. Phys. 27 583–593 (1956).CrossRefGoogle Scholar
  11. 11.
    Mason, W. P., Physical Acoustics and the Properties of Solids, Van Nostrand, Princeton, 1959, pp. 209–224.Google Scholar
  12. 12.
    Lifshitz, E. M. and Parkhomovskii, G. D., Zh. Eksperim. i Teoret., Fiz. 20, 175–182 (1950).Google Scholar
  13. 13.
    Bhatia, A. B., “Scattering of High-Frequency Sound Waves in Polycrystalline Materials,” J. Acoust. Soc. Amer. 31, 16–23 (1959).CrossRefGoogle Scholar
  14. 14.
    Bhatia, A. B. and Moore, R. A., “Scattering of High-Frequency Sound Waves in Polycrystalline Materials II,” J. Acoust. Soc. Amer. 31, 1140–1142 (1959).CrossRefGoogle Scholar
  15. 15.
    Merkulov, L. G., “Investigation of Ultrasonic Scattering in Metals,” Sov. Phys. — Tech. Phys. 1 (1), 59–69 (Oct. 1956), from J. Tech. Phys. (USSR) 26, 64–73 (1956).Google Scholar
  16. 16.
    Mason, W. P. and McSkimin, H. J., “Energy Losses of Sound Waves in Metals Due to Scattering and Diffusion,” J. Appl. Phys. 19, 940–946 (1948).CrossRefGoogle Scholar
  17. 17.
    Papadakis, E. P., “Grain Size Distribution in Metals and Its Influence on Ultrasonic Attenuation Measurements,” J. Acoust. Soc. Amer. 33, 1616–1621 (1961).CrossRefGoogle Scholar
  18. 18.
    Papadakis, E. P., “From Micrograph to Grain Size Distribution With Ultrasonic Applications,” J. Appl. Phys. 35, 1586–1594 (1964).CrossRefGoogle Scholar
  19. 19.
    Kamigaki, K., “Ultrasonic Attenuation in Steel and Cast Iron,” Sci. Rep. RITU Tohoku Univ., Sendai, Japan, A-9, 48–77 (1957).Google Scholar
  20. 20.
    Papadakis, E. P., “Ultrasonic Attenuation and Velocity in Three Transformation Products in Steel,” J. Appl. Phys. 35, 1474–1482 (1964).CrossRefGoogle Scholar
  21. 21.
    Papadakis, E. P., “Ultrasonic Attenuation and Velocity in S.A.E. 52100 Steel Quenched from Various Temperatures,” Met. Trans. 1, 1053–1057 (1970).Google Scholar
  22. 22.
    Papadakis, E. P. and Reed, E. L., “Ultrasonic Detection of Changes in the Elastic Properties of a 70–30 Iron-Nickel Alloy Upon Heat Treatment,” J. Appl. Phys. 32, 682–687 (1961).CrossRefGoogle Scholar
  23. 23.
    Papadakis, E. P., “Influence of Preferred Orientation on Ultrasonic Grain Scattering,” J. Appl. Phys. 36, 1738–1740 (1965).CrossRefGoogle Scholar
  24. 24.
    Morse, P. M., Vibration and Sound, 2nd Edition, McGraw-Hill, New York, 1948, pp. 347–352.Google Scholar
  25. 25.
    Morse, P. M. and Ingard, K. U., Theoretical Acoustics, McGraw-Hill, New York, 1968, pp. 401–407.Google Scholar
  26. 26.
    Lord Rayleigh, Theory of Sound, Macmillan Co., New York, 1929, Vol. II, p. 152.Google Scholar
  27. 27.
    Huntington, H. B., “On Ultrasonic Scattering by Polycrystals,” J. Acoust. Soc. Amer. 22, 362–364 (1950).CrossRefGoogle Scholar
  28. 28.
    Papadakis, E. P., “Revised Grain Scattering Formulas and Tables,” J. Acoust. Soc. Amer. 37, 703–710 (1965).CrossRefGoogle Scholar
  29. 29.
    Papadakis, E. P., “Ultrasonic Attenuation Caused by Scattering in Polycrystalline Metals,” J. Acoust. Soc. Amer. 37, 711–717 (1965).CrossRefGoogle Scholar
  30. 30.
    Papadakis, E. P., “Ultrasonic Attenuation in S.A.E. 3140 and 4150 Steel,” J. Acoust. Soc. Amer. 32, 1628–1639 (1960).CrossRefGoogle Scholar
  31. 31.
    Papadakis, E. P., “Ultrasonic Study of Simulated Crystal Symmetries in Polycrystalline Aggregates,” IEEE Trans. SU-11, 9–29 (1964).Google Scholar
  32. 32.
    Plenard, E. “The Elastic Behavior of Cast Iron,” National Metal Congress, Cleveland, 1964.Google Scholar
  33. 33.
    Fuller, A. G., Emerson, P. J. and Sergeant, G. F., “A Report on the Effect Upon Mechanical Properties of Variations in Graphite Form in Irons Having Varying Amounts of Ferrite and Pear lite in the Matrix Structure....,” AFS Trans. 88, 21–50 1980).Google Scholar
  34. 34.
    Sergeant, G. F. and Fuller, A. G., “The Effect Upon Mechanical Properties of Variation in Graphite Form in Irons Having Varying Amounts of Carbide in the Matrix Structure....,” AFS Trans. 88, 545–574 (1980).Google Scholar
  35. 35.
    Patterson, B. R. and Bates, C. E., “Nondestructive Property Prediction in Grey Cast Iron Using Ultrasonic Techniques,” AFS Trans. 89, 369–378 (1981).Google Scholar
  36. 36.
    Henderson, H. E., “Ultrasonic Velocity Technique for Quality Assurance of Ductile Iron Castings,” The Iron Worker 37 (3), Summer 1973.Google Scholar
  37. 37.
    Kovacs, B. V. and Cole, G. “On the Interaction of Acoustic Waves With S. G. Iron Castings,” Trans. AFS 83, 497–510 (1977).Google Scholar
  38. 38.
    Henderson, H. E., “The Effect of Heat Treatment on Ultrasonic Velocity of Ductile Iron Castings,” The Iron Worker 40 (3), Summer 1976.Google Scholar
  39. 39.
    Papadakis, E. P., “Morphological Severity Factor for Graphite Shape in Cast Iron and Its Relation to Ultrasonic Velocity and Tensile Properties,” AFS Trans. (to be published).Google Scholar
  40. 40.
    Papadakis, E. P., “Ultrasonic Velocity and Attenuation: Measurement Methods With Scientific and Industrial Applications,” in Physical Acoustics: Principles and Methods, Vol. XII, W. P. Mason and R. N. Thurston, editors, Academic Press, New York, 1976, pp. 343–348.Google Scholar
  41. 41.
    Lysaght, V. E., Indentation Hardness Testing, Reinhold, N.Y., 1949, pp. 134–135 and 150–153.Google Scholar
  42. 42.
    Giza, P. and Papadakis, E. P., “Eddy Current Tests for Hardness Certification of Gray Iron Castings,” Mater. Eval. 37(8), 45–50, 55 (July 1979).Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Emmanuel P. Papadakis
    • 1
  1. 1.Manufacturing Processes LaboratoryFord Motor CompanyRedfordUSA

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