NDTnet - March 1996, Vol.1 No.03

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Chapter VI

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CONCLUSIONS
The specialized techniques [l5] that are available at the Acoustic and Ultrasonic Properties of Materials Laboratory allow us to perform difficult ultrasonic velocity measurements as well as other kinds of acoustic measurement, including acoustic emission detection. We are continuously upgrading techniques through ongoing research projects, and stay abreast of new methods through close contact with researchers around the world. The personnel at the Acoustic Laboratory are always available to discuss and assist with unique problems from requestors.
ACKNOWLEDGMENTS
The author wishes to express his appreciation to D. R. Green for his valuable experimental contributions, including his discovery of Saran Wrap as an ultrasonic coupling agent, to George Yanes for his assistance in computer programming and electronic instrumentation, and to Dr. C. A. Tatro for his valuable consultation.
REFERENCES
  1. R. Truell, C. Elbaum, and B. B. Chick, Ultrasonic Methods in Solid State Physics (Academic Press, New York, 1969), pp. 53-158, 183-186, 365-368.
  2. T. F. Hueter and R. H. Bolt, Sonics (John Wiley and Sons, Inc., New York, 1955), pp. 32-38.
  3. H. J. McSkimin, J. Acoust. Soc. Am. 33,(1),12-16 (1961).
  4. H. J. McSkimin and P. Andreatch, J. Acoust. Soc. Am. 34, 609-615 (1962).
  5. H. J. McSkimin, J. Acoust. Soc. Am. 33,(1), 12-16 (1961).
  6. E. P. Papadakis, J. Acoust. Soc. Am. 42, 1045-1051 (1967).
  7. E. P. Papadakis, J. Acoust. Soc. Am. 40, 863-876 (1966).
  8. J. F. Nye, Physical Properties of Crystals (Oxford University Press, London, 1957).
  9. B. Carlin, Ultrasonics (McGraw-Hill, New York, 1960), pp. 33-36.
  10. R. Goldman, Ultrasonic Technology (Reinhold Publishing Corp., New York, 1962).
  11. H. L. Dunegan, "High Temperature Dynamic Modulus Measurements by Use of Ultrasonics," Materials Evaluation 22 (6), 266-272 (1964).
  12. H. J. McSkimin, Physical Acoustics, W. P. Mason, Ed. (Academic Press, New York and London, 1966), vol. 1, part A, pp. 272-334.
  13. M. B. Reynolds, "The Determination of the Elastic Constants of Metals by the Ultrasonic Pulse Technique," Trans. Am. Soc. for Metals 45, 839-861 (1953).
  14. C. F. Cline, H. L. Dunegan, and G. W. Henderson, J. Acoust. Soc. Am. 38(4), 1944-1948 (1967).
  15. L. C. Lynnworth, Materials Evaluation, 25(12), 265-277 (1967).
  16. L. E. Kinsler and A. R. Frey, Fundamentals of Acoustics (John Wiley & Sons, New York, 1962), 2nd ed.
  17. F. Filipczynski, A. Pawlowski, and J. Wehr, Ultrasonic Methods of Testing Materials (Butterworth & Co., London, 1966). [Translation].
  18. C. F. Brockelsby, J. S. Palfreeman, and R. W. Gibson, Ultrasonic Delay Lines (London Iliffe, Book Dorset House, Stanford Street, London, 1963).
  19. H. J. McSkimin, J. Acoust. Soc. Am. 37(5), 864-871 (1965).
  20. H. Seki, A. Granato, and R. Truell, J. Acoust. Soc. Am. 28(2), 230-238 (1956).
  21. R. C. McMaster, Ed., Nondestructive Testing Handbook (American Society for Nondestructive Testing, The Ronald Press Co., New York, 1959), vol. 2, p. 43.11.
  22. O. L. Anderson, Physical Acoustics, W. P. Mason, Ed. (Academic Press, New York and London, 1965), vol. 3, part B, pp. 43-95.
  23. O. L. Anderson, E. Schreiber, and R. C. Lieberman, Review of Geophysics 6(4), 491-524 (1968).
  24. D.M. Egle, A.E. Brown, "Considerations for the Detection of Acoustic Emission Waves in Thin Plates", J. Acoust. Soc. Am. 57(3), 1975.
  25. E. P. Papadakis, J. Acoust. Soc. Am. Vol. 44, No. 5, 1437-1441 (1968).
ABOUT THE REFERENCES
A larger list of references could undoubtedly have been presented. However, each of these references contains an ample supply of references, should a more extensive investigation be warranted.

The first fifteen references are discussed in the text of this report. Of the remaining eight, the ASNT handbook [21] contains a most liberal review of techniques, along with some limited theory. This handbook is currently under revision, and when the new edition becomes available, it may contain much of the information on pulse overlap and pulse superposition contained in references 1, 3, 4, 5, 6, 7, 19, and 20. References 22 and 23 contain information on the techniques of determining the dynamic elastic moduli in geologic formation, and much of this theory is applicable to a variety of other structural materials. References 16 and 17 contain general ultrasonic theory and information on methods, similar to the information presented in references 2, 9, and 10.

Recent advancements in the technology of detecting and propagating ultrasonic waves in filaments and thin wires l5,l8 have been of great value to some industries concerned with product quality control, and measurements of elastic constants over extreme temperature ranges. These advancements were made possible by new designs in ultrasonic transducers. Should this technology become required at LLNL, equipment is commercially available for use from -273°C to 5000°C.

Appendix A
Interdepartmental letterhead
Mail Station L - 333
Ext: 2-7089
Current Date

TO : Client
FROM: Al Brown
SUBJECT: DYNAMIC MODULI FOR COMMERCIAL GRADE VANADIUM The ultrasonic velocities were measured on vanadium plate in preparation for ultrasonic inspection of tubing. The estimated accuracy for the ultrasonic velocities is ±1%. It should be noted that the listed values may be specimen specific.
Specimen I.D. Vanadium
Geometry (cm) Plate
Thickness (mm) 1.55
Density (kg/m 3 ) 6,134
Frequency, MHz (Vl) 30.00
Frequency, MHz (Vs) 20.00
Longitudinal Velocity (m/s) 5,965
Shear Velocity (m/s) 2,626
Thin Rod Velocity (m/s) 4,362
Rayleigh Velocity (m/s) 2,465
Poisson's Ratio 0.3798
Young's Modulus (GPa) 116.7
Shear Modulus (GPa) 42.3
LameŽ Modulus (GPa) 133.7
Bulk Modulus (GPa) 161.9

Lower test frequencies were found inadequate. At 30 MHz, there are approximately 8 wavelengths of material thickness thereby avoiding the possibility of wave interference. The proposed tubing of the same material has a nominal wall thickness of 0.635 mm (0.025 inch), about 3 wavelengths thick at 30 MHz. A 30 MHz, highly damped broad band transducer will probably suffice if used with a wide bandwidth, high frequency receiver. A crack width of 50.8 mm (0.002 inch) will be approximately one quarter wavelength and will reflect the sound at 30 MHz if the crack length is in-plane and is at least 3.5 wavelengths (0.8 mm) long oriented normal to the sound propagation direction. A 30 MHz transducer with a spherical focal length of one inch should be able to detect a flaw of 8 nm 2 (13 microinch exp. 2 ) area.
Appendix B

ATTENUATION OF ULTRASOUND

GENERAL EQUATIONS:

For pulse-echo:

Where:
I2/I1 = ratio of intensities at two points a unit distance apart, and I2 < I1.
P2/P1 = ratio of pressures at two points a unit distance apart, and P2 < P1.
a = attenuation constant (nepers/unit distance)
a' = 8.686 a (dB/cm)
A = l a (nepers/wavelength) where l equals velocity/frequency
A 1 = 8.686 l a (dB/wavelength)

ATTENUATION RESULTS FROM:

  1. Beam spread (finite transducer size)
  2. Field effects
  3. Couplant mismatch (direct couplant reflection loss, waterbuffer)
  4. Transducer loading (couplant or specimen)
  5. Sample geometry (defect reflection: size, shape, surface, impedance)
  6. Diffraction pattern (losses from beam divergence, wave front phase effects)
  7. Non parallelism (rough surfaces)
  8. Absorption:
    a) Dislocation damping (radiation damage, internal oxidation)
    b) Motion of domain walls
    c) Magnetic "rotation" effect near saturation
    d) Visco-elastic losses (thermo-elastic losses, diffusion of atoms)
  9. Scattering:
    a) By small objects
    b) By extended (internal) surfaces (reflection)
    c) By wave front phase effects (bending and distortion) due to space variation, velocity, refraction index
  10. Diffusion
  11. Viscous damping losses
  12. Relaxation losses
And, finally, attenuation caused by grain size, yield strength, crystalline damage, impact strength, and hardness.
Appendix C

ATTENUATION MEASUREMENTS 25

BUFFER ROD TECHNIQUE

The reflection coefficient at the buffer-sample interface must have a moderate value so that the transmitted and reflected portions of the wave at the buffer-sample interface have comparable amplitudes. Nearly equal acoustic impedances in the two materials are required.

The loss per echo of the multiple echoes in the buffer rod must be sufficient in the short buffer case to ensure that these echoes do not interfere with the echoes returning from the sample.

In the long buffer rod, the attenuation should be very low. In either case, the sample echoes should not coincide with the buffer echoes, but have well-separated echoes.

Short buffer with long specimen




Long buffer with short specimen









FORWARD PROPAGATION
R = ( Z2 - Z1 )/ ( Z2 + Z1 )
T = R + 1 = ( Z2 - Z1 )/( Z2 + Z1 ) + 1

REVERSE PROPAGATION
R ' = ( Z1 - Z2 )/(Z1 + Z2 )
T ' = ( Z1 - Z2 )/(Z1 + Z2 ) + 1

DEFINITIONS
A 0 = R = ( Z2 - Z1 )/( Z2 + Z1 )First Interface Reflection, Buffer-Specimen
A 1 = TT ' = [ ( Z2 - Z1 )/( Z2 + Z1 ) + 1 ] [( Z1 - Z2 )/( Z1 + Z2 ) + 1 ) ]
A 1 = 4 Z2 Z1 /( Z1 + Z2 )² First Reflection from Specimen Back Surface
But: A 1 oo R and T=R+1 T '=1-R
Therefore: A1 = TT ' = (R + 1)(1 - R) = 1 - R²
And: A2 = TR ' T ' = ( R + 1)(1 - R)( R _) = R _(1 - R ²)
Where R _is the phase reversal on the second reflection: numerically the same as R, but reversed polarity.

ATTENUATION
A1 = ( 1- R² ) e (exp) -a2L
A2 = R ( 1- R² ) e (exp) -a4L
a = nepers per unit length

AMPLITUDE RATIO
B0 = A0 / A1 = R e (exp) -a2L / ( 1- R² )
B2 = A2 / A1 = R e (exp) -a2L
B0B2 = [(R e (exp) -a2L ) R e (exp) -a2L] / (1- R²) = [ (1)R² ] / [ 1 - R² ]
R = [ B0 B2 / (1 + B0 B2 )]½
R = { (A2 /A1) (A0/A1) / [1 + (A2/A1) (A0/A1)]} ½
a = [ ln ( R / B2 ) ]/ 2L
a = { ln [[((A2/A1) (A0/A1)) / (1 + (A2/A1)(A0/A1))]½ /(A2/A1)]}/ 2L

ACOUSTIC IMPEDANCE PRESSURE WAVES INTENSITY POWER DENSITY

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Rolf Diederichs 13.Febr.1996, info@ndt.net

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