Abstract
The scattering of an ultrasonic wave in an elastically inhomogeneous medium results in a frequency dependent velocity and attenuation of the wave. The ultrasonic attenuation and dispersion are therefore sensitive to the microstructure of the material. Since the microstructure also has an important effect on material properties there is considerable interest in the development of ultrasonic techniques for the determination of fracture toughness, hardness, impact strength, yield strength and tensile strength for example [1]. Variations in the microstructure within a sample and from sample to sample may arise from composition fluctuations, inclusions, grain growth due to faulty heat treatment, incorrect fibre fraction in composites, porosity and microcracking. In contrast to the elastic constants of the material, which can be obtained from ultrasonic measurements at a single frequency, the determination of the above mentioned properties requires the measurement of the frequency dependence of the velocity or attenuation. An example is the use of ultrasonics to predict the yield strength of plain carbon steel [2]. This prediction is based on the Hall-Petch relations, which relate the yield strength and impact transition temperature to the mean grain size, an important parameter determining the frequency dependence of the ultrasonic attenuation.
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References
SAYERS, C.M., Characterisation of microstructures using ultrasonics, in Ultrasonic Methods in Evaluation of Inhomogeneous Materials edited by A. Alippi and W.G. Mayer, pp 175–183, Martinus Nijhoff, 1987.
KLINMAN, R., WEBSTER, G.R., MARSH, F.J. AND STEPHENSON, E.T. (1980) Ultrasonic prediction of grain size, strength and toughness in plain carbon steel, Mat. Eval., 38, 26.
YING, C.F. AND TRUELL, R. (1956) Scattering of a plane longitudinal wave by a spherical obstacle in an isotropically elastic solid, J. Appl. Phys., 27, 1086–1097.
FOLDY, L.L. (1945) The multiple scattering of waves, Phys. Rev, 67 107–119.
LAX, M. (1952) Multiple scattering of waves II. The effective field in dense systems, Phys. Rev., 85, 621–629.
URICK, R.J. AND AMENT, W.S. (1949) The propagation of sound in composite media, J. Acoust. Soc. Am., 21, 115–119.
WATERMAN, P.C. AND TRUELL, R. (1961) Multiple scattering of waves, J. Math. Phys., 2,512–537.
TWERSKY, V. (1962) J. Opt. Soc. Am., 52, 145.
LLOYD, P. AND BERRY, M.V. (1967) Proc. Phys. Soc., 91, 678.
SAYERS, C.M. AND SMITH, R.L. (1983) Ultrasonic velocity and attenuation in an epoxy matrix containing lead inclusions, J. Phys. D, 16, 1189–1194.
KINRA, V.K., KER, E. AND DATTA, S.K. (1982) Mech. Res. Comm., 9, 109.
SAYERS, C.M. (1981) Ultrasonic velocity dispersion in porous materials, J. Phys. D, 14, 413–420.
LLOYD, P. (1967) Proc. Phys. Soc., 90, 207.
LLOYD, P. (1967) Proc. Phys. Soc., 90, 217.
SAYERS, C.M. (1980) On the propagation of ultrasound in highly concentrated mixtures and suspensions, J. Phys. D, 13, 179–184.
SAYERS, C.M. AND SMITH, R.L. (1982) The propagation of ultrasound in porous media, Ultrasonics, 20, 201–205.
SAYERS, C.M. AND TAIT, C.E. (1984) Ultrasonic properties of transducer backings, Ultrasonics, 22, 57–60.
TITTMAN, B.R., MORRIS, W.L. AND RICHARDSON, J.M. (1980) Appl. Phys. Lett., 36, 199.
FRANZBLAU, M.C. AND KRAFT, D.W. (1971) J. Appl. Phys., 42, 5261.
PAPADAKIS, E.P. AND PETERSEN, B.W. (1979) Ultrasonic velocity as a predictor of density in sintered powder meta parts, Mat. Evai, 37, 76.
REYNOLDS, W.N. AND WILKINSON, S.J. (1977) A.E.R.E. Report R8974.
NAGARAJAN, A. (1971) J. Appl. Phys., 42, 3693.
RANACHOWSKI, J. (1971) Proc Conf. on Acoustics of Solid Media, Warsaw ed L. Filipczynski et al. p203.
WINKLER, K.W. (1983) Frequency dependent ultrasonic properties of high-porosity sandstones, J. Geophys. Res. B, 88, 9493–9499.
ELLIOT, R.J., KRUMHANSL, J.A. AND LEATH, P.L. (1974) The theory and properties of randomly disordered crystals and related physical systems, Rev. Mod. Phys., 46, 465–543.
BERRYMAN, J.G. (1979) Theory of elastic properties of composite materials, Appl. Phys. Leu., 35, 856–858.
BERRYMAN, J.G. (1979) Long-wavelength propagation in composite elastic media I. Spherical inclusions, J. Acoust. Soc. Am., 68, 1809–1819.
BERRYMAN, J.G. (1979) Long-wavelength propagation in composite elastic media II. Ellipsoidal inclusions, J. Acoust. Soc. Am., 68, 1820–1831.
THOMPSON, R.B., SPITZIG, W.A. AND GRAY, T.A. Relative effects of porosity and grain size on ultrasonic wave propagation in iron compacts.
BOOCOCK, J., FURZER, A.S. AND MATTHEWS, J.R. (1972) The effect of porosity on the elastic moduli of CO2 as measured by an ultrasonic technique, A.E.R.E. Report M2565.
O’CONNELL, R.J. AND BUDIANSKY, B. (1974) Seismic velocities in dry and saturated cracked solids, J. Geophys. Res., 79, 5412–5426.
BUDIANSKY, B. AND O’CONNELL, R.J. (1976) Elastic moduli of a cracked solid, Int. J. Solids Structures, 12, 81–97.
HOENIG, A. (1979) Elastic moduli of a non-randomly cracked body, Int. J. Solids Structures, 15, 137–154.
BRUNER, W.M. (1976) Comment on ‘Seismic velocities in dry and saturated cracked solids’ by R.J. O’Connell and B. Budiansky, J. Geophys. Res., 81, 2573–2576.
HENYEY, F.S. AND POMPHREY, N. (1982) Self-consistent moduli of a cracked solid, Geophys. Res. Lett., 9, 903–906.
HUDSON, J.A. (1980) Overall properties of a cracked solid, Math. Proc. Camb. Phil. Soc, 88 371–384.
HUDSON, J.A. (1981) Wave speeds and attenuation of elastic waves in material containing cracks, Geophys. J. Royal Astr. Soc, 64, 133–150.
HUDSON, J.A. (1986) A higher order approximation to the wave propagation constants for a cracked solid, Geophys. J. Royal Astr. Soc., 87, 265–274.
HILL, R. (1963) Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids, 11, 357–372.
SAYERS, C.M. AND KACHANOV, M. (1991) A simple technique for finding effective elastic constants of cracked solids for arbitrary crack orientation statistics, Int. J. Solids Structures, 12, 81–97.
ESHELBY, J.D. (1957), The determination of the elastic field of an Ellipsoidal inclusion and related problems. Proc. Roy. Soc, A241, 376–396.
HOENIG, A. (1978) The behaviour of a flat elliptical crack in an anisotropic body, Int. J. solids Structures, 14, 925–934.
CHARLAIX, E. (1986) Percolation threshold of a random array of discs: a numerical simulation, J. Phys. A, 19, L351-L354.
LAWS, N. AND DVORAK, G.J. (1987) The effect of fibre breaks and aligned penny-shaped cracks on the stiffness and energy release rates in unidirectional composites, Int. J. Solids Structures, 23, 1269–1283.
MILTON, G. (1984) The coherent potential approximation is a realizable effective medium scheme, preprint.
NORRIS, A.N. (1985) A differential scheme for the effective moduli of composites. Mechanics of Materials, 4, 1–16.
SAYERS, C.M. (1988a) Inversion of ultrasonic wave velocity measurements to obtain the microcrack orientation distribution function in rocks, Ultrasonics, 26, 73–77.
SAYERS, C.M. (1988b) Stress-induced ultrasonic wave velocity anisotropy in fractured rock, Ultrasonics, 26, 311–317.
ROE, R.J. (1964) Description of crystallite orientation in polycrystalline materials having fibre texture, J. Chem. Phys., 40, 2608–2615.
ROE, R.J. (1965) Description of crystallite orientation in polycrystalline materials — III: General solution to pole figure inversion, J. Appl. Phys., 36, 2024–2031.
ROE, R.J. (1966) Inversion of pole figures for materials having cubic crystal symmetry, J. AppL Phys., 37, 2069–2072.
MORRIS, P.R. (1969) Averaging fourth-rank tensors with weight functions. J. Appl. Phys., 40, 447–448.
MUSGRAVE, M.J.P., Crystal Acoustics, Holden-Day, San Fransisco, 1970.
BIRCH, F. (1960) The velocity of compressional waves in rocks to 10 kilobars. Part 1, J. Geophys. Res., 65, 1083–1102.
BIRCH, F. (1961) The velocity of compressional waves in rocks to 10 kilobars. Part 2, J. Geophys. Res., 66, 2199–2224.
THILL, R.E., WILLARD, R.J. and BUR, T.R. (1969) Correlation of longi-tudinal velocity variation with rock fabric, J. Geophys. Res., 74, 4897–4909.
BATZLE, M.L., SIMMONS, G. and SIEGFRIED, R.W. (1980) Microcrack closure in rocks under stress: direct observation, J. Geophys. Res., 85, 7072–7090.
NUR, A. and G. SIMMONS, Stress-induced velocity anisotropy in rock: an experimental study, J. Geophys. Res., 74, 6667–6674, 1969.
PATERSON, M.S., Experimental Rock Deformation — The Brittle Field, Springer, Berlin, 254 pp., 1978.
KRANZ, R.L., Microcracks in rock: A review, Tectonophysics 100, 449–480, 1983.
SAYERS, C.M. and J.G. van MUNSTER, Microcrack-induced seismic anisotropy of sedimentary rocks, accepted for publication in J. Geophys. Res.
SAYERS, C.M., J.G. VAN MUNSTER and M.S. KING, Stress-induced ultrasonic anisotropy in Berea sandstone, Int. J. Rock Mech., 27, 429–436, 1990.
CASTAGNA, J.P., M.L. BATZLE and R.L. EASTWOOD, Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks, Geophysics, 50, 571–581, 1985.
LO, T., K.B. COYNER and M.N. TOKSOZ, Experimental determination of elastic anisotropy of Berea sandstone, Geophysics, 51, 164–171, 1986.
HATHERLEY, M. and HUTCHINSON, W.B., An introduction to textures in metals, monograph no. 5, London, Institution of Metallurgists.
HUTCHINSON, W.B., (1984) Int. Metall. Rev., 29, 25–42.
STICKELS, C.A. and MOULD, P.R., (1970) Met. Trans., 1, 1303–1312.
DAVIES, G.J., GOODWILL, D.J. and KALLEND, J.S. (1972) Met. Trans., 3, 1627–1631.
SAYERS, C.M. (1982) Ultrasonic velocities in anisotropic polycrystalline aggregates, J. Phys. D, 15, 2157–2167.
SAYERS, C.M. (1986) Angular dependent ultrasonic wave velocities in aggregates of hexagonal crystals, Ultrasonics 24, 289–291.
SAYERS, C.M. (1987) The elastic anisotropy of polycrystalline aggregates of Zirconium and its alloys, J. Nucl. Mat. 144, 211–213
SAYERS, C.M. (1987) Elastic wave anisotropy in the upper mantle, Geo-phys. J. Roy. Astr. Soc. 88, 417–424
SAYERS, C.M. (1987) Orientation of olivine in dunite from elastc wave velocity measurements, Geophys. Res. Lett. 14, 1050–1052.
BUNGE, H.J. (1965) Z. Metallic., 56, 872.
BUNGE, H.J. (1968) Krist. Tech., 3, 431.
PURSEY, H. and COX, H.L. (1954) Phil. Mag., 45, 295.
HILL, R. (1957) The elastic behaviour of a crystaline aggregate, Proc. Phys. Soc, A65, 349–354.
SAYERS, C.M. and PROUDFOOT, G.G. (1986) Angular dependence of the ultrasonic SH wave velocity in rolled metal sheets, J. Mech. Phys. Solids 34, 579–592.
SAYERS, C.M. Texture independent determination of residual stress in polycrystalline aggregates using Rayleigh waves. J. Phys. D., L179-L184 (1984).
SAYERS C.M. Angular dependence of the Rayleigh surface velocity in polycrystalline metals with small anisotropy. Proc. Roy. Soc. A 400, 175–182 (1985).
SAYERS, C.M., ALLEN, D.R., HAINES, G.E. and PROUDFOOT, G.G., Texture and stress determination in metals by using ultrasonic Rayleigh waves and neutron diffraction, Phil. Trans. Royal Soc. 320, 187–200 (1986).
ALLEN D.R., LANGMAN R. and SAYERS C.M. Ultrasonic SH wave velocity in textured aluminium plates. Ultrasonics, September 1985, 215–222.
ALLEN, A.J., HUTCHINGS, M.T., SAYERS, C.M., ALLEN, D.R. and SMITH, R.L. (1983) Use of neutron diffraction texture measurements to establish a model for calculation of ultrasonic velocities in highly oriented austenitic weld material, J. Appl. Phys., 54, 555–560.
ALLEN, D.R. and LANGMAN, R. (1985) AERE-R11573.
LANGMAN, R. and ALLEN, D.R. (1985) AERE-R11598.
KUPPERMAN, D.S. and REIMANN, K.J., (1980) I.E.E.E. Trans Sonics Ultrasonics SU-27, 7.
MACDONALD, D.E., (1981) I.E.E.E. Trans Sonics Ultrasonics SU-28, 75.
BIOT, M.A., (1940) J. Appl. Phys. 11, 522.
THURSTON, R.N., (1965) J. Acoust. Soc. Am 37, 348.
THOMPSON, R.B., SMITH, J.F. and LEE, S.S. (1983) Rev. Prog. NDE 2, ed. D.O. Thompson and D.E. Chimenti, Plenum Press, New York.
THOMPSON, R.B., LEE, S.S. and SMITH, J.F. (1984) Rev. Prog. NDE 3, ed. D.O. Thompson and D.E. Chimenti, Plenum Press, New York.
LEE, S.S., SMITH, J.F. and THOMPSON, R.B., (1985) Rev. Prog. NDE 4, ed. D.O. Thompson and D.E. Chimenti, Plenum Press, New York.
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Sayers, C.M. (1993). Ultrasound in Solids with Porosity, Microcracking and Polycrystalline Structuring. In: The Evaluation of Materials and Structures by Quantitative Ultrasonics. CISM International Centre for Mechanical Sciences, vol 330. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4315-5_17
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DOI: https://doi.org/10.1007/978-3-7091-4315-5_17
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