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Elastic Properties of Porous Ceramics

Published online by Cambridge University Press:  21 February 2011

H. M. Ledbetter ,
M. Lei  and
S. K. Datta
H. M. Ledbetter
Affiliation:
Institute for Materials Science and Engineering, National Institute of Standards and Technology, Boulder, Colorado 80303
M. Lei
Affiliation:
Institute for Materials Science and Engineering, National Institute of Standards and Technology, Boulder, Colorado 80303
S. K. Datta
Affiliation:
Department of Mechanical Engineering and CIRES University of Colorado, Boulder, Colorado 80309
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Abstract

Using theoretical models, we consider the sound velocities and elastic constants of ceramics containing pores. As an example, we consider alumina. However, the approach applies to all ceramics. As a point of departure, we consider spherical pores. For all the usual elastic constants–Young modulus, shear modulus, bulk modulus, Poisson ratio–we give relationships for both the forward and inverse cases: predicting the porous ceramic properties and estimating the pore-free ceramic properties. Following a suggestion by Hasselman and Fulrath that sintering or hot pressing can produce cylindrical pores, we derive a relationship for the elastic constants of a distribution of randomly oriented long cylinders (c/a + ∞, the prolate-spheroid limit). This model predicts elastic constants lower than for spherical pores, but well above measurement. We obtain agreement with observation by assuming the pores are oblate spheroids. For alumina, the necessary aspect ratio equals oneninth. Besides pore aspect ratio, the model requires only the pore-free alumina elastic constants. It contains no adjustable parameters.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 142: Symposium U – Nondestructive Monitoring of Materials Properties , 1988 , 275
Copyright
Copyright © Materials Research Society 1989

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References

1. Wachtman, J.B., in Mechanical and Thermal Properties of Ceramics. Spec. Publ. 303 (Nat. Bur. Stands., Washington, 1969), p. 139.Google Scholar
2. Phani, K.K. and Niyogi, S.K., J. Mater. Sci. 22, 257 (1987).Google Scholar
3. Wang, J.C., J. Mater. Sci. 19, 801 (1984).Google Scholar
4. Wang, J.C., J. Mater. Sci. 19, 809 (1984).Google Scholar
5. Sayers, C.M., J. Phys. D: Appl. Phys. 14, 413 (1981).Google Scholar
6. Sayers, C.M. and Smith, R.L., Ultrasonics 20, 201 (1982).CrossRefGoogle Scholar
7. Hasselman, D.P.H. and Fulrath, R.M., J. Am. Ceram. Soc. 48, 545 (1965).CrossRefGoogle Scholar
8. Ledbetter, H.M. and Datta, S.K., J. Acoust. Soc. Am. 79, 239 (1986).Google Scholar
9. Eshelby, J.D., Proc. Roy. Soc. Land. A241, 376 (1957).Google Scholar
10. Hashin, Z., J. Appl. Mech. 29, 143 (1962).Google Scholar
11. Tefft, W.E., J. Res. Nat. Bur. Stand. 70A, 277 (1966).Google Scholar
12. Knudsen, F.P., J. Am. Ceram. Soc. 45, 94 (1962).Google Scholar
13. Ledbetter, H.M., Datta, S.K., and Kriz, R.D., Acta Metall. 32, 2225 (1984).Google Scholar
14. Budiansky, B. and O'Connell, R.J., Int. J. Solids Struct. 12, 81 (1976).Google Scholar