Abstract
A new equationE =E 0 (1 −aP)n whereE andE 0 are the Young's moduli at porosity,P, and zero, respectively, a andn are material constants, has been derived semi-empirically for describing the porosity dependence of Young's modulus of brittle solids. The equation satisfies quite well the exact theoretical solution for the values of Young's moduli at different porosities for model systems with ideal and non-ideal packing geometry. The equation shows excellent agreement with the data Onα- andβ-alumina over a wide range of porosity. Unlike the existing porosity-elastic modulus equations, the proposed equation satisfies the boundary conditions and is inherently capable of treating isometric closed pores as well as non-isometric interconnected pores. The parameters a and n provide information about the packing geometry and pore structure of the material.
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References
R. M. Spriggs,J. Amer. Ceram. Soc. 44 (1961) 628.
F. P. Knudsen,ibid. 45 (1962) 94.
I. Soroka andP. J. Sereda,ibid. 51 (1968) 337.
R. D. Carnahan,ibid. 51 (1968) 223.
D. F. Porter, A S. Reed andDavid Lewis III,ibid. 60 (1977) 345.
D. P. H. Hasselman,ibid. 45 (1962) 452.
J. C. Wang,J. Mater. Sci 19 (1984) 801.
R. L. Coble andW. D. Kingery,J. Amer. Ceram. Soc. 39 (1956) 377.
J. R. G. Evans, R. Stevens andS. R. Tan,Trans. J. Brit. Ceram. Soc. 83 (1984) 43.
K. K. Schiller, in “Mechanical Properties of Non-Metallic Brittle Materials”, edited by W. H. Walton (Butterworth, London, 1958) p. 35.
F. P. Knudsen,J. Amer. Ceram. Soc. 42 (1959) 376.
J. B. Wachtman Jr, W. E. Tefft, D. G. Lam Jr andR. P. Stinchfield,J. Res. Nat. Bur. Stand. 64A (1960) 213.
David Lweis III,Ceram. Bull. 57 (1978) 434.
W. H. Duckworth, J. K. Johnston, L. R. Jackson andH. Z. Schofield, “Mechanical properties of Ceramic Bodier”, Rand Report No. R-209, Bottelle Memorial Institute, Columbus, Ohio (1950).
R. M. Spriggs andT. Vasilos, “Effect of grain size and porosity on transverse bend strength and elastic modulus of hot pressed alumina and magnesia”, paper presented at the Sixty Third Annual Meeting, The American Ceramic Society, Toronto, Ontario, Canada, 24 April (1961).
S. M. Lang, “Properties of High-temperature ceramics and cermets — Elasticity and Density at Room Temperature”, National Bureau of Standards Monograph no. 6 (NBS, Washington, 1960) p. 45.
H. Z. Schofield, J. F. Lynch andW. H. Duckworth, “Fundamental Studies of Ceramic Materials”, Final Summary Report, Bottelle Memorial Institute Report to office of Naval Research, Navy Dept. Contract No. N5 ORL - 111, 31 March (1949).
B. L. Majumder,Trans. Indian Ceram. Soc. 11 (1952) 168.
D. H. Chung, “Elastic and Anelastic Properties of Fine Grained Polycrystalline Alumina at Elevated Temperatures”, Bulletin of Research Department, Monthly Report No. 297, State University of New York College of Ceramics at Alfred University March (1961).
J. K. Mackenzie,Proc. Phys. Soc. (London) 63B (1950) 2.
D. P. H. Hasselman andR. M. Fulrath,J. Amer. Ceram. Soc. 47 (1964) 52.
K. K. Phani, S. K. Niyogi, A. K. Maitra andM. Roy Choudhury,J. Mater. Sci. 21 (1986) 4335.
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Phani, K.K., Niyogi, S.K. Young's modulus of porous brittle solids. J Mater Sci 22, 257–263 (1987). https://doi.org/10.1007/BF01160581
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DOI: https://doi.org/10.1007/BF01160581