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Poisson's ratio of porous and microcracked solids: Theory and application to oxide superconductors

Published online by Cambridge University Press:  03 March 2011

Martin L. Dunn  and
Hassel Ledbetter
Martin L. Dunn
Affiliation:
Department of Mechanical Engineering, Center for Acoustics, Mechanics, and Materials, University of Colorado, Boulder, Colorado 80309-0427
Hassel Ledbetter
Affiliation:
Materials Science and Engineering Laboratory, National Institute of Standards and Technology, Boulder, Colorado 80303
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Abstract

We present a theoretical study of the effective Poisson's ratio of elastic solids weakened by porosity and microcracks. Explicit expressions of the effective Poisson's ratio are obtained using the Mori-Tanaka mean-field approach as applied to macroscopically isotropic solids containing randomly distributed and randomly oriented spheroidal pores. We focus on the influence of pore shape and concentration and devote special attention to the limiting cases of spherical, penny-shape, and needle-shape pores. A key result of this study is that the effective Poisson's ratio depends only on pore concentration, pore shape, and Poisson's ratio of the bulk solid. In other words, it is independent of any other elastic constants of the bulk solid. Also, the ratio of the shear and bulk moduli behaves similarly. Unlike other elastic constants which monotonically decrease with pore concentration, Poisson's ratio may increase, decrease, or remain unchanged as a function of pore concentration, depending on the pore shape and Poisson's ratio of the bulk solid. We discuss ramifications of these findings with regard to the elastic constants of oxide superconductors, especially the bismuth cuprates, which show unusually low Poisson's ratios. We also discuss these low Poisson's ratios, including the possibility of negative Poisson's ratios.

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Articles
Information
Journal of Materials Research , Volume 10 , Issue 11 , November 1995 , pp. 2715 - 2722
Copyright
Copyright © Materials Research Society 1995

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References

REFERENCES

1Köster, W. and Franz, H., Metall. Rev. 6, 1 (1961).CrossRefGoogle Scholar
2Ledbetter, H.M., J. Phys. Chem. Solids 34, 721 (1973).CrossRefGoogle Scholar
3Ledbetter, H.M., Z. Naturforsch. 31a, 1539 (1976).CrossRefGoogle Scholar
4Ledbetter, H. M., Lei, M., Hermann, A., and Sheng, Z., Physica 225C, 397 (1994).CrossRefGoogle Scholar
5Eschrig, H., in Physics of High-Tc Superconductors (Springer, Berlin, 1992), p. 45.CrossRefGoogle Scholar
6Ledbetter, H. M. and Kim, S., unpublished.Google Scholar
7Cohen, R. E., Pickett, W. E., Krakauer, H., and Boyer, L. L., Physica 153C, 202 (1988).CrossRefGoogle Scholar
8Iguchi, E. and Yonezawa, Y., Jpn. J. Appl. Phys. Lett. 26, L1492 (1987).CrossRefGoogle Scholar
9Kress, W., Schroder, U., Prade, J., Kulkarni, A. D., and de Wette, F.W., Physica 153C, 221 (1988).CrossRefGoogle Scholar
10Ledbetter, H.M., J. Mater. Res. 7, 2905 (1992).CrossRefGoogle Scholar
11Ledbetter, H.M. and Lei, M., J. Mater. Res. 6, 2253 (1991).CrossRefGoogle Scholar
12Lei, M., Sarrao, J., Visscher, W., Bell, T., Thompson, J., Migliori, A., Weep, U., and Veal, B., Phys. Rev. B 47, 6154 (1993).CrossRefGoogle Scholar
13Ledbetter, H.M., Kim, S., and Roshko, A., Z. Phys. B Condensed Matter 89, 275 (1992).CrossRefGoogle Scholar
14Ledbetter, H. M., Kim, S., Goldfarb, R., and Togano, K., Phys. Rev. B 39, 9689 (1989).CrossRefGoogle Scholar
15C-Y. Chu, Routbort, J., Chen, N., Biondo, A., Kupperman, D., and Goretta, K., Supercond. Sci. Technol. 5, 306 (1992).Google Scholar
16Dominec, J., Vasek, P., Svoboda, P., Plechacek, V., and Laermans, C., Mod. Phys. Lett. B 6, 1049 (1992).CrossRefGoogle Scholar
17Mackenzie, J. K., Proc. Phys. Soc. London B63, 2 (1950).CrossRefGoogle Scholar
18Christensen, R. M., Mechanicals of Composite Materials (John Wiley, New York, 1979).Google Scholar
19Kachanov, M., Tsukrov, I., and Shafiro, B., Appl. Mech. Rev. 47, S151 (1994).CrossRefGoogle Scholar
20Zhao, Y. H., Tandon, G.P., and Weng, G.J., Acta Mech. 76, 105 (1989).CrossRefGoogle Scholar
21Mori, T. and Tanaka, K., Acta Metall. 21, 571 (1973).CrossRefGoogle Scholar
22Hashin, Z. and Shtrikman, T., J. Mech. Phys. Solids 11, 127 (1963).CrossRefGoogle Scholar
23Zimmerman, R.W., Mech. Res. Commun. 19, 563 (1992).CrossRefGoogle Scholar
24Zimmerman, R.W., Mech. Mater. 12, 17 (1991).CrossRefGoogle Scholar
25Zimmerman, R.W., Appl. Mech. Rev. 47, S38 (1993).CrossRefGoogle Scholar
26Hill, R., J. Mech. Phys. Solids 11, 357 (1963).CrossRefGoogle Scholar
27Eshelby, J.D., Proc. R. Soc. London A241, 376 (1957).Google Scholar
28Benveniste, Y., Mech. Mater. 6, 147 (1987).CrossRefGoogle Scholar
29Weng, G.J., Int. J. Engng. Sci. 22, 845 (1984).CrossRefGoogle Scholar
30Weng, G.J., Int. J. Engng. Sci. 28, 1111 (1990).CrossRefGoogle Scholar
31Weng, G.J., Int. J. Engng. Sci. 30, 83 (1992).CrossRefGoogle Scholar
32Benveniste, Y., Dvorak, G.J., and Chen, T., J. Mech. Phys. Solids 39, 927 (1991).CrossRefGoogle Scholar
33Ferrari, M., Mech. Mater. 11, 251 (1991).CrossRefGoogle Scholar
34Willis, J.R., J. Mech. Phys. Solids 25, 185 (1977).CrossRefGoogle Scholar
35Dunn, M. L. and Taya, M., Proc. R. Soc. London A443, 265 (1993).Google Scholar
36Dunn, M. L. and Taya, M., J. Am. Ceram. Soc. 76 (7), 1697 (1993).CrossRefGoogle Scholar
37Walpole, L.J., J. Mech. Phys. Solids 17, 235 (1969).CrossRefGoogle Scholar
38Norris, A.N., J. Appl. Mech. 56, 83 (1989).CrossRefGoogle Scholar
39Hashin, Z., J. Appl. Mech. 29, 143 (1962).CrossRefGoogle Scholar
40Hill, R., J. Mech. Phys. Solids 12, 199 (1964).CrossRefGoogle Scholar
41Kachanov, M., Adv. Appl. Mech. 30, 259 (1993).CrossRefGoogle Scholar
42Bristow, J.R., Brit. J. Appl. Phys. 11, 81 (1960).CrossRefGoogle Scholar
43Budiansky, B. and O'Connell, R.J., Int. J. Solids Struct. 12, 81 (1976).CrossRefGoogle Scholar
44Lakes, R., Science 235, 1038 (1987).CrossRefGoogle Scholar
45Ledbetter, H.M., Kim, S., and Togano, K., Physica 185C, 935 (1991).CrossRefGoogle Scholar
46Ledbetter, H.M., unpublished.Google Scholar
47Milstein, F. and Huang, K., Phys. Rev. B 18, 2529 (1978).CrossRefGoogle Scholar
48Mackrodt, W., Supercond. Sci. Technol. 1, 343 (1988).CrossRefGoogle Scholar
49Ledbetter, H. M. and Kim, S., unpublished.Google Scholar
50Junod, A., in Physical Properties of High-Temperature Superconductors II (World Scientific, Singapore, 1990), p. 13.CrossRefGoogle Scholar
51Ledbetter, H.M., Lei, M., and Kim, S., Phase Transitions 23, 61 (1990).CrossRefGoogle Scholar
52Ledbetter, H.M., Physica 235–240C, 1325 (1994).CrossRefGoogle Scholar
53Leibfried, G. and Ludwig, W., Solid State Phys. 12, 275 (1961).CrossRefGoogle Scholar
54Gao, Y., Lee, P., Coppens, P., Subramanlan, M., and Sleight, A., Science 241, 954 (1988).CrossRefGoogle Scholar
55Yamamoto, A., Onoda, M., Takayama-Muromzchi, E., Izumi, F., Ishigaki, T., and Asano, H., Phys. Rev. B 42, 4228 (1990).CrossRefGoogle Scholar
56Gavarri, J. R., Monnereau, O., Vacquier, G., Carel, C., and Vettier, C., Physica 172C, 213 (1990).CrossRefGoogle Scholar
57Keskar, N. and Chelikovsky, J., Nature (London) 358, 222 (1992).CrossRefGoogle Scholar
58Fukumoto, A., Phys. Rev. B 42, 7462 (1990).CrossRefGoogle Scholar