Abstract
The deviatoric transformation strain of an inclusion is modeled by applying an equivalent distribution of dislocations along a surface which exhibits a discontinuous change in the transformation strains. This method is applied to qualitatively model the twin structures generated in transformation toughened ceramics. For this case, the transformation shear strain of the inclusion is assumed to consist of a number of symmetrical pairs of (twinning) shears in a rectangular grain. The elastic energy is derived and expressed in terms of elementary functions. With one pair of shears, the inclusion induced toughening effect in the presence of a crack is calculated by applying a recent solution of the crack-dislocation interaction problem. Numerical results show that the toughening due to the inclusion (as compared to that due to dilatation) is not negligible if the inclusion is located within a distance equal to several grain sizes from the crack tip. Moreover, the toughening depends strongly on the orientation of the inclusion relative to the crack.
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References
Asaro, R. J. and Barnett, D. M. (1975), The non-uniform transformation strain problem for an anisotropic ellipsoidal inclusion, J. Mech. Phys. Solids, 23, 77–83.
Becher, P. F., Swain, M. V., and Sómiya, S. (1987), Advanced Structural Ceramics, MRS, Vol. 78, Materials Research Society, Pittsburgh.
Becher, P. F. and Tiegs, T. N. (1987), Toughening behavior involving multiple mechanisms: Whisker reinforcement and zirconia toughening, J. Amer. Ceram. Soc., 70, 651–54.
Bilby, B. A., Bullough, R., and Smith, E. (1955), Continuous distribution of dislocations, Proc. Roy. Soc. London, A231, 263–273.
Chen, I.-W. and Morel, P. E. (1986), Implications of transformation plasticity in ZrO2-containing ceramics, J. Amer. Ceram. Soc., 69, 181–89.
Evans, A. G. and Cannon, R. M. (1986), Toughening of brittle solids by martensitic transformations, Acta Metallurgica, 34, 761–800.
McMeeking, R. and Evans, A. G. (1982), Mechanics of transformation toughening in brittle materials, J. Amer. Ceram. Soc., 65, 242–45.
Muddle, B. C. and Hannink, R. H. J. (1986), Crystallography of the tetragonal to monoclinic transformation in MgO partially stabilized zirconia, J. Amer. Ceram. Soc., 69, 547–55.
Mura, T. (1987), Micromechanics of Defects in Solids, 2nd ed., Martinus Nijhoff, Dordrecht.
Mura, T., Jasiuk, I., and Tsuchida, B. (1985), The stress field of a sliding inclusion, Int. J. Solids Structures, 21, 1165–1179.
Mura, T., Mori, T., and Kato, M. (1976), The elastic field caused by a general ellipsoidal inclusion and the application to martensite formulation, J. Mech. Phys. Solids,24305–18.
Rose, L. R. F. (1987), The mechanics of transformation toughening, Proc. Roy. Soc. London, A412, 169–97.
Thomson, R. (1986), Physics of fracture, in Solid State Physics, Vol. 39, edited by H. Ehrenreich and D. Turnbull, Academic Press, New York, pp. 1–129.
Weertman, J., Lin I.-H., and Thomson, R. (1983), Double ship plane crack model, Acta Metallurgica, 31, 473–486.
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© 1990 Springer-Verlag New York Inc.
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Chang, SJ., Becher, P.F. (1990). Crack Tip Toughening by Inclusions with Pairs of Shear Transformations. In: Weng, G.J., Taya, M., Abé, H. (eds) Micromechanics and Inhomogeneity. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8919-4_6
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DOI: https://doi.org/10.1007/978-1-4613-8919-4_6
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