Abstract
A new micromechanics constitutive model for pure dilatant transformation plasticity of structure ceramics is proposed in this paper. Based on the thermodynamics, micromechanics and microscalet→m transformation mechanism analysis of the TZP and PSZ ZrO2-containing ceramics, an analytic expressions of the Helmholtz and complementary free energy of the constitutive element for the case of pure dilatant transformation is derived for the first time in a self-consistent manner. By the analysis of energy dissipation in the forward and reverse transformations, the micromechanics constitutive law is derived in the framework of Hill-Rice's internal variable constitutive theory.
Similar content being viewed by others
References
McMeeking R. and Evans, A. G. Mechanisms of transformation toughening in brittle materials,J. Am. Ceram. Soc.,65, 5 (1982), 242–45.
Budiansky B., Hutchinson J.W. and Lambropoulos J.C., Continuum theory of dilatant transformation toughening in ceramics,Int. J. Solids Struct.,19, 4 (1983) 337–55.
Chen I-Wei and P. E. Reyes Morel, Implications of transformation plasticity in ZrO2-containing ceramics: I, shear and dilatation effect,J. Am. Ceram. Soc.,69, 3 (1986), 181–189.
Chen I-Wei and P. E. Reyes Morel, Transformation plasticity and transformation toughening in Mg-PSZ and Ce-TZP, Mat. Res. Soc. Symp. Proc., Vol. 78, (1987).
Sun Q. P., Yu S. W. and Hwang K. C., Experimental and numerical research on transformation plasticity and transformation toughening of Ce-TZP ceramics, to be presented at 92th Annual Meeting of the American Ceramic Society, Texas, (April 1990).
Reyes Morel P. E., Cherng J. S. and Chen I Wei, Transformation plasticity of Ce-TZP—the shape memory effect, Presented at the 89th Annual Meeting of the American Ceramic Society, (1987).
Lambropoulos, J. C., Shear, shape and orientation effects in transformation toughening,Int. J. Solids Struct. 22, 10, (1986), 1083–1106.
Mura T., Micromechanics of Defects in Solids, Martinus Nijhoff, The Hague, The Netherlands (1987).
Mori, T. and Tanaka K., Average stress in matrix and average elastic energy of materials with misfitting inclusions,Acta, Metall.,21 5 (1973), 571–574.
Rice, J. R., Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms. In Constitutive Equations in Plasticity (Edited by Ali S. Argon). MIT Press, Cambridge, MA (1975), 23–79.
Rice J. R., Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity,J. M. P. S.,19, (1971), 433–455.
Chen I-Wei and Chiao, Y-H. Theory and experiment of martensitic nucleation in ZrO2-containing ceramics and ferrous alloys,Acta Metall.,33, 10 (1985), 1827–1845.
Chen I-Wei, Chiao Y-H. and Tsuzaki K., Statistics of martensitic nucleation,Acta Metall.,33, 10 (1985) 1847–59.
Eshelby J. D., Energetic forces and energy momentum tensor, Inelastic Behavior of Solid, Edited by Kanninen, et all., (1970).
Author information
Authors and Affiliations
Additional information
The project is supported by the National Natural Science Foundation of China.
Rights and permissions
About this article
Cite this article
Qingping, S., Shouwen, Y. & Kehchih, H. A micromechanics constitutive model for pure dilatant martensitic transformation of ZrO2-containing ceramics. Acta Mech Sinica 6, 141–150 (1990). https://doi.org/10.1007/BF02488445
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02488445