Acta Mechanica Sinica

, Volume 6, Issue 4, pp 324–332 | Cite as

A micromechanics constitutive theory for forward transformation plasticity with shear and dilatation effect: I, nonproportional loading history

  • Hwang Kehchih
  • Sun Qingping
  • Yu Shouwen


A micromechanics constitutive theory which takes into account both the dilatation and shear effects of the transformation is proposed to describe the macroscopic plastic behavior of structure ceramics during forward transformation under different temperatures. Under some basic assumptions, the analytic expressions of the Helmholtz and complementary free energy of the constitutive element are derived in a self-consistent manner by using the Mori-Tanaka's method which takes into account the interaction between the transformed inclusions. In the framework of Hill-Rice's internal variable constitutive theory, the forward transformation yield function and incremental stress strain relations, in analogy to the theory of metal plasticity, for non-proportional loading histories are obtained.

Key Words

shear effect internal variables constitutive element 


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  1. [1]
    McMeeking R. and Evens A. G. Mechanisms of transformation toughening in brittle materials,J. Am. Ceram. Soc.,65, 5 (1982) 242–45.CrossRefGoogle Scholar
  2. [2]
    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.zbMATHCrossRefGoogle Scholar
  3. [3]
    Lambropoulos J. C., Shear, shape and orientation effects in transformation toughening,Int. J. Solids Struct.,22, 10 (1986), 1083–1106.CrossRefGoogle Scholar
  4. [4]
    Chen I. W. and Reyes Morel P. E., Implications of transformation plasticity in ZrO2- containing ceramics: I, shear and dilatation effect,J. Am. Ceram. Soc.,69, 3 (1986), 181–189.CrossRefGoogle Scholar
  5. [5]
    Chen I. W. and Reyes Morel P. E., Transformation plasticity and transformation toughening in Mg-PSZ and Ce-TZP, Mat. Res. Soc. Symp. Proc.,78 (1987).Google Scholar
  6. [6]
    Reyes Morel P. E., Cherng J. S. and Chen I. W., Transformation plasticity of Ce-TZP—the shape memory effect, Presented at the 89th Annual Meeting of the American Ceramic Society (1987).Google Scholar
  7. [7]
    Sun Q. P., Yu S. W. and Hwang K. C., Experimental and numerical research on transformation plasticity and transformation toughening of Ce-TZP ceramics, presented at the 90th Annual Meeting of the American Ceramic Society held in Texas, U. S. A., Apr. (1990).Google Scholar
  8. [8]
    Sun Q. P., Yu S. W. and Hwang K. C., A micromechanics constitutive model for pure dilatant martensitic transformation of ZrO2-containing ceramics, Acta Mechanica Sinica,6, 2 (1990).Google Scholar
  9. [9]
    Eshelby J. D., The determination of the elastic field of an ellipsoidal inclusions, and the related problems. Proc. R. Soc. Lond., A241, 376 (1957).Google Scholar
  10. [10]
    Sun Q. P., PhD thesis, Department of Engineering Mechanics, Tsinghua University, Beijing, China.Google Scholar
  11. [11]
    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.CrossRefGoogle Scholar
  12. [12]
    Mura, T., Micromechanics of Defects in Solids. Martinus Nijhoff, The Hague, The Netherlands (1987).Google Scholar
  13. [13]
    Rice J. R., Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanism. In Constitutive Relation of plasticity (Edited by Ali S. Argon), MIT Press, Cambridge, MA (1975), 23–79.Google Scholar
  14. [14]
    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.zbMATHCrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1990

Authors and Affiliations

  • Hwang Kehchih
    • 1
  • Sun Qingping
    • 1
  • Yu Shouwen
    • 1
  1. 1.Department of Engineering MechanicsTsinghua UniversityBeijingChina

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