Micromechanical Superplastic Model for the Analysis of Inhomogeneous Deformation in Heterogeneous Microstructure

비균일 조직에 따른 불균일 변형 해석을 위한 미시역학적 초소성 모텔

  • Kim, Tae-Won
  • 김태원
  • Published : 2001.12.01


A micromechanical model is presented for superplasticity in which heterogeneous microstructures are coupled with deformation behavior. The effects of initial distributions of grain size, and their evolutions on the mechanical properties can be predicted by the model. Alternative stress rate models such as Jaumann rate and rotation incremental rate have been employed to analyze uniaxial loading and simple shear problems and the appropriate modeling was studied on the basis of hypoelasticity and elasto-viscoplasticity. The model has been implemented into finite element software so that full process simulation can be carried out. Tests have been conducted on Ti-6Al-4V alloy and the microstructural features such as grain size, distributions of grain size, and volume fraction of each phase were examined for the materials that were tested at different strain rates. The experimentally observed stress-strain behavior on a range of initial grain size distributions has been shown to be correctly predicted. In addition, the effect of volume fraction of the phases and concurrent grain growth were analyzed. The dependence of failure strain on strain rate has been explained in terms of the change in mechanism of grain growth that occurs with changing strain rate.


Micromechanics;Inhomogeneous Deformation;Failure;Heterogeneous Microstructure;State Variable;Superplasticity


  1. Prager, W., 'An Elementary Disussion of Definitions of Stress Rate,' 1961, Quart. Appl. Math., Vol. 18, pp. 403-407
  2. Kurzydlowski, K.J. and Ralph, B., 1995, The Quantiative Description of the Microstructure of Materials, CRC Press, New York
  3. Wart, J.A. and Paton, N.E., 1983, 'Enhanced Superplasticity and Strength in Modified Ti-6Al-4V Alloys,' Met.Trans.A, Vol. 14A, pp. 2535-2544
  4. Taylor, G.l., 1938, 'Plastic Strain in Metals,' J. Inst. Metals, Vol. 62, pp. 307-324
  5. Spencer, A.J.M., 1980, Continuum Mechanics.Longman Group Limited, London
  6. Iwasaki, H., Hayami, s., Higashi, K. and Tanimura, S., 1990, 'Instability of Superplastic Aluminium Alloys,' Superplasticity in Metals, Ceramics and Intermetallic (Ed. M. J. Mayo, M.Kobayashi, J. Wadsworth), Proc. Symp., California, USA, pp. 233-238
  7. Ghosh, A.K. and Hamilton, C.H., 1979, 'Mechanical Behavior and Hardening Characteristics of a Superplastic Ti-6Al-4V Alloy,' Met. Trans. A, Vol. 10A, pp. 699-706
  8. Nieh, T.G., Wadworth, J. and Sherby, O.D., 1997, Superplasticity in Metals and Ceramics, Cambridge University Press, Cambridge
  9. Khan, A.S. and Huang, S., 1995, Continuum Theory of Plasticity, Wiley, New York
  10. Kim, T.-W. and Dunne, F.P.E., 1997, 'Determination of Superplastic Constitutive Equations and Strain Rate Sensitivites for Aerospace Alloys,' Proc. Instn. Mech. Engrs., Vol. 211, Part G, pp. 367-380
  11. Suh, Y.S., 1998, 'The Influence of Plastic-Strain Induced Anisotropy Modeled as Combined Isotropic Kinematic Harening in the Tension-Torsion Starining Problem (I),' KSME Int. J., Vol. 12, No. 4, pp. 572-582
  12. Suh, Y.S., 1998, 'The Influence of Plastic-Strain Induced Anisotropy Modeled as Combined Isotropic Kinematic Hardening in the Tension-Torsion Starining Problem(II),' KSME Int. J., Vol. 12, No. 4, pp. 583-597
  13. Lemaire, L. and Chaboche, J.-L., 1990, Mechanics of Solid Materials, Cambridge University Press, Cambridge
  14. Haghi, M., 1995, 'A Frame Work for Constitutive Relations and Failure Criteria for Materials with Distributed Properties, with Application to Prous Vixcoplasticity,' J. of. Mech. Phys. Solid, Vol. 43, pp. 573-597
  15. Stouffer, D.C. and Dame, L.T., 1996, Inelastic Deformation of Metals, John Wiley & Sons, Inc., New York
  16. Lai, W.M., Rubin, D. and Krempl, E., 1978, Intreduction to Continuum Mechanics, Pergamon Press Oxford
  17. Mosher, D.A. and Dawson, P.R., 1996, 'A state Variable Constitutive Model for Superplastlic Ti-6Al4V Based on Grain Size,' J. of Eng. Mater.Tech., Vol. 118, pp. 162-168
  18. Paton, N.E. and Hamitlon, C.H., 1979, 'Microstructural Influence on Superplasticity in Ti-6Al-4V,' Met. Trans., Vol. 10A, pp. 241-250
  19. Shi, L. and Northwood, D.O., 1995, 'Grain Size Effect in High Temperature Creep and Superplastic Deformation of Polycrystalline Materials,' Mater. Sci. Forum, Vol. 189, pp. 335-340
  20. Ghosh,A.K. and Raj, R., 1986, 'A Model for the Evolution of Grain Size Distribution During Superplastic Deformation,' Acta. Met. Mater., Vol. 34, No. 3, pp. 447-456
  21. Zhou, M. and Dunne, F.P.E., 1996, 'Mechanisms Based Consitutive Equations for the Superplastic Behaviour of a Titanium Alloy,' J. of. Strain Analysis, Vol. 31, pp 65-73
  22. Wood, R.D. and Bonet. J., 1994, 'Aspects of the Numirical Simulation of SPF Including Material Parameter Evalution,' Superplasticity : 60 Years after Pearson (Ed. N.Ridlyey). Proc. Conf., UMIST. UK, pp. 206-217
  23. Winkler, P.-J., 1990, 'Superplasticity in use : A Critical Review of its Staus,Trends and Limtes,' Superplasticity in Metals, Ceramics and Intermetallic(Ed. M. J.Mayo, M.Kobayashi, J.Wadswotrh). Proc. Symp., California, USA, pp. 123-136
  24. Johnson, R.H., 1970, 'Superplasticity,' Met. Rev. 15, pp. 115-134