Experimental Validation of Two-dimensional Finite Element Method for Simulating Constitutive Response of Polycrystals During High Temperature Plastic Deformation

  • Sumit Agarwal
  • Clyde L. Briant
  • Paul E. Krajewski
  • Allan F. Bower
  • Eric M. Taleff


A finite element method was recently designed to model the mechanisms that cause superplastic deformation (A.F. Bower and E. Wininger, A Two-Dimensional Finite Element Method for Simulating the Constitutive Response and Microstructure of Polycrystals during High-Temperature Plastic Deformation, J. Mech. Phys. Solids, 2004, 52, p 1289–1317). The computations idealize the solid as a collection of two-dimensional grains, separated by sharp grain boundaries. The grains may deform plastically by thermally activated dislocation motion, which is modeled using a conventional crystal plasticity law. The solid may also deform by sliding on the grain boundaries, or by stress-driven diffusion of atoms along grain boundaries. The governing equations are solved using a finite element method, which includes a front-tracking procedure to monitor the evolution of the grain boundaries and surfaces in the solid. The goal of this article is to validate these computations by systematically comparing numerical predictions to experimental measurements of the elevated-temperature response of aluminum alloy AA5083 (M.-A. Kulas, W.P. Green, E.M. Taleff, P.E. Krajewski, and T.R. McNelley, Deformation Mechanisms in Superplastic AA5083 materials. Metall. Mater. Trans. A, 2005, 36(5), p 1249–1261). The experimental work revealed that a transition occurs from grain-boundary sliding to dislocation (solute-drag) creep at approximately 0.001/s for temperatures between 425 and 500 °C. In addition, increasing the grain size from 7 to 10 μm decreased the transition to significantly lower strain rates. Predictions from the finite element method accurately predict the effect of grain size on the transition in deformation mechanisms.


aluminum constitutive response deformation mechanisms dislocation creep finite element simulations grain-boundary sliding superplastic forming 



This work was performed as part of the General Motors Collaborative Research Laboratory on Computational Materials Research at Brown University. Research at The University of Texas was funded by General Motors.


  1. 1.
    Barnes A.J. (1994) Superplastic Forming of Aluminum Alloys. Mater. Sci. Forum 170–172:701–714CrossRefGoogle Scholar
  2. 2.
    J.G. Schroth, “General Motors Quick Plastic Forming process,” Advances in Superplasticity and Superplastic Forming, E.M. Taleff, P.A. Friedman, P.E. Krajewski, R.S. Mishra, and J.G. Schroth, Eds., TMS, 2004, p 9–20Google Scholar
  3. 3.
    Verma R., Ghosh A.K., Kim S., Kim C. (1995) Grain Refinement and Superplasticity in 5083 Al. Mater. Sci. Eng. A191:143–150CrossRefGoogle Scholar
  4. 4.
    Verma R., Friedman P.A., Ghosh A.K., Kim S., Kim C. (1996) Characterization of Superplastic Deformation Behavior of a Fine Grain 5083 Al Alloy Sheet. Metall. Mater. Trans. A 27A:1889–1898Google Scholar
  5. 5.
    Khaleel M.A., Smith M.T., Pitman S.G. (1997) The Effect of Strain Rate History on the Ductility in Superplastic AA-5083. Scripta Mater. 37(12):1909–1915CrossRefGoogle Scholar
  6. 6.
    Iwasaki H., Hosokawa H., Mori T., Tagata T., Higashi K. (1998) Quantitative Assessment of Superplastic Deformation Behavior in a Commercial 5083 Alloy. Mat. Sci. Eng. A. A252:199–202CrossRefGoogle Scholar
  7. 7.
    Patankar S.N., Jen T.M. (1998) Strain Rate Insensitive Plasticity in Aluminum Alloy 5083. Scripta Mater. 38(8):1255–1261CrossRefGoogle Scholar
  8. 8.
    Hsiao I.C., Huang J.C. (1999) Development of Low Temperature Superplasticity in Commercial 5083 Al-Mg Alloys. Scripta Mater. 40(6):697–703CrossRefGoogle Scholar
  9. 9.
    Martin C.F., Blandin J.J., Salvo L. (2001) Variations in Microstructure and Texture during High Temperature Deformation of Al–Mg Alloy. Mater. Sci. Eng. A 297:212–222CrossRefGoogle Scholar
  10. 10.
    Cleveland R.M., Ghosh A.K., Bradley J.R. (2003) Comparison of Superplastic Behavior in Two 5083 Aluminum Alloys. Mater. Sci. Eng. A. A351(1–2):228–236Google Scholar
  11. 11.
    Sherby O.D., Wadsworth J. (1989) Superplasticity-Recent Advances and Future Directions. Prog. Mater. Sci. 33:169–221CrossRefGoogle Scholar
  12. 12.
    Kulas M.-A., Green W.P., Taleff E.M., Krajewski P.E., McNelley T.R. (2005) Deformation Mechanisms in Superplastic AA5083 materials. Metall. Mater. Trans. A 36(5):1249–1261CrossRefGoogle Scholar
  13. 13.
    Agarwal S., Krajewski P.E., Briant C.L. (2004) Texture Development and Dynamic Recrystallization in AA5083 during Superplastic Forming at Various Strain Rates. Taleff E.M., Friedman P.A., Krajewski P.E., Mishra R.S., Schroth J.G. (eds) Advances in Superplasticity and Superplastic Forming, Charlotte, TMS, p 95–108Google Scholar
  14. 14.
    Bower A.F., Wininger E. (2004) A Two-Dimensional Finite Element Method for Simulating the Constitutive Response and Microstructure of Polycrystals during High-Temperature Plastic Deformation. J. Mech. Phys. Solids 52:1289–1317CrossRefGoogle Scholar
  15. 15.
    Pierce D., Asaro R.J., Needleman A. (1983) Material Rate Dependence and Localized Deformation in Crystalline Solids. Acta Metall. 31:1951–1976CrossRefGoogle Scholar
  16. 16.
    H. Frost, M.F. Ashby, Deformation Mechanism Maps, 1st ed., Chap. 4, Pergamon Press, 1982, p 20–29Google Scholar
  17. 17.
    Raj R., Ashby M.F. (1971) On Grain Boundary Sliding and Diffusion Creep. Metal. Trans. 2(4):1113–1127Google Scholar

Copyright information

© ASM International 2007

Authors and Affiliations

  • Sumit Agarwal
    • 1
  • Clyde L. Briant
    • 1
  • Paul E. Krajewski
    • 2
  • Allan F. Bower
    • 1
  • Eric M. Taleff
    • 3
  1. 1.Division of EngineeringBrown UniversityProvidenceUSA
  2. 2.General Motors R&D CenterWarrenUSA
  3. 3.Department of Mechanical EngineeringThe University of Texas at AustinAustinUSA

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