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RESEARCH PAPERS

Modeling of Anisotropic Deformation in Superplastic Sheet Metal Stretching

[+] Author and Article Information
Fadi K. Abu-Farha, Marwan K. Khraisheh

Center for Manufacturing and Department of Mechanical Engineering, University of Kentucky, Lexington, KY 40506

J. Eng. Mater. Technol 127(1), 159-164 (Feb 22, 2005) (6 pages) doi:10.1115/1.1839216 History: Received March 23, 2004; Revised July 15, 2004; Online February 22, 2005
Copyright © 2005 by ASME
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References

Hamilton, C., Zbib, H., Johnson, C., and Richter, C., 1991, “Dynamic Grain Coarsening, Its Effects on Flow Localization in Superplastic Deformation,” 2nd SAMPE Symposium, Chipa, Japan, pp. 272–279.
Dutta,  A., and Mukherjee,  M., 1992, “Superplastic Forming: An Analytical Approach,” Mater. Sci. Eng., A157, pp. 9–13.
Carrino,  L., and Guiliano,  G., 1997, “Modeling of Superplastic Blow Forming,” Int. J. Mech. Sci., 39, pp. 193–199.
Zhang,  K., Hamilton,  C., Zbib,  H., and Khraisheh,  M., 1995, “Observation of Transient Effects in Superplastic Deformation of Pb–Sn Eutectic Alloy,” Scr. Metall. Mater., 32, pp. 919–923.
Khraisheh,  M., Zbib,  H., Hamilton,  C., and Bayoumi,  A., 1997, “Constitutive Modeling of Superplastic Deformation. Part I: Theory and Experiments,” Int. J. Plast., 13, pp. 143–164.
Khraisheh, M., and Abu-Farha, F., 2003, “Microstructure-Based Modeling of Anisotropic Superplastic Deformation,” Transactions of NAMRI/SME, Hamilton, Ontario, Canada, Vol. 31, pp. 41–46.
Abu-Farha,  F., and Khraisheh,  M., 2004, “Constitutive Modeling of Deformation-Induced Anisotropy in Superplastic Materials,” Mater. Sci. Forum, 447-448, pp. 165–170.
Dafalias,  Y.-F., 1990, “The Plastic Spin in Viscoplasticity,” Int. J. Solids Struct., 26, pp. 149–163.
Siegert,  K., Jäger,  S., and Vulcan,  M., 2003, “Pneumatic Bulging of Magnesium AZ 31 Sheet Metals at Elevated Temperatures,” CIRP Annals. Manufacturing Technology, 52, pp. 241–244.
Banabic, D., Balan, T., and Comsa, D.-S., 1999, “Closed Form Solutions for Bulging Through Elliptical Dies,” SheMet’99, pp. 623–626.
Ding,  X., Zbib,  H., and Hamilton,  C., 1997, “On the Stability of Bi-Axial Stretching with Application to the Optimization of Superplastic Blow-Forming,” Trans. ASME, 119, pp. 26–31.
Yang,  H., and Mukhrjee,  A., 1992, “An Analysis of the Superplastic Forming of a Circular Sheet Diaphragm,” Int. J. Mech. Sci., 34(4), pp. 283–297.

Figures

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Stress–strain state under biaxial loading
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σ11 at ε̇1=10−3 s−1 for different values of k
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σ22 at ε̇1=10−3 s−1 for different values of k
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Anisotropic yield surfaces at different values of ϕ0, compared to von Mises
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Evolution of the anisotropic angle ϕ at k=−0.5 for different values of ε̇1
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Schematic representation of free blow forming of a circular sheet
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The effect of anisotropy and grain-growth on the pressure–time profiles at ε̇e=2×10−3 s−1 for the case of strain-balanced biaxial stretching
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The effect of anisotropy and grain-growth on the pressure–time profile at ε̇e=2×10−3 s−1 for the case of stress-balanced biaxial stretching
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The effect of anisotropy and grain-growth on the pressure–time profile at ε̇e=2×10−3 s−1, a comparison between strain-balanced and stress-balanced biaxial stretching cases
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Expected shapes of a bulged circular sheet for different values of k. (a) Incomplete hemisphere (k<1); (b) perfect hemisphere (k=1); (c) over-bulged hemisphere (k>1)
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Longitudinal and transverse cross sections of the three domes. (a) Incomplete hemisphere (k<1); (b) perfect hemisphere (k=1); (c) over-bulged hemisphere (k>1)

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