Currently available models describing superplastic deformation are mostly based on uniaxial tensile test data and assume isotropic behavior, thus leading to limited predictive capabilities of material deformation and failure. In this work we present a multi-axial microstructure-based constitutive model that describes the anisotropic superplastic deformation within the continuum theory of viscoplasticity with internal variables. The model accounts for microstructural evolution and employs a generalized anisotropic dynamic yield function. The anisotropic yield function can describe the evolution of the initial state of anisotropy through the evolution of unit vectors defining the direction of anisotropy during deformation. The generalized model is then reduced to the plane stress condition to simulate sheet metal stretching in superplastic blow forming using pressurized gas. Different ratios of biaxial stretching were investigated, including the case simulating the uniaxial loading condition, where the model successfully captured the uniaxial experimental data. The model is also used to develop a new forming pressure profile that accounts for anisotropy and microstructural evolution.

1.
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.
2.
Dutta
,
A.
, and
Mukherjee
,
M.
,
1992
, “
Superplastic Forming: An Analytical Approach
,”
Mater. Sci. Eng.
,
A157
, pp.
9
13
.
3.
Carrino
,
L.
, and
Guiliano
,
G.
,
1997
, “
Modeling of Superplastic Blow Forming
,”
Int. J. Mech. Sci.
,
39
, pp.
193
199
.
4.
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
.
5.
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
.
6.
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.
7.
Abu-Farha
,
F.
, and
Khraisheh
,
M.
,
2004
, “
Constitutive Modeling of Deformation-Induced Anisotropy in Superplastic Materials
,”
Mater. Sci. Forum
,
447-448
, pp.
165
170
.
8.
Dafalias
,
Y.-F.
,
1990
, “
The Plastic Spin in Viscoplasticity
,”
Int. J. Solids Struct.
,
26
, pp.
149
163
.
9.
Siegert
,
K.
,
Ja¨ger
,
S.
, and
Vulcan
,
M.
,
2003
, “
Pneumatic Bulging of Magnesium AZ 31 Sheet Metals at Elevated Temperatures
,”
CIRP Annals.
Manufacturing Technology,
52
, pp.
241
244
.
10.
Banabic, D., Balan, T., and Comsa, D.-S., 1999, “Closed Form Solutions for Bulging Through Elliptical Dies,” SheMet’99, pp. 623–626.
11.
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
.
12.
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
.
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