This paper describes an inverse approach (IA) formulation for the analysis of tubes under free hydroforming conditions. The IA formulation is derived from that of Guo et al. established for flat sheet hydroforming analysis using constant strain triangular membrane elements. First, an incremental analysis of free hydroforming for a hot-dip galvanized (HG/Z140) DP600 tube is performed using the Marc finite element code. The deformed geometry obtained at the last converged increment is then used as the final configuration in the inverse analysis. This comparative study allows an assessment of the predictive capability of the inverse analysis. The results are compared with the experimental values determined by Asnafi and Skogsga¨rdh. After that, a procedure based on a forming limit diagram (FLD) is described as a means to adjust the process parameters such as the axial feed and internal pressure. Finally, the adjustment process is illustrated through a re-analysis of the same tube using the inverse approach.

1.
Asnafi
,
N.
,
1999
, “
Analytical Modeling of Tube Hydroforming
,”
Thin-Walled Struct.
,
34
, pp.
295
330
.
2.
Asnafi
,
N.
, and
Skogsga¨rdh
,
A.
,
2000
, “
Theoretical and Experimental Analysis of Stroke-Controlled Tube Hydroforming
,”
Mater. Sci. Eng., A
,
A279
, pp.
95
110
.
3.
Chenot, J. L., Wood, R. D., and Zienkiewicz, O. C., eds, 1992, “Numerical Methods in Industrial Forming Processes,” NUMIFORM 92. A. A. Balkema, Rotterdam, Netherlands.
4.
Owen, D. R. J., Onate, E., and Hinton, E., eds, 1997, “Computational Plasticity—Fundamentals and Applications,” COMPLAS V, CIMNE, Barcelona, Spain.
5.
Guo
,
Y. Q.
,
Batoz
,
J. L.
,
Detraux
,
J. M.
, and
Duroux
,
P.
,
1990
, “
Finite Element Procedures for Strain Estimations of Sheet Metal Forming Parts
,”
Int. J. Numer. Methods Eng.
,
30
, pp.
1385
1401
.
6.
Guo
,
Y. Q.
,
Batoz
,
J. L.
,
Naceur
,
H.
,
Bouabdallah
,
S.
,
Mercier
,
F.
, and
Barlet
,
O.
,
2000
, “
Recent Developments on The Analysis and Optimum Design of Sheet Metal Forming Parts Using a Simplified Inverse Approach
,”
Comput. Struct.
,
78
, pp.
133
148
.
7.
Batoz
,
J. L.
,
Guo
,
Y. Q.
, and
Mercier
,
F.
,
1998
, “
The Inverse Approach with Simple Triangular Shell Elements for Large Strain Predictions of Sheet Metal Forming Parts
,”
Eng. Comput.
,
15
(
7
), pp.
864
892
.
8.
Chung
,
K.
,
Barlat
,
F.
,
Brem
,
J. C.
,
Lege
,
D. J.
, and
Richmond
,
O.
,
1997
, “
Blank Shape Design for a Planar Anisotropic Sheet Based on Ideal Forming Design Theory and FEM Analysis
,”
Int. J. Mech. Sci.
,
39
, pp.
105
120
.
9.
Chung
,
K.
,
Yoon
,
J.-W.
, and
Richmond
,
O.
,
2000
, “
Ideal Sheet Forming with Frictional Constraints
,”
Int. J. Plast.
16
, pp.
595
610
.
10.
Lee
,
C. H.
, and
Huh
,
H.
,
1998
, “
Blank Design and Strain Estimates for Sheet Metal Forming Processes by A Finite Element Inverse Approach with Initial Guess of Linear Deformation
,”
J. Mater. Process. Technol.
,
82
, pp.
145
155
.
11.
Yoon, J.-W., Chung, K., Pourboghrat, F., Barlat, F., and Shah, K. N., 2002, “Preform Design for Hydroforming of Extruded Parts Based on Ideal Forming Design Theory,” Plasticity, Damage and Fracture at Macro, Micro and Nano Scales, Proceedings of Plasticity 02, A. S. Khan and O. Lopez-Pamies, eds., NEAT Press, Maryland, pp. 460–462.
12.
Nguyen, B. N., Johnson, K. I., Davies, R. W., and Khaleel, M. A., 2002, “Inverse Analysis of Tube Free Hydroforming,” Plasticity, Damage and Fracture at Macro, Micro and Nano Scales, Proceedings of Plasticity 02, A. S. Khan and O. Lopez-Pamies, eds., NEAT Press, Maryland, pp. 427–429.
13.
Nguyen, B. N., Johnson, K. I., Davies, R. W., and Khaleel, M. A., 2002, “A Computation Tool for Hydroforming Prediction Using an Inverse Approach,” SAE Technical Paper Series, Paper # 2002-01-0785, SAE 2002 World Congress, Detroit, Michigan, March 2002.
14.
Hill
,
R.
,
1948
, “
A Theory of The Yielding and Plastic Flow of Anisotropic Metals
,”
Proc. R. Soc. London, Ser. A
,
A193
, pp.
281
297
.
15.
Lemaitre, J., and Chaboche, J. L., 1985, Me´canique des Mate´riaux Solides, Bordas, Paris.
You do not currently have access to this content.