A family of closed-form formulas for calculating minimum corner-fill radii in planar sections of tube hydroformed products is introduced. Corner forming limit diagrams relating the limiting major strain to the minimum corner-fill radius are introduced. The theory accounts for friction effects and accommodates regular shaped polygon die sections. This effort represents an exploration into a method for design and analysis of tube hydroforming processes without employing the finite element method and while using a closed form approach for capturing friction effects. Good agreement with experimental results is observed.

1.
Mackerle
,
J.
, 2004, “
Finite Element Analyses and Simulations of Sheet Metal Forming Processes
,”
Eng. Comput.
0264-4401,
21
(
7–8
), pp.
891
940
.
2.
Hillmann
,
M.
, and
Weiher.
,
J.
, 1995, “
Simulation of Metal Forming Processes With Respect to MPP-Systems
,”
FGCS, Future Gener. Comput. Syst.
0167-739X,
11
(
4–5
), pp.
431
437
.
3.
Karima
,
M.
, 1994, “
Practical Application of Process Simulation in Stamping
,”
J. Mater. Process. Technol.
0924-0136,
46
(
3–4
), pp.
309
320
.
4.
Kleiber
,
M.
,
Rojek
,
J.
, and
Stocki
,
R.
, 2002, “
Reliability Assessment for Sheet Metal Forming Operations
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
191
(
39–40
), pp.
4511
4532
.
5.
Rojek
,
J.
,
Jovicevic
,
J.
, and
Onate
,
E.
, 1996, “
Industrial Applications of Sheet Stamping Simulation Using New Finite Element Models
,”
J. Mater. Process. Technol.
0924-0136,
60
(
1–4
), pp.
243
247
.
6.
Dong
,
H. Z.
,
Teck
,
C. B.
,
Jiang
,
R. D.
, and
Lin
,
Z. Q.
, 2002, “
Study on Geometry Modeling in the Dynamic Stamping Simulation of a Die
,”
J. Mater. Process. Technol.
0924-0136,
127
(
2
), pp.
261
265
.
7.
Wang
,
H. B.
,
Xu
,
W. L.
,
Lin
,
Z. Q.
,
Yang
,
Y. Y.
, and
Wang
,
Z. R.
, 2002, “
Stamping and Stamping Simulation With a Blankholder Gap
,”
J. Mater. Process. Technol.
0924-0136,
120
(
1–3
), pp.
62
67
.
8.
Koc
,
M.
, and
Altan
,
T.
, 2001, “
An Overall Review of the Tube Hydroforming (THF) Technology
,”
J. Mater. Process. Technol.
0924-0136,
108
, pp.
384
393
.
9.
Asnafi
,
N.
, 1999, “
Analytical Modeling of Tube Hydroforming
,”
Thin-Walled Struct.
0263-8231,
34
, pp.
295
330
.
10.
Asnafi
,
N.
, and
Skogsgardh
,
A.
, 2000, “
Theoretical and Experimental Analysis of Stroke-Controlled Tube Hydroforming
,”
Mater. Sci. Eng., A
0921-5093,
279
, pp.
95
110
.
11.
Rimkus
,
W.
,
Bauer
,
H.
, and
Mihsein
,
M. J. A.
, 2000, “
Design of Load-Curves for Hydroforming Applications
,”
J. Mater. Process. Technol.
0924-0136,
108
, pp.
97
105
.
12.
Sokolowski
,
T.
,
Gerke
,
K.
,
Ahmetoglu
,
M.
, and
Altan
,
T.
, 2000, “
Evaluation of Tube Formability and Material Characteristics: Hydraulic Bulge Testing of Tubes
,”
J. Mater. Process. Technol.
0924-0136,
98
, pp.
34
40
.
13.
Carleer
,
B.
,
van der Kevie
,
G.
,
de Winter
,
L.
, and
van Velduizen
,
B.
, 2000, “
Analysis of the Effect on Material Properties on the Hydroforming Process of Tubes
,”
J. Mater. Process. Technol.
0924-0136,
104
, pp.
158
166
.
14.
Koc
,
M.
, and
Altan
,
T.
, 2002, “
Prediction of Forming Limits and Parameters in the Tube Hydroforming Process
,”
Int. J. Mach. Tools Manuf.
0890-6955,
42
, pp.
123
138
.
15.
Hill
,
R.
, 1953, “
On Discontinuous Plastic States With Special Reference to Localized Necking in Thin Sheets
,”
J. Mech. Phys. Solids
0022-5096,
1
, pp.
19
30
.
16.
Swift
,
H. W.
, 1952, “
Plastic Instability Under Plane Stress
,”
J. Mech. Phys. Solids
0022-5096,
1
, pp.
1
18
.
17.
Lei
,
L. P.
,
Kim
,
J.
, and
Kang
,
B. S.
, 2002, “
Bursting Failure Prediction in Tube Hydroforming Processes by Using Rigid-Plastic FEM Combined With Ductile Fracture Criterion
,”
Int. J. Mech. Sci.
0020-7403,
44
, pp.
1411
1428
.
18.
Oyane
,
M.
,
Sato
,
T.
,
Okimoto
,
K.
, and
Shima
,
S.
, 1980, “
Criteria for Ductile Fracture and Their Applications
,”
J. Mech. Work. Technol.
0378-3804,
4
, pp.
65
81
.
19.
Xing
,
H. L.
, and
Makinouchi
,
A.
, 2001, “
Numerical Analysis and Design for Tubular Hydroforming
,”
Int. J. Mech. Sci.
0020-7403,
43
, pp.
1009
1026
.
20.
Kim
,
S.
, and
Kim
,
Y.
, 2002, “
Analytical Study for Tube Hydroforming
,”
J. Mater. Process. Technol.
0924-0136,
128
, pp.
232
239
.
21.
Kim
,
J.
,
Kim
,
S. W.
,
Song
,
W. J.
, and
Kang
,
B. S.
, 2005, “
Analytical and Numerical Approach to Prediction of Forming Limit in Tube Hydroforming
,”
J. Mater. Process. Technol.
0924-0136,
47
, pp.
1023
1037
.
22.
Koc
,
M.
,
Aue-u-lan
,
Y.
, and
Altan
,
T.
, 2001, “
On the Characteristics of Tubular Materials for Hydroforming—Experimentation and Analysis
,”
Int. J. Mach. Tools Manuf.
0890-6955,
41
, pp.
761
772
.
23.
Chow
,
C. L.
, and
Yang
,
X. J.
, 2002, “
Bursting for Fixed Tubular and Restrained Hydroforming
,”
J. Mater. Process. Technol.
0924-0136,
130–131
, pp.
107
114
.
24.
Nefussi
,
G.
, and
Combesure
,
A.
, 2002, “
Coupled Buckling and Plastic Instability for Tube Hydroforming
,”
Int. J. Mech. Sci.
0020-7403,
44
, pp.
899
914
.
25.
Lee
,
M. Y.
,
Sohn
,
S. M.
,
Kang
,
C. Y.
, and
Lee
,
S. Y.
, 2002, “
Study of Hydroforming Process for Automobile Radiator Support Members
,”
J. Mater. Process. Technol.
0924-0136,
130–131
, pp.
115
120
.
26.
Smith
,
L. M.
,
Ganeshmurthy
,
S.
, and
Alladi
,
K.
, 2003, “
Double-Sided High-Pressure Tubular Hydroforming
,”
J. Mater. Process. Technol.
0924-0136,
3
, pp.
599
608
.
27.
Jain
,
N.
, and
Wang
,
J.
, 2004, “
Finite Element Analysis of Dual Hydroforming Processes
,”
J. Mater. Process. Technol.
0924-0136,
145
, pp.
59
65
.
28.
Nemat-Alla
,
M.
, 2003, “
Reproducing Hoop Stress-Strain Behavior for Tubular Material Using Lateral Compression Test
,”
Int. J. Mech. Sci.
0020-7403,
45
, pp.
605
621
.
29.
Ngaile
,
G.
,
Jaeger
,
S.
, and
Altan
,
T.
, 2004, “
Lubrication in Tube Hydroforming (THF) Part II. Performance Evaluation of Lubricants Using LDH Test and Paer-Shaped Tube Expansion Test
,”
J. Mater. Process. Technol.
0924-0136,
146
, pp.
116
123
.
30.
Levy
,
B.
,
Van Tyne
,
C. J.
, and
Stringfield
,
J. M.
, 2004, “
Characterizing Steel Tube for Hydroforming Applications
,”
J. Mater. Process. Technol.
0924-0136,
150
, pp.
280
289
.
31.
Brunet
,
M.
,
Boumaiza
,
G.
, and
Nefussi
,
G.
, 2004, “
Unified Failure Analysis for Yubular Hydroforming
,”
J. Mater. Process. Technol.
0924-0136,
148
, pp.
269
277
.
32.
Kulkarni
,
A.
,
Biswas
,
P.
,
Narasimhan
,
R.
,
Luo
,
A.
,
Mishra
,
R.
,
Stoughton
,
T. B.
, and
Sachdev
,
A.
, 2004, “
An Experimental and Numerical Study of Necking Initiation in Aluminum Alloy Tubes During Hydroforming
,”
Int. J. Mech. Sci.
0020-7403,
46
, pp.
1727
1746
.
33.
Strano
,
M.
, and
Altan
,
T.
, 2004, “
An Inverse Energy Approach to Determine the Flow Stress of Tubular Materials for Hydroforming Applications
,”
J. Mater. Process. Technol.
0924-0136,
146
, pp.
92
96
.
34.
Li
,
H. Y.
,
Wang
,
X. S.
,
Yuan
,
S. J.
,
Miao
,
Q. B.
, and
Wang
,
Z. R.
, 2004, “
Typical Stress States of Tube Hydroforming and Their Distribution on the Yield Ellipse
,”
J. Mater. Process. Technol.
0924-0136,
151
, pp.
345
349
.
35.
Song
,
W. J.
,
Kim
,
S. W.
,
Kim
,
J.
, and
Kang
,
B. S.
, 2005, “
Analytical and Numerical Analysis of Bursting Failure Prediction in Tube Hydroforming
,”
J. Mater. Process. Technol.
0924-0136,
164–165
, pp.
1618
1623
.
36.
Yuan
,
S. J.
,
Lin
,
G.
,
Huang
,
X. R.
,
Wang
,
X. S.
,
Xie
,
W. C.
, and
Wang
,
Z. R.
, 2004, “
Hydroforming of Typical Hollow Components
,”
J. Mater. Process. Technol.
0924-0136,
151
, pp.
203
207
.
37.
Abrantes
,
J. P.
,
Szabo-Ponce
,
A.
, and
Batalha
,
G. F.
, 2005, “
Experimental and Numerical Simulation of Tube Hydroforming (THF)
,”
J. Mater. Process. Technol.
0924-0136,
164–165
, pp.
1140
1147
.
38.
Rama
,
S. C.
,
Ma
,
K.
,
Smith
,
L. M.
, and
Zhang
,
J. M.
, 2003, “
A Two-Dimensional Approach for Simulation of Hydroforming Expansion of Tubular Cross-Sections Without Axial Feed
,”
J. Mater. Process. Technol.
0924-0136,
141
, pp.
420
430
.
39.
Hwang
,
Y. M.
, and
Chen
,
W. C.
, 2003, “
Analysis and Finite Element Simulation of Tube Expansion in a Rectangular Cross Sectional Die
,”
Proc. Inst. Mech. Eng., Part B
0954-4054,
217
, pp.
127
135
.
40.
Smith
,
L. M.
, and
Sun
,
T.
, in press, “
Analytical Model for Tubular Hydroforming Analysis
,”
J. Mater. Process. Technol.
41.
Hwang
,
Y. M.
, and
Chen
,
W. C.
, 2005, “
Analysis of Tube Hydroforming in a Square Cross-Sectional Die
,”
Int. J. Plast.
0749-6419,
21
, pp.
1815
1833
.
42.
Smith
,
L. M.
,
Averill
,
R.
,
Lucas
,
J.
,
Stoughton
,
T. B.
, and
Matin
,
P.
, 2003, “
Influence of Transverse Normal Stress on Sheet Metal Formability
,”
Int. J. Plast.
0749-6419,
19
, pp.
1567
1583
.
43.
Morphy
,
G.
, 1998, “
Tube Hydroforming: Dimensional Capability Analysis of a High Volume Automotive Structural Component Production Process
,” SAE Technical Paper Series
980450
, International Congress & Exposition, February, Detroit, MI, Session: Sheet Metal Stamping.
44.
Auto/Steel Partnership Tube Hydroforming Committee, 2000, United States Automotive Manufacturing Partnership, Town Center, Southfield, MI.
45.
Smith
,
L. M.
, and
Sengupta
,
S.
, 2002, “
Organization and Interpretation of Phase One Tubular Hydroforming Experimental Data
,” Report to Auto Steel Partnership, Southfield, MI, August.
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