An accurate analytical method is normally the preferred choice in engineering practice since this approach usually does not require additional software and can be applied for different situations. A number of analytical methods have been proposed for the air bending process, however, none of them has the capacity to deal with large radius bending. Large radius bending is characterized by a high ratio of the punch radius to the die opening and it is often applied for high-strength steels because of their limited bendability. This bending mode is used to fulfill the imposed level of maximum strain during the forming process. This contribution develops an analytical solution based on the assumption that the bent plate profile can be represented by two straight lines and a circular segment. Three different hardening laws—linear, Swift, and Aerens—are used for the bending moment calculation. Unit moment measurements are used in order to avoid extrapolation of hardening curves obtained by tensile testing. The model is compared with a wide range of experiments using the coefficient of determination, relative and absolute average errors, in addition to the mean standard error. The analytical prediction based on the circular approximation is found to be an accurate and robust tool for the calculation of the major bending characteristics for large radius air bending of high-strength steels.

References

References
1.
Vorkov
,
V.
,
Aerens
,
R.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
,
2017
, “
Experimental Investigation of Large Radius Air Bending
,”
Int. J. Adv. Manuf. Technol.
,
92
(
9–12
), pp.
3553
3569
.
2.
Marciniak
,
Z.
, and
Duncan
,
J. L.
,
1992
,
Mechanics of Sheet Metal Forming
,
Edward Arnold
,
London
.
3.
Lange
,
K.
,
1985
,
Handbook of Metal Forming
,
McGraw-Hill Book Company
,
New York
.
4.
Altan
,
T.
, and
Tekkaya
,
A. E.
,
2012
,
Sheet Metal Forming: Processes and Applications
,
ASM International
, Materials Park, OH.
5.
Kim
,
H.
,
Nargundkar
,
N.
, and
Altan
,
T.
,
2007
, “
Prediction of Bend Allowance and Springback in Air Bending
,”
ASME J. Manuf. Sci. Eng.
,
129
(
2
), pp.
342
351
.
6.
Wang
,
C.
,
Kinzel
,
G.
, and
Altan
,
T.
,
1993
, “
Mathematical Modeling of Plane-Strain Bending of Sheet and Plate
,”
J. Mater. Process. Technol.
,
39
(
3–4
), pp.
279
304
.
7.
Yang
,
X.
,
Choi
,
C.
,
Sever
,
N. K.
, and
Altan
,
T.
,
2016
, “
Prediction of Springback in Air-Bending of Advanced High Strength Steel (DP780) Considering Young's Modulus Variation and With a Piecewise Hardening Function
,”
Int. J. Mech. Sci.
,
105
, pp.
266
272
.
8.
Yang
,
X.
,
Kardes
,
N.
,
Choi
,
C.
, and
Taylan
,
A.
,
2011
, “
Investigating Springback in Bending of Advanced High-Strength Steel—Part II Springback Prediction
,”
STAMPING J.
, pp. 8–9https://ercnsm.osu.edu/sites/ercnsm.osu.edu/files/uploads/642-1.pdf.
9.
Aerens
,
R.
, and
Masselis
,
S.
,
2000
, “
Air Bending
,” Scientific and Technical Research Center of the Metal Fabrication Industry (CRIF/WTCM/SIRRIS), Leuven, Belgium, Report No. MC 110.
10.
De Vin
,
L. J.
,
Streppel
,
A. H.
, and
Kals
,
H. J. J.
,
1994
, “
Tolerancing and Sheet Bending in Small Batch Part Manufacturing
,”
CIRP Annals
,
43
(
1
), pp.
421
424
.
11.
De Vin
,
L. J.
,
Streppel
,
A. H.
,
Singh
,
U. P.
, and
Kals
,
H. J. J.
,
1996
, “
A Process Model for Air Bending
,”
J. Mater. Process. Technol.
,
57
(
1–2
), pp.
48
54
.
12.
Elkins
,
K. L.
, and
Sturges
,
R. H.
,
1999
, “
Springback Analysis and Control in Small Radius Air Bending
,”
ASME J. Manuf. Sci. Eng.
,
121
(
4
), pp.
679
688
.
13.
Vorkov
,
V.
,
Aerens
,
R.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
,
2015
, “
Influence of a Single Bend in the Bumping Process of Large Radius Air Bending
,”
Key Eng. Mater.
,
651
, pp.
1090
1095
.
14.
Vorkov
,
V.
,
Aerens
,
R.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
,
2015
, “
On the Identification of a Loading Scheme in Large Radius Air Bending
,”
Key Eng. Mater.
,
639
, pp.
155
162
.
15.
Vorkov
,
V.
,
Aerens
,
R.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
,
2014
, “
Springback Prediction of High-Strength Steels in Large Radius Air Bending Using Finite Element Modeling Approach
,”
Procedia Eng.
,
81
, pp.
1005
1010
.
16.
Vorkov
,
V.
,
Konyukhov
,
A.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
,
2016
, “
Contact Modelling of Large Radius Air Bending With Geometrically Exact Contact Algorithm
,”
J. Phys.: Conf. Ser.
,
734
(3), p. 032076.
17.
Vorkov
,
V.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
, “
Finite Element Modeling of Large Radius Bending Operation
,”
Int. J. Manuf. Res.
(under review).
18.
Vorkov
,
V.
,
Aerens
,
R.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
,
2017
, “
Accurate Prediction of Large Radius Air Bending Using Regression
,”
Procedia Eng.
,
207
, pp.
1623
1628
.
19.
Vorkov
,
V.
,
Aerens
,
R.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
,
2018
, “
Two Regression Approaches for Prediction of Large Radius Air Bending
,”
Int. J. Mater. Form.
(in press).
20.
Vorkov
,
V.
,
Aerens
,
R.
,
Vandepitte
,
D.
, and
Duflou
,
J. R.
,
2014
, “
The Multi-Breakage Phenomenon in Air Bending Process
,”
Key Eng. Mater.
,
611
, pp.
1047
1053
.
21.
Samuel
,
K. G.
, and
Rodriguez
,
P.
,
2005
, “
On Power-Law Type Relationships and the Ludwigson Explanation for the Stress-Strain Behaviour of AISI 316 Stainless Steel
,”
J. Mater. Sci.
,
40
(
21
), pp.
5727
5731
.
22.
Aerens
,
R.
,
1997
, “
Characterisation of Material by Bending
,”
Fifth International Conference on Sheet Metal
(SheMet'97), Linkoping, Sweden, June 16–18, pp.
251
262
.
23.
Perduijn
,
A. B.
, and
Hoogenboom
,
S. M.
,
1995
, “
The Pure Bending of Sheet
,”
J. Mater. Process. Technol.
,
51
(
1–4
), pp.
274
295
.
24.
Hoefnagels
,
J. P. M.
,
Ruybalid
,
A. P.
, and
Buizer
,
C. A.
,
2015
, “
A Small-Scale, Contactless, Pure Bending Device for in-Situ Testing
,”
Exp. Mech.
,
55
(
8
), pp.
1511
1524
.
25.
Chatti
,
S.
, and
Fathallah
,
R.
,
2014
, “
A Study of the Variations in Elastic Modulus and Its Effect on Springback Prediction
,”
Int. J. Mater. Form.
,
8
(
1
), pp.
19
29
.
26.
Wagoner
,
R. H.
,
Lim
,
H.
, and
Lee
,
M.-G.
,
2013
, “
Advanced Issues in Springback
,”
Int. J. Plast.
,
45
, pp.
3
20
.
27.
Vorkov
,
V.
,
2017
, “
Complete Experimental Data for Large Radius Bending
,”
The Dataverse Project
, Harvard Dataverse.
28.
Vorkov
,
V.
,
2017
, “
Variability Data for Large Radius Bending
,”
The Dataverse Project
, Harvard Dataverse.
29.
Streppel
,
A. H.
,
De Vin
,
L. J.
,
Brinkman
,
J.
, and
Kals
,
H. J. J.
,
1993
, “
Suitability of Sheet Bending Modelling Techniques in CAPP Applications
,”
J. Mater. Process. Technol.
,
36
(
3
), pp.
339
356
.
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