One of the most widely involved operations in sheet metal forming processes in aircraft industry is bending, particularly, air bending as a simple process. For this reason, the bendability of aluminum alloys is an important material property, which determines the minimum radius to which a sheet may be bent without cracking. Hence, the challenging issue, on which this paper focuses, is to predict this material parameter from other material parameters commonly measured during standard tensile tests. For this prediction, a finite element model and a response surface model are elaborated and, as a result, a relatively simple formula is proposed to calculate the minimum bending radius from the reduction in the area at fracture, the strain hardening exponent, and the yield stress, which are material parameters available from tensile tests.

1.
G.
Sachs
, 1976,
Principles and Methods of Sheet-Metal Fabricating
,
Reinhold
,
New York
.
2.
Sangdahl
,
G. S.
,
Aul
,
E. L.
, and
Sachs
,
G.
, 1948, “
An Investigation of the Stress and Strain States Occurring in Bending Rectangular Bars
,”
Experimental Stress Analysis
,
6
(
1
), pp.
1
18
.
3.
Akeret
,
R.
, 1978, “
Failure Mechanism in the Bending of Aluminium Sheets and Limits of Bendability
,”
Aluminium
,
54
(
2
), pp.
117
123
.
4.
Pourboghrat
,
F.
, and
Stelson
,
K. A.
, 1997, “
Bend Allowance and Developed Length Calculation for Pressbrake Bending
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
119
, pp.
227
237
.
5.
Wang
,
C.
,
Kinzel
,
G.
, and
Altan
,
T.
, 1993, “
Mathematical Modeling of Plane-Strain Bending of Sheet and Plate
,”
J. Mater. Process. Technol.
0924-0136,
39
(
3–4
), pp.
279
304
.
6.
Prasad
,
Y. K. D. V.
, and
Somasundaram
,
S.
, 1993, “
A Mathematical Model for Bend-Allowance Calculation in Automated Sheet-Metal Bending
,”
J. Mater. Process. Technol.
0924-0136,
39
, pp.
337
356
.
7.
Kim
,
H.
,
Nargundkar
,
N.
, and
Altan
,
T.
, 2007, “
Prediction of Bend Allowance and Spring Back in Air Bending
,”
ASME J. Manuf. Sci. Eng.
1087-1357,
129
, pp.
342
351
.
8.
Woznica
,
K.
, and
Klepaczko
,
J. R.
, 2003, “
Modelling of Inelastic Bending of a Metal Sheet With Thermal Coupling
,”
Int. J. Mech. Sci.
0020-7403,
45
, pp.
359
372
.
9.
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.
0924-0136,
57
, pp.
48
54
.
10.
Sarkar
,
J.
,
Kutty
,
T. R. G.
,
Conlon
,
K. T.
,
Wilkinson
,
D. S.
,
Embury
,
J. D.
, and
Lloyd
,
D. J.
, 2001, “
Tensile and Bending Properties of aa5754 Aluminium Alloys
,”
Mater. Sci. Eng., A
0921-5093,
316
, pp.
52
59
.
11.
Ragab
,
A. R.
, and
Saleh
,
C. A.
, 2005, “
Evaluation of Bendability of Sheet Metals Using Void Coalescence Models
,”
Mater. Sci. Eng., A
0921-5093,
395
, pp.
102
109
.
12.
Wisselink
,
H.
, and
Huétink
,
H.
, 2008, “
Prediction of the Bendability of Sheet Metals Using Nonlocal Damage Models
,”
Metal Forming 2008
,
E. J.
Pietrzi
, ed., Krakow, Poland, Sept. 21–24.
13.
Datsko
,
J.
, and
Yang
,
C. T.
, 1960, “
Correlation of Bendability of Materials With Their Tensile Properties
,”
ASME J. Eng. Ind.
0022-0817,
82
(
4
), pp.
309
314
.
15.
Wang
,
C.
,
Kinzel
,
G.
, and
Altan
,
T.
, 1993, “
Process Simulation and Spring Back Control in Plane-Strain Sheet Bending
,” SAE Special Publications No. 944, Society of Automotive Engineers, pp.
45
54
.
16.
Hill
,
R.
, 1948, “
A Theory of the Yielding and Plastic Flow of Anisotropic Metals
,”
Proc. R. Soc. London, Ser. A
0950-1207,
193
, pp.
281
297
.
17.
Hill
,
R.
, 1979, “
Theoretical Plasticity of Textured Aggregates
,”
Math. Proc. Cambridge Philos. Soc.
0305-0041,
85
, pp.
179
191
.
18.
Ragab
,
A. R.
, and
Abbas
,
A. T.
, 1986, “
Assessment of Work-Hardening Characteristics and Limit Strains of Anisotropic Aluminium Sheets in Biaxial Stretching
,”
ASME J. Eng. Mater. Technol.
0094-4289,
108
, pp.
250
255
.
19.
Bressan
,
J. D.
, and
Williams
,
J. A.
, 1983, “
The Use of a Shear Instability Criterion to Predict Local Necking in Sheet Metal Deformation
,”
Int. J. Mech. Sci.
0020-7403,
25
, pp.
155
168
.
20.
Kals
,
J. A. G.
, and
Veenstra
,
P. C.
, 1974, “
On the Critical Radius in Sheet Bending
,”
CIRP Ann.
0007-8506,
23
(
1
), pp.
55
56
.
21.
Leu
,
D. -K.
, 1997, “
A Simplified Approach for Evaluating Bendability and Springback in Plastic Bending of Anisotropic Sheet Metals
,”
J. Mater. Process. Technol.
0924-0136,
66
(
1–3
), pp.
9
17
.
22.
Rolf
,
R. L.
, and
Patrick
,
E. P.
, 1978, “
Bending and Spring Back of Aluminium Alloy Sheet and Plate, Formability Topics—Metallic Materials
,” ASTM STP No. 647, pp.
65
85
.
23.
Hoffman
,
O.
, and
Sachs
,
G.
, 1953,
Theory of Plasticity
,
McGraw-Hill
,
New York
.
24.
Hill
,
R.
, 1950,
The Mathematical Theory of Plasticity
,
Oxford
,
London
, pp.
288
294
.
25.
Ludwik
,
P.
, 1909,
Verlag von Julius Springer
,
Springer
,
Berlin
.
26.
Box
,
G. E. P.
, and
Wilson
,
K. B.
, 1951, “
On the Experimental Attainment of Optimum Conditions (With Discussion)
,”
J. R. Stat. Soc. Ser. B (Methodol.)
0035-9246,
13
(
1
), pp.
1
45
.
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