Finite deformation elastic-plastic analysis of plane-strain pure bending of a strain hardening sheet is presented. The general closed-form solution is proposed for an arbitrary isotropic hardening law assuming that the material is incompressible. Explicit relations are given for most popular conventional laws. The stage of unloading is included in the analysis to investigate the distribution of residual stresses and springback. The paper emphasizes the method of solution and the general qualitative features of elastic-plastic solutions rather than the study of the bending process for a specific material. In particular, it is shown that rigid-plastic solutions can be used to predict the bending moment at sufficiently large strains.
Issue Section:
Technical Briefs
1.
Daxner
, T.
, Rammerstorfer
, F. G.
, Segurado
, J.
, and Pettermann
, H. E.
, 2003, “Numerical Simulations of the Creep Deformation of MMCs in 4-Point Bending Mode
,” ASME J. Eng. Mater. Technol.
0094-4289, 125
(1
), pp. 50
–55
.2.
Eason
, G.
, 1960, “The Elastic-Plastic Bending of a Compressible Curved Bar
,” Appl. Sci. Res.
0003-6994, 9
, pp. 53
–63
.3.
Denton
, A. A.
, 1966, “Plane Strain Bending With Work Hardening
,” J. Strain Anal.
0022-4758, 1
(3
), pp. 196
–203
.4.
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
, pp. 279
–304
.5.
Dadras
, P.
, 2001, “Plane Strain Elastic-Plastic Bending of a Strain-Hardening Curved Beams
,” Int. J. Mech. Sci.
0020-7403, 43
, pp. 39
–56
.6.
Chakrabarty
, J.
, Lee
, W. B.
, and Chan
, K. C.
, 2001, “An Exact Solution for the Elastic/Plastic Bending of Anisotropic Sheet Under Conditions of Plane Strain
,” Int. J. Mech. Sci.
0020-7403, 43
, pp. 1871
–1880
.7.
Chan
, K. C.
, and Wang
, S. H.
, 1999, “Effect of Anisotropy on Springback of Integrated Circuit Leadframes
,” J. Mater. Eng. Perform.
1059-9495, 8
, pp. 368
–374
.8.
Hsueh
, C. H.
, Lee
, S.
, and Chuang
, T. J.
, 2003, “An Alternative Method of Solving Multilayer Bending Problems
,” ASME J. Appl. Mech.
0021-8936, 70
, pp. 151
–154
.9.
Rees
, D. W. A.
, 2007, “Descriptions of Reversed Yielding in Bending
,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062, 221
, pp. 981
–991
.10.
Hill
, R.
, 1950, The Mathematical Theory of Plasticity
, Clarendon
, Oxford
11.
Dadras
, P.
, and Majless
, S. A.
, 1982, “Plastic Bending of Work Hardening Materials
,” ASME J. Eng. Ind.
0022-0817, 104
(3
), pp. 224
–230
.12.
Verguts
, H.
, and Sowerby
, R.
, 1975, “The Pure Plastic Bending of Laminated Sheet metals
,” Int. J. Mech. Sci.
0020-7403, 17
, pp. 31
–51
.13.
Tan
, Z.
, Persson
, B.
, and Magnusson
, C.
, 1995, “Plastic Bending of Anisotropic Sheet Metals
,” Int. J. Mech. Sci.
0020-7403, 37
(4
), pp. 405
–421
.14.
Alexandrov
, S.
, Kim
, J. -H.
, Chung
, K.
, and Kang
, T. -J.
, 2006, “An Alternative Approach to Analysis of Plane-Strain Pure Bending at Large Strains
,” J. Strain Anal. Eng. Des.
0309-3247, 41
(5
), pp. 397
–410
.15.
Lyamina
, E. A.
, 2006, “Plastic Bending of a Strip for a Yield Criterion Depending on the Mean Stress
,” J. Appl. Mech. Tech. Phys.
0021-8944, 47
, pp. 249
–253
.16.
Helsing
, J.
, and Jonsson
, A.
, 2002, “On the Accuracy of Benchmark Tables and Graphical Results in the Applied Mechanics Literature
,” ASME J. Appl. Mech.
0021-8936, 69
, pp. 88
–90
.17.
Gao
, X. -L.
, 1994, “Finite Deformation Elasto-Plastic Solution for the Pure Bending Problem of a Wide Plate of Elastic Linear-Hardening Material
,” Int. J. Solids Struct.
0020-7683, 31
(10
), pp. 1357
–1376
.18.
Xiao
, H.
, Bruhns
, O. T.
, and Meyers
, A.
, 2006, “Elastoplasticity Beyond Small Deformations
,” Acta Mech.
0001-5970, 182
, pp. 31
–111
.19.
Rees
, D. W. A.
, 2006, Basic Engineering Plasticity
, Butterworth-Heinemann
, Oxford
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.