Plane strain bending of a bimetallic sheet at large strains

- Journal title : Structural Engineering and Mechanics
- Volume 58, Issue 4, 2016, pp.641-659
- Publisher : Techno-Press
- DOI : 10.12989/sem.2016.58.4.641

Title & Authors

Plane strain bending of a bimetallic sheet at large strains

Alexandrov, Sergei E.; Kien, Nguyen D.; Manh, Dinh V.; Grechnikov, Fedor V.;

Alexandrov, Sergei E.; Kien, Nguyen D.; Manh, Dinh V.; Grechnikov, Fedor V.;

Abstract

This paper deals with the pure bending of incompressible elastic perfectly plastic two-layer sheets under plane strain conditions at large strains. Each layer is classified by its yield stress, shear modulus of elasticity and its initial percentage thickness in relation to the whole sheet. The solution found is semi-analytic. In particular, a numerical technique is only necessary to solve transcendental equations. The general solution is cumbersome because different analytic expressions for the radial and circumferential stresses should be adopted in different regions of the whole sheet. In particular, there are several alternative ways a plastic region (or plastic regions) can propagate. However, for any given set of material and process parameters the solution to the problem consists of a sequence of rather simple analytic expressions connected by transcendental equations. The general solution is illustrated by a simple example.

Keywords

plane strain bending;bimetallic sheet;elastic/perfectly plastic material;large strains;analytic solution;

Language

English

References

1.

Alexandrov, S. and Hwang, Y.M. (2009), "The bending moment and springback in pure bending of anisotropic sheets", Int. J. Solid. Struct., 46(25-26), 4361-4368.

2.

Alexandrov, S. and Hwang, Y.M. (2010), "Plane strain bending with isotropic strain hardening at large strains", Tran. ASME J. Appl. Mech., 77(6), 064502.

3.

Alexandrov, S. and Hwang, Y.M. (2011), "Influence of Bauschinger effect on springback and residual stresses in plane strain pure bending", Acta Mech., 220(1-4), 47-59.

4.

Alexandrov, S., Kim, J.H., Chung, K. and Kang, T.J. (2006), "An alternative approach to analysis of planestrain pure bending at large strains", J. Strain Anal. Eng. Des., 41(5), 397-410.

5.

Alexandrov, S., Manabe, K. and Furushima, T. (2011), "A general analytic solution for plane strain bending under tension for strain-hardening material at large strains", Arch. Appl. Mech., 81(12), 1935-1952.

6.

Arslan, E. and Sulu, I.Y. (2014), "Yielding of two-layer curved bars under pure bending", ZAMM, 94(9), 713-720.

7.

Chakrabarty, J. (1987), Theory of Plasticity, McGraw-Hill, Singapore.

8.

Hill, R. (1950), The Mathematical Theory of Plasticity, Clarendon Press, Oxford

9.

Kagzi, S.A., Gandhi, A.H., Dave, H.K. and Raval, H.K. (2015), "An analytical model for bending and springback of bimetallic sheets", Mech. Adv. Mater. Struct., 23(1), 80-88.

10.

Lo, K.H. and Conway, H.D. (1975), "Bending of multi-layered curved bars", Int. J. Mech. Sci. 17, 283-291.

11.

Roberts, S.M., Hall, F.R., Bael, A.V., Hartley, P., Pillinger, I., Sturgess, C.E.N., Houtte, P.V. and Aernoudt, E. (1992), "Benchmark tests for 3-D, elasto-plastic, finite-element codes for the modeling of metal forming processes", J. Mater. Proc. Technol., 34, 61-68.

12.

Verguts, H. and Sowerby, R. (1975), "The pure plastic bending of laminated sheet metals", Int. J. Mech. Sci., 17, 31-51.

13.

Xiao, H., Bruhns, O.T. and Meyers, A. (2006), "Elastoplasticity beyond small deformations", Acta Mech., 182, 31-111.