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Structural Engineering and Mechanics Volume 58, Number 4, May25 2016 , pages 641-659 DOI: https://doi.org/10.12989/sem.2016.58.4.641 |
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Plane strain bending of a bimetallic sheet at large strains |
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Sergei E. Alexandrov, Nguyen D. Kien, Dinh V. Manh
and Fedor V. Grechnikov
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| 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 semianalytic. 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. | ||
| Key Words | ||
| plane strain bending; bimetallic sheet; elastic/perfectly plastic material; large strains; analytic solution | ||
| Address | ||
| Sergei E. Alexandrov: Laboratory for Strength and Fracture of Materials and Structures, Institute for Problems in Mechanics, 101-1 Prospect Vernadskogo, 119526, Moscow, Russia Nguyen D. Kien, Dinh V. Manh: Institute of Mechanics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam Fedor V. Grechnikov: Metal Forming Department, Samara State Aerospace University, 34 Moskovskoye shosse, 443086, Samara, Russia | ||