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Technical Briefs

Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

[+] Author and Article Information
Sergei Alexandrov

Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow 119526, Russia

Yeong-Maw Hwang1

Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwanymhwang@mail.nsysu.edu.tw

1

Corresponding author.

J. Appl. Mech 77(6), 064502 (Sep 01, 2010) (6 pages) doi:10.1115/1.4001283 History: Received April 11, 2009; Revised January 23, 2010; Published September 01, 2010; Online September 01, 2010

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.

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Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Geometry of the process

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Figure 2

Dependence of the dimensionless bending moment on the radius of the concave surface for several constitutive equations. The broken line corresponds to a rigid perfectly/plastic material.

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Figure 3

Through-thickness distribution of the radial residual stress at different values of radius rCD at the end of loading (Swift’s law)

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Figure 4

Through-thickness distribution of the circumferential residual stress at different values of radius rCD at the end of loading (Swift’s law)

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Figure 5

Dependence of the radius of the concave surface after unloading on its value at the end of loading

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