An Efficient Method for Describing Plane Strain Bending of Viscoplastic Sheets at Large Strains

2021 ◽  
pp. 23-35
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Alexander Pirumov
Keyword(s):  
Plane Strain ◽  
Efficient Method ◽  
Large Strains

scholarly journals Finite Pure Plane Strain Bending of Inhomogeneous Anisotropic Sheets

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 145
Author(s):  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Yeong-Maw Hwang
Keyword(s):  
Plane Strain ◽  
Yield Criterion ◽  
Large Strains ◽  
Rigid Plastic ◽  
Plastic Properties ◽  
Elastic Plastic ◽  
Starting Point ◽  
The Difference ◽  
Inside Radius ◽  
Elastic Unloading

The present paper concerns the general solution for finite plane strain pure bending of incompressible, orthotropic sheets. In contrast to available solutions, the new solution is valid for inhomogeneous distributions of plastic properties. The solution is semi-analytic. A numerical treatment is only necessary for solving transcendent equations and evaluating ordinary integrals. The solution’s starting point is a transformation between Eulerian and Lagrangian coordinates that is valid for a wide class of constitutive equations. The symmetric distribution relative to the center line of the sheet is separately treated where it is advantageous. It is shown that this type of symmetry simplifies the solution. Hill’s quadratic yield criterion is adopted. Both elastic/plastic and rigid/plastic solutions are derived. Elastic unloading is also considered, and it is shown that reverse plastic yielding occurs at a relatively large inside radius. An illustrative example uses real experimental data. The distribution of plastic properties is symmetric in this example. It is shown that the difference between the elastic/plastic and rigid/plastic solutions is negligible, except at the very beginning of the process. However, the rigid/plastic solution is much simpler and, therefore, can be recommended for practical use at large strains, including calculating the residual stresses.

Plane-Strain Bending With Isotropic Strain Hardening at Large Strains

2010 ◽  
Vol 77 (6) ◽  
Author(s):  
Sergei Alexandrov ◽  
Yeong-Maw Hwang
Keyword(s):  
Strain Hardening ◽  
Plane Strain ◽  
Closed Form Solution ◽  
Bending Moment ◽  
Form Solution ◽  
Isotropic Hardening ◽  
Large Strains ◽  
Rigid Plastic ◽  
Elastic Plastic ◽  
Hardening Law

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.

Plane strain bending of a bimetallic sheet at large strains

2016 ◽  
Vol 58 (4) ◽  
pp. 641-659
Author(s):  
Sergei E. Alexandrov ◽  
Nguyen D. Kien ◽  
Dinh V. Manh ◽  
Fedor V. Grechnikov
Keyword(s):  
Plane Strain ◽  
Large Strains ◽  
Bimetallic Sheet

scholarly journals Plane strain pure bending of sheets with damage evolution at large strains

2011 ◽  
Vol 48 (11-12) ◽  
pp. 1637-1643 ◽  
Author(s):  
Sergei Alexandrov ◽  
Jean-Claude Gelin
Keyword(s):  
Plane Strain ◽  
Damage Evolution ◽  
Large Strains ◽  
Pure Bending

An Alternative Approach to Analysis of Plane-Strain Pure Bending at Large Strains

2006 ◽  
Vol 41 (5) ◽  
pp. 397-410 ◽  
Author(s):  
S Alexandrov ◽  
Ji Hoon Kim ◽  
Kwansoo Chung ◽  
Tae Jin Kang
Keyword(s):  
Plane Strain ◽  
Large Strains ◽  
Pure Bending ◽  
Alternative Approach

The Theoretical Analysis of Metal-Forming Problems in Plane Strain

1952 ◽  
Vol 19 (1) ◽  
pp. 97-103
Author(s):  
E. H. Lee
Keyword(s):  
Plane Strain ◽  
Metal Forming ◽  
Plastic Material ◽  
Large Strains ◽  
Rigid Plastic ◽  
Small Strains ◽  
Plastic Type ◽  
Static Determinacy ◽  
Complete Solutions

Abstract The plastic flow in plane strain of an ideally plastic material subjected to large strains is considered. Elastic strains are negligible and a rigid-plastic type of analysis is adopted. The equations to be satisfied are detailed, and they include stress and velocity equations in the plastic regions, as well as consideration of the stress field in the rigid regions to check the validity of small strains there. Complete solutions satisfying these conditions require the determination of the rigid-plastic boundaries to delineate the regions in which the various conditions must be satisfied. The fallacy of static determinacy of such problems in terms of the stress equations only is emphasized. The study of complete solutions indicates errors in solutions commonly accepted in the literature which are based on the stress equations only. Examples are discussed. The general occurrence of velocities in the boundary conditions of forming problems is pointed out, and the difficulty of setting such problems in terms of boundary stresses only is illustrated by examples.

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