An exact solution for the elastic/plastic bending of anisotropic sheet metal under conditions of plane strain

2001 ◽  
Vol 43 (8) ◽  
pp. 1871-1880 ◽  
Author(s):  
J Chakrabarty ◽  
W.B Lee ◽  
K.C Chan
Keyword(s):  
Exact Solution ◽  
Plane Strain ◽  
Sheet Metal ◽  
Plastic Bending ◽  
Elastic Plastic

Elementary Solutions and Process Sensitivities for Plane-Strain Sheet-Metal Forming

1992 ◽  
Vol 59 (2S) ◽  
pp. S23-S28 ◽  
Author(s):  
M. L. Wenner
Keyword(s):  
Exact Solution ◽  
Plane Strain ◽  
Sheet Metal ◽  
Process Parameters ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Computer Programs ◽  
Equilibrium Equations ◽  
Numerical Errors ◽  
Low Levels

Solutions to simple, plane-strain sheet-metal forming problems are developed using an exact solution to the membrane equilibrium equations and apre-integrated version of the plasticity equations. This approach allows the numerical errors to be driven to very low levels in an economical manner. Both stretch and draw conditions are considered, and solutions are presented for several problems which have been proposed as benchmarks for sheet-metal forming computer programs. The simplicity of this approach allows us to calculate formulas for the sensitivity of the solutions to process parameters. It is demonstrated that draw problems can exhibit very strong dependencies on parameters, especially drawbead restraint force.

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.

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