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.

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.

Rigid-Plastic Meshfree Method for Metal Forming Simulation

2003 ◽  
Author(s):  
Young H. Park
Keyword(s):  
Metal Forming ◽  
Plastic Material ◽  
Meshfree Method ◽  
Large Plastic Deformation ◽  
Rigid Plastic ◽  
Mesh Distortion ◽  
Forming Simulation ◽  
Rigid Plastic Material ◽  
Plastic Analysis ◽  
Main Variable

In this paper, material processing simulation is carried out using a meshfree method. With the use of a meshfree method, the domain of the workpiece is discretized by a set of particles without using a structured mesh to avoid mesh distortion difficulties which occurred during the course of large plastic deformation. The proposed meshfree method is formulated for rigid-plastic material. This approach uses the flow formulation based on the assumption that elastic effects are insignificant in the metal forming operation. In the rigid-plastic analysis, the main variable of the problem becomes flow velocity rather than displacement. A numerical example is solved to validate the proposed method.

A Theoretical Analysis of the Bending into Cylindrical Dies of Metal Strips

1984 ◽  
Vol 198 (2) ◽  
pp. 99-108 ◽  
Author(s):  
T X Yu ◽  
W Johnson
Keyword(s):  
Theoretical Analysis ◽  
Metal Forming ◽  
Plastic Material ◽  
Forming Process ◽  
Rigid Plastic ◽  
Rigid Plastic Material ◽  
Punch Load ◽  
Theoretical Predictions ◽  
Metal Forming Process ◽  
Good Agreement

Based on experiments on the bending of metal strips into cylindrical dies using a semi-circular ended punch (1) a theoretical analysis of this metal forming process is presented to predict the punch load—punch travel characteristic and the clearance between the punch pole and the mid-point of the strip. Elastic/plastic and rigid/plastic material idealizations are employed, and the effect of friction between the strip and the die is also considered. The theoretical predictions show good agreement with the experimental results and are useful for designers.

An Unexpected Feature of a Class of Damage Evolution Models

2016 ◽  
Vol 713 ◽  
pp. 195-198
Author(s):  
Sergei Alexandrov
Keyword(s):  
Metal Forming ◽  
Damage Evolution ◽  
Plastic Material ◽  
Closed Form Solution ◽  
Material Model ◽  
Form Solution ◽  
Friction Condition ◽  
Rigid Plastic ◽  
Damage Evolution Equation ◽  
Rigid Plastic Material

The main objective of the present paper is to demonstrate, by means of a boundary value problem permitting a closed-form solution, that no solution exists under certain conditions in the case of a rigid/plastic material model including a damage evolution equation. The source of this feature of the solution is the sticking friction condition, which is often adopted in the metal forming literature.

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 Rigid Plastic Finite Element Formulation for Sheet Metal Forming Processes

1993 ◽  
Vol 207 (3) ◽  
pp. 167-171 ◽  
Author(s):  
P A F Martins ◽  
M J M Barata Marques
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Yield Criterion ◽  
Large Strain ◽  
Theoretical Development ◽  
Element Formulation ◽  
Rigid Plastic

A rigid plastic finite element model for analysing two-dimensional plane strain sheet metal forming processes is described. The model is based on the large strain formulation using membrane theory, and the material is assumed to be rigid plastic, work hardening and conforms to Hill's anisotropic yield criterion and associated flow rules. The theoretical development follows the work of Kobayashi and Kim on the axisymmetric modelling of sheet metal forming. An application of the model for plane strain cylindrical punch stretching is presented. The results obtained are compared with those provided through an analytical membrane solution described in this work. The agreement found between both solutions is excellent.

scholarly journals The Influence of the Characteristics of Plastic Materials Used in the Performance of the Thoraco-Lumbar Orthoses

2018 ◽  
Vol 55 (1) ◽  
pp. 85-90 ◽  
Author(s):  
Constantin Nanu ◽  
Ion Poeata ◽  
Cezar Popescu ◽  
Lucian Eva ◽  
Bogdan Florin Toma ◽  
...  
Keyword(s):  
Plastic Material ◽  
Burst Fracture ◽  
Rigid Plastic ◽  
Element Analysis ◽  
Plastic Materials ◽  
Plastic Type ◽  
Lumbar Area ◽  
Bone Fragments ◽  
Materials Used ◽  
State Of Tension

The aim of the paper is to identify the of optimal plastic type used in obtaining thoraco-lumbar orthoses - used in the treatments of comminutive fracture, of burst fracture type of the vertebrae in the lumbar area. For this purpose, with the help of Finite Element Analysis (FEA), a theoretical study was carried out on the influence of elastic properties of plastics, used in the achieving of lumbar orthoses, on the state of tension and on the local displacements of the bone fragments from the traumatized area under the condition of the movement from the base of extension and flexion. In the study the force of flexion, the force of extension and the elastic modulus of plastic material varied on three levels. The theoretical results obtained were completed with clinical trials carried out on a total of 26 patients who suffer thoraco-lumbar comminutive fracture, burst fractures type, at vertebra T11 and were immobilized in Boston-type plastic orthoses made of: polypropylene (PP), rigid vinyl polychloride (PVC-D) and polytetrafluoroethylene (PTFE). As a result of observations, it was found that the use of an orthesis made from rigid plastic material, although it appears higher stresses in the traumatized zone, the displacements of bone fragments are smaller, the pains is higher in the fractured zone, the angle of kyphosis (LKA) close to the normal value and a better mobility of the spine (ODI indicator).

Numerical Study of Metal Forming Simulation Using Elasto-Plastic and Rigid-Plastic Meshfree Analysis

2005 ◽  
Author(s):  
Young H. Park
Keyword(s):  
Metal Forming ◽  
Reproducing Kernel ◽  
Numerical Study ◽  
Plastic Material ◽  
Meshfree Method ◽  
Material Model ◽  
Reproducing Kernel Particle Method ◽  
Rigid Plastic ◽  
Plastic Model ◽  
Forming Simulation

In this paper, material processing simulation is carried out using a meshfree method. The domain of the workpiece is discretized using the Lagrangian Reproducing Kernel Particle Method (RKPM) where no external meshes are used. The meshfree method is formulated for elasto-plastic material model as well as rigid-plastic model. For elasto-plastic model, a finite plasticity theory is formulated based on the multiplicative decomposition to handle large deformation problems. A rigid-plastic material model is also employed using flow formulation based on the assumption that elastic effects are insignificant in the metal forming operation. A comparative study between elasto-plastic and rigid-plastic RKPM methods was conducted to demonstrate consistency of the results from elasto-plastic and rigid-plastic simulations for a metal forming application.

Conical Flows in Metal Forming

1972 ◽  
Vol 94 (1) ◽  
pp. 213-222 ◽  
Author(s):  
N. Ahmed
Keyword(s):  
Work Hardening ◽  
Metal Forming ◽  
Plastic Material ◽  
Dead Zone ◽  
Equivalent Stress ◽  
Plastic Region ◽  
Maximum Pressure ◽  
Rigid Plastic ◽  
Hardening Material ◽  
Conical Flows

An improved velocity field based on the solution to an incompressible fluid flow is used to establish an upper bound approach for conical flows in metal forming. From a three parameter characterization of the equivalent stress-equivalent strain data on copper and aluminum, the effects of work hardening on forming stresses, maximum reduction ratios, optimum cone angles, and dead zone angles are studied for drawing, conventional, and hydrostatic extrusion. Results for a rigid-plastic material are obtained as a special case of the work hardening material. Experimental data are offered to show an excellent correlation with theory. A representation for the redundant work factor is developed that incorporates in it the effects of material properties and flow geometry. The existence of maximum pressure well inside the plastic region is pointed out and the possibility of introducing the forming fluid at some distance inside the die to facilitate better lubrication is examined.

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