Plane-strain Process Research Articles

Theoretical modeling, simulation and experimental studies of Al/Cu clad sheet forging

Slab analysis of three layer clad sheet forging process is presented by considering the Von Mises yield criterion and Coulomb friction condition in the plane strain process. A significant phenomenon considered in this paper is evaluation of considering or ignoring the shear stress in the yield criterion and investigating the subsequent effects on the process pressure and force. The pressure distribution and the forging force are investigated for different friction coefficient ratios and width to thickness ratios. In addition, three layer clad sheet forging process is simulated entirely using dynamic explicit solution of ABAQUS/software. Comparisons of analytical results from present model with those from finite element simulation have showed good agreements. Finally, some experiments were performed on forging process of two layer Al/Cu clad sheet to evaluate the bonding quality of sheets.

Upper Bound Solutions of Ring Compression Test

In this paper a particularization of forging process is presented, studying the deformation of a ring specimen. Plastic forming is performed by means of the Upper Bound Theorem and the model of Triangular Rigid Blocks to calculate the minimal charge needed to deform the part. The establishing the part to deform an annular geometry is determined by the so-called Ring Compression Test under its canonical configuration, that allows assimilating to a plane strain process. A new perspective to calculate the neutral plane (radius at which the workpiece material flows in opposite directions) is proposed, a basic element in the solution of the problem.

An exact solution for a model of pressure-dependent plasticity in an un-steady plane strain process

Abstract An incompressible material obeying a pressure-dependent yield condition is confined between two planar plates which are inclined at an angle 2 α . The plates intersect in a hinged line and the angle α slowly decreases from an initial value. An initial/boundary value problem for the flow of the material is formulated and solved for the stress and the velocity fields, the solution being in closed form. The material is assumed to obey a special case of the double slip and rotation model, which generalises the classical plastic potential model and is also a variant of the double shearing model. The solution for the velocity field may exhibit sliding or sticking at the plates. Solutions which exhibit sticking may have a rigidly rotating zone in the region adjacent to the plates. It is shown that sliding occurs when the value of α is less than a certain critical value α c ; that sticking occurs without a rigid zone if α exceeds or equals α c but is less than a second critical value α 0 ; and that sticking with a rigid zone adjacent to the plates occurs if α exceeds α 0 . The values of α c and α 0 coincide for a certain range of model parameters. Solutions which exhibit sliding are singular. Qualitative features of the solution found are compared with those of the solution for the classical plastic potential model.

Application of Image Measurement and Continuum Mechanics to the Direct Measurement of Two-Dimensional Finite Strain in a Complex Fibro-Porous Material

This paper outlines a computational procedure that has been implemented for the direct measurement of finite material strains from digital images taken of a material surface during plane-strain process experiments. The selection of both hardware and software components of the image processing system is presented, and the numerical procedures developed for measuring the 2D material deformations are described. The algorithms are presented with respect to two-roll milling of sugar cane bagasse, a complex fibro-porous material that undergoes large strains during processing to extract the sucrose-rich liquid. Elaborations are made in regard to numerical developments for other forms of experimentation, algorithm calibrations and measurement improvements. Finite 2D strain results are shown for both confined uniaxial compression and two-roll milling experiments.

Prediction of void growth in drawing and extrusion of voided metals

In this work the growth of micro voids during drawing and extrusion processes through conical and wedge-shaped dies is predicted. The solution uses a modified Shield’s analysis for the stress distribution within the die zone together with Gurson–Tvergaard’s yield function and its associated flow rule for voided solids. The effects of the process parameters e.g. area reduction, semi-die angle and friction conditions on void growth are investigated. Moreover the influences of the initial void volume fraction, void shape and strain-hardening on void growth are considered. The analysis is used to estimate the density change in multi-pass drawing process. The predicted density change is compared with available experimental data for axisymmetric and plane-strain processes. The predictions which are in good agreement with the experiments may be of value in investigating the occurrence of central bursting in such processes.

Study on the efficiency of the digging process using the model of excavator bucket

In the first part of the paper, an experimental program is presented investigating the soil cutting problem, with the application of vertical rigid walls at various widths as the working tools. It was found that when the tool width equalled the width of the soil bin, the soil cutting problems might be treated as plane strain processes. For the tools for which no interaction with the sidewalls of the bin was observed, the zone of the plane strain deformations occurred in the central part of the tools. In the second part of this paper a new experimental program of laboratory tests is presented, for a tool model in the shape of an excavator’s bucket equipped with teeth. The experimental verification of the influence of teeth (number of teeth and the position of teeth on the bucket’s inside lip) on the efficiency of the digging cycle is the aim of this paper. For high values of teeth spacing, the superposition of the plane strain deformation mechanism with three-dimensional failure modes within the soil was observed. For the low values of teeth spacing, the teeth did not act as separate three-dimensional objects but as one wide tool built up from several modules. As a consequence, the deformation pattern in front of such an assembly of teeth was again the plane strain deformation pattern.

The criterion for central bursting and its occurrence in drawing and extrusion under plane strain

Central bursting is dealt with, with respect to the collapse of the unique solution. In general, there are two cases bringing about multiplicity: one is a statical multiplicity and the other is a kinematical one. The latter corresponds to localized necking. These two multiplicities occur simultaneously in plane strain processes. In general, it is possible for localized necking to take only two modes, but only one mode can be realized in a plane strain process. The criterion for central bursting is given as (ϵ 1/n)(p/2k) = −1 2 , with p as average pressure, k as shear strength. ϵ 1 as the tensile strain in forming direction, and n as work hardening exponent. The influences of die geometry and manufacturing conditions on the central bursting are examined.

Central bursting in drawing and extrusion under plane strain.

Central bursting is dealt with, with respect to the collapse of a unique solution. In general, there are two cases bringing about multiplicity : one is statical and the other is kinematical one. The latter corresponds to localized necking. These two multiplicities occur simultaneously in plane strain processes. There are two modes which can be realized at localized necking, but only one mode is possible in a plane strain process. The criterion for central bursting is given as(ε1/n)(P/k)=-1, where P=average pressure, k=shear strength, ε1 is the tensile strain in forming direction, and n is work hardening exponent. The influences of die geometry and manufacturing conditions on the central bursting are examined.

A combined eulerian-lagrangian three-dimensional finite-element analysis of edge-rolling

After edge-rolling (heavy width-reduction), the cross-section of a continuously-cast steel slab may be non-rectangular, whereas what is desired is that it should be exactly rectangular. The deformed shape results in an increased number of heavy width- and thickness-reductions having to be imposed on the slab. Since edge-rolling is clearly a three-dimensional forming process, use of plane-strain analysis would be insufficient: a three-dimensional finite-element formulation, based on elastic-plastic material behaviour, has therefore been developed. This three-dimensional formulation has been incorporated into the existing special purpose FEM programme DIEKA, developed at Twente University of Technology by one of the present authors. The former two-dimensional programme DIEKA has already been successfully applied to plane-strain processes such as the cold rolling of strip-material, and axi-symmetric processes such as wire drawing.Using the extended three-dimensional programme, calculations have been made in order to investigate the influence of roller-radii on the resulting cross section of the slab after a width reduction. Experiments for verification and small-scale simulation of the real production process have been carried out using plasticine as a model material.