Academic literature on the topic 'Extrusion process Drawing (Metal-work) Finite element method'

Except at the start and the end of the deformation, processes such as extrusion, drawing, and rolling are kinematically steady state. Steady-state solutions in these processes are needed for equipment design and die design and for controlling product properties. A variety of solutions for different conditions in extrusion and drawing have been obtained by applying the slip-line theory and the upper-bound theorems. Early applications of the finite-element method to the analysis of extrusion have been for the loading of a workpiece that fits the die and container, and for the extrusion of a small amount of it rather than extruding the workpiece until a steady state is reached. An exception is the work by Lee et al. for plane-strain extrusion with frictionless curved dies using the elastic-plastic finite-element method. In view of the computational efficiency, various numerical procedures particularly suited for the analysis of steady-state processes have been developed by several investigators. Shah and Kobayashi analyzed axisymmetric extrusion through frictionless conical dies by the rigid-plastic finite-element method. The technique involves construction of the flow lines from velocities and integration of strain-rates numerically along flow lines to determine the strain distributions. An improvement of the method was made by including friction at the die-workpiece interface. The steady-state deformation characteristics in extrusion and drawing were obtained as functions of material property, die-workpiece interface friction, die angle, and reduction. In kinematically transient or nonsteady-state forming problems, a mesh that requires continuous updating (Lagrangian) is used. In steady-state problems, a mesh fixed in space (Eulerian) is appropriate, since the process configuration does not change with time. For steady-state problems whose solutions depend on the loading history or strain history of the material, combined Eulerian-Lagrangian approaches are necessary. In deformation of rigid-plastic materials under the isothermal conditions, the solution obtained by the finite-element method is in terms of velocities and, hence, strain-rates. In the nonsteady-state processes, the effective strain-rates are added incrementally for each element to determine the effective strains after a certain amount of deformation.

The main concern here is the analysis of plastic deformation processes in the warm and hot forming regimes. When deformation takes place at high temperatures, material properties can vary considerably with temperature. Heat is generated during a metal-forming process, and if dies are at a considerably lower temperature than the workpiece, the heat loss by conduction to the dies and by radiation and convection to the environment can result in severe temperature gradients within the workpiece. Thus, the consideration of temperature effects in the analysis of metal-forming problems is very important. Furthermore, at elevated temperatures, plastic deformation can induce phase transformations and alterations in grain structures that, in turn, can modify the flow stress of the workpiece material as well as other mechanical properties. Since materials at elevated temperatures are usually rate-sensitive, a complete analysis of hot forming requires two considerations—the effect of the rate-sensitivity of materials and the coupling of the metal flow and heat transfer analyses. A material behavior that exhibits rate sensitivity is called viscoplastic. A theory that deals with viscoplasticity was described in Chap. 4. It was shown that the governing equations for deformation of viscoplastic materials are formally identical to those of plastic materials, except that the effective stress is a function of strain, strain-rate, and temperature. The application of the finite-element method to the analysis of metal-forming processes using rigid-plastic materials leads to a simple extension of the method to rigid-viscoplastic materials. The importance of temperature calculations during a metal-forming process has been recognized for a long time. Until recently, the majority of the work had been based on procedures that uncouple the problem of heat transfer from the metal deformation problem. Several researchers have used the following approach. They determined the flow velocity fields in the problem either experimentally or by calculations, and they then used these fields to calculate heat generation. Examples of this approach are the works of Johnson and Kudo on extrusion, and of Tay et al. on machining. Another approach uses Bishop’s numerical method in which heat generation and transportation are considered to occur instantaneously for each time-step with conduction taking place during the time-step.

Slab method of analysis has been used for solving metal forming problems for a long time. However it has been restricted to plane strain and axisymmetric problems due to limitations in its formulations. In this paper a new formulation has been proposed so that it could be applied to three dimensional problems in metal forming. A parametric slab has been considered in this analysis and the force balance on the slab was carried out to obtain equilibrium equations in terms of these parameters. The parameters in fact are related to the geometry of the final extruded shape, the die and the material