Analysis of Cavity Tool Stresses in Channel Angular Extrusion

The Channel Angular Extrusion (CAE) technique is a process, in which a deformable solid material is led to yielding through the intersection of inclined channels. Compared to classic plastic deformation, the process is technically simple but the material experiences, instantly, large plastic deformation. The deformation occurs locally and high internal stresses develop during the process. In most cases the process is used for grain size refinement. Equal Channel Angular Extrusion (ECAE) is a special case where the intersecting channels are of equal cross sections. In this paper, an analytical study of the internal stresses and those developed along CAE tools is presented. A deformation model is introduced for the general process of channel extrusion in which the intersecting channels are not necessarily equal. The procedure splits the material at the intersection of the channels into two zones; one causes the deformation while the other remains rigid. The analysis is also applied to the particular case of ECAE, and the results are compared with those obtained from a finite element analysis and the overall experimental pressure. Introduction The first delivery of most materials is in its softest state so that it could be shaped easily by metal removal or through plastic deformation. Improved mechanical properties usually result from the imposition of strains on metallic materials that cause grain deformation. In order to add homogeneity in the distribution and size of grains the material is subsequently heat treated. When large strains are required, the mechanism for the evolution of small grains is complex, and therefore multiple reductions that employed through traditional forming processes become impractical. An alternative method is driven by the advantages of the Equal Channels Angular Extrusion (ECAE) process [1]. In such a process, a billet of a deformable material is forced to flow, through intersecting channels. However, large initial strain is achievable in a small number of cycles. Although severe plastic deformation occurs, the geometry of the material being deformed remains unchanged and it is possible to use it for the production of sheets of consistent improved properties. The microstructural refinement of the deformed material, which is developed by severe local deformation along the ECAE small shearing zone, has been of interest to many researchers. For example, grain size was shown to decrease with the increasing numbers of extrusions passes applied to a billet [2,3]. As a consequence, it was also shown that, with the evolution of grain refinement and subsequent increase in mechanical properties the measured tool forces increased with the number of passes, despite there was no change in the material geometry [4]. Because the initial geometry and the final geometry are the same, multiple processing has been possible. In an attempt to improve the efficiency and productivity of this process, Rosochowski [5] introduced a 90 degree intersection that is repeated in a number of bends thus creating a three dimensional processing configuration. The workpiece material used in the experiments was soft aluminium. However, it was shown that such a significant increase in the effective strain had caused the yield stress of the workpiece material to increase by almost three times after two passes, through the multiple 90 degree channels. In order to further improve efficiency, and reduce tool and total extrusion pressure, an experimental set-up [6], with sliding die walls, was used in order to reduce friction and wear. New and novel uses of this method seem to require better understanding of the mechanism of deformation and the stress system that evolves in the process. The use of ECAE was extended into other spheres by Osman [7], where it was exploited and formulated to provide a new technical concept for energy dissipation. Deformation through equal channels was realised in the form of a Universal Re-useable Energy Absorption Device(UREAD). Such a new technology appears to have wide domains of application, in parallel with the structural refinement of metallic materials. Most of the research carried out in this area has been on the process of imposing large strains on metallic materials. The Channel Angular Extrusion(CAE) process, in most cases, is asymmetric where localised plastic deformation is dominant, hence the study of the forming stresses, tool forces, energy dissipation and the mechanism of local deformation is important in order to assess the technical capabilities of the process. In this paper, an analytical approach to predict tool stresses and cavity stresses for the general CAE process is presented and results applied to ECAE and compared with those from other techniques. Stress-zone model for CAE Fig.1 shows a two-dimensional schematic diagram of the 90 degree single CAE process with its dimensional properties and parts. The material is forced to deform from the vertical channel into the horizontal channel through widths b and h respectively. The length of the deformable material, L, remaining in the vertical channel is important when considering the force required to cause the deformation, F. Figure 1. 2-D CAE process Figure 2. Stress-zone model When yielding takes place, material flow will depend on the opening in horizontal channel. For example, if the material is forced into an enclosed cavity (h=0), additional hydrostatic pressure becomes predominant and flow is prohibited by the elasticity of the surrounding tools. In contrast the hydrostatic pressure is at its minimal state in the open case of simple compression(L=0). It is therefore assumed that the deformation pattern depends on the width of the horizontal channel. Fig. 2 shows the deformation pattern represented by three zones. A yielding zone seems to exist in the intersection volume between the two channels and begins from the exit surface. The remainder of the intersection volume stays rigid as well as the material in the vertical channel. The deformation of the yielding zone is effected by the local yielding pressure which acts on a portion of the surface of the intersection volume between the two channels. A parameter, k, is introduced which defines the width of the yielding zone in relation to the width of the vertical channel. Hence the width of the yielding zone is given by kb, where k is between zero and one. Also, it is assumed that the yielding process in the intersection between the channels is affected by the rigid material in the vertical channel, hence the following relationships are constructed for the cases where h≤ b; h L k  for h L   0 (1)