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In this paper, an upper bound analysis for novel backward extrusion has been presented. Initially deformation zone has been divided to four separated regions and an admissible velocity field for them has been suggested. Then total power in this process has been calculated for every region and extrusion force has been gained. Moreover investigation of relevance of extrusion force and process powers (friction, deformation, velocity discontinuity) with process parameters has been revealed better understanding in load estimation and process efficiency in this method. Finite element analysis by DEFORMTM3D has been done for validation of upper bound results. Upper bound analysis showed, increasing of initial billet diameter enhances extrusion force by nonlinear relation. In addition big billet size remodels novel backward extrusion to conventional backward extrusion and it proves lower requirement extrusion load in novel backward extrusion in comparison with conventional backward extrusion. Moreover Increasing of first region’s thickness in this process diminishes extrusion force by exponential relation and no considerable change in extrusion force can be seen in a particular thickness domain. Investigation of process parameters in power efficiency shows that bigger extruded part’s diameter creates critical condition in process efficiency because of high friction power. But increasing of thickness enhances power efficiency. Finally upper bound analysis results have a good agreement with FEM.

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In the present paper, drawing process of metal plates through a wedge-shaped die, by proposing new velocity field, has been analyzed by upper bound method and simulated by finite element method (Abaqus software). Among the important cases in upper bound analysis of the forming processes is selection the appropriate boundaries for the deformation zone and offering admissible velocity field that in addition to satisfy the incompressibility condition and boundary conditions, is consistent by the behavior of metal flow in the deformation zone. The entrance boundary of deformation zone has been assumed exponential curve surface and boundary at exit has been assumed cylindrical surface. In the past analyses, metal flow lines in the deformation zone have been assumed straight but in reality it is not. In the present work, velocity field and also geometric shape of the deformation zone, justify that metal flow lines are non-straight. Base on proposed velocity field, internal powers, shear and frictional and also total power have been calculated. Then, according to the plate pulling velocity, required drawing force has been obtained. Finally, analytical results have been compared with the obtained results of FEM. In order to validate the present analysis, obtained results have been compared with other researchers. Also, the effect of various parameters, such as percentage reduction in thickness and shear friction constant on the drawing force and die optimum angle have been investigated.

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This paper attempts to predict the occurrence of central bursting defects in the plane strain extrusion process using upper bound method. For this purpose, the material under deformation is divided into three deformation zones. These deformation zones are separated from each other by the shear boundaries as the exponential functions. Then, an admissible velocity field, including the radial and the angular velocity components are developed for each deformation zone. Strain rates components are determined and mathematical relationships for internal, shear and friction powers are obtained. For a given process conditions, the total power toward geometrical shape of shear boundaries entrance and existence is optimized. Intersection position of the entrance and existence shear boundaries of deformation zone on centerline represents the occurrence of central bursting defects. The effect of process parameters, including semi die angle, reduction in area and friction factor on the defects and the extrusion force are investigated. The analysis results with the FEM simulation (Deform software) and the results of the published papers are compared. The results showed that increase of friction factor and increase the reduction in area decreases the probability of central bursting defects.