An analytical approach for simple shear extrusion process with a linear die profile

• Introducing a new die parameter named maximum inclination angle for simple shear extrusion technique.
• Proposing an analytical approach based on upper-bound theorem to analyze simple shear extrusion process for the first time.
• Minimizing the deformation power by optimization of maximum inclination angle.

In the present work, for the first time, an analytical approach based on upper-bound theorem is proposed to analyze the simple shear extrusion process. In this regard new die parameter named maximum inclination angle is introduced. By this model, the power dissipated on all frictional and velocity discontinuity surfaces is determined and the total power is optimized for two types of die, fixed and movable inlet channel die. To check the validation of the upper-bound model, the process is simulated by the commercial finite element code, Deform-3D. To compare the theoretical results with experiments, a fixed inlet channel die and two dies with movable inlet channel are used to determine the processing force for different cross sections. The developed model predicts that the relative extrusion pressure increases with increasing the constant friction factor; also, for a given value of the constant friction factor and the maximum distortion angle, there is an optimized maximum inclination angle which minimizes the power. Comparing the fixed inlet channel die with the movable inlet channel one, it is seen that the optimized maximum inclination angle is higher in the FIC die.

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