Mathematical plastic flow modeling for equal–channel angular pressing of bismuth chalcogenide base solid solution

In this work, mathematical modeling was used to optimize the geometry of the composite mold for developing the technology of equal−channel angular pressing with three channels for thermoelectric materials. To obtain the maximum degree of deformation in this work, we used a three−channel scheme. Taking into consideration the material characteristics (low resistance to tensile  stresses), we proposed a tapering profile (along  the length)  of the third channel. To analyze the  plastic  flow in the  proposed scheme of equal−channel angular pressing with three channels, we performed mathematical modeling of plastic flow, stress and deformation rates along the rod, deformation homogeneity along the cross−section and absence of stagnant zones in the extruder. The methodical approach is based on the combined use  of the elastic and plastic  solid state approximations according to the fundamentals of the elasticity and plasticity theory. Critical points are identified having the maximum stored energy accumulation without discontinuity of the material. Calculation of the flow velocity in planes perpendicular and  parallel  to the  deformation axis showed a slight difference in the flow rate of the material  for the section plane parallel to the deformation axis. This produces a bend with a large  curvature radius  but  does not  cause cracking of the  material. Calculation of deformations along  the  flow axis allowed  us to detect deformation inhomogeneity. This resulted in the  appearance of small  tensile stresses in the longitudinal  section of the third channel. We show that the plastic  deformation inhomogeneity revealed by modeling can be eliminated by using an equipment design with a greater output channel length. Mathematical modeling shows the suitability of the suggested unconventional design of equal−channel angular pressing equipment for bismuth chalcogenide base solid solutions.

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