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.