The most widespread methods for producing thermoelectric materials are directional solidification techniques: Czochralski, Bridgman methods and zone melting. The other group of methods belongs to a powder metallurgy. However, the powder compressed samples include the disoriented grains, which impair their thermoelectric properties. The more efficient method is the hot extrusion (HE) [1,2]. Its advantages in comparison of crystallization methods are following: the high mechanical strength and uniformity of extruded rod, the possibility of variation of its shape and cross-section, the high productivity and lower costs.

      During HE process a pressed cylindrical billet (with diameter D and height L) is forced by a punch through a die at temperature T ~ 400 °C in according to the scheme shown in Fig. 1. The geometrical parameters of this die and the punch rate have the decisive impact on a product quality and process productivity.

Fig. 1. Scheme of hot extrusion for thermoelectric composite Bi0.4Sb1.6Te3: 1 – ram, 2 – pressed billet, 3 – forming die (θ – angle of curvature, d – diameter,  l – length of cylindrical outlet). V is the punch rate.

      This work presents the numerical simulation of HE process for thermoelectric compound Bi0.4Sb1.6Te3, on the basis of which the evolution of its stress-strain state was investigated at different stages of this process. The numerical model is based on joint elastic-plastic approach. The numerical method uses the finite-element approximation on Lagrangian time-dependent grid, which changes with taking into account of a forming die. Calculations have been carried out by means of MSC Marc^Ò code [3].

      The influence of die geometric parameters was investigated for its following variation: d= 20,  30 mm at l = 10 mm and θ = 100 and 120^o. Mechanical parameters of the material were set as the following: Young's modulus E = 40 GPa, Poisson's ratio ν = 0.3. The critical stress of elastic-plastic transition was set in accordance with the measured «stress-deformation» dependence as σ_o = 102 MPa.

The transverse and longitudinal changes in a composition structure of extruded samples have been investigated by x-ray diffraction measurement, optical and electronic microscopy [4]. In accordance with these experimental data the regions were established, which were responsible for the composition formation and microstructure of these samples. Their comparison with the data of numerical simulation has showed that these regions correspond to a plastic deformation at distance ~ 4 cm from the upper edge of die, where stresses reach the maximum values.

Acknowledgments

This investigation was supported by JSC “ROSATOM” (the state contract: Н.4б.44.90.13.1050), and Russian Foundation for Basic Research (the grants: 11-08-00966, 12-02-01126).

References

[1] Sabo Ye.P. // J. Thermoelectricity. 2005. V. 3. P. 52-68.

[2] Yang J., Chen R., Fan X. et al.  // J. Allows&Compounds. 2007. V. 429. P. 156-162.

[3] License certificate of MSC Marc^Ò: RE007990PCS. 2008.

[4] Lavrentev M.G., Osvenskii V.B., Mezhennii M.V. et al. // J. Thermoelectricity. 2012. V. 4. P. 36-42.

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