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Abstract. This article is focused on a 2-D fluid dynamics description of punch shape geometry improvement for Equal Channel Angular Extrusion (ECAE) or Equal Channel Angular Pressing (ECAP) of viscous incompressible continuum through acute-angled Segal 2θ -dies with 2θ < 90 • . It has been shown both experimentally with physical simulation and theoretically with computational fluid dynamics that for the best efficiency under the stated conditions, the geometric condition required is for the taper angle 2θ 0 of the inclined oblique punch to be equal to the 2θ angle between the inlet and outlet channels of the Segal 2θ -die. Experimentally and theoretically determined rational geometric condition for the ECAP punch shape is especially prominent and significant for ECAP through the acute angled Segal 2θ -dies. With the application of Navier-Stokes equations in curl transfer form it has been shown that for the stated conditions, the introduction of an oblique inclined 2θ 0 -punch results in dead zone area downsizing and macroscopic rotation reduction during ECAP of a viscous incompressible continuum. The derived results can be significant when applied to the improvement of ECAP processing of both metal and polymer materials through Segal 2θ -dies.

The present article is focused on a 2D computational fluid mechanics study of local viscous flow dynamics and the formation character of rotary modes of deformation during Equal Channel Multiple Angular Extrusion (ECMAE) of a polymer workpiece fluid model through a U-shaped die with parallel slants in channel intersection zones. The present local flow problem was experimentally analyzed using physical simulation methods and theoretically studied with numerical fluid mechanics techniques. The computational approach has been grounded on the numerical finite difference solution of the boundary value problem for the Navier-Stokes equations in the curl transfer form for the local viscous flow of incompressible Newtonian fluid through a U-shaped rectangular die with parallel slants. The derived research results allow us to draw a conclusion that the implementation of a geometric design of parallel slants within a 2-turn U-shaped die results in localization of the maximum tangential stresses within the workpiece volume to the vicinity of these parallel slants during ECMAE.

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<p>It is a common practice in pressure forming to make an Equal Channel Angular Extrusion (ECAE) of a workpiece through a die with channel intersection angle 2θ = 90° using a standard punch of brick or cylindrical shape with 2θ₀ = 90°. However Nejadseyfi et al (2015) have applied a beveled 2θ₀-punch to the process of ECAE through a standard angular die of Segal geometry with 2θ = 90° and 2θ₀ ≠ 2θ. The scope of the article is focused on an alternative numerical study of Nejadseyfi-ECAE-Scheme using techniques of Computational Fluid Dynamics (CFD). A finite-difference method was applied to the numerical solution of the boundary value problem for the Navier-Stokes equations in the form of a vorticity transfer equation. The complex of 2D plots for CFD-derived fields of flow lines and flow velocities and 3D plots for spatial distributions of flow velocities and tangential stresses were firstly derived for Nejadseyfi-ECAE-Scheme during viscous flow of polymer workpiece models through angular die with 2θ = 90° for the different punch inclination angles 30° ≤ 2θ₀ ≤ 150°. It was found that Nejadseyfi-ECAE-Scheme provides enhancement of the rotary modes of intensive deformations during ECAE. Results provide visualization of velocity gradients and macroscopic rotation and the illustration of Nejadseyfi et al’s ideas from an alternative CFD-based viewpoint.</p>

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