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.

The scope of the present article is the study of the fracture initiation from initial spherical flaws in incompressible propellant materials. Using a constitutive law, derived from the neo-Hookean strain energy function, one may deduce the relation between the radial pressure applied at infinity and the corresponding extension ratio, at the surface of the cavity. An equation which defines the critical extension ratio for a given value of a parameter, κ, was derived and the corresponding critical load, pc, is related to the critical cavity extension ratio. Plots for the extension ratio and normalized pressure were provided solving the appropriate equation derived from the analysis. The failure of the cavity is associated with the incremental energy transfer at a constant critical stress between the applied work, internal strain energy and surface energy. The influence of the surface energy on the radial deformation of an initially intact sphere is presented and it turns out that a characteristic cavitation phenomenon occurs instead of the bifurcation. A mathematical formula is derived for the pressure, per unit current area, which is valid for a general form of incompressible elastic strain energy function. Using the derived formula one may deduce the relation between the radial pressure and the corresponding extension ratio at the surface of the cavity. In an incompressible material of given modulus and surface energy it is proved that a critical field stress exists at which a small internal cavity may grow in size where the significant quantities are the radial and tangential strains.

Equal Channel Angular Extrusion (ECAE), sometimes referred to as Equal Channel Angular Pressing (ECAP), is a Severe Plastic Deformation technique. However the energy-power parameters of ECAE have not been fully addressed in previous known publications. The present article is focused on the punching pressure, accumulated plastic strain, and dead metal zone geometry estimation during ECAE of metal workpieces through a 2θ-die with a channel intersection angle of 2θ>0º and 2θ≠90º. Computational analytical results for ECAE technological parameters have been analytically derived for planar flow of a plastic, incompressible, non-hardening metal workpiece in an angular Segal die with 2θ>0º and 2θ≠90º. This is accomplished through the use of an Upper Bound Method (UBM) with Discontinuous Velocity Field (DVF) introduction. The development of the Dead Zone (DZ) for metal ECAE through a 2θ-die with 2θ>0º and 2θ≠90º has been analytically investigated. The obtained computational results for 2θ-die have been compared with the slip line analytic solutions of Segal for non-rectangular 2θ-dies of the same geometry. Good agreement between the two computational results has been found. The physical modeling techniques using plasticine have confirmed the appearance of a dead zone and material flow dynamics during ECAE through the Segal 2θ-die.

In present paper the Equal Channel Angular Extrusion (ECAE) through a rectangular die was firstly physically simulated using plasticine and then theoretically analyzed by upper bound method. Physical simulation was used to identify the deformation zone and as a background for the following theoretical ECAE analysis by rigid block model. The plane strain deformation mode and ideal plasticity of an extruded material were assumed. The dependencies of ECAE pressure, accumulated shear and dimension of a "dead zone" upon friction factor were analytically determined. The rise in ECAE pressure, accumulated shear and size of a "dead zone" with the increase in friction was predicted. The obtained results were compared with the slip line based solution and a good agreement between them was found. Finally the results of upper bound analysis were discussed together with the results of experimental investigations and finite element analysis of ECAE mechanics published elsewhere.