Study of ECAE mechanics by upper bound rigid block model with two degrees of freedom

The mechanics of equal channel angular extrusion (ECAE) in a rectangular die was studied by upper bound method and rigid block model of deformation with two variables (two degrees of freedom). The appearance of a dead zone in the die external corner was assumed and verified by physical simulation using plasticine as a modeling material. The obtained dependences of ECAE pressure, total ECAE shear and geometrical parameters of dead zone upon friction factor were compared with corresponding results of upper bound rigid block analysis with one variable (one degree of freedom) and with the results of slip line analysis published by the authors elsewhere. It was demonstrated that an increase in degrees of freedom in an ECAE rigid block model from one to two results in much better approximation of the reference data of slip line analysis. The authors believe that an increase in the numbers of degrees of freedom and flexibility of a rigid block model generally leads to a better accuracy in modeling of other metal forming processes as well. As an example, the ECAE pressure of the aluminum 6061 alloy was calculated and compared with the experimental data from literature. A good agreement between them was found. The importance of consideration of friction in the inlet and outlet die channels was emphasized.