An upper-bound analysis for equal-channel angular extrusion

Two-parameter Rigid Block Approach to Upper Bound Analysis of Equal Channel Angular Extrusion Through a Segal 2θ-die

“…Many contributions have been focused on the introduction of slip line fields 25,26 , Upper Bound Method (UBM) with continuous trial velocity fields [1][2][3][4][5][6][8][9][10][12][13][14][15]24,27 , kinematically admissible analytical approaches 11,28 , FEM computational techniques 2,8,9,11,17,18,23 , Navier-Stokes equations 16,20,21 etc. Segal 25,26 has grounded his analytic approach to ECAE metal flow with the introduction of slip line fields.…”

“…Milind 4,5 , Faraji et al 6 , Laptev et al 7 , Luri et al 8 , Luri & Luis 9 , Medeiros et al 10 , Narooei & Karimi Taheri [12][13][14] , Paydar et al 15 , Perig & Laptev 19 , Perig 22 , Reihanian et al 24 , Talebanpour & Ebrahimi 27 and others. Altan et al 3 have addressed the Upper Bound Method (UBM) with continuous trial velocity fields for description of metal ECAE motion through the Segal die. The main computational approach 3 has been based on the use of a cylindrical coordinate system with the center of a symmetrical metal deformation zone, definition of a kinematically admissible velocity field for metal flow, evaluation of the only non-zero strain rate field component d(ε rθ )/dt, formulation of an equation for dissipated power balance and further minimization of the derived expression for dissipated plastic power by optimization parameter differentiation.…”

“…Berta et al 29 outline comparable experimental ECAE data on the structure of the treated metal blanks at various channel angles 2θ=90° and 2θ=120° [ 29] . It is necessary to note that many analytical computational approaches [1][2][3][4][5][6][8][9][10][12][13][14][15]24,27 initially determine the shape of the dead metal zone CED in an angular Segal 2θ-die (Figures 3-6). …”

“…Moreover, the two-parameter rigid block approach to the two-parameter UBM of metal flow during ECAE with trial Discontinuous Velocity Field (DVF) introduction and accounting for the complex geometry of dead zone CEDF (Figures 3-6) for metal flow through a Segal 2θ-die has not been addressed in proper way in previous known publications [1][2][3][4][5][6][7][8][9][10][12][13][14][15]19,22,24,27 . All previous research [1][2][3][4][5][6][7][8][9][10][12][13][14][15]19,22,24,27 has not fully addressed the complex geometry of the dead metal zone CEDF (Figures 3-6) nor the influence of complex dead zone geometry CEDF (Figures 3-6) on the character of metal flow during workpiece ECAE through a Segal 2θ-die applying a two-parameter UBM in the form of a two-parameter RBM with trial DVF. This insufficient analysis of energy-power parameters during ECAE with an introduction of the two-parameter UBM with DVF was the stimulus, which resulted in the research reported in the present article.…”

Analysis of equal channel angular extrusion by upper bound method and rigid blocks model

“…Despite the simple design of ECAE tool, the homogeneity of material flow, needed pressure and resulting strains are strongly influenced by a number of process parameters like tool geometry, external friction, rheology of extruded material etc. Therefore the mechanics of ECAE attracts attention of many researchers and was investigated by both theoretical and experimental means [5][6][7][8][9] . The theoretical contributions have been focused on application of the Slip Line Theory 10 , Upper Bound Analysis 5,11-13 , Finite Difference Analysis and Finite Element Modeling 6,14,15 .…”