A Finite Element Investigation into the Changing Channel Angular Extrusion of Brass Alloy

This study investigates a novel changing channel angular (CCA) extrusion process, in which high strains are induced within the billet by passing it through a series of channels of unequal cross-sections arranged such that they form specified internal angles. Using commercial DEFORM 2D rigid-plastic finite element code, the plastic deformation behavior of CuZn37 brass alloy is examined during one-turn and two-turn CCA extrusion processing in dies with internal angles of φ =90, 120, 135 or 150, respectively. The simulations focus specifically on the effects of the processing conditions on the effective strain, the rotation angle and the effective stress induced within the extruded billet. The numerical results provide valuable insights into the shear plastic deformation behavior of CuZn37 brass alloy during the CCA extrusion process. Introduction In general, rolling, extrusion and forging processes subject the working material to very high strains. The resulting plastic deformation causes a significant change in the physical and mechanical properties of the material. Accordingly, there are significant benefits to be gained from deforming metallic alloys under very high levels of plastic strain. The equal channel angular (ECA) extrusion process (also known as equal channel angular pressing (ECAP)) was first developed by Segal et al. [1-2] as a means of inducing large plastic strains within metallic workpieces without causing a significant change in their outer dimensions. More recently, Liu et al. [3] presented a novel changing channel angular (CCA) extrusion method designed to reduce the tensile stress within the workpiece and to increase the hydrostatic pressure during the extrusion process. Kim [4] used commercial DEFORM 2D software to perform a finite element analysis (FEA) investigation into the formation of corner gaps between the die and the workpiece during the plane strain ECAP process. In analyzing the multiple-pass ECAP process, Figueiredo et al. [5] neglected the strain path effect and predicted the material deformation behavior in each pass using a single stress-effective strain curve. Meanwhile, the present authors [6] applied a FE method to investigate the plastic deformation behavior of Ti-6Al-4V titanium alloy during oneand two-turn ECA extrusion. The current study uses DEFORM 2D FE code to investigate the plastic deformation behavior of CuZn37 brass alloy during oneand two-turn CCA extrusion processing, in which high strains are induced within the billet by passing it through a series of channels of unequal cross-sections arranged such that they form specified internal angles. The simulations focus particularly on the effects of the CCA processing conditions on the distributions of the effective strain, rotation angle and effective stress, respectively, within the extruded workpiece. Analytical method According to Kim and Yang [7], the FE formulation for rigid-plastic deformation in a material subject to work hardening has the form 0 ) ( ) ' ( = ∆ + − + ∆ + ∫ ∫ ∫ dS v f f dV K dV H t i i V V S i v v w w w f δ α ε δ ε ε δ ε α σ     (1) Materials Science Forum Vol. 594 (2008) pp 90-95 Online available since 2008/Aug/19 at www.scientific.net © (2008) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/MSF.594.90 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 210.60.80.67-01/10/09,19:56:20) where ' ' ) 2 / 3 ( ij ijσ σ σ = , ij ijε ε ε    ) 3 / 2 ( = and ii v ε ε   = . Additionally, K, ' ij σ , H’ and αare the penalty constant, the deviatoric stress, the strain-hardening rate and the work-hardening effect constant ( 1 0 ≤ ≤ α ), respectively. Finally, w V and f S are the volume and tractional boundary surface of the workpiece, respectively. The DEFORM FE 2D simulations performed in this study are based on a flow formulation approach using an updated Lagrangian procedure. The nonlinear equations in the FE software are solved using a direct iteration method combined with the Newton-Raphson scheme. In the solution procedure, the direct iteration method is used to generate a suitable initial estimate for the Newton-Raphson method, which is then employed to obtain a rapid convergence to the final solution. The termination criteria specified for the iteration procedure are as follows: a velocity error norm of 001 . 0 / ≤ ∆ v v and a force error norm of 01 . 0 / ≤ ∆ F F , where v is 2 / 1 ) ( v vT . Simulation process analysis and discussion The current simulations are based upon the following assumptions: (1) both the container and the die are rigid bodies; (2) the extrusion billet is a rigid-plastic material; and (3) the friction factors between the extrusion billet and the ram, container and die are constant. Fig. 1 presents the stress-strain relationship for the current CuZn37 brass alloy. Meanwhile, Fig. 2 illustrates the various CCA die set configurations. As shown, the billets are pressed through channels of unequal cross-sections oriented with internal angles of φ =90, 120, 135 or 150, respectively. For each orientation angle, the simulations consider both one-turn and two-turn extrusion processing. Flow Stress = f (Temperature =600C, Strain Rate = 0.3s, Strain) (MPa) 0 0.2 0.4 0.6 0.8 1 Strain 84 86 88 90 92 94 96