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Research Papers

A Simplified Model for Assessing the Work-Hardening Effect in the Analysis of Plate Drawing Processes by Upper Bound Method

[+] Author and Article Information
E. M. Rubio

Department of Manufacturing Engineering,  National Distance University of Spain (UNED), C/ Juan del Rosal 12, Ciudad Universitaria, E-28040-Madrid, Spainerubio@ind.uned.es

A. Sanz-Lobera

Department of Materials and Aerospace Production,  Polytechnic University of Madrid (UPM), Pl. Cardenal Cisneros s/n, E-28040 Madrid, Spain

M. Marcos

Department of the Mechanical Engineering and Industrial Design,  University of Cadiz (UCA), C/ Chile s/n, E-11003-Cádiz, Spain

M. A. Sebastián

Department of Manufacturing Engineering,  National Distance University of Spain (UNED), C/ Juan del Rosal 12, Ciudad Universitaria, E-28040-Madrid, Spain

J. Manuf. Sci. Eng 134(2), 021003 (Apr 04, 2012) (10 pages) doi:10.1115/1.4005791 History: Received May 14, 2010; Revised December 02, 2011; Published March 30, 2012; Online April 04, 2012

This work presents an analysis of the plate drawing processes carried out in converging dies. The analysis has been made by the upper bound method (UBM), modeling the plastic deformation zone by triangular rigid zones (TRZ), and considering that the processes occur under plane strain and partial friction conditions. The goal is to evaluate how the work-hardening suffered by materials when they are cold-worked affects the energy required to carry out a certain process. In order to achieve this objective, the paper proposes a simplified model for calculating the shear yield stress, k, along the contact surface between die and material when theoretical work-hardening materials are used. The results obtained with this simplified procedure do not differ significantly from those obtained with the complete model, even in the more drastic conditions tried. This result confirms that the simplified model can successfully substitute for the complete model with less calculation.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Real (R) effective flow stress–strain curves for annealed copper UNS C11000, aluminum UNS A91100, and stainless steel UNS S34000 and the four different types of theoretical work-hardening materials T1, T2, T3, and T4 that were tried to model each one of them

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Figure 2

Geometrical layout of plate drawing process

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Figure 3

Triangular rigid (N-2)-zone model

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Figure 4

(a) Triangular rigid one-zone model; (b) kinematic model; (c) geometric model

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Figure 8

Value of the shear yield stress, k, along the discontinuities lines AB, BC, and AC for annealed copper, UNS C11000, and reduction values of: (a) r = 0.1, (b) r = 0.2, (c) r = 0.3, and (d) r = 0.4 obtained by the simplification purposed in this work

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Figure 9

Configurations of the plastic deformation zone with: (a) 3 TRZ (N = 5); (b) 5 TRZ (N = 7)

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Figure 10

Comparison of the results obtained for theoretical work-hardening material of the annealed copper UNS C11000 using 1, 3, and 5 TRZ (N = 3, 5, and 7) for: (a) α = 5, m = 0; (b) α = 5, m = 0.4; (c) α = 10, m = 0; and (d) α = 10, m = 0.4

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Figure 11

Comparison of the results obtained for rigid perfectly plastic (denoted by UBM_RPP), theoretical work-hardening (denoted by UBM_TWH), and simplified work-hardening (denoted by UBM_SWH), materials for: α = 1 deg–60 deg; r = 0.2; m = 0.5 and: (a) annealed copper UNS C11000; (b) aluminum UNS A91100; and (c) stainless steel UNS S34000

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Figure 12

Comparison between the results obtained for the theoretical (UBM_TWH) and for the simplified (UBM_SWH) annealed copper UNS C11000 for α = 1 deg–60 deg and: (a) r = 0.10, m = 0.1; (b) r = 0.20, m = 0.5; and (c) r = 0.40, m = 0.8

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Figure 5

Stress–strain curves theoretical (T) and real (R) for aluminum UNS A91100, annealed copper UNS C11000, and stainless steel UNS S34000 used in the study

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Figure 6

Value of the shear yield stress, k, along the discontinuity lines AB, BC, and AC in the rigid perfectly plastic material case

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Figure 7

Value of the shear yield stress, k, along the discontinuities lines AB, BC, and AC with the simplification purposed in this work when work-hardening materials are used

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