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TECHNICAL PAPERS

Modeling the Rotation of Orthotropic Axes of Sheet Metals Subjected to Off-Axis Uniaxial Tension

[+] Author and Article Information
Wei Tong, Hong Tao, Xiquan Jiang

Department of Mechanical Engineering, Yale University, 219 Becton Center, New Haven, CT 06520-8284

J. Appl. Mech 71(4), 521-531 (Sep 07, 2004) (11 pages) doi:10.1115/1.1755694 History: Received February 28, 2003; Revised September 03, 2003; Online September 07, 2004
Copyright © 2004 by ASME
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Figures

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Definitions of the three Cartesian coordinate systems for a monoclinic sheet metal: (a) the principal axes of stress (σ123); (b) the principal axes of the current material texture frame XYZ; and (c) the sheet material coordinate system X0Y0Z0. The principal axis of σ3 always coincides with Z0-axis and Z-axis to ensure the planar plastic flow of the sheet metal. The in-plane axes X and Y of the texture frame are defined to be the principal straining directions of the sheet metal under equal biaxial tension (σ123=0). The material coordinate system X0Y0Z0 undergoes the same rigid body rotation as the sheet metal itself and it may be chosen to coincide with the initial texture frame of the sheet metal (the initial texture frame of an orthotropic sheet metal is defined by its rolling (RD), transverse (TD), and normal (ND) directions). The loading orientation angle θ is defined as the angle between the principal axis of σ1 and the X-axis of the material texture frame. The relative rotation ω12 of the texture frame with respect to the material coordinate system of the sheet metal is due to the macroscopic plastic spin ω̇12,28.
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The amount of rotation ω12 of the material texture frame due to plastic spin at a fixed uniaxial plastic strain ε1 of 20% as a function of the initial loading orientation angle θ0 with three different k values according to Eq. (13b) (D=1 is used for all data points)
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The current loading orientation angle θ and the amount of rotation ω12 of the material texture frame due to plastic spin as a function of uniaxial plastic strain ε1 with three different initial loading orientation angles θ0 and three different k values according to Eq. (13) (kD=10 is used for all data points)
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Comparison of the model description (solid and dashed lines) and the experimental data (filled symbols) of a steel sheet reported by Boehler and Koss 10 and Losilla et al. 45 on the rotation ω12 of the material texture frame due to plastic spin as a function of uniaxial plastic strain ε1 with different initial loading orientation angles θ0=30deg, 45 deg, and 60 deg. The solid lines are given by Eq. (14) with d1=7,d2=10 and d3=−3 (all other coefficients are zero). The dashed lines are given by Eq. (13b) with k=2 and D=9 (the initial loading orientation angles of 30 deg, 46 deg, and 60 deg were used).
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Comparison of the model description (solid and dashed lines) and the experimental data (filled symbols) of a steel sheet reported by Kim and Yin 11 on the rotation ω12 of the material texture frame due to plastic spin as a function of uniaxial plastic strain ε1 with different initial loading orientation angles θ0=30deg, 45 deg, and 60 deg. The solid lines are given by Eq. (14) with d1=−8,d2=17 and d3=3 (all other coefficients are zero). The dashed lines are given by Eq. (13b) with k=2 and D=12.5 (the initial loading orientation angles of 30 deg, 46 deg, and 60 deg were used).
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Comparison of the model description (solid and dashed lines) and the experimental data (filled symbols) of an aluminum sheet reported by Bunge and Nielsen 12 on the amount of rotation ω12 of the material texture frame due to plastic spin at a fixed uniaxial plastic strain ε1 of 20% with 11 different initial loading orientation angles θ0. The solid line is given by Eq. (13b) with k=2 and D=0.45.

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