Research Papers

Investigation of Preferred Orientations in Planar Polycrystals

[+] Author and Article Information
M. R. Tonks

T-3,  Los Alamos National Laboratory, Los Alamos, NM, 87545; Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

A. J. Beaudoin, D. A. Tortorelli

Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

F. Schilder

Department of Mathematics, University of Surrey, Guildford, GU2 7XH, UK

Note that these definitions are slightly different from those employed by Prantil et al. (9), in which Λ̇c is the rate of stretching and Γ̇c is the rate shearing.

J. Appl. Mech 75(5), 051001 (Jul 02, 2008) (10 pages) doi:10.1115/1.2912930 History: Received February 21, 2007; Revised February 25, 2008; Published July 02, 2008

More accurate manufacturing process models come from better understanding of texture evolution and preferred orientations. We investigate the texture evolution in the simplified physical framework of a planar polycrystal with two slip systems used by Prantil (1993, “An Analysis of Texture and Plastic Spin for Planar Polycrystal  ,” J. Mech. Phys. Solids, 41(8), pp. 1357–1382). In the planar polycrystal, the crystal orientations behave in a manner similar to that of a system of coupled oscillators represented by the Kuramoto model. The crystal plasticity finite element method and the stochastic Taylor model (STM), a stochastic method for mean-field polycrystal plasticity, predict the development of a steady-state texture not shown when employing the Taylor hypothesis. From this analysis, the STM appears to be a useful homogenization method when using representative standard deviations.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

Single planar crystal structure

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Figure 2

Geometric representation of the order parameter, with the corresponding θj plotted on the unit circle

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Figure 3

The order parameter calculated from Eq. 21 with θj=2θc at several time instants for various loadings and simulation methods. The shading of the data points represents the corresponding time as dictated by the scale bar.

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Figure 4

The deformed mesh at the indicated times due to the indicated macrodeformation, where θ is the rigid-body rotation of the polycrstal at the time t. The shading of each element represents the orientation of the crystal in degrees as dictated by the legend. Elements of interest in the mesh are outlined in black.

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Figure 5

fΛc, fΓc, and fΩc from CPFEM with Ω=−π, Γ=0, and Λ=1.2 at t=2.2s. The bars are a histogram approximation of the PDF and the black line is a normal distribution with the measured μ and σ.

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Figure 6

The standard deviations of Ωc, Λc, and Γc with time from CPFEM analyses

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Figure 7

Relationship between the PDF of ηc and λ for several standard deviations σ=σΓc=σΛc

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Figure 8

r versus time at several standard deviations σ=σΓc=σΛc

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Figure 9

Steady-state ODF at several standard deviations σ=σΓc=σΛc



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