0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2008 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Single planar crystal structure

Grahic Jump Location
Figure 2

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

Grahic Jump Location
Figure 9

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
Figure 6

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

Grahic Jump Location
Figure 7

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

Grahic Jump Location
Figure 8

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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In