0
Research Papers

Scale-Dependent Homogenization of Inelastic Random Polycrystals

[+] Author and Article Information
Shivakumar I. Ranganathan

Department of Mechanical Science and Engineering,  University of Illinois at Urbana-Champaign, Urbana, IL 61801srangan3@uiuc.edu

Martin Ostoja-Starzewski

Department of Mechanical Science and Engineering,  University of Illinois at Urbana-Champaign, Urbana, IL 61801martinos@uiuc.edu

J. Appl. Mech 75(5), 051008 (Jul 15, 2008) (9 pages) doi:10.1115/1.2912999 History: Received September 01, 2007; Revised November 14, 2007; Published July 15, 2008

Rigorous scale-dependent bounds on the constitutive response of random polycrystalline aggregates are obtained by setting up two stochastic boundary value problems (Dirichlet and Neumann type) consistent with the Hill condition. This methodology enables one to estimate the size of the representative volume element (RVE), the cornerstone of the separation of scales in continuum mechanics. The method is illustrated on the single-phase and multiphase aggregates, and, generally, it turns out that the RVE is attained with about eight crystals in a 3D system. From a thermodynamic perspective, one can also estimate the scale dependencies of the dissipation potential in the velocity space and its complementary potential in the force space. The viscoplastic material, being a purely dissipative material, is ideally suited for this purpose.

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

The homogenization methodology

Grahic Jump Location
Figure 2

Quartet for the selection of dissipation potential (at macroscale)

Grahic Jump Location
Figure 3

The multiplicative decomposition

Grahic Jump Location
Figure 4

Single crystal compression test: L11=L22=0.5, L33=−1, L12=L13=L21=L23=L31=L32=0: (a) Sachs type and (b) Taylor type

Grahic Jump Location
Figure 6

Single crystal and the polycrystalline aggregate yield surfaces at a strain of 0.5 (in the “π-plane”)

Grahic Jump Location
Figure 7

(a) Geometry of eight grains, (b) mesh, (c) deformed view-Neumann problem, (d) deformed view-Dirichlet problem, (e) von Mises stress-Neumann problem, and (f) von Mises stress-Dirichlet problem

Grahic Jump Location
Figure 8

Bounds on the aggregate response

Grahic Jump Location
Figure 9

(a) Deformed view in the Neumann problem (two-phase material), (b) deformed view in the Dirichlet problem (two-phase material), (c) the von Mises stress in the Neumann problem, and (d) the von Mises stress in the Dirichlet problem

Grahic Jump Location
Figure 10

Bounds on the multiphase aggregate response

Grahic Jump Location
Figure 5

(a) The polycrystal compression test: L11=L22=0.5, L33=−1, L12=L13=L21=L23=L31=L32=0, (b) texture-Taylor type, and (c) texture-Sachs type

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