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Technical Briefs

Singular Stress Fields at the Intersection of a Grain Boundary and a Stress-Free Edge in a Columnar Polycrystal

[+] Author and Article Information
E. D. Reedy

 Sandia National Laboratories, P.O. Box 5800, Albuquerque, NM 87185-0346edreedy@sandia.gov

J. Appl. Mech 78(1), 014502 (Oct 13, 2010) (4 pages) doi:10.1115/1.4002118 History: Received May 17, 2010; Revised June 22, 2010; Posted July 07, 2010; Published October 13, 2010; Online October 13, 2010

The singular stress field generated at the intersection of a grain boundary and a stress-free edge is investigated for a columnar polycrystal. An idealized, plane strain geometry that embeds four columnar cubic crystals within an effective isotropic media is analyzed. This idealized problem permits a detailed finite element analysis that can resolve the nature of stress singularities. Particular emphasis is placed on characterizing the magnitude of the stress fields and defining the size of the region dominated by the singularity. The effects of crystal and grain boundary orientation combinations and crystal properties are examined.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

Radial stress dependence at pt1 (θ=0 deg) and pt2 (θ=180 deg) for baseline geometry and material

Grahic Jump Location
Figure 3

FEA results showing the variation in −λ with γa at pt1 of the baseline configuration with γa=γc=−γd, and γb=0 deg are compared with asymptotic-λ values determined using the Stroh formalism for anisotropic elasticity

Grahic Jump Location
Figure 1

Geometry of problem analyzed; loaded by uniformly displacing right edge relative to fixed left edge in a direction parallel to the stress-free edge to generate a nominally uniform σ11=σ∗

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