Research Papers

A Predictive Framework for Dislocation-Density Pile-Ups in Crystalline Systems With Coincident Site Lattice and Random Grain Boundaries

[+] Author and Article Information
David M. Bond

North Carolina State University,
Raleigh, NC 27695-7190
e-mail: dmbond@ncsu.edu

Mohammed A. Zikry

College of Engineering,
North Carolina State University,
Campus Box 7910/3154 EBIII,
Centennial Campus,
Raleigh, NC 27695-7190
e-mail: zikry@ncsu.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 16, 2016; final manuscript received September 9, 2016; published online February 13, 2017. Assoc. Editor: Xi Chen.

J. Eng. Mater. Technol 139(2), 021023 (Feb 13, 2017) (8 pages) Paper No: MATS-16-1184; doi: 10.1115/1.4035494 History: Received June 16, 2016; Revised September 09, 2016

Evolving dislocation-density pile-ups at grain-boundaries (GBs) spanning a wide range of coincident site lattice (CSL) and random GB misorientations in face-centered cubic (fcc) bicrystals and polycrystalline aggregates has been investigated. A dislocation-density GB interaction scheme coupled to a dislocation-density-based crystalline plasticity formulation was used in a nonlinear finite element (FE) framework to understand how different GB orientations and GB-dislocation-density interactions affect local and overall behavior. An effective Burger's vector of residual dislocations was obtained for fcc bicrystals and compared with molecular dynamics (MDs) predictions of static GB energy, as well as dislocation-density transmission at GB interfaces. Dislocation-density pile-ups and accumulations of residual dislocations at GBs and triple junctions (TJs) were analyzed for a polycrystalline copper aggregate with Σ1, Σ3, Σ7, Σ13, and Σ21 CSLs and random high-angle GBs to understand and predict the effects of GB misorientation on pile-up formation and evolution. The predictions indicate that dislocation-density pile-ups occur at GBs with significantly misoriented slip systems and large residual Burger's vectors, such as Σ7, Σ13, and Σ21 CSLs and random high-angle GBs, and this resulted in heterogeneous inelastic deformations across the GB and local stress accumulations. GBs with low misorientations of slip systems had high transmission, no dislocation-density pile-ups, and lower stresses than the high-angle GBs. This investigation provides a fundamental understanding of how different representative GB orientations affect GB behavior, slip transmission, and dislocation-density pile-ups at a relevant microstructural scale.

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Fig. 1

Comparison of static MD calculated GB energy from Ref. [26] and average effective Burger's vector calculated for the [111] and [001] rotation axes for an fcc bicrystal

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Fig. 2

Average effective Burger's vector for the [111] rotation axis with CSL bicrystals showing the grain boundary transmission factor of the most active slip system at a nominal strain of 5%

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Fig. 3

Grain boundary misorientations determined using rotation matrices of each grain. The rotation matrices, R, were obtained by combining three successive rotations described by the Euler angles for each grain.

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Fig. 4

Microstructural polycrystal model with GB orientations indicated

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Fig. 5

(a) Normal stress and (b) GB residual dislocation-density at 3% nominal strain with maximum normal stress regions marked. Region 1 is a Σ7 CSL GB, and region 2 and region 3 are near triple junctions.

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Fig. 6

Behavior for the most active slip systems in grains A and B at 3% nominal strain: (a) immobile dislocation-density for (11¯1)[011], (b) GBTF for (11¯1)[011], (c) immobile dislocation-density for (1¯1¯1)[011], and (d) GBTF for (1¯1¯1)[011]

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Fig. 7

Normalized normal stress and grain boundary residual dislocation-density at the Σ7 CSL GB

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Fig. 8

Behavior at triple junction at 3% nominal strain: (a) GBTF for most active slip system (11¯1)[011], (b) grain boundary residual dislocation-density, (c) immobile dislocation-density for slip system (11¯1)[011], and (d) normal stress

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Fig. 9

Slip direction and immobile dislocation-density of the most active slip system of grains A, B, and C at the triple junction

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Fig. 10

Shear slip behavior: (a) near the TJ with sampling lines and CSL GBs indicated, (b) shear slip across Σ1 CSL GB, (c) shear slip across Σ13 CSL GB, and (d) shear slip across the Σ7 CSL GB




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