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Title: Analytic model of the γ -surface deviation and influence on the stacking fault width between partial dislocations

Abstract

The stacking fault width (R$$_{eq}$$) between partial dislocations within an FCC crystalline lattice characterizes the onset of numerous plastic flow mechanisms, as well as the relationship between material strength and grain size. Continuum models traditionally consider a complete unit of dislocation slip (b) along the $$\langle{110}$$$$\rangle$$ direction distributed between two discrete partial dislocations, each with a fixed partial Burgers vector (bp), which bound a stacking fault. Across the stacking fault, the vectorial slip is assumed to be constant, yielding a constant intrinsic stacking fault energy density, $$\gamma$$$$_{isf}$$ Here, we demonstrate that the vectorial displacement path taken in accomplishing a complete unit of slip (b) deviates from the expected displacement path containing the local minima, $$\gamma$$$$_{isf}$$ leading to a correction in the nominally derived stacking fault width. The magnitude of the correction depends on both the net orientation of the dislocation within the lattice, and also the degree of relaxation of each partial Burgers vector along the $$\langle{\bar{1}12}$$$$\rangle$$ direction. We derive a simple analytic model for the corrected stacking fault width, explicitly accounting for the deviation, by introducing a variable ξ (0 < ξ < 1), which governs the magnitude of each partial dislocation component along the $$\langle{\bar{1}12}$$$$\rangle$$ direction. Significantly, ourmore » model predicts a correction to R$$_{eq}$$ of ~$$\mathscr{O}$$ (|b|) for the nominally screw dislocation, and has no noticeable influence on nominally edge dislocations. We apply our model towards computing the stacking fault width of several FCC metals, and demonstrate excellent agreement both with our own numerical data as well as that obtained from ab initio and Molecular Statics (MS) methods within the literature. Lastly, the results from this study demonstrate that, upon judicious application, discrete linear elastic models are successful in reproducing elastic interactions as computed from higher fidelity models on the spatial scale of metallic dislocation cores.« less

Authors:
 [1];  [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1524373
Alternate Identifier(s):
OSTI ID: 1548632
Report Number(s):
LA-UR-17-29245
Journal ID: ISSN 0927-0256
Grant/Contract Number:  
89233218CNA000001; ER20160156; ER20170679; AC52-06NA25396; 20170679ER
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computational Materials Science
Additional Journal Information:
Journal Volume: 147; Journal Issue: C; Journal ID: ISSN 0927-0256
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; Material Science

Citation Formats

Szajewski, B. A., Hunter, A., and Luscher, D. J. Analytic model of the γ -surface deviation and influence on the stacking fault width between partial dislocations. United States: N. p., 2018. Web. doi:10.1016/j.commatsci.2018.02.021.
Szajewski, B. A., Hunter, A., & Luscher, D. J. Analytic model of the γ -surface deviation and influence on the stacking fault width between partial dislocations. United States. https://doi.org/10.1016/j.commatsci.2018.02.021
Szajewski, B. A., Hunter, A., and Luscher, D. J. 2018. "Analytic model of the γ -surface deviation and influence on the stacking fault width between partial dislocations". United States. https://doi.org/10.1016/j.commatsci.2018.02.021. https://www.osti.gov/servlets/purl/1524373.
@article{osti_1524373,
title = {Analytic model of the γ -surface deviation and influence on the stacking fault width between partial dislocations},
author = {Szajewski, B. A. and Hunter, A. and Luscher, D. J.},
abstractNote = {The stacking fault width (R$_{eq}$) between partial dislocations within an FCC crystalline lattice characterizes the onset of numerous plastic flow mechanisms, as well as the relationship between material strength and grain size. Continuum models traditionally consider a complete unit of dislocation slip (b) along the $\langle{110}$$\rangle$ direction distributed between two discrete partial dislocations, each with a fixed partial Burgers vector (bp), which bound a stacking fault. Across the stacking fault, the vectorial slip is assumed to be constant, yielding a constant intrinsic stacking fault energy density, $\gamma$$_{isf}$ Here, we demonstrate that the vectorial displacement path taken in accomplishing a complete unit of slip (b) deviates from the expected displacement path containing the local minima, $\gamma$$_{isf}$ leading to a correction in the nominally derived stacking fault width. The magnitude of the correction depends on both the net orientation of the dislocation within the lattice, and also the degree of relaxation of each partial Burgers vector along the $\langle{\bar{1}12}$$\rangle$ direction. We derive a simple analytic model for the corrected stacking fault width, explicitly accounting for the deviation, by introducing a variable ξ (0 < ξ < 1), which governs the magnitude of each partial dislocation component along the $\langle{\bar{1}12}$$\rangle$ direction. Significantly, our model predicts a correction to R$_{eq}$ of ~$\mathscr{O}$ (|b|) for the nominally screw dislocation, and has no noticeable influence on nominally edge dislocations. We apply our model towards computing the stacking fault width of several FCC metals, and demonstrate excellent agreement both with our own numerical data as well as that obtained from ab initio and Molecular Statics (MS) methods within the literature. Lastly, the results from this study demonstrate that, upon judicious application, discrete linear elastic models are successful in reproducing elastic interactions as computed from higher fidelity models on the spatial scale of metallic dislocation cores.},
doi = {10.1016/j.commatsci.2018.02.021},
url = {https://www.osti.gov/biblio/1524373}, journal = {Computational Materials Science},
issn = {0927-0256},
number = C,
volume = 147,
place = {United States},
year = {Thu Feb 22 00:00:00 EST 2018},
month = {Thu Feb 22 00:00:00 EST 2018}
}

Journal Article:

Citation Metrics:
Cited by: 5 works
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Figures / Tables:

Figure 1 Figure 1: (a) Schematic of the displacement path (u) across the $$γ$$-surface for an edge dislocation within Pd. The displacement is typically assumed to pass through the minima ($$γ$$$isf$ ). The deviation is indicated by $$ξ$$, where 0 ≤ $$ξ$$ ≤ 1, and $max$ ($$u$$<$$\bar{1}12$$>|$$ξ$$=1)=|b| $$\sqrt{3}$$/6. (b) Illustration of themore » displacement (black: $$u$$<110>($$x$$) and blue: $$u$$<$$\bar{1}12$$>($$x$$)) versus the position ($$x$$), with $$ξ$$ indicating the maximum displacement along $$u$$<$$\bar{1}12$$>($$x$$). (c) Displacement gradient ($∂u$<110>($$x$$)/$∂x$) versus position ($$x$$) illustrating two peaks separated by the stacking fault width, R$eq$.« less

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Works referencing / citing this record:

Phase-field-based calculations of the disregistry fields of static extended dislocations in FCC metals
journal, February 2019


A comparison of different continuum approaches in modeling mixed-type dislocations in Al
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An iterative scheme for the generalized Peierls–Nabarro model based on the inverse Hilbert transform
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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.