A Superposition Framework for Discrete Dislocation Plasticity

M. P. O’Day; W. A. Curtin

doi:10.1115/1.1794167

Journal of Applied Mechanics | Volume 71 | Issue 6 | TECHNICAL PAPERS

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TECHNICAL PAPERS

A Superposition Framework for Discrete Dislocation Plasticity

M. P. O’Day and W. A. Curtin

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M. P. O’Day, W. A. Curtin

Division of Engineering, Brown University, Providence, RI 02912

J. Appl. Mech 71(6), 805-815 (Jan 27, 2005) (11 pages) doi:10.1115/1.1794167 History: Received February 24, 2003; Revised October 30, 2003; Online January 27, 2005

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General discrete dislocation boundary value problem (fields u_DD,σ_DD) is written as the superposition of: (i) dislocation fields in infinite space of homogeneous matrix material (ũ ,σ̃ ) and (ii) corrective fields to account for the inclusion and proper boundary conditions (u⁁ ,σ⁁ )

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New superposition framework showing decomposition into two subsidiary problems: discrete dislocation (DD) subproblem solved with the standard formulation subject to generic boundary conditions, and elastic (EL) subproblem, which contains all specific boundary conditions and loading, solved with standard elastic FE

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Decomposition of the bimaterial fracture problem into DD and EL subproblems

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Comparison of superposition and standard DD methods for rigid substrate: (a) crack growth resistance curves and (b) crack opening displacements

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Normalized applied stress intensity factor |K|/K₀ versus crack extension Δa for various substrate moduli

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(Color online) Dislocations and normalized opening stress σ₂₂/μ×10³ in a 10×13 μm region near the crack tip for various substrate moduli just prior to failure (see triangles in Fig. 5): (a) E₂/E₁=1 with |K|/K₀=1.118, (b) E₂/E₁=2 with |K|/K₀=1.811, (c) E₂/E₁=6 with |K|/K₀=2.304, and (d) E₂/E₁=∞ with |K|/K₀=2.286. The crack opening profiles for each case are plotted below the x axis. All distances are in microns.

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(Color online) Dislocations and normalized opening stress σ₂₂/μ×10³ in a 8×6 μm region near the crack tip for E₂/E₁=2 at four stages of loading (see circles in Fig. 5): (a) |K|/K₀=0.966, (b) 1.208, (c) 1.449, and (d) 1.691. The crack opening profiles at each load are plotted below the x axis. All distances are in microns.

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Schematic of the superposition technique applied to a 2D polycrystalline structure. Each DD problem is independent and thus the computation is easily parallelized.

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O’Day MP, Curtin WA. A Superposition Framework for Discrete Dislocation Plasticity. ASME. J. Appl. Mech. 2005;71(6):805-815. doi:10.1115/1.1794167.

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A Superposition Framework for Discrete Dislocation Plasticity

References

Figures

General discrete dislocation boundary value problem (fields u_DD,σ_DD) is written as the superposition of: (i) dislocation fields in infinite space of homogeneous matrix material (ũ ,σ̃ ) and (ii) corrective fields to account for the inclusion and proper boundary conditions (u⁁ ,σ⁁ )

Decomposition of the bimaterial fracture problem into DD and EL subproblems

Comparison of superposition and standard DD methods for rigid substrate: (a) crack growth resistance curves and (b) crack opening displacements

Normalized applied stress intensity factor |K|/K₀ versus crack extension Δa for various substrate moduli

Schematic of the superposition technique applied to a 2D polycrystalline structure. Each DD problem is independent and thus the computation is easily parallelized.

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Discussions

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A Superposition Framework for Discrete Dislocation Plasticity

References

Figures

General discrete dislocation boundary value problem (fields uDD,σDD) is written as the superposition of: (i) dislocation fields in infinite space of homogeneous matrix material (ũ ,σ̃ ) and (ii) corrective fields to account for the inclusion and proper boundary conditions (u⁁ ,σ⁁ )

Decomposition of the bimaterial fracture problem into DD and EL subproblems

Comparison of superposition and standard DD methods for rigid substrate: (a) crack growth resistance curves and (b) crack opening displacements

Normalized applied stress intensity factor |K|/K0 versus crack extension Δa for various substrate moduli

Schematic of the superposition technique applied to a 2D polycrystalline structure. Each DD problem is independent and thus the computation is easily parallelized.

Tables

Errata

Discussions

Related Content

Journals

Conference Proceedings

eBooks

General discrete dislocation boundary value problem (fields u_DD,σ_DD) is written as the superposition of: (i) dislocation fields in infinite space of homogeneous matrix material (ũ ,σ̃ ) and (ii) corrective fields to account for the inclusion and proper boundary conditions (u⁁ ,σ⁁ )

Normalized applied stress intensity factor |K|/K₀ versus crack extension Δa for various substrate moduli