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Research Papers

A Mesoscale Model of Plasticity: Dislocation Dynamics and Patterning (One-Dimensional)

[+] Author and Article Information
Nasrin Taheri-Nassaj, Hussein M. Zbib

School of Mechanical and Materials Engineering,
Washington State University,
Pullman, WA 99164

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received October 14, 2015; final manuscript received May 27, 2016; published online July 29, 2016. Assoc. Editor: Peter W. Chung.

J. Eng. Mater. Technol 138(4), 041015 (Jul 29, 2016) (9 pages) Paper No: MATS-15-1256; doi: 10.1115/1.4033910 History: Received October 14, 2015; Revised May 27, 2016

In this study, we developed a physically based mesoscale model for dislocation dynamics systems to predict the deformation and spontaneous formation of spatio-temporal dislocation patterns over microscopic space and time. Dislocations and dislocation patterns are emblematic of plastic deformation, a nonlinear, dissipative process involving the dynamics of underlying dislocations as carriers of plastic deformation. The mesoscale model includes a set of nonlinear partial differential equations of reaction–diffusion type. Here, we consider the equations within a one-dimensional framework and analyze the stability of steady-state solutions for these equations to elucidate the associated patterns with their intrinsic length scale. The numerical solution to the model yields the spatial distribution of dislocation patterns over time and provides respective stress–strain curves. Finally, we compare the stress–strain curves associated with the dislocation patterns with the experimental results noted in the literature.

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Copyright © 2016 by ASME
Topics: Dislocations
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References

Figures

Grahic Jump Location
Fig. 1

Dislocation patterns for aluminum with FCC crystalline structure after a total strain of 0.1, when loading is in the 〈111〉 direction: (a), (b), and (c) denote the positive mobile, negative mobile, and immobile dislocation densities

Grahic Jump Location
Fig. 2

Dislocation pattern for aluminum with FCC crystalline structure, when loading is in the 〈100〉 direction, after a total strain of (I) 0.1 and (II) 0.3: (a), (b), and (c) denote the positive mobile, negative mobile, and immobile dislocation densities

Grahic Jump Location
Fig. 3

Dislocation pattern for Fe single crystal with BCC structure, loading in the 〈100〉 direction for a total strain of (I) 0.1, (II) 0.3, and (III) 2, when loading in the 〈111〉 direction: (a), (b), and (c) denote the positive mobile, negative mobile, and immobile dislocation densities

Grahic Jump Location
Fig. 4

Dislocation pattern for Fe single crystal with BCC structure, when loading in the 〈011〉 direction for a total strain of 2: (a), (b), and (c) denote the positive mobile, negative mobile, and immobile dislocation densities

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Fig. 5

Stress–strain curve for aluminum with FCC crystalline structure, comparison between simulation and experiments

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Fig. 6

Stress–strain curve for Fe single crystal with BCC crystalline structure, comparison between simulation and experiments

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