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TECHNICAL PAPERS

A Multiscale Model of Plasticity Based on Discrete Dislocation Dynamics

[+] Author and Article Information
Hussein M. Zbib

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920

Tomas Diaz de la Rubia, Vasily Bulatov

Lawrence Livermore National Laboratory, Materials Science and Technology Division, Chemistry and Materials Science Directorate, Mail Stop L-353, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550

J. Eng. Mater. Technol 124(1), 78-87 (May 28, 2001) (10 pages) doi:10.1115/1.1421351 History: Received January 25, 2001; Revised May 28, 2001
Copyright © 2002 by ASME
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References

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Rhee,  M., Stolken,  J., Zbib,  H. M., Hirth,  J. P., and Diaz de la Rubia,  T., 2001, “Dislocation Dynamics Using Anisotropic Elasticity: Methodology and Analysis,” Mater. Sci. Eng., A A309-310, pp. 288–293.
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Hirth,  J. P., Rhee,  M., and Zbib,  H. M., 1996, “Modeling of Deformation by a 3D Simulation of Multipole, Curved Dislocations,” J. Computer-Aided Materials Design, 3, pp. 164–166.
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Zbib, H. M., and De La Rubia, T. D., 2002, “Multiscale Model of Plasticity,” Int. J. Plasticity, in press.
Zbib, H. M., Rhee, M., and Hirth, J. P., 1996, “3D Simulation of Curved Dislocations: Discretization and Long Range Interactions,” Advances in Engineering Plasticity and its Applications, T. Abe and T. Tsuta, eds., Pergamon, NY, pp. 15–20.
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Khraishi,  T. A., Zbib,  H. M., Hirth,  J. P., and Khaleel,  M., 2000, “Analytical Solution for The Stress-Displacement Field of Glide Dislocation Loop,” Int. J. Eng. Sci., 38, pp. 251–266.
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Demir,  I., Zbib,  H. M., and Khaleel,  M., 2001, “On Crack Propagation in the Case of Multiple Cracks, Inclusions and Voids,” Theor. Appl. Fract. Mech., in press.

Figures

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Numerical accuracy of dislocation mesh (a) Effect of mesh size on self stress of a dislocation loop, maximum error is 3 percent for the finest mesh size when compared to the exact solution (from Khraishi et al. 2000). (b) The bow-out of a pinned pure edge dislocation under an applied shear stress of 13 MPa for different mesh sizes, at various time steps up to the stable configuration.
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Numerical simulation of micro-shear bands development using the coupled FEA-DD model. (a) The initial dislocation state; Frank-Read sources originating from prismatic loops; (b) the finite element mesh.
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(a,b) The history of dislocation path during single-slip deformation, (c) distribution of effective plastic strain
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(a,b) The history of dislocation path during double-slip deformation, (c) distribution of effective plastic strain, (d) distribution of effective stress
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(a) Production of dislocations from FR sources, (b) dislocation distribution at a later stage resulting from both dislocation emission from FR sources and cross-slip, (c) distribution of effective stress, (d) distribution of effective plastic strain
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(a) dislocation distribution at a later stage of deformation resulting from both dislocation emission from FR sources and cross-slip, (b) distribution of effective plastic strain. Constant strain rate.
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The predicted stress-strain curves for various slip conditions
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The evolution of dislocation density for various slip and loading conditions
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Distribution of effective plastic strain rate for the case of double slip under constant stress with free boundary condition, showing the development of steps at the surfaces. (Deformed configuration with displacement magnified by a factor of 100.)
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Displacement of upper surface when subjected to an impact constant force

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