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TECHNICAL PAPERS

Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling

[+] Author and Article Information
Tariq A. Khraishi

Department of Mechanical Engineering, University of New Mexico, Albuquerque, NM 87131e-mail: khraishi@me.unm.edu

Hussein M. Zbib

School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164e-mail: zbib@mme.wsu.edu

J. Eng. Mater. Technol 124(3), 342-351 (Jun 10, 2002) (10 pages) doi:10.1115/1.1479694 History: Received September 04, 2001; Revised March 15, 2002; Online June 10, 2002
Copyright © 2002 by ASME
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References

Yoffe,  E., 1961, “A Dislocation at a Free Surface,” Philos. Mag., 6, pp. 1147–1155.
Bacon, D. J., and Groves, P. P., 1970, “The Dislocation in a Semi-Infinite Isotropic Medium,” Fundamental Aspects of Dislocation Theory, J. A. Simmons, R. de Witt, and R. Bullough, eds, Spec. Publ. 317, I, pp. 35–45.
Groves,  P. P., and Bacon,  D. J., 1970, “The Dislocation Loop Near a Free Surface,” Philos. Mag., 22, pp. 83–91.
Maurissen,  Y., and Capella,  L., 1974, “Stress Field of a Dislocation Segment Parallel to a Free Surface,” Philos. Mag., 29(5), pp. 1227–1229.
Maurissen,  Y., and Capella,  L., 1974, “Stress Field of a Dislocation Segment Perpendicular to a Free Surface,” Philos. Mag., 30(3), pp. 679–683.
Comninou,  M., and Dunders,  J., 1975, “The Angular Dislocation in a Half Space,” J. Elast., 5(3–4), pp. 203–216.
Gosling,  T. J., and Willis,  J. R., 1994, “A Line-Integral Representation For the Stresses Due to an Arbitrary Dislocation in an Isotropic Half-Space,” J. Mech. Phys. Solids, 42(8), pp. 1199–1221.
Lothe,  J., Indenbom,  V. L., and Chamrov,  V. A., 1982, “Elastic Fields and Self-Force of Dislocations Emerging at the Free Surfaces of an Anisotropic Halfspace,” Phys. Status Solidi B, 111, pp. 671–677.
Zbib,  H. M., Rhee,  M., and Hirth,  J. P., 1998, “On Plastic Deformation and the Dynamics of 3D Dislocations,” Int. J. Mech. Sci., 40(2–3), pp. 113–127.
Rhee,  M., Zbib,  H. M., Hirth,  J. P., Huang,  H., and de la Rubia,  T., 1998, “Models for Long/Short-Range Interactions and Cross Slip in 3D Dislocation Simulation of BCC Single Crystals,” Modelling Simul. Mater. Sci. Eng., 6, pp. 467–492.
Hirth, J. P., and Lothe, J., 1982, Theory of Dislocations, Krieger Publishing Company, Malabar, FL.
Devincre,  B., 1995, “Three-Dimensional Stress Field Expressions for Straight Dislocation Segments,” Solid State Commun., 93(11), pp. 875–878.
Hills, D. A., Kelly, P. A., Dai, D. N., and Korsunsky, A. M., 1996, Solution of Crack Problems: The Distributed Dislocation Technique, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Khraishi,  T. A., Hirth,  J. P., Zbib,  H. M., and Khaleel,  M. A., 2000, “The Displacement, and Strain-Stress Fields of a General Circular Volterra Dislocation Loop,” Int. J. Eng. Sci., 38(3), pp. 251–266.
Khraishi,  T. A., Zbib,  H. M., Hirth,  J. P., and de la Rubia,  T. D., 2000, “The Stress Field of a General Circular Volterra Dislocation Loop: Analytical and Numerical Approaches,” Philos. Mag. Lett., 80(2), pp. 95–105.
Chapra, S., and Canale, R., 1998, Numerical Methods for Engineers With Programming and Software Applications, WCB McGraw-Hill, Boston.
Khraishi, T., 2000, “The Treatment of Boundary Conditions in Three-Dimensional Dislocation Dynamics Analysis,” PhD dissertation, Washington State University.
Khraishi,  T. A., Zbib,  H. M., and de la Rubia,  T. D., 2001, “The Treatment of Traction-Free Boundary Condition in Three-Dimensional Dislocation Dynamics Analysis Using Generalized Image Stress Analysis,” Mater. Sci. Eng., A, 309–310, pp. 283–287.

Figures

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A dislocation segment inside a computational box
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Segment A1B1 beneath a surface with ascribed local coordinate system
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A mesh of rectangular elements, representing prismatic dislocation loops, covering area S upon which surface traction annulment is sought. The inset shows one of these prismatic dislocation loops.
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Faces of a DD computational box uniformly meshed with square elements representing prismatic dislocation loops
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A dislocation segment in a DD computational box reflected off of the six external box surfaces
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Comparisons of the stresses from the current work (TK) versus the work by Maurissen and Capella (MC) for a sub-surface vertical segment. Stresses are in Pa. The segment points in the positive z-direction, has a zero y-component of b, and a length of 100b. The stresses are plotted along an axis parallel to the y-axis at a depth of 400b. The surface is 20,000b on each side and has a mesh density of 10×10 loops.
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Same as Fig. 6 but with a surface mesh density of 30×30 loops.
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Same as Fig. 6 but with a surface mesh density of 50×50 loops
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The Peach-Koehler force pulling a subsurface horizontal segment towards the surface versus the segment depth for a fixed segment length
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The Peach-Koehler force pulling a subsurface horizontal segment towards the surface versus the segment length for a fixed segment depth
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Stress-strain diagrams from DD simulations for one operational Frank-Read source in a cubic cell that is 10,000b in side length. The source is close to the cell’s external surfaces. The continuous line correspond to no treatment of the traction-free boundary condition, and the dashed lines corresponds to an external surface mesh density of 10×10 loops, 20×20 loops, and 30×30 loops.

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