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A Mesh-Independent Brute-Force Approach for Traction-Free Corrections in Dislocation Problems

DOI: 10.4236/mnsms.2021.111001, PP. 1-18

Keywords: Free Surfaces, Dislocation Theory, Dislocation Dynamics, Peach-Koehler Force

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Abstract:

Simulation of dislocation dynamics opens the opportunity for researchers and scientists to observe in-depth many plastic deformation phenomena. In 2D or 3D media, modeling of physical boundary conditions accurately is one of the keys to the success of dislocation dynamics (DD) simulations. The scope of analytical solutions is restricted and applies to specific configurations only. But in dynamics simulations, the dislocations’ shape and orientation change over time thus limiting the use of analytical solutions. The authors of this article present a mesh-based generalized numerical approach based on the collocation point method. The method is applicable to any number of dislocations of any shape/orientation and to different computational domain shapes. Several verifications of the method are provided and successful implementation of the method in 3D DD simulations have been incorporated. Also, the effect of free surfaces on the Peach-Koehler force has been computed. Lastly, the effect of free surfaces on the flow stress of the material has been studied. The results clearly showed a higher force with increased closeness to the free surface and with increased dislocation segment length. The simulations’ results also show a softening effect on the flow stress results due to the effect of the free surfaces.

References

[1]  Hull, D. and Bacon, D.J. (2011) Introduction to Dislocations. Butterworth-Heinemann, Oxford.
https://doi.org/10.1016/B978-0-08-096672-4.00002-5
[2]  Hirth, J.P. and Lothe, J. (1982) Theory of Dislocations. John Wiley & Sons, Hoboken.
[3]  Eshelby, J.D. and Stroh, A.N. (1951) CXL. Dislocations in Thin Plates. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 42, 1401-1405.
https://doi.org/10.1080/14786445108560958
[4]  Jeans, J. (1925) Mathematical Theory of Electricity and Magnetism. CUP Archive.
[5]  Yoffe, E.H. (1961) A Dislocation at a Free Surface. Philosophical Magazine, 6, 1147-1155.
https://doi.org/10.1080/14786436108239675
[6]  Bastecká, J. (1964) Interaction of Dislocation Loop with Free Surface. Czechoslovak Journal of Physics, 14, 430-442.
https://doi.org/10.1007/BF01689476
[7]  Groves, P.P. and Bacon, D.J. (1970) The Dislocation in a Semi-Infinite Isotropic Medium. Fundamental Aspects of Dislocation Theory, 1, 35-45.
[8]  Groves, P.P. and Bacon, D.J. (1970) The Dislocation Loop near a Free Surface. Philosophical Magazine, 22, 83-91.
https://doi.org/10.1080/14786437008228153
[9]  Maurissen, Y. and Capella, L. (1974) Stress Field of a Dislocation Segment Parallel to a Free Surface. Philosophical Magazine, 29, 1227-1229.
https://doi.org/10.1080/14786437408226608
[10]  Maurissen, Y. and Capella, L. (1974) Stress Field of a Dislocation Segment Perpendicular to a Free Surface. Philosophical Magazine, 30, 679-683.
https://doi.org/10.1080/14786439808206591
[11]  Comninou, M. and Dundurs, J. (1975) The Angular Dislocation in a Half Space. Journal of Elasticity, 5, 203-216.
https://doi.org/10.1007/BF00126985
[12]  Lothe, J., Indenbom, V.L. and Chamrov, V.A. (1982) Elastic Field and Self-Force of Dislocations Emerging at the Free Surfaces of an Anisotropic Halfspace. Physica Status Solidi (B), 111, 671-677.
https://doi.org/10.1002/pssb.2221110231
[13]  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. Journal of the Mechanics and Physics of Solids, 42, 1199-1221.
https://doi.org/10.1016/0022-5096(94)90032-9
[14]  Devincre, B. (1995) Three Dimensional Stress Field Expressions for Straight Dislocation Segments. Solid State Communictions, 93, 875-878.
https://doi.org/10.1016/0038-1098(94)00894-9
[15]  Kubin, L., Canova, G., Condat, M., Devincre, B., Pontikis, V. and Brechet, Y. (1992) Dislocation Microstructures and Plastic Flow: A 3D Simulation. Solid State Phenomena, 23-24, 455-472.
https://doi.org/10.4028/www.scientific.net/SSP.23-24.455
[16]  Canova, G.R. and Fivel, M.C. (1999) Developing Rigorous Boundary Conditions to Simulations of Discrete Dislocation Dynamics. Modelling and Simulation in Materials Science and Engineering, 7, 753-768.
https://doi.org/10.1088/0965-0393/7/5/308
[17]  Hartmaier, A., Fivel, M.C., Canova, G.R. and Gumbsch, P. (1999) Image Stresses in a Free-Standing Thin Film. Modelling and Simulation in Materials Science and Engineering, 7, 781-793.
https://doi.org/10.1088/0965-0393/7/5/310
[18]  El-Azab, A. (2000) The Boundary Value Problem of Dislocation Dynamics. Modelling and Simulation in Materials Science and Engineering, 8, 37-54.
https://doi.org/10.1088/0965-0393/8/1/304
[19]  Deng, J., El-Azab, A. and Larson, B.C. (2008) On the Elastic Boundary Value Problem of Dislocations in Bounded Crystals. Philosophical Magazine, 88, 3527-3548.
https://doi.org/10.1080/14786430802558544
[20]  Zhou, C., Biner, S.B. and LeSar, R. (2010) Discrete Dislocation Dynamics Simulations of Plasticity at Small Scales. Acta Materialia, 58, 1565-1577.
https://doi.org/10.1016/j.actamat.2009.11.001
[21]  Crone, J.C., Munday, L.B. and Knap, J. (2015) Capturing the Effects of Free Surfaces on Void Strengthening with Dislocation Dynamics. Acta Materialia, 101, 40-47.
https://doi.org/10.1016/j.actamat.2015.08.067
[22]  Jing, P., Khraishi, T., Young, J.A. and Wirth, B.D. (2005) Multi-Scale Simulations of the Effects of Irradiation-induced Voids and Helium Bubbles on the Mechanical Properties of Aluminum. Philosophical Magazine, 85, 757-767.
https://doi.org/10.1080/14786430412331319958
[23]  Jing, P., Khraishi, T., Zepeda-Ruiz, L.A. and Wirth, B.D. (2009) The Elastic Fields of Sub-Surface Dislocation Loops: A Comparison between Analytical Continuum-Theory Solutions and Atomistic Calculations. International Journal of Theoretical and Applied Multiscale Mechanics, 1, 71-85.
https://doi.org/10.1504/IJTAMM.2009.022472
[24]  Khraishi, T.A. and Zbib, H.M. (2001) Dislocation Dynamics Simulations of the Interaction between a Short Rigid Fiber and a Glide Circular Dislocation Pile-Up. Computational Materials Science, 24, 310-322.
https://doi.org/10.1016/S0927-0256(01)00253-1
[25]  Khraishi, T.A. and Zbib, H.M. (2002) Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling. Journal of Engineering Materials and Technology, 124, 342-351.
https://doi.org/10.1115/1.1479694
[26]  Yan, L., Khraishi, T.A., Shen, Y.-L. and Horstemeyer, M.F. (2004) A Distributed-Dislocation Method for Treating Free-Surface Image Stresses in Three-Dim-ensional Dislocation Dynamics Simulations. Modelling and Simulation in Materials Science and Engineering, 12, S289-S301.
https://doi.org/10.1088/0965-0393/12/4/S01
[27]  Siddique, A.B. and Khraishi, T. (2020) Numerical Methodology for Treating Static and Dynamic Dislocation Problems near a Free Surface. Journal of Physics Communications, 4, Article ID: 055005.
https://doi.org/10.1088/2399-6528/ab8ff9
[28]  Siddique, A.B. and Khraishi, T.A. (2020) A Dislocation Near a Cylindrical Hole: A Numerical Treatment. Proceedings of the 2020 ASEE Gulf-Southwest Annual Conference, 23-29 April 2020, 3.
https://peer.asee.org/35939
[29]  Chapra, S.C. and Canale, R.P. (1998) Numerical Methods for Engineers. McGraw-Hill, New York.
[30]  Khraishi, T.A., Yan, L. and Shen, Y.-L. (2004) Dynamic Simulations of the Interaction between Dislocations and Dilute Particle Concentrations in Metal-Matrix Composites (MMCs). International Journal of Plasticity, 20, 1039-1057.
https://doi.org/10.1016/j.ijplas.2003.10.003
[31]  Zbib, H.M., Rhee, M. and Hirth, J. (1998) On Plastic Deformation and the Dynamics of 3D Dislocations. International Journal of Mechanical Sciences, 40, 113-127.
https://doi.org/10.1016/S0020-7403(97)00043-X
[32]  Meyers, M.A. and Chawla, K.K. (1998) Mechanical Behavior of Materials. Cambridge University Press, Cambridge.

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