On dislocation patterning: Multiple slip effects in the rate equation approach |
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| Institution: | 1. Metallurgy and Materials Engineering Department, Federal University of Rio de Janeiro-PO Box 68505, 21941-972 Rio de Janeiro, Brazil;2. Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, B-1050 Brussels, Belgium;3. Laboratory of Mechanics and Materials, Polytechnic School, Aristotle University of Thessaloniki, GR-54124, Thessaloniki, Greece;4. Center for the Mechanics of Material Instabilities and Manufacturing Processes Michigan Technological University, MI 49931, Houghton, USA;1. Graduate School of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan;2. College of Science and Engineering, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan;3. Research Laboratory, Structural Strength Department, IHI Corporation, 1, Shin-Nakahara-Cho, Isogo-ku, Yokohama 235-8501, Japan;4. Research Organization of Science and Technology, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan;1. Lawrence Livermore National Laboratory, Livermore, CA 94550, United States;2. Institut fur Angewandte Mathematik, Universitat Bonn, 53115 Bonn, Germany;3. University of Pennsylvania, Philadelphia, PA 19104-6315, United States;1. Department of Mechanical Engineering, School of Engineering, University of Nairobi, P.O. Box 30197-00100, Nairobi, Kenya;2. Department of Mechanical Engineering, Jomo Kenyatta University of Agriculture and Technology, P.O. Box 62000-00200, Nairobi, Kenya;3. DST-NRF Centre of Excellence in Strong Materials, University of the Witwatersrand, Private Bag 3, WITS 2050, South Africa;4. School of Chemical and Metallurgical Engineering, University of the Witwatersrand, Private Bag 3, WITS 2050, South Africa;5. African Materials Science and Engineering Network (AMSEN), A RISE Network, South Africa;1. Department of Mechanical Engineering, Whiting School of Engineering, The Johns Hopkins University, Baltimore, MD 21218-2682, USA;2. Air Force Research Laboratory, Materials and Manufacturing Directorate, Wright-Patterson AFB, OH 45433-7817, USA;3. Institute of Mechanical Engineering, EPFL, Lausanne, Switzerland;4. UES Inc., 4401 Dayton-Xenia Road, Dayton, OH 45432-1894, USA |
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| Abstract: | Strain localization and dislocation pattern formation are typical features of plastic deformation in metals and alloys. Glide and climb dislocation motion, along with accompanying production/annihilation processes, lead to the occurrence of instabilities of initially uniform dislocation distributions. These instabilities result to the development of various types of dislocation microstructures (dislocation cells, slip and kink bands, persistent slip bands, labyrinth structures, etc.), depending on the externally applied loading and the intrinsic lattice constraints. The term “dislocation patterning” was introduced over 20 years ago by the third author and a corresponding “gradient dislocation dynamics” framework was suggested to describe such phenomena. In the W–A model proposed at that time by the last two authors, it was shown how coupled nonlinear evolution equations of the reaction-diffusion type for the forest (immobile) and gliding (mobile) dislocation densities can generate dislocation microstructures which correspond to walls perpendicular to the slip direction for Cu-crystals oriented for single slip under cyclic loading conditions. This model is adapted to the multiple slip case here. Weakly nonlinear analysis predicts that dislocation patterns should correspond to domains of walls perpendicular to each slip direction and separated by domain walls in the same orientations. This result is confirmed by numerical analysis and experimental observations. The present model generalizes the original W–A model to the case of multiple slip and considers also explicitly gradient effects by allowing for non-uniform dislocation velocities and internal stress effects. |
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