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Materials 2017, 10(3), 289; doi:10.3390/ma10030289

The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals

Institute of Continuum Mechanics and Material Mechanics, Hamburg University of Technology, 21073 Hamburg, Germany
Institute of Materials Research, Materials Mechanics, Helmholtz-Zentrum Geesthacht, 21502 Geesthacht, Germany
Chair of Solid Mechanics, School of Mechanical Engineering and Safety Engineering, University of Wuppertal, 42119 Wuppertal, Germany
Author to whom correspondence should be addressed.
Academic Editor: Martin O. Steinhauser
Received: 25 January 2017 / Revised: 1 March 2017 / Accepted: 3 March 2017 / Published: 16 March 2017
(This article belongs to the Special Issue Computational Multiscale Modeling and Simulation in Materials Science)
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The mechanical behavior of single crystalline, micro-sized copper is investigated in the context of cantilever beam bending experiments. Particular focus is on the role of geometrically necessary dislocations (GNDs) during bending-dominated load conditions and their impact on the characteristic bending size effect. Three different sample sizes are considered in this work with main variation in thickness. A gradient extended crystal plasticity model is presented and applied in a three-dimensional finite-element (FE) framework considering slip system-based edge and screw components of the dislocation density vector. The underlying mathematical model contains non-standard evolution equations for GNDs, crystal-specific interaction relations, and higher-order boundary conditions. Moreover, two element formulations are examined and compared with respect to size-independent as well as size-dependent bending behavior. The first formulation is based on a linear interpolation of the displacement and the GND density field together with a full integration scheme whereas the second is based on a mixed interpolation scheme. While the GND density fields are treated equivalently, the displacement field is interpolated quadratically in combination with a reduced integration scheme. Computational results indicate that GND storage in small cantilever beams strongly influences the evolution of statistically stored dislocations (SSDs) and, hence, the distribution of the total dislocation density. As a particular example, the mechanical bending behavior in the case of a physically motivated limitation of GND storage is studied. The resulting impact on the mechanical bending response as well as on the predicted size effect is analyzed. Obtained results are discussed and related to experimental findings from the literature. View Full-Text
Keywords: cantilever beam bending; size effect; geometrically necessary dislocations; crystal plasticity; finite element method cantilever beam bending; size effect; geometrically necessary dislocations; crystal plasticity; finite element method

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Husser, E.; Bargmann, S. The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals. Materials 2017, 10, 289.

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