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

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 bend...

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Autores principales: Husser, Edgar, Bargmann, Swantje
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5503410/
https://www.ncbi.nlm.nih.gov/pubmed/28772657
http://dx.doi.org/10.3390/ma10030289
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author Husser, Edgar
Bargmann, Swantje
author_facet Husser, Edgar
Bargmann, Swantje
author_sort Husser, Edgar
collection PubMed
description 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.
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spelling pubmed-55034102017-07-28 The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals Husser, Edgar Bargmann, Swantje Materials (Basel) Article 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. MDPI 2017-03-16 /pmc/articles/PMC5503410/ /pubmed/28772657 http://dx.doi.org/10.3390/ma10030289 Text en © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Husser, Edgar
Bargmann, Swantje
The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals
title The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals
title_full The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals
title_fullStr The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals
title_full_unstemmed The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals
title_short The Role of Geometrically Necessary Dislocations in Cantilever Beam Bending Experiments of Single Crystals
title_sort role of geometrically necessary dislocations in cantilever beam bending experiments of single crystals
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5503410/
https://www.ncbi.nlm.nih.gov/pubmed/28772657
http://dx.doi.org/10.3390/ma10030289
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