Courte, Luca and Bhattacharya, Kaushik and Dondl, Patrick (2020) Bounds on precipitate hardening of line and surface defects in solids. Zeitschrift für Angewandte Mathematik und Mechanik, 71 (3). Art. No. 99. ISSN 0044-2275. doi:10.1007/s00033-020-01327-3. https://resolver.caltech.edu/CaltechAUTHORS:20200702-080619417
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Abstract
The yield behavior of crystalline solids is determined by the motion of defects like dislocations, twin boundaries and coherent phase boundaries. These solids are hardened by introducing precipitates—small particles of a second phase. It is generally observed that the motion of line defects like dislocations are strongly inhibited or pinned by precipitates while the motion of surface defects like twin and phase boundaries are minimally affected. In this article, we provide insight into why line defects are more susceptible to the effect of precipitates than surface defects. Based on mathematical models that describe both types of motion, we show that for small concentrations of a nearly periodic arrangement of precipitates, the critical force that is required for a surface defect to overcome a precipitate is smaller than that required for a line defect. In particular, the critical forces for surface and line defects scale with the radius of precipitates to the second and first power, respectively.
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| Additional Information: | © 2020 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Received 24 April 2019; Revised 14 January 2020; Published 03 June 2020. Open Access funding provided by Projekt DEAL. LC and KB acknowledge the support of the Army Research Laboratory under Cooperative Agreement No. W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. The opportunity to conduct this research has been made possible by the SURF program of the California Institute of Technology. PWD acknowledges partial funding by the German Scholars Organization/Carl-Zeiss-Stiftung in the form of the “Wissenschaftler-Rückkehrprogramm”. | ||||||||||
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| Subject Keywords: | Dislocations, Twin boundaries, Evolution of defects, Pinning, Precipitate hardening, Scaling laws, Viscosity solutions | ||||||||||
| Issue or Number: | 3 | ||||||||||
| Classification Code: | MSC: 35D40, 35Q74, 35R11, 35K93, 74C99 | ||||||||||
| DOI: | 10.1007/s00033-020-01327-3 | ||||||||||
| Record Number: | CaltechAUTHORS:20200702-080619417 | ||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200702-080619417 | ||||||||||
| Official Citation: | Courte, L., Bhattacharya, K. & Dondl, P. Bounds on precipitate hardening of line and surface defects in solids. Z. Angew. Math. Phys. 71, 99 (2020). https://doi.org/10.1007/s00033-020-01327-3 | ||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
| ID Code: | 104200 | ||||||||||
| Collection: | CaltechAUTHORS | ||||||||||
| Deposited By: | Tony Diaz | ||||||||||
| Deposited On: | 02 Jul 2020 15:16 | ||||||||||
| Last Modified: | 16 Nov 2021 18:29 |
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