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Title: Towards Using Eshelby Calculations to Enhance Kinetic Model for Zirconium Hydride Precipitation

Abstract

A C++ library (called Eshelby) was implemented in fiscal year 2015 based upon the formulas documented in this report. The library implements a generalized version of Eshelby's inclusion problem. The library was written as a set of functions which can be called from another program; the principle intended use cases are kinetic models of precipitate formation in zirconium claddings where use of the Eshelby library provides needed elastic energy density calculations, as well as calculations of stress and strain in and around precipitates; it is intended that the library will be made open source. For isotropic inclusions in the form of oblate and prolate ellipsoids, the Eshelby library can be used for nearly any relevant/appropriate shape parameters to calculate strains, stresses and energy density at interior and exterior points. The Eshelby library uses a combination of analytical formulas and numerical routines making it very extensible. For example, the library can can easily be extended to include inclusions such as spheres since analytical expressions exist for the required elliptic integrals; similarly, general ellipsoids do not have analytical results for the required elliptic integrals but those integrals can be numerically evaluated and thus fit naturally into the Eshelby library. This report documentsmore » all formulas implemented in the Eshelby library and presents some demonstration calculations relevant to the intended application.« less

Authors:
 [1];  [1];  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Multiscale Science
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Storage and Transportation Technologies
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1504854
Report Number(s):
SAND-2015-8831
607393
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English

Citation Formats

Mitchell, John Anthony, Tikare, Veena, and Weck, Philippe F. Towards Using Eshelby Calculations to Enhance Kinetic Model for Zirconium Hydride Precipitation. United States: N. p., 2015. Web. doi:10.2172/1504854.
Mitchell, John Anthony, Tikare, Veena, & Weck, Philippe F. Towards Using Eshelby Calculations to Enhance Kinetic Model for Zirconium Hydride Precipitation. United States. doi:10.2172/1504854.
Mitchell, John Anthony, Tikare, Veena, and Weck, Philippe F. Thu . "Towards Using Eshelby Calculations to Enhance Kinetic Model for Zirconium Hydride Precipitation". United States. doi:10.2172/1504854. https://www.osti.gov/servlets/purl/1504854.
@article{osti_1504854,
title = {Towards Using Eshelby Calculations to Enhance Kinetic Model for Zirconium Hydride Precipitation},
author = {Mitchell, John Anthony and Tikare, Veena and Weck, Philippe F.},
abstractNote = {A C++ library (called Eshelby) was implemented in fiscal year 2015 based upon the formulas documented in this report. The library implements a generalized version of Eshelby's inclusion problem. The library was written as a set of functions which can be called from another program; the principle intended use cases are kinetic models of precipitate formation in zirconium claddings where use of the Eshelby library provides needed elastic energy density calculations, as well as calculations of stress and strain in and around precipitates; it is intended that the library will be made open source. For isotropic inclusions in the form of oblate and prolate ellipsoids, the Eshelby library can be used for nearly any relevant/appropriate shape parameters to calculate strains, stresses and energy density at interior and exterior points. The Eshelby library uses a combination of analytical formulas and numerical routines making it very extensible. For example, the library can can easily be extended to include inclusions such as spheres since analytical expressions exist for the required elliptic integrals; similarly, general ellipsoids do not have analytical results for the required elliptic integrals but those integrals can be numerically evaluated and thus fit naturally into the Eshelby library. This report documents all formulas implemented in the Eshelby library and presents some demonstration calculations relevant to the intended application.},
doi = {10.2172/1504854},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2015},
month = {10}
}