skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

This content will become publicly available on February 10, 2020

Title: Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields

Abstract

We report that since the 1950s, a large body of work has been published on connecting the curvature of a crystal lattice to geometrically necessary dislocations densities of a crystal lattice. Studying dislocation transmission through grains and across their boundaries requires the lattice curvature to be preserved. However, traditional crystal plasticity models and their numerical implementations do not formally preserve lattice curvature. In this paper, a continuous crystal lattice orientation finite element method (LOFEM) is proposed to rectify this impediment to the inclusion of dislocation-based constitutive models. The methodology is first presented, and then it is demonstrated for tension and compression deformations of a copper polycrystal. It is shown that under the same deformation histories, the lattice continuity constraint alters the evolving state in comparison to the traditional approach, including retarding the rate at which the crystallographic texture strengthens under monotonic deformation. Lastly, taking advantage of the finite element representation of the lattice orientation, the Nye tensor is computed on lattices misoriented by deformation and is subsequently used to compute evolving dislocation density distributions.

Authors:
 [1];  [1]
  1. Cornell Univ., Ithaca, NY (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1497974
Report Number(s):
LLNL-JRNL-757791
Journal ID: ISSN 0022-5096; 945769
Grant/Contract Number:  
AC52-07NA27344; SC0004913
Resource Type:
Accepted Manuscript
Journal Name:
Journal of the Mechanics and Physics of Solids
Additional Journal Information:
Journal Volume: 126; Journal Issue: C; Journal ID: ISSN 0022-5096
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Crystal lattice orientation; Crystal plasticity; Finite elements; Dislocations

Citation Formats

Carson, Robert, and Dawson, Paul. Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields. United States: N. p., 2019. Web. doi:10.1016/j.jmps.2019.02.006.
Carson, Robert, & Dawson, Paul. Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields. United States. doi:10.1016/j.jmps.2019.02.006.
Carson, Robert, and Dawson, Paul. Sun . "Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields". United States. doi:10.1016/j.jmps.2019.02.006.
@article{osti_1497974,
title = {Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields},
author = {Carson, Robert and Dawson, Paul},
abstractNote = {We report that since the 1950s, a large body of work has been published on connecting the curvature of a crystal lattice to geometrically necessary dislocations densities of a crystal lattice. Studying dislocation transmission through grains and across their boundaries requires the lattice curvature to be preserved. However, traditional crystal plasticity models and their numerical implementations do not formally preserve lattice curvature. In this paper, a continuous crystal lattice orientation finite element method (LOFEM) is proposed to rectify this impediment to the inclusion of dislocation-based constitutive models. The methodology is first presented, and then it is demonstrated for tension and compression deformations of a copper polycrystal. It is shown that under the same deformation histories, the lattice continuity constraint alters the evolving state in comparison to the traditional approach, including retarding the rate at which the crystallographic texture strengthens under monotonic deformation. Lastly, taking advantage of the finite element representation of the lattice orientation, the Nye tensor is computed on lattices misoriented by deformation and is subsequently used to compute evolving dislocation density distributions.},
doi = {10.1016/j.jmps.2019.02.006},
journal = {Journal of the Mechanics and Physics of Solids},
number = C,
volume = 126,
place = {United States},
year = {2019},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on February 10, 2020
Publisher's Version of Record

Save / Share: