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 November 18, 2020

Title: Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals

Abstract

The accuracy of the stresses predicted from crystal plasticity-based finite element formulation depends on estimation and control of the errors associated with the discretization. In the current work, the errors in the stress distribution are estimated in virtual polycrystalline samples of α-phase titanium (hexagonal close-packed phase of Ti–6Al–4V). To estimate the error, the stress field, which does not possess inter-element continuity, is smoothed over a grain using an L 2 projection, thereby providing continuous stress distributions with inter-element continuity. The differences between the continuous (smooth) and discontinuous (raw) stress fields are calculated at individual Gauss quadrature points and used to estimate errors for corresponding elements and grains. Error estimations are performed for a Voronoi-tessellated microstructure, an equiaxed microstructure, and two microstructures with varying grain sizes for tensile loading extending into the fully plastic regime (≈ 5% extension). Magnitudes of the errors are found to depend on microstructural characteristics, particularly the shape and size of grains. Samples having variations in grain size or having less spherical grains exhibited higher errors than samples with uniformly sized, equiaxed grains, with the size variations having a more pronounced effect. In conclusion, errors correlate with proximity to grain boundaries at small (elastic) strains and withmore » deformation-induced features (deformation bands) at large strains.« less

Authors:
 [1];  [1]; ORCiD logo [1]
  1. Cornell Univ., Ithaca, NY (United States). Sibley School of Mechanical and Aerospace Engineering
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1575866
Report Number(s):
LLNL-JRNL-787804
Journal ID: ISSN 2193-9764; 985546
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Integrating Materials and Manufacturing Innovation
Additional Journal Information:
Journal Name: Integrating Materials and Manufacturing Innovation; Journal ID: ISSN 2193-9764
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; Crystal plasticity; Virtual polycrystals; Stress distributions; Finite elements; Error estimation

Citation Formats

Chatterjee, Kamalika, Carson, Robert A., and Dawson, Paul R. Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals. United States: N. p., 2019. Web. doi:10.1007/s40192-019-00158-z.
Chatterjee, Kamalika, Carson, Robert A., & Dawson, Paul R. Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals. United States. doi:10.1007/s40192-019-00158-z.
Chatterjee, Kamalika, Carson, Robert A., and Dawson, Paul R. Mon . "Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals". United States. doi:10.1007/s40192-019-00158-z.
@article{osti_1575866,
title = {Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals},
author = {Chatterjee, Kamalika and Carson, Robert A. and Dawson, Paul R.},
abstractNote = {The accuracy of the stresses predicted from crystal plasticity-based finite element formulation depends on estimation and control of the errors associated with the discretization. In the current work, the errors in the stress distribution are estimated in virtual polycrystalline samples of α-phase titanium (hexagonal close-packed phase of Ti–6Al–4V). To estimate the error, the stress field, which does not possess inter-element continuity, is smoothed over a grain using an L2 projection, thereby providing continuous stress distributions with inter-element continuity. The differences between the continuous (smooth) and discontinuous (raw) stress fields are calculated at individual Gauss quadrature points and used to estimate errors for corresponding elements and grains. Error estimations are performed for a Voronoi-tessellated microstructure, an equiaxed microstructure, and two microstructures with varying grain sizes for tensile loading extending into the fully plastic regime (≈ 5% extension). Magnitudes of the errors are found to depend on microstructural characteristics, particularly the shape and size of grains. Samples having variations in grain size or having less spherical grains exhibited higher errors than samples with uniformly sized, equiaxed grains, with the size variations having a more pronounced effect. In conclusion, errors correlate with proximity to grain boundaries at small (elastic) strains and with deformation-induced features (deformation bands) at large strains.},
doi = {10.1007/s40192-019-00158-z},
journal = {Integrating Materials and Manufacturing Innovation},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on November 18, 2020
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Hexahedral Mesh Generation for Computational Materials Modeling
journal, January 2017


Investigating the limits of polycrystal plasticity modeling
journal, February 2005


An optimal control approach to a posteriori error estimation in finite element methods
journal, May 2001


Determining the strengths of HCP slip systems using harmonic analyses of lattice strain distributions
journal, February 2018


The influence of mechanical constraints introduced by β annealed microstructures on the yield strength and ductility of Ti-6Al-4V
journal, June 2017

  • Kasemer, Matthew; Quey, Romain; Dawson, Paul
  • Journal of the Mechanics and Physics of Solids, Vol. 103
  • DOI: 10.1016/j.jmps.2017.03.013

The Proof and Measurement of Association between Two Things
journal, January 1904

  • Spearman, C.
  • The American Journal of Psychology, Vol. 15, Issue 1
  • DOI: 10.2307/1412159

Sensitivity of Crystal Stress Distributions to the Definition of Virtual Two-Phase Samples
journal, January 2019

  • Poshadel, Andrew C.; Gharghouri, Michael A.; Dawson, Paul R.
  • Metallurgical and Materials Transactions A, Vol. 50, Issue 3
  • DOI: 10.1007/s11661-018-5085-2

On slip initiation in equiaxed α/β Ti-6Al-4V
journal, September 2017


A posteriori error estimation in finite element analysis
journal, March 1997

  • Ainsworth, Mark; Oden, J. Tinsley
  • Computer Methods in Applied Mechanics and Engineering, Vol. 142, Issue 1-2
  • DOI: 10.1016/S0045-7825(96)01107-3

Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing
journal, April 2011

  • Quey, R.; Dawson, P. R.; Barbe, F.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 17-20
  • DOI: 10.1016/j.cma.2011.01.002

Adaptive mesh refinement and automatic remeshing in crystal plasticity finite element simulations
journal, August 2009

  • Resk, H.; Delannay, L.; Bernacki, M.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 17, Issue 7
  • DOI: 10.1088/0965-0393/17/7/075012

Topology-faithful nonparametric estimation and tracking of bulk interface networks
journal, December 2016


A simple error estimator and adaptive procedure for practical engineerng analysis
journal, February 1987

  • Zienkiewicz, O. C.; Zhu, J. Z.
  • International Journal for Numerical Methods in Engineering, Vol. 24, Issue 2
  • DOI: 10.1002/nme.1620240206

Prediction of tensile stiffness and strength of Ti-6Al-4V using instantiated volume elements and crystal plasticity
journal, September 2018


A posteriori error estimation techniques in practical finite element analysis
journal, January 2005


Optimal polyhedral description of 3D polycrystals: Method and application to statistical and synchrotron X-ray diffraction data
journal, March 2018

  • Quey, Romain; Renversade, Loïc
  • Computer Methods in Applied Mechanics and Engineering, Vol. 330
  • DOI: 10.1016/j.cma.2017.10.029