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:
-
- 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
- Alternate Identifier(s):
- OSTI ID: 1547765
- 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. https://doi.org/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. https://doi.org/10.1016/j.jmps.2019.02.006. https://www.osti.gov/servlets/purl/1497974.
@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 = {Sun Feb 10 00:00:00 EST 2019},
month = {Sun Feb 10 00:00:00 EST 2019}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 3 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
On the effects of reorientation and shear transfer during twin formation: Comparison between high resolution electron backscatter diffraction experiments and a crystal plasticity finite element model
journal, September 2016
- Abdolvand, Hamidreza; Wilkinson, Angus J.
- International Journal of Plasticity, Vol. 84
A model of crystal plasticity based on the theory of continuously distributed dislocations
journal, April 2001
- Acharya, Amit
- Journal of the Mechanics and Physics of Solids, Vol. 49, Issue 4
Constitutive analysis of finite deformation field dislocation mechanics
journal, February 2004
- Acharya, Amit
- Journal of the Mechanics and Physics of Solids, Vol. 52, Issue 2
Grain-size effect in viscoplastic polycrystals at moderate strains
journal, October 2000
- Acharya, A.; Beaudoin, A. J.
- Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 10
Overview of fatigue performance of Cu processed by severe plastic deformation
journal, September 1999
- Agnew, S. R.; Vinogradov, A. Yu.; Hashimoto, S.
- Journal of Electronic Materials, Vol. 28, Issue 9
Vacancy dipoles in fatigued copper
journal, October 1976
- Antonopoulos, J. G.; Brown, L. M.; Winter, A. T.
- The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, Vol. 34, Issue 4
Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density
journal, March 1999
- Arsenlis, A.; Parks, D. M.
- Acta Materialia, Vol. 47, Issue 5
Review on slip transmission criteria in experiments and crystal plasticity models
journal, November 2015
- Bayerschen, E.; McBride, A. T.; Reddy, B. D.
- Journal of Materials Science, Vol. 51, Issue 5
The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals
journal, September 2009
- Bieler, T. R.; Eisenlohr, P.; Roters, F.
- International Journal of Plasticity, Vol. 25, Issue 9
Characterizing heterogeneous intragranular deformations in polycrystalline solids using diffraction-based and mechanics-based metrics
journal, May 2017
- Carson, Robert; Obstalecki, Mark; Miller, Matthew
- Modelling and Simulation in Materials Science and Engineering, Vol. 25, Issue 5
The missing term in the decomposition of finite deformation
journal, January 2014
- Clayton, J. D.; Hartley, C. S.; McDowell, D. L.
- International Journal of Plasticity, Vol. 52
A model of extrusions and intrusions in fatigued metals I. Point-defect production and the growth of extrusions
journal, August 1981
- Essmann, U.; Gösele, U.; Mughrabi, H.
- Philosophical Magazine A, Vol. 44, Issue 2
A crystal plasticity model that incorporates stresses and strains due to slip gradients
journal, April 2008
- Gerken, J.; Dawson, P.
- Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 4
Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation
journal, January 2016
- Gottschalk, D.; McBride, A.; Reddy, B. D.
- Computational Materials Science, Vol. 111
Slip band–grain boundary interactions in commercial-purity titanium
journal, September 2014
- Guo, Y.; Britton, T. B.; Wilkinson, A. J.
- Acta Materialia, Vol. 76
A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations
journal, January 2002
- Gurtin, Morton E.
- Journal of the Mechanics and Physics of Solids, Vol. 50, Issue 1
The finite deformation of rate-dependent polycrystals—II: A comparison of the self-consistent and Taylor methods
journal, January 1991
- Harren, S. V.
- Journal of the Mechanics and Physics of Solids, Vol. 39, Issue 3
Measurement of geometrically necessary dislocation density with high resolution electron backscatter diffraction: Effects of detector binning and step size
journal, February 2013
- Jiang, J.; Britton, T. B.; Wilkinson, A. J.
- Ultramicroscopy, Vol. 125
Assessment of geometrically necessary dislocation levels derived by 3D EBSD
journal, October 2015
- Konijnenberg, P. J.; Zaefferer, S.; Raabe, D.
- Acta Materialia, Vol. 99
Modeling crystallographic texture evolution with finite elements over neo-Eulerian orientation spaces
journal, January 1998
- Kumar, Ashish; Dawson, Paul R.
- Computer Methods in Applied Mechanics and Engineering, Vol. 153, Issue 3-4
Experimental lower bounds on geometrically necessary dislocation density
journal, August 2010
- Kysar, J. W.; Saito, Y.; Oztop, M. S.
- International Journal of Plasticity, Vol. 26, Issue 8
A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations
journal, May 2006
- Ma, A.; Roters, F.; Raabe, D.
- Acta Materialia, Vol. 54, Issue 8
Extrusions and intrusions in fatigued metals. Part 1. State of the art and history†
journal, June 2009
- Man, J.; Obrtlík, K.; Polák, J.
- Philosophical Magazine, Vol. 89, Issue 16
On modelling the elasto-viscoplastic response of metals using polycrystal plasticity
journal, November 1998
- Marin, E. B.; Dawson, P. R.
- Computer Methods in Applied Mechanics and Engineering, Vol. 165, Issue 1-4
The cyclic hardening and saturation behaviour of copper single crystals
journal, May 1978
- Mughrabi, H.
- Materials Science and Engineering, Vol. 33, Issue 2
Some geometrical relations in dislocated crystals
journal, March 1953
- Nye, J. F.
- Acta Metallurgica, Vol. 1, Issue 2
Connecting heterogeneous single slip to diffraction peak evolution in high-energy monochromatic X-ray experiments
journal, May 2014
- Pagan, Darren C.; Miller, Matthew P.
- Journal of Applied Crystallography, Vol. 47, Issue 3
Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction
journal, June 2008
- Pantleon, W.
- Scripta Materialia, Vol. 58, Issue 11
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
Intra-grain orientation distributions in hot-deformed aluminium: Orientation dependence and relation to deformation mechanisms
journal, November 2015
- Quey, R.; Driver, J. H.; Dawson, P. R.
- Journal of the Mechanics and Physics of Solids, Vol. 84
Microtexture tracking in hot-deformed polycrystalline aluminium: Comparison with simulations
journal, April 2010
- Quey, R.; Piot, D.; Driver, J. H.
- Acta Materialia, Vol. 58, Issue 6
Finite element approximation of field dislocation mechanics
journal, January 2005
- Roy, A.
- Journal of the Mechanics and Physics of Solids, Vol. 53, Issue 1
Texture predictions using a polycrystal plasticity model incorporating neighbor interactions
journal, January 1996
- Sarma, Gorti B.; Dawson, Paul R.
- International Journal of Plasticity, Vol. 12, Issue 8
Stress and deformation heterogeneity in individual grains within polycrystals subjected to fully reversed cyclic loading
journal, June 2015
- Wong, Su Leen; Obstalecki, Mark; Miller, Matthew P.
- Journal of the Mechanics and Physics of Solids, Vol. 79
Works referencing / citing this record:
Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals
journal, November 2019
- Chatterjee, Kamalika; Carson, Robert A.; Dawson, Paul R.
- Integrating Materials and Manufacturing Innovation, Vol. 8, Issue 4