Non-orthogonal computational grids for studying dislocation motion in phase field approaches

Peng, Xiaoyao; Hunter, Abigail; Beyerlein, Irene J.; Lebensohn, Ricardo A.; Dayal, Kaushik; Martinez, Enrique

doi:10.1016/j.commatsci.2021.110834

Non-orthogonal computational grids for studying dislocation motion in phase field approaches

Journal Article · Mon Sep 06 00:00:00 EDT 2021 · Computational Materials Science

DOI:https://doi.org/10.1016/j.commatsci.2021.110834· OSTI ID:1834531

^[1]; Hunter, Abigail ^[1]; ^[2]; Lebensohn, Ricardo A. ^[1]; ^[3]; ^[4]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of California, Santa Barbara, CA (United States)
Carnegie Mellon Univ., Pittsburgh, PA (United States)
Clemson Univ., SC (United States)

In this work, new non-orthogonal computational grids are implemented into a phase field model called Phase Field Dislocation Dynamics (PFDD). We demonstrate that the new non-orthogonal grid can accommodate multiple slip planes in either the face centered cubic (FCC) or body centered cubic (BCC) crystallographic systems. Here, we show that they avoid numerical errors induced when modeling glide on inclined slip planes in an orthogonal grid. The Gibbs effect that arises in the orthogonal or rotated orthogonal grids is substantially diminished when a non-orthogonal grid is employed. A few test cases demonstrate the effectiveness of using non-orthogonal grids in solving systems with multiple non-planar slip systems.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: Clemson University; National Science Foundation (NSF); US Department of the Navy, Office of Naval Research (ONR); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1834531

Report Number(s):: LA-UR--21-25715

Journal Information:: Computational Materials Science, Journal Name: Computational Materials Science Vol. 200; ISSN 0927-0256

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (45)

The Gibbs-Wilbraham phenomenon: An episode in fourier analysis Hewitt, Edwin; Hewitt, Robert E. Archive for History of Exact Sciences, Vol. 21, Issue 2 https://doi.org/10.1007/BF00330404	journal	January 1979
An approximate analytical 2D-solution for the stresses and strains in eigenstrained cubic materials Dreyer, W.; M�ller, W. H.; Olschewski, J. Acta Mechanica, Vol. 136, Issue 3-4 https://doi.org/10.1007/BF01179256	journal	September 1999
A phase-field theory of dislocation dynamics, strain hardening and hysteresis in ductile single crystals Koslowski, M.; Cuitiño, A. M.; Ortiz, M. Journal of the Mechanics and Physics of Solids, Vol. 50, Issue 12 https://doi.org/10.1016/S0022-5096(02)00037-6	journal	December 2002
A numerical method for computing the overall response of nonlinear composites with complex microstructure Moulinec, H.; Suquet, P. Computer Methods in Applied Mechanics and Engineering, Vol. 157, Issue 1-2 https://doi.org/10.1016/S0045-7825(97)00218-1	journal	April 1998
Physics and phenomenology of strain hardening: the FCC case Kocks, U. F.; Mecking, H. Progress in Materials Science, Vol. 48, Issue 3 https://doi.org/10.1016/S0079-6425(02)00003-8	journal	January 2003
Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations Wang, Y. U.; Jin, Y. M.; Cuitiño, A. M. Acta Materialia, Vol. 49, Issue 10 https://doi.org/10.1016/S1359-6454(01)00075-1	journal	June 2001
Length scale and time scale effects on the plastic flow of fcc metals Horstemeyer, M. F.; Baskes, M. I.; Plimpton, S. J. Acta Materialia, Vol. 49, Issue 20 https://doi.org/10.1016/S1359-6454(01)00149-5	journal	December 2001
Phase field methods and dislocations Rodney, D.; Le Bouar, Y.; Finel, A. Acta Materialia, Vol. 51, Issue 1 https://doi.org/10.1016/S1359-6454(01)00379-2	journal	January 2003
Phase field model of dislocation networks Shen, C.; Wang, Y. Acta Materialia, Vol. 51, Issue 9 https://doi.org/10.1016/S1359-6454(03)00058-2	journal	May 2003
Incorporation of γ-surface to phase field model of dislocations: simulating dislocation dissociation in fcc crystals Shen, C.; Wang, Y. Acta Materialia, Vol. 52, Issue 3 https://doi.org/10.1016/j.actamat.2003.10.014	journal	February 2004
Nucleation and propagation of dislocations in nanocrystalline fcc metals Van Swygenhoven, H.; Derlet, P. M.; Frøseth, A. G. Acta Materialia, Vol. 54, Issue 7 https://doi.org/10.1016/j.actamat.2005.12.026	journal	April 2006
Phase field modeling of defects and deformation Wang, Yunzhi; Li, Ju Acta Materialia, Vol. 58, Issue 4 https://doi.org/10.1016/j.actamat.2009.10.041	journal	February 2010
Effect of microstructural uncertainty on the yield stress of nanocrystalline nickel Cao, Lei; Koslowski, Marisol Acta Materialia, Vol. 61, Issue 4 https://doi.org/10.1016/j.actamat.2012.11.018	journal	February 2013
Relationship between monolayer stacking faults and twins in nanocrystals Hunter, A.; Beyerlein, I. J. Acta Materialia, Vol. 88 https://doi.org/10.1016/j.actamat.2014.12.045	journal	April 2015
Effects of the stacking fault energy fluctuations on the strengthening of alloys Zeng, Yifei; Cai, Xiaorong; Koslowski, Marisol Acta Materialia, Vol. 164 https://doi.org/10.1016/j.actamat.2018.09.066	journal	February 2019
A dislocation density based constitutive law for BCC materials in crystal plasticity FEM Ma, A.; Roters, F.; Raabe, D. Computational Materials Science, Vol. 39, Issue 1 https://doi.org/10.1016/j.commatsci.2006.04.014	journal	March 2007
FFT-based methods for the mechanics of composites: A general variational framework Brisard, S.; Dormieux, L. Computational Materials Science, Vol. 49, Issue 3 https://doi.org/10.1016/j.commatsci.2010.06.009	journal	September 2010
A 3D phase field dislocation dynamics model for body-centered cubic crystals Peng, Xiaoyao; Mathew, Nithin; Beyerlein, Irene J. Computational Materials Science, Vol. 171 https://doi.org/10.1016/j.commatsci.2019.109217	journal	January 2020
Spectral methods for full-field micromechanical modelling of polycrystalline materials Lebensohn, Ricardo A.; Rollett, Anthony D. Computational Materials Science, Vol. 173 https://doi.org/10.1016/j.commatsci.2019.109336	journal	February 2020
Spectral discrete dislocation dynamics with anisotropic short range interactions Kohnert, Aaron A.; Capolungo, Laurent Computational Materials Science, Vol. 189 https://doi.org/10.1016/j.commatsci.2020.110243	journal	March 2021
Fourier-based schemes for computing the mechanical response of composites with accurate local fields Willot, François Comptes Rendus Mécanique, Vol. 343, Issue 3 https://doi.org/10.1016/j.crme.2014.12.005	journal	March 2015
A phase field dislocation dynamics model for a bicrystal interface system: An investigation into dislocation slip transmission across cube-on-cube interfaces Zeng, Y.; Hunter, A.; Beyerlein, I. J. International Journal of Plasticity, Vol. 79 https://doi.org/10.1016/j.ijplas.2015.09.001	journal	April 2016
Development of a new consistent discrete green operator for FFT-based methods to solve heterogeneous problems with eigenstrains Eloh, Komlavi Sényo; Jacques, Alain; Berbenni, Stéphane International Journal of Plasticity, Vol. 116 https://doi.org/10.1016/j.ijplas.2018.10.011	journal	May 2019
The effect of local chemical ordering on Frank-Read source activation in a refractory multi-principal element alloy Smith, Lauren T. W.; Su, Yanqing; Xu, Shuozhi International Journal of Plasticity, Vol. 134 https://doi.org/10.1016/j.ijplas.2020.102850	journal	November 2020
Stress-dependence of dislocation dissociation, nucleation and annihilation in elastically anisotropic Cu He, Tengwu; Ji, Yanzhou; Qi, Yuming International Journal of Plasticity, Vol. 138 https://doi.org/10.1016/j.ijplas.2021.102927	journal	March 2021
A FFT-based formulation for discrete dislocation dynamics in heterogeneous media Bertin, N.; Capolungo, L. Journal of Computational Physics, Vol. 355 https://doi.org/10.1016/j.jcp.2017.11.020	journal	February 2018
Atomistically determined phase-field modeling of dislocation dissociation, stacking fault formation, dislocation slip, and reactions in fcc systems Rezaei Mianroodi, Jaber; Svendsen, Bob Journal of the Mechanics and Physics of Solids, Vol. 77 https://doi.org/10.1016/j.jmps.2015.01.007	journal	April 2015
The role of partial mediated slip during quasi-static deformation of 3D nanocrystalline metals Cao, Lei; Hunter, Abigail; Beyerlein, Irene J. Journal of the Mechanics and Physics of Solids, Vol. 78 https://doi.org/10.1016/j.jmps.2015.02.019	journal	May 2015
Three-dimensional phase-field model of dislocations for a heterogeneous face-centered cubic crystal Ruffini, Antoine; Le Bouar, Yann; Finel, Alphonse Journal of the Mechanics and Physics of Solids, Vol. 105 https://doi.org/10.1016/j.jmps.2017.04.008	journal	August 2017
A phase field model for dislocations in hexagonal close packed crystals Albrecht, C.; Hunter, A.; Kumar, A. Journal of the Mechanics and Physics of Solids, Vol. 137 https://doi.org/10.1016/j.jmps.2019.103823	journal	April 2020
Modeling dislocations with arbitrary character angle in face-centered cubic transition metals using the phase-field dislocation dynamics method with full anisotropic elasticity Xu, Shuozhi; Su, Yanqing; Beyerlein, Irene J. Mechanics of Materials, Vol. 139 https://doi.org/10.1016/j.mechmat.2019.103200	journal	December 2019
Stacking fault emission from grain boundaries: Material dependencies and grain size effects Hunter, A.; Beyerlein, I. J. Materials Science and Engineering: A, Vol. 600 https://doi.org/10.1016/j.msea.2014.02.030	journal	April 2014
Shock deformation of face-centred-cubic metals on subnanosecond timescales Bringa, E. M.; Rosolankova, K.; Rudd, R. E. Nature Materials, Vol. 5, Issue 10 https://doi.org/10.1038/nmat1735	journal	September 2006
Improved phase field model of dislocation intersections Zheng, Songlin; Zheng, Dongchang; Ni, Yong npj Computational Materials, Vol. 4, Issue 1 https://doi.org/10.1038/s41524-018-0075-x	journal	April 2018
The core structure, recombination energy and Peierls energy for dislocations in Al Schoeck, Gunther Philosophical Magazine A, Vol. 81, Issue 5 https://doi.org/10.1080/01418610108214434	journal	May 2001
The generalized Peierls–Nabarro model Schoeck, G. Philosophical Magazine A, Vol. 69, Issue 6 https://doi.org/10.1080/01418619408242240	journal	June 1994
A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics Bertin, N.; Upadhyay, M. V.; Pradalier, C. Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue 6 https://doi.org/10.1088/0965-0393/23/6/065009	journal	August 2015
Fast Fourier transform discrete dislocation dynamics Graham, J. T.; Rollett, A. D.; LeSar, R. Modelling and Simulation in Materials Science and Engineering, Vol. 24, Issue 8 https://doi.org/10.1088/0965-0393/24/8/085005	journal	October 2016
Effect of texture and grain size on the residual stress of nanocrystalline thin films Cao, Lei; Sengupta, Arkaprabha; Pantuso, Daniel Modelling and Simulation in Materials Science and Engineering, Vol. 25, Issue 7 https://doi.org/10.1088/1361-651X/aa80fb	journal	August 2017
A comparison of different continuum approaches in modeling mixed-type dislocations in Al Xu, Shuozhi; Smith, Lauren; Mianroodi, Jaber R. Modelling and Simulation in Materials Science and Engineering, Vol. 27, Issue 7 https://doi.org/10.1088/1361-651X/ab2d16	journal	July 2019
Understanding dislocation mechanics at the mesoscale using phase field dislocation dynamics Beyerlein, I. J.; Hunter, A. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 374, Issue 2066 https://doi.org/10.1098/rsta.2015.0166	journal	April 2016
Atomic-scale simulations of the mechanical deformation of nanocrystalline metals Schiøtz, J.; Vegge, T.; Di Tolla, F. D. Physical Review B, Vol. 60, Issue 17 https://doi.org/10.1103/PhysRevB.60.11971	journal	November 1999
Semidiscrete Variational Peierls Framework for Dislocation Core Properties Bulatov, Vasily V.; Kaxiras, Efthimios Physical Review Letters, Vol. 78, Issue 22 https://doi.org/10.1103/PhysRevLett.78.4221	journal	June 1997
The Design and Implementation of FFTW3 Frigo, M.; Johnson, S. G. Proceedings of the IEEE, Vol. 93, Issue 2 https://doi.org/10.1109/JPROC.2004.840301	journal	February 2005
The Role of Collinear Interaction in Dislocation-Induced Hardening Madec, R. Science, Vol. 301, Issue 5641 https://doi.org/10.1126/science.1085477	journal	September 2003

Similar Records

Phase-field dislocation modeling of cross-slip

Journal Article · Sun Jan 02 19:00:00 EST 2022 · Journal of Materials Science · OSTI ID:1840885

Phase field dislocation dynamics (PFDD) modeling of non-Schmid behavior in BCC metals informed by atomistic simulations

Journal Article · Fri Apr 23 20:00:00 EDT 2021 · Journal of the Mechanics and Physics of Solids · OSTI ID:1781381

Phase-field modeling of the interactions between an edge dislocation and an array of obstacles

Journal Article · Thu Dec 23 19:00:00 EST 2021 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:1976973

Related Subjects

36 MATERIALS SCIENCE
FFT method
Non-orthogonal grids
Non-planar slip
Phase field model

Non-orthogonal computational grids for studying dislocation motion in phase field approaches

Citation Formats

References (45)

Similar Records

Related Subjects