On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms

Lin, Peng; Vivekanandan, Vignesh; Starkey, Kyle; Anglin, Benjamin; Geller, Clint; El-Azab, Anter

doi:10.1016/j.ijplas.2021.102943

Title: On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms

Journal Article · Fri Jan 29 00:00:00 EST 2021 · International Journal of Plasticity

DOI:https://doi.org/10.1016/j.ijplas.2021.102943· OSTI ID:1852411

^[1];

^[1]; Starkey, Kyle ^[1];

^[2];

^[2]; El-Azab, Anter ^[1]

Purdue Univ., West Lafayette, IN (United States)
Naval Nuclear Laboratory, West Mifflin, PA (United States)

Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan's law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test was first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. Finally, the simulations show that dislocations exhibit some self-organized structures as the strain is increased.

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Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; National Science Foundation (NSF); USDOE

Grant/Contract Number:: SC0017718; 1663311

OSTI ID:: 1852411

Alternate ID(s):: OSTI ID: 1784589

Journal Information:: International Journal of Plasticity, Vol. 138, Issue C; ISSN 0749-6419

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (56)

Continuous distribution of moving dislocations Mura, T. Philosophical Magazine, Vol. 8, Issue 89 https://doi.org/10.1080/14786436308213841	journal	May 1963
Implementation of annihilation and junction reactions in vector density-based continuum dislocation dynamics Lin, Peng; El-Azab, Anter Modelling and Simulation in Materials Science and Engineering, Vol. 28, Issue 4 https://doi.org/10.1088/1361-651X/ab7d90	journal	March 2020
Dislocation Mean Free Paths and Strain Hardening of Crystals Devincre, B.; Hoc, T.; Kubin, L. Science, Vol. 320, Issue 5884 https://doi.org/10.1126/science.1156101	journal	June 2008
Revisiting dislocation reactions and their role in uniaxial deformation of copper single crystal micro-pillars Mishra, Ashish; Alankar, Alankar Modelling and Simulation in Materials Science and Engineering, Vol. 27, Issue 5 https://doi.org/10.1088/1361-651X/ab1e09	journal	May 2019
Thermodynamically consistent continuum dislocation dynamics Hochrainer, Thomas Journal of the Mechanics and Physics of Solids, Vol. 88 https://doi.org/10.1016/j.jmps.2015.12.015	journal	March 2016
Dislocation Networks and the Microstructural Origin of Strain Hardening Sills, Ryan B.; Bertin, Nicolas; Aghaei, Amin Physical Review Letters, Vol. 121, Issue 8 https://doi.org/10.1103/PhysRevLett.121.085501	journal	August 2018
Computational modelling of mesoscale dislocation patterning and plastic deformation of single crystals Xia, Shengxu; El-Azab, Anter Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue 5 https://doi.org/10.1088/0965-0393/23/5/055009	journal	May 2015
Numerical implementation of static Field Dislocation Mechanics theory for periodic media Brenner, R.; Beaudoin, A. J.; Suquet, P. Philosophical Magazine, Vol. 94, Issue 16 https://doi.org/10.1080/14786435.2014.896081	journal	March 2014
Coupling the Phase Field Method for diffusive transformations with dislocation density-based crystal plasticity: Application to Ni-based superalloys Cottura, M.; Appolaire, B.; Finel, A. Journal of the Mechanics and Physics of Solids, Vol. 94 https://doi.org/10.1016/j.jmps.2016.05.016	journal	September 2016
Latent hardening in copper and aluminium single crystals Franciosi, P.; Berveiller, M.; Zaoui, A. Acta Metallurgica, Vol. 28, Issue 3 https://doi.org/10.1016/0001-6160(80)90162-5	journal	March 1980
Continuum modeling of dislocation plasticity: Theory, numerical implementation, and validation by discrete dislocation simulations Sandfeld, Stefan; Hochrainer, Thomas; Zaiser, Michael Journal of Materials Research, Vol. 26, Issue 5 https://doi.org/10.1557/jmr.2010.92	journal	March 2011
Constitutive analysis of finite deformation field dislocation mechanics Acharya, Amit Journal of the Mechanics and Physics of Solids, Vol. 52, Issue 2 https://doi.org/10.1016/S0022-5096(03)00093-0	journal	February 2004
Toward a physical model for strain hardening in fcc crystals Kubin, Ladislas; Devincre, Benoit; Hoc, Thierry Materials Science and Engineering: A, Vol. 483-484 https://doi.org/10.1016/j.msea.2007.01.167	journal	June 2008
The Forces Exerted on Dislocations and the Stress Fields Produced by Them Peach, M.; Koehler, J. S. Physical Review, Vol. 80, Issue 3 https://doi.org/10.1103/PhysRev.80.436	journal	November 1950
Dislocation multiplication mechanisms – Glissile junctions and their role on the plastic deformation at the microscale Stricker, Markus; Weygand, Daniel Acta Materialia, Vol. 99 https://doi.org/10.1016/j.actamat.2015.07.073	journal	October 2015
Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part II Roy, A.; Acharya, A. Journal of the Mechanics and Physics of Solids, Vol. 54, Issue 8 https://doi.org/10.1016/j.jmps.2006.01.012	journal	August 2006
Continuum theory of evolving dislocation fields Sedláček, R.; Schwarz, C.; Kratochvíl, J. Philosophical Magazine, Vol. 87, Issue 8-9 https://doi.org/10.1080/14786430600972921	journal	March 2007
A stochastic crystal plasticity model with size-dependent and intermittent strain bursts characteristics at micron scale Lin, Peng; Liu, Zhanli; Cui, Yinan International Journal of Solids and Structures, Vol. 69-70 https://doi.org/10.1016/j.ijsolstr.2015.05.024	journal	September 2015
Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I Acharya, A.; Roy, A. Journal of the Mechanics and Physics of Solids, Vol. 54, Issue 8 https://doi.org/10.1016/j.jmps.2006.01.009	journal	August 2006
Dislocation transport using an explicit Galerkin/least-squares formulation Varadhan, S. N.; Beaudoin, A. J.; Acharya, A. Modelling and Simulation in Materials Science and Engineering, Vol. 14, Issue 7 https://doi.org/10.1088/0965-0393/14/7/011	journal	September 2006
Some geometrical relations in dislocated crystals Nye, J. F. Acta Metallurgica, Vol. 1, Issue 2 https://doi.org/10.1016/0001-6160(53)90054-6	journal	March 1953
Computational 3-dimensional dislocation elastodynamics Cui, Yinan; Po, Giacomo; Pellegrini, Yves-Patrick Journal of the Mechanics and Physics of Solids, Vol. 126 https://doi.org/10.1016/j.jmps.2019.02.008	journal	May 2019
Continuum representation of systems of dislocation lines: A general method for deriving closed-form evolution equations Monavari, Mehran; Sandfeld, Stefan; Zaiser, Michael Journal of the Mechanics and Physics of Solids, Vol. 95 https://doi.org/10.1016/j.jmps.2016.05.009	journal	October 2016
The discrete-continuum connection in dislocation dynamics: I. Time coarse graining of cross slip Xia, Shengxu; Belak, James; El-Azab, Anter Modelling and Simulation in Materials Science and Engineering, Vol. 24, Issue 7 https://doi.org/10.1088/0965-0393/24/7/075007	journal	September 2016
Theoretical and numerical investigations of single arm dislocation source controlled plastic flow in FCC micropillars Cui, Y. N.; Lin, P.; Liu, Z. L. International Journal of Plasticity, Vol. 55 https://doi.org/10.1016/j.ijplas.2013.11.011	journal	April 2014
Continuum dislocation dynamics: Towards a physical theory of crystal plasticity Hochrainer, Thomas; Sandfeld, Stefan; Zaiser, Michael Journal of the Mechanics and Physics of Solids, Vol. 63 https://doi.org/10.1016/j.jmps.2013.09.012	journal	February 2014
A mesoscale continuum approach of dislocation dynamics and the approximation by a Runge-Kutta discontinuous Galerkin method Schulz, Katrin; Wagner, Lydia; Wieners, Christian International Journal of Plasticity, Vol. 120 https://doi.org/10.1016/j.ijplas.2019.05.003	journal	September 2019
A link between microstructure evolution and macroscopic response in elasto-plasticity: Formulation and numerical approximation of the higher-dimensional continuum dislocation dynamics theory Sandfeld, Stefan; Thawinan, Ekkachai; Wieners, Christian International Journal of Plasticity, Vol. 72 https://doi.org/10.1016/j.ijplas.2015.05.001	journal	September 2015
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
Link between the microscopic and mesoscopic length-scale description of the collective behavior of dislocations Groma, I. Physical Review B, Vol. 56, Issue 10 https://doi.org/10.1103/PhysRevB.56.5807	journal	September 1997
A three-dimensional continuum theory of dislocation systems: kinematics and mean-field formulation Hochrainer, T.; Zaiser, M.; Gumbsch, P. Philosophical Magazine, Vol. 87, Issue 8-9 https://doi.org/10.1080/14786430600930218	journal	March 2007
Temporal statistics and coarse graining of dislocation ensembles Deng, Jie; El-Azab, Anter Philosophical Magazine, Vol. 90, Issue 27-28 https://doi.org/10.1080/14786435.2010.497472	journal	September 2010
Non-local crystal plasticity model with intrinsic SSD and GND effects Evers, L. Journal of the Mechanics and Physics of Solids, Vol. 52, Issue 10 https://doi.org/10.1016/j.jmps.2004.03.007	journal	October 2004
Dislocation multiplication in stage II deformation of fcc multi-slip single crystals Stricker, Markus; Sudmanns, Markus; Schulz, Katrin Journal of the Mechanics and Physics of Solids, Vol. 119 https://doi.org/10.1016/j.jmps.2018.07.003	journal	October 2018
Low-strain fatigue in AISI 316L steel surface grains: a three-dimensional discrete dislocation dynamics modelling of the early cycles I. Dislocation microstructures and mechanical behaviour Déprés, C.; Robertson *, C. F.; Fivel, M. C. Philosophical Magazine, Vol. 84, Issue 22 https://doi.org/10.1080/14786430410001690051	journal	August 2004
On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals Arsenlis, A. Journal of the Mechanics and Physics of Solids, Vol. 52, Issue 6 https://doi.org/10.1016/j.jmps.2003.12.007	journal	June 2004
Unravelling the physics of size-dependent dislocation-mediated plasticity El-Awady, Jaafar A. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms6926	journal	January 2015
Dynamical Theory of Dislocations Kosevich, A. M. Soviet Physics Uspekhi, Vol. 7, Issue 6 https://doi.org/10.1070/PU1965v007n06ABEH003688	journal	June 1965
A comparison of a statistical-mechanics based plasticity model with discrete dislocation plasticity calculations Yefimov, S.; Groma, I.; van der Giessen, E. Journal of the Mechanics and Physics of Solids, Vol. 52, Issue 2 https://doi.org/10.1016/S0022-5096(03)00094-2	journal	February 2004
Multiple slip dislocation patterning in a dislocation-based crystal plasticity finite element method Grilli, N.; Janssens, K. G. F.; Nellessen, J. International Journal of Plasticity, Vol. 100 https://doi.org/10.1016/j.ijplas.2017.09.015	journal	January 2018
A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales Liu, Z. L.; Liu, X. M.; Zhuang, Z. International Journal of Plasticity, Vol. 25, Issue 8 https://doi.org/10.1016/j.ijplas.2008.11.006	journal	August 2009
Statistical mechanics treatment of the evolution of dislocation distributions in single crystals El-Azab, A. Physical Review B, Vol. 61, Issue 18 https://doi.org/10.1103/PhysRevB.61.11956	journal	May 2000
Annihilation and sources in continuum dislocation dynamics Monavari, Mehran; Zaiser, Michael Materials Theory, Vol. 2, Issue 1 https://doi.org/10.1186/s41313-018-0010-z	journal	March 2018
Finite element approximation of field dislocation mechanics Roy, A. Journal of the Mechanics and Physics of Solids, Vol. 53, Issue 1 https://doi.org/10.1016/j.jmps.2004.05.007	journal	January 2005
A new dislocation-density-function dynamics scheme for computational crystal plasticity by explicit consideration of dislocation elastic interactions Leung, H. S.; Leung, P. S. S.; Cheng, B. International Journal of Plasticity, Vol. 67 https://doi.org/10.1016/j.ijplas.2014.09.009	journal	April 2015
Numerical study of the size-dependent deformation morphology in micropillar compressions by a dislocation-based crystal plasticity model Lin, Peng; Liu, Zhanli; Zhuang, Zhuo International Journal of Plasticity, Vol. 87 https://doi.org/10.1016/j.ijplas.2016.09.001	journal	December 2016
Multipole expansion of continuum dislocations dynamics in terms of alignment tensors Hochrainer, T. Philosophical Magazine, Vol. 95, Issue 12 https://doi.org/10.1080/14786435.2015.1026297	journal	March 2013
Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations Zaiser, M.; Miguel, M. -Carmen; Groma, I. Physical Review B, Vol. 64, Issue 22 https://doi.org/10.1103/PhysRevB.64.224102	journal	November 2001
Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics Groma, I.; Csikor, F. F.; Zaiser, M. Acta Materialia, Vol. 51, Issue 5 https://doi.org/10.1016/S1359-6454(02)00517-7	journal	March 2003
Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity Sudmanns, Markus; Stricker, Markus; Weygand, Daniel Journal of the Mechanics and Physics of Solids, Vol. 132 https://doi.org/10.1016/j.jmps.2019.103695	journal	November 2019
Collective behaviour of dislocations in a finite medium Kooiman, M.; Hütter, M.; Geers, M. G. D. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2014, Issue 4 https://doi.org/10.1088/1742-5468/2014/04/P04028	journal	April 2014
Physical analyses of crystal plasticity by DD simulations Devincre, B.; Kubin, L.; Hoc, T. Scripta Materialia, Vol. 54, Issue 5 https://doi.org/10.1016/j.scriptamat.2005.10.066	journal	March 2006
Gradient single-crystal plasticity with free energy dependent on dislocation densities Gurtin, Morton E.; Anand, Lallit; Lele, Suvrat P. Journal of the Mechanics and Physics of Solids, Vol. 55, Issue 9 https://doi.org/10.1016/j.jmps.2007.02.006	journal	September 2007
Numerical investigations of helical dislocations based on coupled glide-climb model Liu, Fengxian; Liu, Zhan-li; Lin, Peng International Journal of Plasticity, Vol. 92 https://doi.org/10.1016/j.ijplas.2017.02.015	journal	May 2017
Pattern formation in a minimal model of continuum dislocation plasticity Sandfeld, Stefan; Zaiser, Michael Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue 6 https://doi.org/10.1088/0965-0393/23/6/065005	journal	July 2015
Numerical implementation of static Field Dislocation Mechanics theory for periodic media Brenner, R.; Beaudoin, A. J.; Suquet, P. Carnegie Mellon University https://doi.org/10.1184/r1/6466379.v1	text	January 2014

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Title: On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms

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