A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals

Berbenni, Stéphane; Taupin, Vincent; Lebensohn, Ricardo A.

doi:10.1016/j.jmps.2019.103808

Title: A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals

Journal Article · Sat Nov 30 00:00:00 EST 2019 · Journal of the Mechanics and Physics of Solids

DOI:https://doi.org/10.1016/j.jmps.2019.103808· OSTI ID:1578028

Berbenni, Stéphane ^[1]; Taupin, Vincent ^[1];

^[2]

Univ. de Lorraine, Metz (France); Univ. de Lorraine, Lorraine (France)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

A numerical implementation of a non-local polycrystal plasticity theory based on a mesoscale version of the field dislocation mechanics theory (MFDM) of Acharya and Roy (2006) is presented using small-strain elasto-viscoplastic fast Fourier transform-based (EVPFFT) algorithm developed by Lebensohn et al. (2012). In addition to considering plastic flow and hardening only due to SSDs (statistically stored dislocations) as in the classic EVPFFT framework, the proposed method accounts for the evolution of GND (geometrically necessary dislocations) densities solving a hyperbolic-type partial differential equation, and GND effects on both plastic flow and hardening. This allows consideration of an enhanced strain-hardening law that includes the effect of the GND density tensor. The numerical implementation of a reduced version of the MFDM is presented in the framework of the FFT-based augmented Lagrangian procedure of Michel et al. (2001). A Finite Differences scheme combined with discrete Fourier transforms is applied to solve both incompatibility and equilibrium equations. The numerical procedure named MFDM-EVPFFT is used to perform full field simulations of polycrystal plasticity considering different grain sizes and their mechanical responses during monotonic tensile and reversible tension-compression tests. Using Voronoi tessellation and periodic boundary conditions, voxelized representative volume elements (RVEs) with different grain sizes are generated. With MFDM-EVPFFT, a Hall-Petch type scaling law is obtained in contrast with the conventional crystal plasticity EVPFFT. In the case of reversible plasticity, a stronger Bauschinger effect is observed with the MFDM-EVPFFT approach in comparison with conventional EVPFFT. Here, the origin of these differences is analyzed in terms of heterogeneity, GND density and stress evolutions during the compression stage.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

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

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1578028

Alternate ID(s):: OSTI ID: 1776109

Report Number(s):: LA-UR-19-31410

Journal Information:: Journal of the Mechanics and Physics of Solids, Vol. 135, Issue C; ISSN 0022-5096

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 33 works

Citation information provided by
Web of Science

References (144)

A model of crystal plasticity based on the theory of continuously distributed dislocations Acharya, Amit Journal of the Mechanics and Physics of Solids, Vol. 49, Issue 4 https://doi.org/10.1016/S0022-5096(00)00060-0	journal	April 2001
Driving forces and boundary conditions in continuum dislocation mechanics Acharya, Amit Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 459, Issue 2034 https://doi.org/10.1098/rspa.2002.1095	journal	June 2003
Jump condition for GND evolution as a constraint on slip transmission at grain boundaries Acharya, A. Philosophical Magazine, Vol. 87, Issue 8-9 https://doi.org/10.1080/14786430600951537	journal	March 2007
Microcanonical Entropy and Mesoscale Dislocation Mechanics and Plasticity Acharya, Amit Journal of Elasticity, Vol. 104, Issue 1-2 https://doi.org/10.1007/s10659-011-9328-3	journal	March 2011
Lattice incompatibility and a gradient theory of crystal plasticity Acharya, A. Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 8 https://doi.org/10.1016/S0022-5096(99)00075-7	journal	August 2000
Grain-size effect in viscoplastic polycrystals at moderate strains Acharya, A.; Beaudoin, A. J. Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 10 https://doi.org/10.1016/S0022-5096(00)00013-2	journal	October 2000
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
Continuum theory and methods for coarse-grained, mesoscopic plasticity Acharya, Amit; Roy, Anish; Sawant, Aarti Scripta Materialia, Vol. 54, Issue 5 https://doi.org/10.1016/j.scriptamat.2005.10.070	journal	March 2006
A study of the heterogeneity of plastic deformation in IF steel by EBSD Allain-Bonasso, Nathalie; Wagner, Francis; Berbenni, Stéphane Materials Science and Engineering: A, Vol. 548 https://doi.org/10.1016/j.msea.2012.03.068	journal	June 2012
Validation of a numerical method based on Fast Fourier Transforms for heterogeneous thermoelastic materials by comparison with analytical solutions Anglin, B. S.; Lebensohn, R. A.; Rollett, A. D. Computational Materials Science, Vol. 87 https://doi.org/10.1016/j.commatsci.2014.02.027	journal	May 2014
The plastic deformation of polycrystalline aggregates Armstrong, R.; Codd, I.; Douthwaite, R. M. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, Vol. 7, Issue 73 https://doi.org/10.1080/14786436208201857	journal	January 1962
Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density Arsenlis, A.; Parks, D. M. Acta Materialia, Vol. 47, Issue 5 https://doi.org/10.1016/S1359-6454(99)00020-8	journal	March 1999
Modeling the evolution of crystallographic dislocation density in crystal plasticity Arsenlis, Athanasios; Parks, David M. Journal of the Mechanics and Physics of Solids, Vol. 50, Issue 9 https://doi.org/10.1016/S0022-5096(01)00134-X	journal	September 2002
The deformation of plastically non-homogeneous materials Ashby, M. F. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics, Vol. 21, Issue 170 https://doi.org/10.1080/14786437008238426	journal	February 1970
Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals Balint, D. S.; Deshpande, V. S.; Needleman, A. International Journal of Plasticity, Vol. 24, Issue 12 https://doi.org/10.1016/j.ijplas.2007.08.005	journal	December 2008
Gradients of geometrically necessary dislocations from white beam microdiffraction Barabash, R. I.; Ice, G. E.; Pang, J. W. L. Materials Science and Engineering: A, Vol. 400-401 https://doi.org/10.1016/j.msea.2005.03.036	journal	July 2005
Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model Barbe, Fabrice; Decker, Luc; Jeulin, Dominique International Journal of Plasticity, Vol. 17, Issue 4 https://doi.org/10.1016/S0749-6419(00)00061-9	journal	January 2001
Intergranular and intragranular behavior of polycrystalline aggregates.Part 2: Results Barbe, Fabrice; Forest, Samuel; Cailletaud, Georges International Journal of Plasticity, Vol. 17, Issue 4 https://doi.org/10.1016/S0749-6419(00)00062-0	journal	January 2001
Spatial correlation in grain misorientation distribution Beausir, Benoît; Fressengeas, Claude; Gurao, Nilesh P. Acta Materialia, Vol. 57, Issue 18 https://doi.org/10.1016/j.actamat.2009.07.035	journal	October 2009
Intra-granular plastic slip heterogeneities: Discrete vs. Mean Field approaches Berbenni, S.; Berveiller, M.; Richeton, T. International Journal of Solids and Structures, Vol. 45, Issue 14-15 https://doi.org/10.1016/j.ijsolstr.2008.02.028	journal	July 2008
Impact of the grain size distribution on the yield stress of heterogeneous materials Berbenni, S.; Favier, V.; Berveiller, M. International Journal of Plasticity, Vol. 23, Issue 1 https://doi.org/10.1016/j.ijplas.2006.03.004	journal	January 2007
A numerical spectral approach for solving elasto-static field dislocation and g-disclination mechanics Berbenni, Stéphane; Taupin, Vincent; Djaka, Komlan Sénam International Journal of Solids and Structures, Vol. 51, Issue 23-24 https://doi.org/10.1016/j.ijsolstr.2014.08.009	journal	November 2014
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
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
An extension of the self-consistent scheme to plastically-flowing polycrystals Berveiller, M.; Zaoui, A. Journal of the Mechanics and Physics of Solids, Vol. 26, Issue 5-6 https://doi.org/10.1016/0022-5096(78)90003-0	journal	October 1978
A two-dimensional discrete dislocation simulation of the effect of grain size on strengthening behaviour Biner, S. B.; Morris, J. R. Modelling and Simulation in Materials Science and Engineering, Vol. 10, Issue 6 https://doi.org/10.1088/0965-0393/10/6/303	journal	September 2002
Elastic anisotropy and yield surface estimates of polycrystals Brenner, R.; Lebensohn, R. A.; Castelnau, O. International Journal of Solids and Structures, Vol. 46, Issue 16 https://doi.org/10.1016/j.ijsolstr.2009.04.001	journal	August 2009
Gradient-dependent deformation of two-phase single crystals Busso, E. Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 11 https://doi.org/10.1016/S0022-5096(00)00006-5	journal	November 2000
Orientation gradients and geometrically necessary dislocations in ultrafine grained dual-phase steels studied by 2D and 3D EBSD Calcagnotto, Marion; Ponge, Dirk; Demir, Eralp Materials Science and Engineering: A, Vol. 527, Issue 10-11 https://doi.org/10.1016/j.msea.2010.01.004	journal	April 2010
A study of microstructural length scale effects on the behaviour of FCC polycrystals using strain gradient concepts Cheong, K. S.; Busso, E. P.; Arsenlis, A. International Journal of Plasticity, Vol. 21, Issue 9 https://doi.org/10.1016/j.ijplas.2004.11.001	journal	September 2005
Role of discrete intra-granular slip bands on the strain-hardening of polycrystals Collard, Christophe; Favier, Véronique; Berbenni, Stéphane International Journal of Plasticity, Vol. 26, Issue 2 https://doi.org/10.1016/j.ijplas.2009.07.004	journal	February 2010
Grain size effects on plastic strain and dislocation density tensor fields in metal polycrystals Cordero, N. M.; Forest, S.; Busso, E. P. Computational Materials Science, Vol. 52, Issue 1 https://doi.org/10.1016/j.commatsci.2011.02.043	journal	February 2012
Size effects in generalised continuum crystal plasticity for two-phase laminates Cordero, N. M.; Gaubert, A.; Forest, S. Journal of the Mechanics and Physics of Solids, Vol. 58, Issue 11 https://doi.org/10.1016/j.jmps.2010.06.012	journal	November 2010
Six decades of the Hall–Petch effect – a survey of grain-size strengthening studies on pure metals Cordero, Z. C.; Knight, B. E.; Schuh, C. A. International Materials Reviews, Vol. 61, Issue 8 https://doi.org/10.1080/09506608.2016.1191808	journal	June 2016
Plastic heterogeneities of a copper multicrystal deformed in uniaxial tension: experimental study and finite element simulations Delaire, F.; Raphanel, J. L.; Rey, C. Acta Materialia, Vol. 48, Issue 5 https://doi.org/10.1016/S1359-6454(99)00408-5	journal	March 2000
A numerical spectral approach to solve the dislocation density transport equation Djaka, K. S.; Taupin, V.; Berbenni, S. Modelling and Simulation in Materials Science and Engineering, Vol. 23, Issue 6 https://doi.org/10.1088/0965-0393/23/6/065008	journal	August 2015
Field Dislocation Mechanics for heterogeneous elastic materials: A numerical spectral approach Djaka, Komlan Sénam; Villani, Aurélien; Taupin, Vincent Computer Methods in Applied Mechanics and Engineering, Vol. 315 https://doi.org/10.1016/j.cma.2016.11.036	journal	March 2017
Simulation of residual stress and elastic energy density in thermal barrier coatings using fast Fourier transforms Donegan, S. P.; Rollett, A. D. Acta Materialia, Vol. 96 https://doi.org/10.1016/j.actamat.2015.06.019	journal	September 2015
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 spectral method solution to crystal elasto-viscoplasticity at finite strains Eisenlohr, P.; Diehl, M.; Lebensohn, R. A. International Journal of Plasticity, Vol. 46 https://doi.org/10.1016/j.ijplas.2012.09.012	journal	July 2013
An investigation of back stress formulations under cyclic loading El-Naaman, S. A.; Nielsen, K. L.; Niordson, C. F. Mechanics of Materials, Vol. 130 https://doi.org/10.1016/j.mechmat.2019.01.005	journal	March 2019
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
An interpretation of size-scale plasticity in geometrically confined systems Espinosa, H. D.; Berbenni, S.; Panico, M. Proceedings of the National Academy of Sciences, Vol. 102, Issue 47 https://doi.org/10.1073/pnas.0508572102	journal	November 2005
Discrete dislocation dynamics simulations to interpret plasticity size and surface effects in freestanding FCC thin films Espinosa, H. D.; Panico, M.; Berbenni, S. International Journal of Plasticity, Vol. 22, Issue 11 https://doi.org/10.1016/j.ijplas.2006.01.007	journal	November 2006
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
A fast numerical scheme for computing the response of composites using grid refinement Eyre, D. J.; Milton, G. W. The European Physical Journal Applied Physics, Vol. 6, Issue 1 https://doi.org/10.1051/epjap:1999150	journal	April 1999
A phenomenological theory for strain gradient effects in plasticity Fleck, N. A.; Hutchinson, J. W. Journal of the Mechanics and Physics of Solids, Vol. 41, Issue 12 https://doi.org/10.1016/0022-5096(93)90072-N	journal	December 1993
A reformulation of strain gradient plasticity Fleck, N. A.; Hutchinson, J. W. Journal of the Mechanics and Physics of Solids, Vol. 49, Issue 10 https://doi.org/10.1016/S0022-5096(01)00049-7	journal	October 2001
Guidelines for Constructing Strain Gradient Plasticity Theories Fleck, N. A.; Hutchinson, J. W.; Willis, J. R. Journal of Applied Mechanics, Vol. 82, Issue 7 https://doi.org/10.1115/1.4030323	journal	July 2015
A mathematical basis for strain-gradient plasticity theory—Part I: Scalar plastic multiplier Fleck, N. A.; Willis, J. R. Journal of the Mechanics and Physics of Solids, Vol. 57, Issue 1 https://doi.org/10.1016/j.jmps.2008.09.010	journal	January 2009
Discrete dislocation plasticity: a simple planar model Giessen, E. Van der; Needleman, A. Modelling and Simulation in Materials Science and Engineering, Vol. 3, Issue 5 https://doi.org/10.1088/0965-0393/3/5/008	journal	September 1995
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
Experimental characterization of the intragranular strain field in columnar ice during transient creep Grennerat, F.; Montagnat, M.; Castelnau, O. Acta Materialia, Vol. 60, Issue 8 https://doi.org/10.1016/j.actamat.2012.03.025	journal	May 2012
A unified treatment of strain gradient plasticity Gudmundson, P. Journal of the Mechanics and Physics of Solids, Vol. 52, Issue 6 https://doi.org/10.1016/j.jmps.2003.11.002	journal	June 2004
Strain rate jump induced negative strain rate sensitivity (NSRS) in aluminum alloy 2024: Experiments and constitutive modeling Gupta, Satyapriya; Beaudoin, Armand Joseph; Chevy, Juliette Materials Science and Engineering: A, Vol. 683 https://doi.org/10.1016/j.msea.2016.12.010	journal	January 2017
A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations Gurtin, Morton E. Journal of the Mechanics and Physics of Solids, Vol. 50, Issue 1 https://doi.org/10.1016/S0022-5096(01)00104-1	journal	January 2002
Thermodynamics applied to gradient theories involving the accumulated plastic strain: The theories of Aifantis and Fleck and Hutchinson and their generalization Gurtin, Morton E.; Anand, Lallit Journal of the Mechanics and Physics of Solids, Vol. 57, Issue 3 https://doi.org/10.1016/j.jmps.2008.12.002	journal	March 2009
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
A discrete dislocation analysis of the Bauschinger effect in microcrystals Guruprasad, P. J.; Carter, W. J.; Benzerga, A. A. Acta Materialia, Vol. 56, Issue 19 https://doi.org/10.1016/j.actamat.2008.07.019	journal	November 2008
The Deformation and Ageing of Mild Steel: III Discussion of Results Hall, E. O. Proceedings of the Physical Society. Section B, Vol. 64, Issue 9 https://doi.org/10.1088/0370-1301/64/9/303	journal	September 1951
Mechanism-based strain gradient crystal plasticity—I. Theory Han, Chung-Souk; Gao, Huajian; Huang, Yonggang Journal of the Mechanics and Physics of Solids, Vol. 53, Issue 5 https://doi.org/10.1016/j.jmps.2004.08.008	journal	May 2005
Hall–Petch relation and boundary strengthening Hansen, Niels Scripta Materialia, Vol. 51, Issue 8 https://doi.org/10.1016/j.scriptamat.2004.06.002	journal	October 2004
Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization Haouala, S.; Lucarini, S.; LLorca, J. Journal of the Mechanics and Physics of Solids, Vol. 134 https://doi.org/10.1016/j.jmps.2019.103755	journal	January 2020
Continuum micro-mechanics of elastoplastic polycrystals Hill, R. Journal of the Mechanics and Physics of Solids, Vol. 13, Issue 2 https://doi.org/10.1016/0022-5096(65)90023-2	journal	April 1965
The influence of grain boundaries on mechanical properties Hirth, J. P. Metallurgical Transactions, Vol. 3, Issue 12 https://doi.org/10.1007/BF02661312	journal	December 1972
Evolution of intragranular stresses and dislocation densities during cyclic deformation of polycrystalline copper Jiang, Jun; Benjamin Britton, T.; Wilkinson, Angus J. Acta Materialia, Vol. 94 https://doi.org/10.1016/j.actamat.2015.04.031	journal	August 2015
Effects of the grain size and shape on the flow stress: A dislocation dynamics study Jiang, Maoyuan; Devincre, Benoit; Monnet, Ghiath International Journal of Plasticity, Vol. 113 https://doi.org/10.1016/j.ijplas.2018.09.008	journal	February 2019
Mixed boundary conditions for FFT-based homogenization at finite strains Kabel, Matthias; Fliegener, Sascha; Schneider, Matti Computational Mechanics, Vol. 57, Issue 2 https://doi.org/10.1007/s00466-015-1227-1	journal	December 2015
Cyclic response of copper single crystal micro-beams Kiener, D.; Motz, C.; Grosinger, W. Scripta Materialia, Vol. 63, Issue 5 https://doi.org/10.1016/j.scriptamat.2010.05.014	journal	September 2010
Assessment of geometrically necessary dislocation levels derived by 3D EBSD Konijnenberg, P. J.; Zaefferer, S.; Raabe, D. Acta Materialia, Vol. 99 https://doi.org/10.1016/j.actamat.2015.06.051	journal	October 2015
Zur plastischen verformung des vielkristalls Kröner, E. Acta Metallurgica, Vol. 9, Issue 2 https://doi.org/10.1016/0001-6160(61)90060-8	journal	February 1961
Dislocation Microstructures and Plastic Flow: A 3D Simulation Kubin, Ladislas P.; Canova, G.; Condat, M. Solid State Phenomena, Vol. 23-24 https://doi.org/10.4028/www.scientific.net/SSP.23-24.455	journal	January 1992
Effects of grain size distribution and stress heterogeneity on yield stress of polycrystals: A numerical approach Lavergne, F.; Brenner, R.; Sab, K. Computational Materials Science, Vol. 77 https://doi.org/10.1016/j.commatsci.2013.04.061	journal	September 2013
N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform A. Lebensohn, R. Acta Materialia, Vol. 49, Issue 14 https://doi.org/10.1016/S1359-6454(01)00172-0	journal	August 2001
Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper Lebensohn, Ricardo A.; Brenner, Renald; Castelnau, Olivier Acta Materialia, Vol. 56, Issue 15 https://doi.org/10.1016/j.actamat.2008.04.016	journal	September 2008
Modeling void growth in polycrystalline materials Lebensohn, Ricardo A.; Escobedo, Juan P.; Cerreta, Ellen K. Acta Materialia, Vol. 61, Issue 18 https://doi.org/10.1016/j.actamat.2013.08.004	journal	October 2013
Modeling viscoplastic behavior and heterogeneous intracrystalline deformation of columnar ice polycrystals Lebensohn, R. A.; Montagnat, M.; Mansuy, P. Acta Materialia, Vol. 57, Issue 5 https://doi.org/10.1016/j.actamat.2008.10.057	journal	March 2009
Dilatational viscoplasticity of polycrystalline solids with intergranular cavities Lebensohn, R. A.; Idiart, M. I.; Castañeda, P. Ponte Philosophical Magazine, Vol. 91, Issue 22 https://doi.org/10.1080/14786435.2011.561811	journal	August 2011
An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials Lebensohn, Ricardo A.; Kanjarla, Anand K.; Eisenlohr, Philip International Journal of Plasticity, Vol. 32-33 https://doi.org/10.1016/j.ijplas.2011.12.005	journal	May 2012
Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms Lebensohn, Ricardo A.; Needleman, Alan Journal of the Mechanics and Physics of Solids, Vol. 97 https://doi.org/10.1016/j.jmps.2016.03.023	journal	December 2016
A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys Lebensohn, R. A.; Tomé, C. N. Acta Metallurgica et Materialia, Vol. 41, Issue 9 https://doi.org/10.1016/0956-7151(93)90130-K	journal	September 1993
Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms Lee, S. -B.; Lebensohn, R. A.; Rollett, A. D. International Journal of Plasticity, Vol. 27, Issue 5 https://doi.org/10.1016/j.ijplas.2010.09.002	journal	May 2011
Yield stress strengthening in ultrafine-grained metals: A two-dimensional simulation of dislocation dynamics Lefebvre, S.; Devincre, B.; Hoc, T. Journal of the Mechanics and Physics of Solids, Vol. 55, Issue 4 https://doi.org/10.1016/j.jmps.2006.10.002	journal	April 2007
A damage model for crack prediction in brittle and quasi-brittle materials solved by the FFT method Li, Jia; Tian, Xiao-Xiao; Abdelmoula, Radhi International Journal of Fracture, Vol. 173, Issue 2 https://doi.org/10.1007/s10704-011-9671-1	journal	January 2012
On the accuracy of spectral solvers for micromechanics based fatigue modeling Lucarini, S.; Segurado, J. Computational Mechanics, Vol. 63, Issue 2 https://doi.org/10.1007/s00466-018-1598-1	journal	July 2018
An affine formulation for the self-consistent modeling of elasto-viscoplastic heterogeneous materials based on the translated field method Mareau, Charles; Berbenni, Stéphane International Journal of Plasticity, Vol. 64 https://doi.org/10.1016/j.ijplas.2014.08.011	journal	January 2015
Micromechanical modelling of twinning in polycrystalline materials: Application to magnesium Mareau, Charles; Daymond, Mark R. International Journal of Plasticity, Vol. 85 https://doi.org/10.1016/j.ijplas.2016.07.007	journal	October 2016
An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals Masson, R.; Bornert, M.; Suquet, P. Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 6-7 https://doi.org/10.1016/S0022-5096(99)00071-X	journal	June 2000
Kinetics of flow and strain-hardening Mecking, H.; Kocks, U. F. Acta Metallurgica, Vol. 29, Issue 11 https://doi.org/10.1016/0001-6160(81)90112-7	journal	November 1981
Homogenization of elastic–viscoplastic heterogeneous materials: Self-consistent and Mori-Tanaka schemes Mercier, S.; Molinari, A. International Journal of Plasticity, Vol. 25, Issue 6 https://doi.org/10.1016/j.ijplas.2008.08.006	journal	June 2009
A computational scheme for linear and non‐linear composites with arbitrary phase contrast Michel, J. C.; Moulinec, H.; Suquet, P. International Journal for Numerical Methods in Engineering, Vol. 52, Issue 12 https://doi.org/10.1002/nme.275	journal	September 2001
Effects of grain interaction on deformation in polycrystals Mika, David P.; Dawson, Paul R. Materials Science and Engineering: A, Vol. 257, Issue 1 https://doi.org/10.1016/S0921-5093(98)00824-7	journal	November 1998
A self consistent approach of the large deformation polycrystal viscoplasticity Molinari, A.; Canova, G. R.; Ahzi, S. Acta Metallurgica, Vol. 35, Issue 12 https://doi.org/10.1016/0001-6160(87)90297-5	journal	December 1987
Plastic deformation of freestanding thin films: Experiments and modeling Nicola, L.; Xiang, Y.; Vlassak, J. J. Journal of the Mechanics and Physics of Solids, Vol. 54, Issue 10 https://doi.org/10.1016/j.jmps.2006.04.005	journal	October 2006
Non-uniform plastic deformation of micron scale objects Niordson, Christian F.; Hutchinson, John W. International Journal for Numerical Methods in Engineering, Vol. 56, Issue 7 https://doi.org/10.1002/nme.593	journal	January 2003
Computational strain gradient crystal plasticity Niordson, Christian F.; Kysar, Jeffrey W. Journal of the Mechanics and Physics of Solids, Vol. 62 https://doi.org/10.1016/j.jmps.2013.08.014	journal	January 2014
Strain gradient effects on cyclic plasticity Niordson, Christian F.; Legarth, Brian Nyvang Journal of the Mechanics and Physics of Solids, Vol. 58, Issue 4 https://doi.org/10.1016/j.jmps.2010.01.007	journal	April 2010
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
Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations Ohno, Nobutada; Okumura, Dai Journal of the Mechanics and Physics of Solids, Vol. 55, Issue 9 https://doi.org/10.1016/j.jmps.2007.02.007	journal	September 2007
Grain-Size Dependent Yield Behavior Under Loading, Unloading and Reverse Loading Ohno, Nobutada; Okumura, Dai; Shibata, Tomoyuki International Journal of Modern Physics B, Vol. 22, Issue 31n32 https://doi.org/10.1142/S0217979208051406	journal	December 2008
FFT-based modelling of transformation plasticity in polycrystalline materials during diffusive phase transformation Otsuka, Takayuki; Brenner, Renald; Bacroix, Brigitte International Journal of Engineering Science, Vol. 127 https://doi.org/10.1016/j.ijengsci.2018.02.008	journal	June 2018
Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction Pantleon, W. Scripta Materialia, Vol. 58, Issue 11 https://doi.org/10.1016/j.scriptamat.2008.01.050	journal	June 2008
A crystal plasticity FFT based study of deformation twinning, anisotropy and micromechanics in HCP materials: Application to AZ31 alloy Paramatmuni, Chaitanya; Kanjarla, Anand K. International Journal of Plasticity, Vol. 113 https://doi.org/10.1016/j.ijplas.2018.10.007	journal	February 2019
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
Role of discrete intragranular slip on lattice rotations in polycrystalline Ni: Experimental and micromechanical studies Perrin, C.; Berbenni, S.; Vehoff, H. Acta Materialia, Vol. 58, Issue 14 https://doi.org/10.1016/j.actamat.2010.04.033	journal	August 2010
A new mean field micromechanical approach to capture grain size effects Pipard, J. -M.; Nicaise, N.; Berbenni, S. Computational Materials Science, Vol. 45, Issue 3 https://doi.org/10.1016/j.commatsci.2008.06.012	journal	May 2009
Mechanical response of multicrystalline thin films in mesoscale field dislocation mechanics Puri, Saurabh; Das, Amit; Acharya, Amit Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 11 https://doi.org/10.1016/j.jmps.2011.06.009	journal	November 2011
Plastic deformation of multicrystalline thin films: Grain size distribution vs. grain orientation Puri, Saurabh; Roy, Anish Computational Materials Science, Vol. 52, Issue 1 https://doi.org/10.1016/j.commatsci.2011.03.001	journal	February 2012
Modeling dislocation sources and size effects at initial yield in continuum plasticity Puri, Saurabh; Roy, Anish; Acharya, Amit Journal of Mechanics of Materials and Structures, Vol. 4, Issue 9 https://doi.org/10.2140/jomms.2009.4.1603	journal	January 2009
The deformation behaviour of grain boundary regions in polycrystalline aluminium Randle, V.; Hansen, N.; Jensen, D. Juul Philosophical Magazine A, Vol. 73, Issue 2 https://doi.org/10.1080/01418619608244382	journal	February 1996
Interplay of martensitic phase transformation and plastic slip in polycrystals Richards, A. W.; Lebensohn, R. A.; Bhattacharya, K. Acta Materialia, Vol. 61, Issue 12 https://doi.org/10.1016/j.actamat.2013.03.053	journal	July 2013
Grain-size dependent accommodation due to intragranular distributions of dislocation loops Richeton, T.; Berbenni, S.; Berveiller, M. Acta Materialia, Vol. 57, Issue 5 https://doi.org/10.1016/j.actamat.2008.11.024	journal	March 2009
Modelling the transport of geometrically necessary dislocations on slip systems: application to single- and multi-crystals of ice Richeton, T.; Le, Lt; Chauve, T. Modelling and Simulation in Materials Science and Engineering, Vol. 25, Issue 2 https://doi.org/10.1088/1361-651X/aa5341	journal	January 2017
Continuity constraints at interfaces and their consequences on the work hardening of metal–matrix composites Richeton, T.; Wang, G. F.; Fressengeas, C. Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 10 https://doi.org/10.1016/j.jmps.2011.07.006	journal	October 2011
Stress hot spots in viscoplastic deformation of polycrystals Rollett, A. D.; Lebensohn, R. A.; Groeber, M. Modelling and Simulation in Materials Science and Engineering, Vol. 18, Issue 7 https://doi.org/10.1088/0965-0393/18/7/074005	journal	September 2010
Assessing reliability of fatigue indicator parameters for small crack growth via a probabilistic framework Rovinelli, Andrea; Guilhem, Yoann; Proudhon, Henry Modelling and Simulation in Materials Science and Engineering, Vol. 25, Issue 4 https://doi.org/10.1088/1361-651X/aa6c45	journal	May 2017
Predicting the 3D fatigue crack growth rate of small cracks using multimodal data via Bayesian networks: In-situ experiments and crystal plasticity simulations Rovinelli, Andrea; Sangid, Michael D.; Proudhon, Henry Journal of the Mechanics and Physics of Solids, Vol. 115 https://doi.org/10.1016/j.jmps.2018.03.007	journal	June 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
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
Phenomenological mesoscopic field dislocation mechanics, lower-order gradient plasticity, and transport of mean excess dislocation density Roy, A.; Puri, S.; Acharya, A. Modelling and Simulation in Materials Science and Engineering, Vol. 15, Issue 1 https://doi.org/10.1088/0965-0393/15/1/S14	journal	December 2006
A new class of micro–macro models for elastic–viscoplastic heterogeneous materials Sabar, Hafid; Berveiller, Marcel; Favier, Veronique International Journal of Solids and Structures, Vol. 39, Issue 12 https://doi.org/10.1016/S0020-7683(02)00256-1	journal	June 2002
Influence of grain size on orientation changes during plastic deformation Scheriau, S.; Pippan, R. Materials Science and Engineering: A, Vol. 493, Issue 1-2 https://doi.org/10.1016/j.msea.2007.08.092	journal	October 2008
Simulation of dislocations on the mesoscopic scale. I. Methods and examples Schwarz, K. W. Journal of Applied Physics, Vol. 85, Issue 1 https://doi.org/10.1063/1.369429	journal	January 1999
Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials Shanthraj, P.; Eisenlohr, P.; Diehl, M. International Journal of Plasticity, Vol. 66 https://doi.org/10.1016/j.ijplas.2014.02.006	journal	March 2015
FFT-based interface decohesion modelling by a nonlocal interphase Sharma, Luv; Peerlings, Ron H. J.; Shanthraj, Pratheek Advanced Modeling and Simulation in Engineering Sciences, Vol. 5, Issue 1 https://doi.org/10.1186/s40323-018-0100-0	journal	April 2018
The role of strain gradients in the grain size effect for polycrystals Smyshlyaev, V. P.; Fleck, N. A. Journal of the Mechanics and Physics of Solids, Vol. 44, Issue 4 https://doi.org/10.1016/0022-5096(96)00009-9	journal	April 1996
Multi-scale modeling of the mechanical behavior of polycrystalline ice under transient creep Suquet, P.; Moulinec, H.; Castelnau, O. Procedia IUTAM, Vol. 3 https://doi.org/10.1016/j.piutam.2012.03.006	journal	January 2012
Size effects on the hardening of channel-type microstructures: A field dislocation mechanics-based approach Taupin, V.; Berbenni, S.; Fressengeas, C. Acta Materialia, Vol. 60, Issue 2 https://doi.org/10.1016/j.actamat.2011.10.033	journal	January 2012
On particle size effects: An internal length mean field approach using field dislocation mechanics Taupin, V.; Berbenni, S.; Fressengeas, C. Acta Materialia, Vol. 58, Issue 16 https://doi.org/10.1016/j.actamat.2010.06.034	journal	September 2010
Effects of Size on the Dynamics of Dislocations in Ice Single Crystals Taupin, V.; Varadhan, S.; Chevy, J. Physical Review Letters, Vol. 99, Issue 15 https://doi.org/10.1103/PhysRevLett.99.155507	journal	October 2007
The dependence of polycrystal work hardening on grain size Thompson, Anthony W.; Baskes, Michael I.; Flanagan, William F. Acta Metallurgica, Vol. 21, Issue 7 https://doi.org/10.1016/0001-6160(73)90158-2	journal	July 1973
A higher order elasto-viscoplastic model using fast Fourier transforms: Effects of lattice curvatures on mechanical response of nanocrystalline metals Upadhyay, M. V.; Capolungo, L.; Taupin, V. International Journal of Plasticity, Vol. 83 https://doi.org/10.1016/j.ijplas.2016.04.007	journal	August 2016
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
Lattice incompatibility and strain-aging in single crystals Varadhan, S.; Beaudoin, A. J.; Fressengeas, C. Journal of the Mechanics and Physics of Solids, Vol. 57, Issue 10 https://doi.org/10.1016/j.jmps.2009.06.007	journal	October 2009
Mesoscopic scale simulation of dislocation dynamics in fcc metals: Principles and applications Verdier, M.; Fivel, M.; Groma, I. Modelling and Simulation in Materials Science and Engineering, Vol. 6, Issue 6 https://doi.org/10.1088/0965-0393/6/6/007	journal	November 1998
Deformation patterning in finite-strain crystal plasticity by spectral homogenization with application to magnesium Vidyasagar, A.; Tutcuoglu, Abbas D.; Kochmann, Dennis M. Computer Methods in Applied Mechanics and Engineering, Vol. 335 https://doi.org/10.1016/j.cma.2018.03.003	journal	June 2018
An accelerated FFT algorithm for thermoelastic and non-linear composites Vinogradov, V.; Milton, G. W. International Journal for Numerical Methods in Engineering, Vol. 76, Issue 11 https://doi.org/10.1002/nme.2375	journal	December 2008
A unifying scaling for the Bauschinger effect in highly confined thin films: a discrete dislocation plasticity study Waheed, S.; Hao, R.; Bhowmik, A. Modelling and Simulation in Materials Science and Engineering, Vol. 25, Issue 5 https://doi.org/10.1088/1361-651X/aa733e	journal	June 2017
Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction Wallis, David; Hansen, Lars N.; Ben Britton, T. Ultramicroscopy, Vol. 168 https://doi.org/10.1016/j.ultramic.2016.06.002	journal	September 2016
A finite strain elastic–viscoplastic self-consistent model for polycrystalline materials Wang, H.; Wu, P. D.; Tomé, C. N. Journal of the Mechanics and Physics of Solids, Vol. 58, Issue 4 https://doi.org/10.1016/j.jmps.2010.01.004	journal	April 2010
A micromechanical theory of grain-size dependence in metal plasticity Weng, G. J. Journal of the Mechanics and Physics of Solids, Vol. 31, Issue 3 https://doi.org/10.1016/0022-5096(83)90021-2	journal	January 1983
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
Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures Wulfinghoff, Stephan; Forest, Samuel; Böhlke, Thomas Journal of the Mechanics and Physics of Solids, Vol. 79 https://doi.org/10.1016/j.jmps.2015.02.008	journal	June 2015
Cosserat continuum modelling of grain size effects in metal polycrystals Zeghadi, Asmahana; Forest, Samuel; Gourgues, Anne-Françoise PAMM, Vol. 5, Issue 1 https://doi.org/10.1002/pamm.200510021	journal	December 2005

Cited By (1)

Stress fields of finite-size dislocation walls and prediction of back stress induced by geometrically necessary dislocations at grain boundaries Jiang, Maoyuan; Monnet, Ghiath; Devincre, Benoit Journal of the Mechanics and Physics of Solids, Vol. 143 https://doi.org/10.1016/j.jmps.2020.104071	journal	October 2020

Similar Records

A numerical study of reversible plasticity using continuum dislocation mechanics

Journal Article · Thu Dec 16 00:00:00 EST 2021 · Comptes Rendus. Physique · OSTI ID:1578028

Berbenni, Stéphane; Lebensohn, Ricardo A

A FFT-based numerical implementation of mesoscale field dislocation mechanics: Application to two-phase laminates

Journal Article · Fri Jan 04 00:00:00 EST 2019 · International Journal of Solids and Structures · OSTI ID:1578028

Djaka, Komlan S.; Berbenni, Stéphane; Taupin, Vincent; +1 more

A crystal plasticity model incorporating the effects of precipitates in superalloys: Application to tensile, compressive, and cyclic deformation of Inconel 718

Journal Article · Thu Sep 14 00:00:00 EDT 2017 · International Journal of Plasticity · OSTI ID:1578028

Ghorbanpour, Saeede; Zecevic, Milovan; Kumar, Anil; +5 more

Related Subjects

36 MATERIALS SCIENCE
Field dislocation mechanics
Elastoviscoplastic
FFT
Polycrystal
Grain size effects

Title: A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals

Citation Formats

References (144)

Cited By (1)

Similar Records

Related Subjects