Comptes Rendus
A numerical study of reversible plasticity using continuum dislocation mechanics
Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 295-312.

In this contribution, an elasto-viscoplastic fast Fourier transform-based (EVPFFT) numerical implementation of the Mesoscale Field Dislocation Mechanics (MFDM) formulation, called MFDM-EVPFFT, is applied to study the reversible plastic behavior of periodic two-phase crystalline composites with an elasto-viscoplastic plastic matrix and a purely elastic second phase. Periodic laminate microstructures of this kind with different periods (i.e. sizes) are considered to examine the size dependence of the Bauschinger effect and hardening during cyclic loading. Comparisons with classic composite effects obtained with conventional crystal plasticity are discussed. Specifically, the MFDM-EVPFFT results shed light on the hardening mechanisms due to piling-up/unpiling-up of geometrically-necessary dislocations (GND) during reverse loading.

Première publication :
Publié le :
DOI : 10.5802/crphys.54
Mots clés : Hardening mechanisms, Geometrically-necessary dislocations, Bauschinger effect, Size effect, FFT
Stéphane Berbenni 1, 2 ; Ricardo A. Lebensohn 3

1 Université de Lorraine, Arts et Métiers Paris Tech, CNRS, LEM3, F-57000 Metz, France
2 Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures (DAMAS), Université de Lorraine, France
3 Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87845, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRPHYS_2021__22_S3_295_0,
     author = {St\'ephane Berbenni and Ricardo~A. Lebensohn},
     title = {A numerical study of reversible plasticity using continuum dislocation mechanics},
     journal = {Comptes Rendus. Physique},
     pages = {295--312},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {22},
     number = {S3},
     year = {2021},
     doi = {10.5802/crphys.54},
     language = {en},
}
TY  - JOUR
AU  - Stéphane Berbenni
AU  - Ricardo A. Lebensohn
TI  - A numerical study of reversible plasticity using continuum dislocation mechanics
JO  - Comptes Rendus. Physique
PY  - 2021
SP  - 295
EP  - 312
VL  - 22
IS  - S3
PB  - Académie des sciences, Paris
DO  - 10.5802/crphys.54
LA  - en
ID  - CRPHYS_2021__22_S3_295_0
ER  - 
%0 Journal Article
%A Stéphane Berbenni
%A Ricardo A. Lebensohn
%T A numerical study of reversible plasticity using continuum dislocation mechanics
%J Comptes Rendus. Physique
%D 2021
%P 295-312
%V 22
%N S3
%I Académie des sciences, Paris
%R 10.5802/crphys.54
%G en
%F CRPHYS_2021__22_S3_295_0
Stéphane Berbenni; Ricardo A. Lebensohn. A numerical study of reversible plasticity using continuum dislocation mechanics. Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 295-312. doi : 10.5802/crphys.54. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.54/

[1] L. Nicola; Y. Xiang; J. Vlassak; E. VanderGiessen; A. Needleman Plastic deformation of freestanding thin films: experiments and modeling, J. Mech. Phys. Solids, Volume 54 (2006), pp. 2089-2110 | DOI

[2] P. J. Guruprasad; W. J. Carter; A. A. Benzerga A discrete dislocation analysis of the Bauschinger effect in microcrystals, Acta Mater., Volume 56 (2008), pp. 5477-5491 | DOI

[3] D. S. Balint; V. S. Deshpande; A. Needleman; E. Van der Giessen Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals, Int. J. Plast., Volume 24 (2010), pp. 2149-2172 | DOI

[4] C. Zhou; R. LeSar Dislocation dynamics simulations of the Bauschinger effect in metallic thin films, Comput. Mater. Sci., Volume 54 (2012), pp. 350-355 | DOI

[5] M. Jiang; B. Devincre; G. Monnet Effects of the grain size and shape on the flow stress: A dislocation dynamics study, Int. J. Plast., Volume 113 (2019), pp. 111-124 | DOI

[6] S. Waheed; R. Hao; A. Bhowmik; D. S. Balint; F. Giuliani A unifying scaling for the Bauschinger effect in highly confined thin films: a discrete dislocation plasticity study, Model. Simul. Mater. Sci. Eng., Volume 25 (2017) no. 5, 054003 | DOI

[7] M. E. Gurtin A gradient theory of single-crystal viscoplasticity that accounts for the geometrically necessary dislocations, J. Mech. Phys. Solids, Volume 50 (2002), pp. 5-32 | DOI

[8] N. Ohno; D. Okumura Higher-order stress and grain size effects due to self-energy of geometrically dislocations, J. Mech. Phys. Solids, Volume 55 (2007), pp. 1879-1898 | DOI

[9] N. Ohno; D. Okumura; T. Shibata Grain size dependent yield behavior under loading, unloading and reverse loading, Int. J. Mod. Phys. B, Volume 22 (2008), pp. 5937-5942 | DOI

[10] N. M. Cordero; A. Gaubert; S. Forest; E. P. Busso; F. Galerneau; S. Kruch Size effects in generalised continuum crystal plasticity for two-phase laminates, J. Mech. Phys. Solids, Volume 58 (2010), pp. 1963-1994 | DOI

[11] K. Danas; V. S. Deshpande; N. A. Fleck Compliant interfaces: a mechanism for relaxation of dislocation pile-ups in a sheared single crystal, Int. J. Plast., Volume 26 (2010), pp. 1792-1805 | DOI

[12] S. Wulfinghoff; S. Forest; T. Böhlke Strain gradient plasticity modeling of cyclic behavior of laminate structures, J. Mech. Phys. Solids, Volume 79 (2015), pp. 1-20 | DOI

[13] S. A. El-Naaman; K. L. Nielsen; C. F. Niordson An investigation of back stress formulations under cyclic loading, Mech. Mater., Volume 130 (2019), pp. 76-87 | DOI

[14] M. Rys; H. Petryk Gradient crystal plasticity models with a natural length scale in the hardening law, Int. J. Plast., Volume 111 (2018), pp. 168-187 | DOI

[15] A. Panteghini; L. Bardella; C. F. Niordson A potential for higher-order phenomenological strain gradient plasticity to predict reliable response under non-proportional loading, Proc. R. Soc. Lond. A, Volume 475 (2019), 0258

[16] M. Jebahi; L. Cai; F. Abed-Meraim Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation, Int. J. Plast., Volume 126 (2020), 102617 | DOI

[17] I. Groma; F. F. Csikor; M. Zaiser Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics, Acta Mater., Volume 51 (2003), pp. 1271-1281 | DOI

[18] M. Zaiser; T. Hochrainer Some steps towards a continuum representation of 3D dislocation systems, Scr. Mater., Volume 54 (2006), pp. 717-721 | DOI

[19] S. Sandfeld; T. Hochrainer; P. Gumbsch; M. Zaiser Numerical implementation of 3D continuum theory of dislocation dynamics and application to micro-bending, Philos. Mag., Volume 90 (2010) no. 27–28, pp. 3697-3728 | DOI

[20] T. Hochrainer; S. Sandfeld; M. Zaiser; P. Gumbsch Continuum dislocation dynamics: towards a physically theory of plasticity, J. Mech. Phys. Solids, Volume 63 (2014), pp. 167-178 | DOI

[21] K. Schulz; D. Dickel; S. Schmitt; S. Sandfeld; D. Weygand Analysis of dislocation pile-ups using a dislocation-based continuum theory, Modell. Simul. Mater. Sci. Eng., Volume 22 (2010), 025008

[22] A. Acharya; A. Roy Size effects and idealized dislocation microstructure at small scales: Predictions of a phenomenological model of mesoscopic field dislocation mechanics: Part I, J. Mech. Phys. Solids, Volume 54 (2006), pp. 1687-1710 | DOI

[23] A. Roy; A. Acharya Size effects and idealized dislocation microstructure at small scales: Predictions of a phenomenological model of mesoscopic field dislocation mechanics: Part II, J. Mech. Phys. Solids, Volume 54 (2006), pp. 1711-1743 | DOI

[24] A. Roy; S. Puri; A. Acharya Phenomenological mesoscopic field dislocation mechanics, lower-order gradient plasticity, and transport of mean excess dislocation density, Modell. Simul. Mater. Sci. Eng., Volume 15 (2007), pp. 167-180 | DOI

[25] A. Acharya Microcanonical entropy and mesoscale dislocation mechanics and plasticity, J. Elasticity, Volume 104 (2011), pp. 23-44 | DOI

[26] S. Puri; A. Das; A. Acharya Mechanical response of multicrystalline thin films in mesoscale field dislocation mechanics, J. Mech. Phys. Solids, Volume 59 (2011), pp. 2400-2417 | DOI

[27] S. Puri; A. Roy Plastic deformation of multicrystalline thin films: Grain size distribution vs. grain orientation, Comput. Mater. Sci., Volume 52 (2012), pp. 20-24 | DOI

[28] R. Arora; A. Acharya Dislocation pattern formation in finite deformation crystal plasticity, Int. J. Solids Struct., Volume 184 (2020), pp. 114-135 | DOI

[29] R. A. Lebensohn; A. Needleman Numerical implementation of non-local polycrystal plasticity using fast Fourier transforms, J. Mech. Phys. Solids, Volume 97 (2016), pp. 333-351 | DOI

[30] A. Acharya A model of crystal plasticity based on the theory of continuously distributed dislocations, J. Mech. Phys. Solids, Volume 49 (2001), pp. 761-784 | DOI

[31] A. Acharya Driving forces and boundary conditions in continuum dislocation mechanics, Proc. R. Soc. Lond. A, Volume 459 (2003), pp. 1343-1363 | DOI

[32] A. Roy; A. Acharya Finite element approximation of field dislocation mechanics, J. Mech. Phys. Solids, Volume 53 (2005), pp. 143-170 | DOI

[33] S. Varadhan; A. J. Baudoin; A. Acharya; C. Fressengeas Dislocation transport using Galerkin/least squares formulation, Model. Simul. Mater. Sci. Eng., Volume 14 (2006), pp. 1245-1270 | DOI

[34] V. Taupin; S. Varadhan; J. Chevy; C. Fressengeas; A. J. Beaudoin; M. Montagnat; P. Duval Effects of size on the dynamics of dislocations in ice single crystals, Phys. Rev. Lett., Volume 99 (2007), 155507 | DOI

[35] T. Richeton; G. F. Wang; C. Fressengeas Continuity constraints at the interfaces and their consequences on the work hardening of metal-matrix composites, J. Mech. Phys. Solids, Volume 59 (2011), pp. 2023-2043 | DOI

[36] T. Richeton; L. T. Le; T. Chauve; M. Bernacki; S. Berbenni; M. Montagnat Modelling the transport of geometrically necessary dislocations on slip systems: application to single and multi-crystals of ice, Modell. Simul. Mater. Sci. Eng., Volume 25 (2017), 025010 | DOI

[37] S. Gupta; A. J. Beaudoin; J. Chevy Strain rate jump induced negative strain rate sensitivity (NSRS) in aluminium alloy 2024: Experiments and constitutive modeling, Mater. Sci. Eng. A, Volume 683 (2017), pp. 143-152 | DOI

[38] H. Moulinec; P. Suquet A fast numerical method for computing the linear and non linear properties of composites, C. R. Acad. Sci. Paris II, Volume 318 (1994), pp. 1417-1423

[39] H. Moulinec; P. Suquet A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Meth. Appl. Mech. Eng., Volume 157 (1998), pp. 69-94 | DOI

[40] J. C. Michel; H. Moulinec; P. Suquet A computational scheme for linear and non-linear composites with arbitrary phase contrast, Int. J. Numer. Meth. Eng., Volume 52 (2001), pp. 139-160 | DOI

[41] R. A. Lebensohn N-site modeling of a 3D viscoplatic polycrystal using fast Fourier transform, Acta Mater., Volume 49 (2001), pp. 2723-2737 | DOI

[42] R. A. Lebensohn; R. Brenner; O. Castelnau; A. Rollett Orientation image-based micromechanical modelling of subgrain texture evolution in polycrystalline copper, Acta Mater., Volume 56 (2008), pp. 3914-3926 | DOI

[43] B. Liu; D. Raabe; F. Roters; P. Eisenlohr; R. A. Lebensohn Comparison of finite element and fast Fourier transform crystal plasticity solvers for texture prediction, Model. Simul. Mater. Sci. Eng., Volume 18 (2009), 085005

[44] R. A. Lebensohn; A. K. Kanjarla; P. Eisenlohr An elasto-viscoplastic formulation based on Fast Fourier Transforms for the prediction of micromechanical fields in polycrystalline materials, Int. J. Plast., Volume 32–33 (2012), pp. 59-69 | DOI

[45] P. Suquet; H. Moulinec; O. Castelnau; M. Montagnat; N. Lahellec; F. Grennerat; P. Duval; R. Brenner Multi-scale modeling of the mechanical behavior of polycrystalline ice under transient creep, Procedia IUTAM, Volume 3 (2012), pp. 76-90 | DOI

[46] P. Shanthraj; P. Eisenlohr; M. Diehl; F. Roters Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials, Int. J. Plast., Volume 66 (2015), pp. 31-45 | DOI

[47] S. Lucarini; J. Segurado On the accuracy of spectral solvers for micromechanics based fatigue modeling, Comput. Mech., Volume 63 (2019), pp. 365-382 | DOI

[48] A. Marano; L. Gélébart; S. Forest Intragranular localization induced by softening crystal plasticity analysis of slip and kink bands localization modes from high resolution FFT-simulations results, Acta Mater., Volume 175 (2018), pp. 262-275 | DOI

[49] S. Haouala; S. Lucarini; J. Llorca; J. Segurado Simulation of the Hall-Petch effect in FCC polycrystals by means of strain gradient crystal plasticity and FFT homogenization, J. Mech. Phys. Solids, Volume 134 (2020), 103755 | DOI

[50] R. Brenner; A. J. Beaudoin; P. Suquet; A. Acharya Numerical implementation of static field dislocation mechanics theory for periodic media, Philos. Mag., Volume 94 (2014) no. 16, pp. 1764-1787 | DOI

[51] S. Berbenni; V. Taupin; K. S. Djaka; C. Fressengeas A numerical spectral approach for solving elasto-static field dislocation and g-disclination mechanics, Int. J. Solids Struct., Volume 51 (2014), pp. 4157-4175 | DOI

[52] K. S. Djaka; V. Taupin; S. Berbenni; C. Fressengeas A numerical spectral approach to solve the dislocation density transport equation, Model. Simul. Mater. Sci. Eng., Volume 23 (2015) no. 6, 065008

[53] K. S. Djaka; A. Villani; V. Taupin; L. Capolungo; S. Berbenni Field dislocation mechanics for heterogeneous elastic materials: A numerical spectral approach, Comput. Methods Appl. Mech. Eng., Volume 315 (2017), pp. 921-942 | DOI

[54] K. S. Djaka; S. Berbenni; V. Taupin; R. A. Lebensohn A FFT-based numerical implementation of mesoscale field dislocation mechanics: application to two-phase laminates, Int. J. Solids Struct., Volume 184 (2020), pp. 136-152 | DOI

[55] S. Berbenni; V. Taupin; R. A. Lebensohn A fast Fourier transform-based mesoscale field dislocation mechanics study of grain size effects and reversible plasticity in polycrystals, J. Mech. Phys. Solids, Volume 135 (2020), 103808 | DOI

[56] J. Genée; S. Berbenni; N. Gey; R. A. Lebensohn; F. Bonnet Particle interspacing effects on the mechanical behavior of a Fe-TiB 2 metal matrix composite using FFT-based mesoscopic field dislocation mechanics, Adv. Model. Simul. Eng. Sci., Volume 7 (2020), 6 | DOI

[57] N. Bertin; M. V. Upadhyay; C. Pradalier; L. Capolungo A FFT-based formulation for efficient mechanical fields computation in isotropic and anisotropic periodic discrete dislocation dynamics, Model. Simul. Mater. Sci. Eng., Volume 23 (2015), 065009 | DOI

[58] J. T. Graham; A. D. Rollett; R. LeSar Fast Fourier transform discrete dislocation dynamics, Model. Simul. Mater. Sci. Eng., Volume 8 (2016), 085005

[59] N. Bertin; L. Capolungo A FFT-based formulation for discrete dislocation dynamics in heterogeneous media, J. Comput. Phys., Volume 355 (2018), pp. 366-384 | DOI

[60] M. F. Ashby Deformation of plastically non-homogeneous materials, Philos. Mag., Volume 21 (1970), pp. 399-424 | DOI

[61] Ekkehart Kröner Kontinuumstheorie der Versetzungen und Eigenspannungen, Ergebnisse der Angewewandte Mathematik, 5, Springer Verlag, Berlin, 1958 | DOI

[62] T. Mura Continuous distribution of moving dislocations, Philos. Mag., Volume 89 (1963), pp. 843-857 | DOI

[63] J. F. Nye Some geometrical relations in dislocated crystals, Acta Mater., Volume 1 (1953), pp. 153-162 | DOI

[64] Ekkehart Kröner et al. Continuum Theory of Defects, Physics of defects (R. Balian; M. Kléman; J.-P. Poirier, eds.), North Holland, New York, 1981, pp. 217-315

[65] F. Willot Fourier-based schemes for computing the mechanical response of composites with accurate local fields, C. R. Méc., Volume 343 (2015), pp. 232-245 | DOI

[66] A. Acharya Jump condition for GND evolution as a constraint on slip transmission at grain boundaries, Philos. Mag., Volume 87 (2007), pp. 1349-1359 | DOI

[67] J. D. Atkinson; L. M. Brown; W. M. Stobbs The work-hardening of copper-silica. IV. The Bauschinger effect and plastic relaxation, Philos. Mag., Volume 30 (1974), pp. 1247-1280 | DOI

[68] S. F. Corbin; D. S. Wilkinson; J. D. Embury The Bauschinger effect in a particulate reinforced Al alloy, Mater. Sci. Eng. A, Volume 207 (1996) no. 1, pp. 1-11 | DOI

[69] C. Rey; A. Zaoui Slip heterogeneities in deformed aluminium bi-crystals, Acta Metall., Volume 28 (1980), pp. 687-697 | DOI

[70] H. Mughrabi Dislocation clustering and long-range internal stresses in monotonically and cyclically deformed metal crystals, Rev. Phys. Appl., Volume 23 (1988), pp. 367-379 | DOI

[71] C. Rey; G. Saada The elastic field of periodic dislocation networks, Philos. Mag., Volume 33 (1976), pp. 825-841 | DOI

[72] S. Forest Some links between Cosserat, strain gradient crystal plasticity and the statistical theory of dislocations, Philos. Mag., Volume 88 (2008), pp. 30-32 | DOI

[73] K. Tanaka; T. Mura A dislocation model for fatigue crack initiation, ASME J. Appl. Mech., Volume 48 (1981), pp. 97-103 | DOI

[74] R. J. Asaro Elastic-plastic memory and kinematic-type hardening, Acta Metall., Volume 23 (1975), pp. 1255-1265 | DOI

[75] R. Taillard; A. Pineau Room temperature tensile properties of Fe-19wt.%Cr alloys precipitation hardened by the intermetallic compound NiAl, Mater. Sci. Eng., Volume 56 (1982), pp. 219-231 | DOI

[76] R. Stoltz; R. Pelloux The Bauschinger effect in precipitation strengthened aluminum alloys, Metall. Trans. A, Volume 7 (1975), pp. 1295-1306 | DOI

[77] H. Proudhon; W. Poole; X. Wang; Y. Bréchet The role of internal stresses on the plastic deformation of the Al–Mg–Si–Cu alloy AA611, Philos. Mag., Volume 88 (2008), pp. 621-640 | DOI

Cité par Sources :

Commentaires - Politique


Ces articles pourraient vous intéresser

Generalised continuum modelling of grain size effects in polycrystals

Nicolas M. Cordero; Samuel Forest; Esteban P. Busso

C. R. Méca (2012)


Foreword: Plasticity and Solid State Physics

Samuel Forest; David Rodney

C. R. Phys (2021)


Grain size effects and weakest link theory in 3D crystal plasticity simulations of polycrystals

Lionel Gélébart

C. R. Phys (2021)