Comptes Rendus
Efficient simulation of single and poly-crystal plasticity based on the pencil glide mechanism
Comptes Rendus. Mécanique, Volume 348 (2020) no. 10-11, pp. 847-876.

The present work demonstrates that the pencil glide mechanism is a physically reliable and a computationally efficient model to simulate the nonlinear behaviour of b.c.c. single and polycrystals. For that purpose, the pencil glide extension of Schmid’s criterion used by Gilormini [1] is incorporated in a single crystal model and in a homogenized polycrystal model accounting for large elastoviscoplastic deformations. The response of the pencil glide model in terms of stress-strain curves and lattice rotation is compared to the prediction based on the consideration of all ({110}111+{112}111) slip systems. In the case of α-iron single crystals both approaches are shown to accurately reproduce recent experimental results [2, 3]. The comparison is extended to α-iron polycrystals behaviour under tension, compression, rolling and simple shear loading conditions. The evolution of crystallographic textures obtained either based on pencil glide or using the 24 slip systems is analyzed and compared to classical experimental results from the literature. Limitations of the approach, especially in the case of simple shear textures, are also pointed out. The pencil glide approach can be viewed as a reduced order model enhancing computational efficiency of crystal plasticity simulations involving many slip mechanisms.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.5802/crmeca.44
Mots clés : Crystal plasticity, Pencil glide, Single crystal, Polycrystal, b.c.c. crystal, Homogenization, Texture

Lu Tuan Le 1 ; Kais Ammar 1 ; Samuel Forest 1

1 MINES ParisTech, PSL University, Centre des matériaux (CMAT), CNRS UMR 7633, BP 87 91003 Evry, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMECA_2020__348_10-11_847_0,
     author = {Lu Tuan Le and Kais Ammar and Samuel Forest},
     title = {Efficient simulation of single and poly-crystal plasticity based on the pencil glide mechanism},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {847--876},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {10-11},
     year = {2020},
     doi = {10.5802/crmeca.44},
     language = {en},
}
TY  - JOUR
AU  - Lu Tuan Le
AU  - Kais Ammar
AU  - Samuel Forest
TI  - Efficient simulation of single and poly-crystal plasticity based on the pencil glide mechanism
JO  - Comptes Rendus. Mécanique
PY  - 2020
SP  - 847
EP  - 876
VL  - 348
IS  - 10-11
PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.44
LA  - en
ID  - CRMECA_2020__348_10-11_847_0
ER  - 
%0 Journal Article
%A Lu Tuan Le
%A Kais Ammar
%A Samuel Forest
%T Efficient simulation of single and poly-crystal plasticity based on the pencil glide mechanism
%J Comptes Rendus. Mécanique
%D 2020
%P 847-876
%V 348
%N 10-11
%I Académie des sciences, Paris
%R 10.5802/crmeca.44
%G en
%F CRMECA_2020__348_10-11_847_0
Lu Tuan Le; Kais Ammar; Samuel Forest. Efficient simulation of single and poly-crystal plasticity based on the pencil glide mechanism. Comptes Rendus. Mécanique, Volume 348 (2020) no. 10-11, pp. 847-876. doi : 10.5802/crmeca.44. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.44/

[1] P. Gilormini The theory of rate sensitive pencil glide application to rolling textures, Acta Metall., Volume 37 (1989), pp. 2093-2101 | DOI

[2] L. Le; P. Franciosi Expectable specific features of BCC crystal plastic flow and consistency with the Schmid law, Phil. Mag., Volume 93 (2013), pp. 3589-3611 | DOI

[3] P. Franciosi; L. Le; G. Monnet; C. Kahloun; M.-H. Chavanne Investigation of slip system activity in iron at room temperature by SEM and AFM in-situ tensile and compression tests of iron single crystals, Int. J. Plast., Volume 65 (2015), pp. 226-249 | DOI

[4] G. Taylor; C. Elam The distortion of iron crystals, Proc. R. Soc. Lond. A, Volume 112 (1926), pp. 337-361

[5] P. Gilormini; B. Bacroix; J. Jonas Theoretical analyses of 111 pencil glide in b.c.c. crystals, Acta Metall., Volume 36 (1988), pp. 231-256 | DOI

[6] R. Becker Pencil glide formulation for polycrystal modelling, Scr. Metall. Mater., Volume 32 (1995), pp. 2051-2054 | DOI

[7] G. Taylor Plastic strain in metals, J. Inst. Metals, Volume 62 (1938), pp. 307-324

[8] G. Sachs Zur Ableitung einer Fliessbedingung, Z. Verein. Dtsch. Ing., Volume 72 (1928), pp. 734-736

[9] J. Bishop; R. Hill A theory of the plastic distortion of a polycrystalline aggregate under combined stresses, Lond. Edinburgh Dublin Phil. Mag. J. Sci., Volume 42 (1951) no. 327, pp. 414-427 | DOI | MR | Zbl

[10] H. Honnef; H. Mecking A method for the determination of the active slip systems and orientation changes during single crystal deformation, Proceedings of the 5th International Conference on Texture of Materials, Springer Verlag, 1978, pp. 265-275 | DOI

[11] H. Mecking Low temperature deformation of polycrystals, Proceedings of the 2th International Symposium on Metallurgy and Materials Science: Deformation of Polycrystals, Danmarks Tekniske Universitet, 1981, pp. 73-86

[12] U. Kocks; G. Canova How many slip systems and which?, Deformation of polycrystals: Mechanisms and Microstructures, 2nd International Symposium on Metallurgy and Materials Science (N. Hansen; A. Horsewell; T. Leffers; H. E. Liholt, eds.), Risø National Laboratory, Roskilde, Denmark, 1981, pp. 35-44

[13] P. Van Houtte On the equivalence of the relaxed taylor theory and the bishop-hill theory for partially constrained plastic deformation of crystals, Mater. Sci. Eng., Volume 55 (1982), pp. 69-77 | DOI

[14] M. Arminjon Théorie d’une classe de modèles de Taylor Hétérogènes: application aux textures de déformation des aciers, Acta. Metall., Volume 35 (1987), p. 615 | DOI

[15] M. Arminjon; C. Donadille Présentaion d’un modèle polycrystallin extrémal: application aux aciers d’un modèle approché, Mém. Et. Sci. Revue Métall., Volume 87 (1990), p. 359

[16] A. Molinari Extensions of the self-consistent tangent model, Model. Simul. Mater. Sci. Eng., Volume 7 (1999), pp. 683-697 | DOI

[17] R. Lebensohn; C. Tome A self-consistent visco-plastic model: calculation of rolling textures of anisotropic materials, Mater. Sci. Eng. A, Volume 175 (1994), pp. 71-82 | DOI

[18] M. Berveiller; A. Zaoui An Extension of the self-consistent scheme to plastically flowing polycrystals, J. Mech. Phys. Solids, Volume 26 (1979), pp. 325-344 | DOI | Zbl

[19] P. Lipinski; J. Krier; M. Berveiller Elastoplasticité des métaux en grandes déformations: comportement global et évolution de la structure interne, Rev. Phys. Appl., Volume 25 (1990), pp. 361-388 | DOI

[20] G. Cailletaud A micromechanical approach to inelastic behaviour of metals, Int. J. Plast., Volume 8 (1992), pp. 55-73 | DOI | Zbl

[21] S. Forest; P. Pilvin Modelling finite deformation of polycrystals using local objective frames, Z. Angew. Math. Mech., Volume 79 (1999), pp. 199-202 | DOI | Zbl

[22] K. Sai; G. Cailletaud; S. Forest Micro-mechanical modeling of the inelastic behavior of directionally solidiffed materials, Mech. Mat., Volume 38 (2006) no. 3, pp. 203-217 | DOI

[23] G. Martin; N. Ochoa; K. Sai; E. Hervé-Luanco; G. Cailletaud A multiscale model for the elastoviscoplastic behavior of directionally solidified alloys: application to FE structural computations, Int. J. Solids Struct., Volume 51 (2014), pp. 1175-1187 | DOI

[24] G. Cailletaud; F. Coudon Scale transition rules applied to crystal plasticity, Materials with Internal Structure: Multiscale and Multifield Modeling and Simulation (P. Trovalusci, ed.), Springer International Publishing, 2016, pp. 1-15

[25] F. Coudon; G. Cailletaud; J. Cormier; L. Marcin A multiscale model for nickel-based directionally solidified materials, Int. J. Plast., Volume 115 (2019), pp. 1-17 | DOI

[26] P. Pilvin Une approche inverse pour l’identification d’un modèle polycristallin élastoviscoplastique, 3ème Colloque National en Calcul des Structures, 20–23 mai, Giens, Presses Académiques de l’Ouest, 1997, pp. 207-212

[27] J. Besson; G. Cailletaud; J.-L. Chaboche; S. Forest; M. Blétry Non–Linear Mechanics of Materials, Solid Mechanics and Its Applications, 167, Springer-Verlag, Berlin, Heidelberg, 2009

[28] N. Hfaiedh; A. Roos; H. Badreddine; K. Saanouni Interaction between ductile damage and texture evolution in finite polycrystalline elastoplasticity, Int. J. Damage Mech., Volume 28 (2019), pp. 481-501 | DOI

[29] J. Mandel Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques, Int. J. Solids Struct., Volume 9 (1973), pp. 725-740 | DOI | Zbl

[30] A. Krawietz Efficient integration in the plasticity of crystals with pencil glide and deck glide, Tech. Mech., Volume 21 (2001), pp. 243-250

[31] R. Glüge Glide mechanisms for bundle- and plate-like structures, Tech. Mech., Volume 35 (2015), pp. 62-69

[32] C. Guillemer; M. Clavel; G. Cailletaud Cyclic behavior of extruded magnesium: experimental, microstructural and numerical approach, Int. J. Plast., Volume 27 (2011), pp. 2068-2084 | DOI | Zbl

[33] M. Lindroos; G. Cailletaud; A. Laukkanen; V.-T. Kuokkala Crystal plasticity modeling and characterization of the deformation twinning and strain hardening in Hadfield steels, Mat. Sci. Eng., Volume 720 (2018), pp. 145-159 | DOI

[34] P. Pilvin The Contribution of Micromechanical Approaches to the Modelling of Inelastic Behaviour of Polycrystals, Fourth Int. Conf. on Biaxial/multiaxial Fatigue and Design (London) (A. Pineau; G. Cailletaud; T. Lindley, eds.) (ESIS), Volume 21, Mechanical Engineering Publications, 1996, pp. 3-19

[35] G. Martin; L. Nazé; G. Cailletaud Numerical multi-scale simulations of the mechanical behavior of β-metastable titanium alloys Ti5553 and Ti17, Procedia Eng., Volume 10 (2011), p. 1803-808 | DOI

[36] P. Pilvin; F. Onimus; R. Brenner; S. Pascal; X. Feaugas; K. Saï Finite element assessment of an affine self-consistent model for hexagonal polycrystals, Eur. J. Mech. - A/Solids, Volume 61 (2017), pp. 345-356 | DOI

[37] T. Gu; J.-R. Medy; V. Klosek; O. Castelnau; S. Forest; E. Hervé-Luanco; F. Lecouturier-Dupouy; H. Proudhon; P.-O. Renault; L. Thilly; P. Villechaise Multiscale modeling of the elasto-plastic behavior of architectured and nanostructured Cu-Nb composite wires and comparison with neutron diffraction experiments, Int. J. Plast., Volume 122 (2019), pp. 1-30 | DOI

[38] A. Bertram; M. Kraska Determination of finite plastic deformations in single crystals, Arch. Mech., Volume 47 (1995), pp. 203-222 | Zbl

[39] D. Caillard Kinetics of dislocations in pure Fe. Part I. In situ straining experiments at room temperature, Acta Mater., Volume 58 (2010), pp. 3493-3503 | DOI

[40] J. Kumagai; S. Takaki; S. Suzuki; H. Kimura Orientation dependence of quasi-three-stage work hardening in high purity iron single crystals, Mater. Sci. Eng., Volume A 129 (1990) no. 2, pp. 207-215 | DOI

[41] B. Jaoul Etude de la plasticité et application aux métaux, 1st published, Presses des Mines de Paris, 1965

[42] G. Monnet; D. Terentyev Structure and mobility of the edge dislocation in BCC iron studied by molecular dynamics, Acta Mater., Volume 57 (2009) no. 5, pp. 1416-1426 | DOI

[43] S. Queyreau; J. Marian; M. Gilbert; B. Wirth Edge dislocation mobilities in bcc Fe obtained by molecular dynamics, Phys. Rev. B, Volume 84 (2011) no. 6, 064106 | DOI

[44] C. Domain; G. Monnet Simulation of screw dislocation motion in iron by molecular dynamics simulations, Phys. Rev. Lett., Volume 95 (2005) no. 21, 215506 | DOI

[45] P. Franciosi Etude théorique et expérimentale du comportement élastoplastique des monocristaux métalliques se déformant par glissement : modélisation pour un chargement complexe quasi-statique, Ph. D. Thesis, Université Paris 13 (1984)

[46] R. Madec; L. Kubin Dislocation Interactions and Symmetries in BCC Crystals, Springer, Netherlands, 2004, pp. 69-78

[47] R. Madec; B. Devincre; L. Kubin From dislocation junctions to forest hardening, Phys. Rev. Lett., Volume 89 (2003), 255508

[48] L. P. Kubin; R. Madec; B. Devincre Dislocation intersections and reactions in FCC and BCC crystals, MRS Proc., Volume 779 (2003), W1.6

[49] R. Madec; B. Devincre; L. Kubin; T. Hoc; D. Rodney The role of collinear interaction in dislocation-induced hardening, Science, Volume 301 (2003), pp. 1879-1882 | DOI

[50] S. Queyreau; G. Monnet; B. Devincre Slip systems interactions in a-iron determined by dislocation dynamics simulations, Int. J. Plast., Volume 25 (2009) no. 2, pp. 361-377 | DOI | Zbl

[51] L. T. Le Etude par essais in situ MEB et AFM sur monocristaux des mécanismes de glissement á température ambiante de la ferrite de pureté commerciale, Ph. D. Thesis, Université Paris Nord (2013)

[52] E. Bruder Mechanical properties of ARMCO ®  iron after large and severe plastic deformation-application potential for precursors to ultrafine grained microstructures, Metals, Volume 8 (2018), pp. 191-203 | DOI

[53] P. Coulomb Les textures dans les métaux de réseau cubique, Dunod, Paris, France, 1972

[54] U. Kocks; C. Tomé; H. R. Wenk Texture and Anisotropy, Cambridge University Press, 1998 | Zbl

[55] A. Das Calculation of crystallographic texture of BCC steels during cold rolling, J. Mat. Eng. Perform., Volume 26 (2017) no. 6, pp. 2708-2720 | DOI

[56] D. Ceccaldi; F. Yala; T. Baudin; R. Penelle; F. Royer; M. Arminjon Deformation textures and plastic anisotropy of steels using the Taylor and nonhomogeneous models, Int. J. Plast., Volume 10 (1994), pp. 643-661 | DOI | Zbl

[57] M. Hoelscher; D. Raabe; K. Luecke Rolling and recrystallization textures of BCC steels, Steel Res. Int., Volume 62 (1991), pp. 567-575 | DOI

[58] S. M’Guil; W. Wen; S. Ahzi; J. J. Gracio Modeling of large plastic deformation behavior and anisotropy evolution in cold rolled bcc steels using the viscoplastic ϕ-model-based grain-interaction, Mat. Sci. Eng.: A, Volume 528 (2011), pp. 5840-5853 | DOI

[59] D. Raabe Investigation of contribution of {123} slip planes to development of rolling textures in bcc metals by use of Taylor models, Mater. Sci. Technol., Volume 11 (1995), pp. 455-460 | DOI

[60] J. Baczynski; J. J. Jonas Texture development during the torsion testing of α-iron and two IF steels, Acta Mater., Volume 44 (1996), pp. 4273-4288 | DOI

[61] O. W. Williams Shear texture in copper, brass, aluminum, iron and zirconium, Trans. Metall. Soc. AIME, Volume 224 (1962), pp. 129-139

[62] C. Kahloun; G. Monnet; S. Queyreau; L. Le; P. Franciosi A comparison of collective dislocation motion from single slip quantitative topographic analysis during in-situ AFM room temperature tensile tests on Cu and Feα crystals, Int. J. Plast., Volume 84 (2016), pp. 277-298 | DOI

[63] J. L. Raphanel; P. Van Houtte Simulation of the rolling textures of b.c.c. metals by means of the relaxed taylor theory, Acta Metall., Volume 33 (1985), pp. 1481-1488 | DOI

[64] L. P. Kubin; R. Madec; B. Devincre Dislocation intersections and reactions in FCC and BCC crystals, MRS Proc., Volume 779 (2003), W1.6

[65] G. Cailletaud; P. Pilvin Utilisation de modèles polycristallins pour le calcul par éléments finis, Rev. Européenne des Éléments Finis, Volume 3 (1994), pp. 515-541 | DOI | Zbl

Cité par Sources :

Commentaires - Politique