Comptes Rendus
Identification methodology of a rate-sensitive constitutive law with mean field and full field modeling approaches for polycrystalline materials
Comptes Rendus. Mécanique, Volume 348 (2020) no. 10-11, pp. 807-826.

The present paper deals with the consideration of the rate-sensitivity mechanical behavior of metallic materials, in the framework of mean field and full field homogenization approaches. We re-examine the possibility of describing properly this rate sensitivity with a simple and widely used power law expressed at the level of the slip system, and we propose a methodology to accelerate the identification of the global material constitutive law for Finite Element (FE) simulations. For such an aim, simulations of a tensile test are conducted, using a simple homogenization model (the Taylor one, used in a relaxed constraint form) and an FE code (Abaqus), both using the same single-crystal rate-dependent constitutive law. It is shown that, provided that the identification of this law is performed with care and well adapted to the examined case (rate-sensitive or insensitive materials, static and/or dynamic ranges), the simple power law can be used to simulate the macroscopic behavior of polycrystalline aggregates in a wide range of strain rate (including both static and dynamic regimes) and strain-rate sensitivity values (up the rate-insensitive limit).

Online First:
Published online:
DOI: 10.5802/crmeca.56
Keywords: Viscoplasticity, Polycrystalline materials, Strain-rate sensitivity, Finite Element, Constitutive law
Yann Charles 1; Chunping Zhang 2; Monique Gaspérini 1; Brigitte Bacroix 3

1 Université Sorbonne Paris Nord, Laboratoire des Sciences des Procédés et des Matériaux, LSPM, CNRS, UPR 3407, F-93430, Villetaneuse, France
2 Département de Génie Mécanique, École de Technologie Supérieure, 1100 Rue Notre-Dame Ouest, Montréal, QC H3C 1K3, Canada
3 CNRS, UPR3407, Laboratoire des Sciences des Procédés et des Matériaux, LSPM, Université Sorbonne Paris Nord, F-93430, Villetaneuse, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Yann Charles and Chunping Zhang and Monique Gasp\'erini and Brigitte Bacroix},
     title = {Identification methodology of a rate-sensitive constitutive law with mean field and full field modeling approaches for polycrystalline materials},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {807--826},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {10-11},
     year = {2020},
     doi = {10.5802/crmeca.56},
     language = {en},
AU  - Yann Charles
AU  - Chunping Zhang
AU  - Monique Gaspérini
AU  - Brigitte Bacroix
TI  - Identification methodology of a rate-sensitive constitutive law with mean field and full field modeling approaches for polycrystalline materials
JO  - Comptes Rendus. Mécanique
PY  - 2020
SP  - 807
EP  - 826
VL  - 348
IS  - 10-11
PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.56
LA  - en
ID  - CRMECA_2020__348_10-11_807_0
ER  - 
%0 Journal Article
%A Yann Charles
%A Chunping Zhang
%A Monique Gaspérini
%A Brigitte Bacroix
%T Identification methodology of a rate-sensitive constitutive law with mean field and full field modeling approaches for polycrystalline materials
%J Comptes Rendus. Mécanique
%D 2020
%P 807-826
%V 348
%N 10-11
%I Académie des sciences, Paris
%R 10.5802/crmeca.56
%G en
%F CRMECA_2020__348_10-11_807_0
Yann Charles; Chunping Zhang; Monique Gaspérini; Brigitte Bacroix. Identification methodology of a rate-sensitive constitutive law with mean field and full field modeling approaches for polycrystalline materials. Comptes Rendus. Mécanique, Volume 348 (2020) no. 10-11, pp. 807-826. doi : 10.5802/crmeca.56.

[1] G. R. Canova; C. Fressengeas; A. Molinari; U. F. Kocks Effect of rate sensitivity on slip system activity and lattice rotation, Acta Metall., Volume 36 (1988) no. 8, pp. 1961-1970 | DOI

[2] L. S. Toth; P. Gilormini; J. J. Jonas Effect of rate sensitivity on the stability of torsion textures, Acta Metall., Volume 36 (1988) no. 12, pp. 3077-3091 | DOI

[3] G. I. Taylor The mechanism of plastic deformation of crystals. Part I. Theoretical, Proc. R. Soc. Lond. A, Volume 145 (1934) no. 855, pp. 362-387 | Zbl

[4] R. A. Lebensohn; C. N. Tome; P. P. Castaneda Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations, Phil. Mag., Volume 87 (2007) no. 28, pp. 4287-4322 | DOI

[5] J. W. Hutchinson Bounds and self-consistent estimates for creep of polycrystalline materials, Proc. R. Soc. Lond. A, Volume 348 (1976), pp. 101-127 | Zbl

[6] I. J. Beyerlein; C. N. Tomé Modeling transients in the mechanical response of copper due to strain path changes, Int. J. Plast., Volume 23 (2007) no. 4, pp. 640-664 | DOI | Zbl

[7] V.-T. Phan; T.-D. Nguyen; Q.-H. Bui; G. Dirras Modelling of microstructural effects on the mechanical behavior of ultrafine-grained Nickel using crystal plasticity finite element model, Int. J. Eng. Sci., Volume 94 (2015), pp. 212-225 | DOI

[8] B. Klusemann; B. Svendsen; H. Vehoff Investigation of the deformation behavior of Fe–3%Si sheet metal with large grains via crystal plasticity and finite-element modeling, Comput. Mater. Sci., Volume 52 (2012) no. 1, pp. 25-32 | DOI

[9] A. S. Khan; J. Liu; J. W. Yoon; R. Nambori Strain rate effect of high purity aluminum single crystals: experiments and simulations, Int. J. Plast., Volume 67 (2015), pp. 39-52 | DOI

[10] A. Shahba; S. Ghosh Crystal plasticity FE modeling of Ti alloys for a range of strain-rates. Part I: a unified constitutive model and flow rule, Int. J. Plast., Volume 87 (2016), pp. 48-68 | DOI

[11] G. Monnet; L. Vincent; B. Devincre Dislocation-dynamics based crystal plasticity law for the low- and high-temperature deformation regimes of bcc crystal, Acta Mater., Volume 61 (2013) no. 16, pp. 6178-6190 | DOI

[12] P. Shanthraj; M. A. Zikry Dislocation density evolution and interactions in crystalline materials, Acta Mater., Volume 59 (2011) no. 20, pp. 7695-7702 | DOI

[13] R. J. Asaro Crystal Plast, J. Appl. Mech., Volume 50 (1983), pp. 921-934 | DOI | Zbl

[14] R. Hill; J. R. Rice Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids, Volume 20 (1972), pp. 401-413 | DOI | Zbl

[15] C. Miehe; J. Schröder A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity, Int. J. Numer. Methods Eng., Volume 50 (2001), pp. 273-298 | DOI | Zbl

[16] J. W. Hutchinson; K. W. Neale Influence of strain-rate sensitivity on necking under uniaxial tension, Acta Metall., Volume 25 (1977) no. 8, pp. 839-846 | DOI

[17] G. Vadillo; J. A. Rodríguez-Martínez; J. Fernández-Sáez On the interplay between strain rate and strain rate sensitivity on flow localization in the dynamic expansion of ductile rings, Int. J. Solids Struct., Volume 49 (2012) no. 3–4, pp. 481-491 | DOI

[18] F. Zhou; J. F. Molinari; K. T. Ramesh Effects of material properties and strain rate on the fragmentation of brittle materials, Int. J. Fract., Volume 139 (2006), pp. 169-196 | DOI | Zbl

[19] R. J. Asaro; A. Needleman Overview no. 42 Texture development and strain hardening in rate dependent polycrystals, Acta Metall., Volume 33 (1985) no. 6, pp. 923-953 | DOI

[20] R. W. Klopp; R. J. Clifton; T. G. Shawki Pressure-shear impact and the dynamic viscoplastic response of metals, Mech. Mater., Volume 4 (1985) no. 3, pp. 375-385 | DOI

[21] Z. Leng; H. Pan; Z. Niu; C. Guo; Q. Zhang; Y. Chang; M. Zhang; F. Jiang Mechanical behavior, deformation and damage mechanisms of Mg–RY–Zn alloy under high strain rate, Mater. Sci. Eng. A, Volume 651 (2016), pp. 336-340 | DOI

[22] A. Bintu; G. Vincze; R. C. Picu; A. B. Lopes Effect of symmetric and asymmetric rolling on the mechanical properties of AA5182, Mater. Design, Volume 100 (2016), pp. 151-156 | DOI

[23] J. Luo; M. Li; W. Yu; H. Li The variation of strain rate sensitivity exponent and strain hardening exponent in isothermal compression of Ti–6Al–4V alloy, Mater. Design, Volume 31 (2010) no. 2, pp. 741-748 | DOI

[24] J. Luo; J. Gao; L. Li; M. Q. Li The flow behavior and the deformation mechanisms of Ti–6Al–2Zr–2Sn–2Mo–1.5Cr–2Nb alloy during isothermal compression, J. Alloys Compd., Volume 667 (2016), pp. 44-52 | DOI

[25] Z. N. Mao; X. H. An; X. Z. Liao; J. T. Wang Opposite grain size dependence of strain rate sensitivity of copper at low vs high strain rates, Mater. Sci. Eng. A, Volume 738 (2018), pp. 430-438 | DOI

[26] L. Peroni; M. Scapin Experimental analysis and modelling of the strain-rate sensitivity of sheet niobium, EPJ Web Conf., Volume 183 (2018), 01014 | DOI

[27] A. Rusinek; J. A. Rodríguez-Martínez; A. Arias A thermo-viscoplastic constitutive model for FCC metals with application to OFHC copper, Int. J. Mech. Sci., Volume 52 (2010) no. 2, pp. 120-135 | DOI

[28] S. Fréchard; A. Redjaïmia; E. Lach; A. Lichtenberger Dynamical behaviour and microstructural evolution of a nitrogen-alloyed austenitic stainless steel, Mater. Sci. Eng. A, Volume 480 (2008) no. 1, pp. 89-95 | DOI

[29] M. Knezevic; M. Zecevic; I. J. Beyerlein; R. A. Lebensohn A numerical procedure enabling accurate descriptions of strain rate-sensitive flow of polycrystals within crystal visco-plasticity theory, Comput. Meth. Appl. Mech. Eng., Volume 308 (2016), pp. 468-482 | DOI | MR | Zbl

[30] S. Kok; A. J. Beaudoin; D. A. Tortorelli A polycrystal plasticity model based on the mechanical threshold, Int. J. Plast., Volume 18 (2002) no. 5, pp. 715-741 | DOI | Zbl

[31] S. Forest; M. B. Rubin A rate-independent crystal plasticity model with a smooth elastic–plastic transition and no slip indeterminacy, Eur. J. Mech. A Solids, Volume 55 (2016), pp. 278-288 | DOI | MR | Zbl

[32] M. Zecevic; M. Knezevic A new visco-plastic self-consistent formulation implicit in dislocation-based hardening within implicit finite elements: application to high strain rate and impact deformation of tantalum, Comput. Meth. Appl. Mech. Eng., Volume 341 (2018), pp. 888-916 | DOI | MR | Zbl

[33] Y. Huang A User-Material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program, 1991 (Unknown)

[34] L. Hu; S. Jiang; Y. Zhang; D. Sun Crystal plasticity finite element simulation of NiTi shape memory alloy based on representative volume element, Met. Mater. Int., Volume 23 (2017), p. 1075 | DOI

[35] D. Peirce; R. J. Asaro; A. Needleman An analysis of nonuniform and localized deformation in ductile single crystals, Acta Metall., Volume 30 (1982) no. 6, pp. 1087-1119 | DOI

[36] R. J. Asaro Micromechanics of crystals and polycrystals, Adv. Appl. Mech. (W. H. John; Y. W. Theodore, eds.), Elsevier, Cambridge, MA, USA, 1983, pp. 1-115

[37] M. Arminjon; B. Bacroix On plastic potentials for anisotropic metals and their derivation from the texture function, Acta Mech., Volume 88 (1991) no. 3–4, pp. 219-243 | DOI | Zbl

[38] G. Sachs Zur Ableitung einer Filebedingung, Z. Vereines Deutscher Ingenieure, Volume 72 (1928), pp. 734-736

[39] A. Kochendorfer Plastiche Eigenschaften von Kristallen und Metallischen Werkstoffen, Springer, Berlin, 1941 | Zbl

[40] B. Bacroix; S. Queyreau; D. Chaubet; E. Siv; T. Chauveau The influence of the cube component on the mechanical behaviour of copper polycrystalline samples in tension, Acta Mater., Volume 160 (2018), pp. 121-136 | DOI

[41] R. Quey; P. R. Dawson; F. Barbe Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing, Comput. Meth. Appl. Mech. Eng., Volume 200 (2011) no. 17, pp. 1729-1745 | DOI | Zbl

[42] Simulia Abaqus Scripting User’s Manual, Dassault Système, Providence, Rhode Island, USA, 2011

[43] A. Salahouelhadj; H. Haddadi Estimation of the size of the RVE for isotropic copper polycrystals by using elastic-plastic finite element homogenisation, Comput. Mater. Sci., Volume 48 (2010) no. 3, pp. 447-455 | DOI

[44] Y. Charles; R. Estevez; E. Maire; Y. Brechet Modelling the competition between interface debonding and particle fracture using a plastic strain dependent cohesive zone, Eng. Fract. Mech., Volume 77 (2010) no. 4, pp. 705-718 | DOI

[45] W. F. Hosford Mechanical Behaviour of Materials, Cambridge University Press, New York, NY, USA, 2010

[46] S. A. Chavez; G. E. Korth; D. M. Harper; T. J. Walker High-temperature tensile and creep data for Inconel 600, 304 stainless steel and SA106B carbon steel, Nucl. Eng. Design, Volume 148 (1994) no. 2, pp. 351-363 | DOI

[47] S. El Shawish; L. Cizelj Combining single-and poly-crystalline measurements for identification of crystal plasticity parameters: application to austenitic stainless steel, Crystals, Volume 7 (2017), p. 181 | DOI

[48] Y. Zhang; S. Jiang; L. Hu; Y. Zhao; D. Sun Investigation of primary static recrystallization in a NiTiFe shape memory alloy subjected to cold canning compression using the coupling crystal plasticity finite element method with cellular automaton, Model. Simul. Mater. Sci. Eng., Volume 25 (2017), 075008 | DOI

[49] K. Teferra; L. Graham-Brady A random field-based method to estimate convergence of apparent properties in computational homogenization, Comput. Meth. Appl. Mech. Eng., Volume 330 (2018), pp. 253-270 | DOI | MR | Zbl

[50] L. Hu; S. Jiang; T. Zhou; J. Tu; L. Shi; Q. Chen; M. Yang Multiscale modeling of polycrystalline NiTi shape memory alloy under various plastic deformation conditions by coupling microstructure evolution and macroscopic mechanical response, Mater. Design, Volume 10 (2017), p. 1172

[51] L. Zhao; P. Chakraborty; M. R. Tonks; I. Szlufarska On the plastic driving force of grain boundary migration: a fully coupled phase field and crystal plasticity model, Comput. Mater. Sci., Volume 128 (2017), pp. 320-330 | DOI

[52] A. Belkhabbaz; B. Bacroix; R. Brenner Investigation of the elastoplastic behavior of FCC polycrytals using a FFT numerical scheme, Roumanian J. Techn. Sci. – Appl. Mech., Volume 60 (2015), pp. 5-23 | MR

[53] N. Christodoulou; J. J. Jonas Flow localization in OFHC Cu and 99.99% Al, Acta Metall., Volume 33 (1985) no. 4, pp. 719-730 | DOI

[54] N. Christodoulou; J. J. Jonas Work hardening and rate sensitivity material coefficients for OFHC Cu and 99.99% Al, Acta Metall., Volume 32 (1984), pp. 1655-1668 | DOI

[55] A. Uenishi; C. Teodosiu Constitutive modelling of the high strain rate behaviour of interstitial-free steel, Int. J. Plast., Volume 20 (2004), pp. 915-936 | DOI | Zbl

[56] J. D. Campbell Dynamic Plasticity of Metals (U. CISM, ed.), Springer, Berlin, 1970 | DOI

Cited by Sources:

Articles of potential interest

Efficient simulation of single and poly-crystal plasticity based on the pencil glide mechanism

Lu Tuan Le; Kais Ammar; Samuel Forest

C. R. Méca (2020)

Multiscale modeling of the effective viscoplastic behavior of Mg 2 SiO 4 wadsleyite: bridging atomic and polycrystal scales

O. Castelnau; K. Derrien; S. Ritterbex; ...

C. R. Méca (2020)