Comptes Rendus
A constitutive model accounting for strain ageing effects on work-hardening. Application to a C–Mn steel
Comptes Rendus. Mécanique, Volume 345 (2017) no. 12, pp. 908-921.

One of the most successful models for describing the Portevin–Le Chatelier effect in engineering applications is the Kubin–Estrin–McCormick model (KEMC). In the present work, the influence of dynamic strain ageing on dynamic recovery due to dislocation annihilation is introduced in order to improve the KEMC model. This modification accounts for additional strain hardening rate due to limited dislocation annihilation by the diffusion of solute atoms and dislocation pinning at low strain rate and/or high temperature. The parameters associated with this novel formulation are identified based on tensile tests for a C–Mn steel at seven temperatures ranging from 20 °C to 350 °C. The validity of the model and the improvement compared to existing models are tested using 2D and 3D finite element simulations of the Portevin–Le Chatelier effect in tension.

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DOI: 10.1016/j.crme.2017.09.005
Keywords: Portevin–Le Chatelier effect, Dislocation density, Identification, FEM simulation, Plasticity, C–Mn steel

Sicong Ren 1; Matthieu Mazière 1; Samuel Forest 1; Thilo F. Morgeneyer 1; Gilles Rousselier 1

1 MINES ParisTech, PSL Research University, MAT–Centre des matériaux, CNRS UMR 7633, BP 87, 91003 Évry, France
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Sicong Ren; Matthieu Mazière; Samuel Forest; Thilo F. Morgeneyer; Gilles Rousselier. A constitutive model accounting for strain ageing effects on work-hardening. Application to a C–Mn steel. Comptes Rendus. Mécanique, Volume 345 (2017) no. 12, pp. 908-921. doi : 10.1016/j.crme.2017.09.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.09.005/

[1] Z.Y. Jiang; Q.C. Zhang; H.F. Jiang; Z.J. Chen; X.P. Wu Spatial characteristics of the Portevin–Le Chatelier deformation bands in Al-4at% Cu polycrystals, Mater. Sci. Eng. A, Volume 403 (2005) no. 1, pp. 154-164

[2] N. Ranc; D. Wagner Some aspects of Portevin–Le Chatelier plastic instabilities investigated by infrared pyrometry, Mater. Sci. Eng. A, Volume 394 (2005) no. 1, pp. 87-95

[3] T. Böhlke; G. Bondár; Y. Estrin; M.A. Lebyodkin Geometrically non-linear modeling of the Portevin–Le Chatelier effect, Comput. Mater. Sci., Volume 44 (2009) no. 4, pp. 1076-1088

[4] S.C. Ren, T.F. Morgeneyer, M. Mazière, S. Forest, G. Rousselier, Portevin–Le chatelier effect triggered by complex loading paths in an Al–Cu aluminium alloy. Submitted for publication.

[5] H. Dierke; F. Krawehl; S. Graff; S. Forest; J. Šachl; H. Neuhäuser Portevin–Le Chatelier effect in Al–Mg alloys: influence of obstacles—experiments and modelling, Comput. Mater. Sci., Volume 39 (2007) no. 1, pp. 106-112

[6] H. Louche; P. Vacher; R. Arrieux Thermal observations associated with the Portevin–Le Chatelier effect in an Al–Mg alloy, Mater. Sci. Eng. A, Volume 404 (2005) no. 1, pp. 188-196

[7] R.C. Picu; G. Vincze; F. Ozturk; J.J. Gracio; F. Barlat; A.M. Maniatty Strain rate sensitivity of the commercial aluminum alloy AA5182-O, Mater. Sci. Eng. A, Volume 390 (2005) no. 1, pp. 334-343

[8] H. Halim; D.S. Wilkinson; M. Niewczas The Portevin–Le Chatelier (PLC) effect and shear band formation in an AA5754 alloy, Acta Mater., Volume 55 (2007) no. 12, pp. 4151-4160

[9] H.D. Wang; C. Berdin; M. Mazière; S. Forest; C. Prioul; A. Parrot; P. Le-Delliou Experimental and numerical study of dynamic strain ageing and its relation to ductile fracture of a C–Mn steel, Mater. Sci. Eng. A, Volume 547 (2012), pp. 19-31

[10] J. Belotteau Comportement et rupture d'un acier au C–Mn en présence de vieillissement sous déformation, Ecole Centrale Paris, Paris, 2009 (PhD dissertation)

[11] L. Fournier; D. Delafosse; T. Magnin Oxidation induced intergranular cracking and Portevin–Le Chatelier effect in nickel base superalloy 718, Mater. Sci. Eng. A, Volume 316 (2001) no. 1, pp. 166-173

[12] K.B.S. Rao; S. Kalluri; G.R. Halford; M.A. McGaw Serrated flow and deformation substructure at room temperature in inconel 718 superalloy during strain controlled fatigue, Scr. Metall. Mater., Volume 32 (1995) no. 4, pp. 493-498

[13] K. Prasad; S.V. Kamat Transient flow behaviour in a near alpha titanium alloy timetal 834 in the dynamic strain aging regime, Mater. Sci. Eng. A, Volume 490 (2008) no. 1, pp. 477-480

[14] J.K. Chakravartty; S.L. Wadekar; T.K. Sinha; M.K. Asundi Dynamic strain-ageing of A203D nuclear structural steel, J. Nucl. Mater., Volume 119 (1983) no. 1, pp. 51-58

[15] M.T. Miglin; W.A. Van Der Sluys; R.J. Futato; H.A. Domian Effects of strain aging in the unloading compliance J test, Elastic–Plastic Fracture Test Methods: The User's Experience, ASTM International, 1985

[16] P. Gomiero; Y. Bréchet; F. Louchet; A. Tourabi; B. Wack Microstructure and mechanical properties of a 2091 AlLi alloy-III. Quantitative analysis of Portevin–Le Chatelier instabilities and relation to toughness in Al–Li, Al–Cu–Mg and Al–Li–Cu–Mg (2091) alloys, Acta Metall. Mater., Volume 40 (1992) no. 4, pp. 863-871

[17] K.C. Kim; J.T. Kim; J.I. Suk; U.H. Sung; H. Kwon Influences of the dynamic strain aging on the J–R fracture characteristics of the ferritic steels for reactor coolant piping system, Nucl. Eng. Des., Volume 228 (2004) no. 1, pp. 151-159

[18] D. Wagner; J.C. Moreno; C. Prioul Dynamic strain aging sensitivity of heat affected zones in C–Mn steels, J. Nucl. Mater., Volume 252 (1998) no. 3, pp. 257-265

[19] E. Amar; A. Pineau Interpretation of ductile fracture toughness temperature dependence of a low strength steel in terms of a local approach, Eng. Fract. Mech., Volume 22(6) (1985) no. 6, pp. 1061-1071

[20] F. Zhang; A.F. Bower; W.A. Curtin The influence of serrated flow on necking in tensile specimens, Acta Mater., Volume 60 (2012), pp. 43-50

[21] A.H. Cottrell; B.A. Bilby Dislocation theory of yielding and strain ageing of iron, Proc. Phys. Soc., Volume 62 (1949) no. 1, p. 49

[22] P. Penning Mathematics of the Portevin–Le Chatelier effect, Acta Metall. Mater., Volume 20 (1972) no. 10, pp. 1169-1175

[23] A. van den Beukel Theory of the effect of dynamic strain aging on mechanical properties, Phys. Status Solidi, Volume 30 (1975) no. 1, pp. 197-206

[24] L.P. Kubin; Y. Estrin The Portevin–Le Chatelier effect in deformation with constant stress rate, Acta Metall. Mater., Volume 33 (1985) no. 3, pp. 397-407

[25] L.P. Kubin; Y. Estrin Evolution of dislocation densities and the critical conditions for the Portevin–Le Chatelier effect, Acta Metall. Mater., Volume 38 (1990) no. 5, pp. 697-708

[26] S. Graff; S. Forest; J.-L. Strudel; C. Prioul; P. Pilvin; J.-L. Béchade Strain localization phenomena associated with static and dynamic strain ageing in notched specimens: experiments and finite element simulations, Mater. Sci. Eng. A, Volume 387 (2004), pp. 181-185

[27] M. Mazière; J. Besson; S. Forest; B. Tanguy; H. Chalons; F. Vogel Numerical aspects in the finite element simulation of the Portevin–Le Chatelier effect, Comput. Methods Appl. Mech. Eng., Volume 199 (2010) no. 9, pp. 734-754

[28] P.G. McCormick Theory of flow localisation due to dynamic strain ageing, Acta Metall. Mater., Volume 36 (1988) no. 12, pp. 3061-3067

[29] S. Zhang; P.G. McCormick; Y. Estrin The morphology of Portevin–Le Chatelier bands: finite element simulation for Al–Mg–Si, Acta Mater., Volume 49 (2001), pp. 1087-1094

[30] A. Benallal; T. Berstad; T. Borvik; O.S. Hopperstad; I. Koutiri; R. Nogueira de Codes An experimental and numerical investigation of AA5083 aluminium alloy in presence of the Portevin–Le Chatelier effect, Int. J. Plast., Volume 24 (2008), pp. 1916-1945

[31] B. Klusemann; G. Fischer; T. Boehlke; B. Svendsen Thermomechanical characterization of Portevin–Le Chatelier bands in AlMg3 (AA5754) and modeling based on a modified Estrin–McCormick approach, Int. J. Plast., Volume 67 (2015), pp. 192-216

[32] T.Q. Li; Y.B. Liu; Z.Y. Cao; D.M. Jiang; L.R. Cheng The tensile properties and high cyclic fatigue characteristics of Mg-5Li-3Al-1.5Zn-2RE alloy, Mater. Sci. Eng. A, Volume 527 (2010), pp. 7808-7811

[33] J.-L. Chaboche; A. Gaubert; P. Kanouté; A. Longuet; F. Azzouz; M. Mazière Viscoplastic constitutive equations of combustion chamber materials including cyclic hardening and dynamic strain aging, Int. J. Plast., Volume 46 (2013), pp. 1-22

[34] M. Mazière Overspeed Burst of Turboengine Disks, Mines ParisTech, 2007 (PhD dissertation)

[35] C. Fressengeas; A.J. Beaudoin; M. Lebyodkin; L.P. Kubin; Y. Estrin Dynamic strain aging: a coupled dislocation—solute dynamic model, Mater. Sci. Eng. A, Volume 400 (2005), pp. 226-230

[36] A. Marais; M. Mazière; S. Forest; A. Parrot; P. Le Delliou Identification of a strain-aging model accounting for Lüders behavior in a C–Mn steel, Philos. Mag., Volume 92 (2012) no. 28–30, pp. 3589-3617

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

[38] D. Caillard Dynamic strain ageing in iron alloys: the shielding effect of carbon, Acta Mater., Volume 112 (2016), pp. 273-284

[39] S.G. Hong; S.B. Lee Mechanism of dynamic strain aging and characterization of its effect on the low-cycle fatigue behavior in type 316l stainless steel, J. Nucl. Mater., Volume 340 (2005) no. 2, pp. 307-314

[40] J. Besson; G. Cailletaud; J.-L. Chaboche; S. Forest Non-Linear Mechanics of Materials, Springer, 2009

[41] U.F. Kocks Laws for work-hardening and low-temperature creep, J. Eng. Mater. Technol., Volume 98 (1976) no. 1, pp. 76-85

[42] H.D. Wang Comportement mécanique et rupture des aciers au C–Mn en présence de vieillissement dynamique, Ecole Centrale Paris, Paris, 2011 (PhD dissertation)

[43] J. Belotteau; C. Berdin; S. Forest; A. Parrot; C. Prioul Mechanical behavior and crack tip plasticity of a strain aging sensitive steel, Mater. Sci. Eng. A, Volume 526 (2009), pp. 156-165

[44] F. Springer; C. Schwink Quantitative investigations on dynamic strain aging in polycrystalline Cu–Mn alloys, Scr. Metall. Mater., Volume 25 (1991), pp. 2739-2744

[45] H.D. Wang; C. Berdin; M. Mazière; S. Forest; C. Prioul; A. Parrot; P. Le-Delliou Portevin–Le Chatelier (PLC) instabilities and slant fracture in C–Mn steel round tensile specimens, Scr. Mater., Volume 64 (2011) no. 5, pp. 430-433

[46] J.R.G. da Silva; R.B. McLellan Diffusion of carbon and nitrogen in BCC iron, Mater. Sci. Eng., Volume 26 (1976), pp. 83-87

[47] L.P. Kubin; K. Chihab; Y. Estrin The rate dependence of the Portevin–Le Chatelier effect, Acta Metall. Mater., Volume 36 (1988) no. 10, pp. 2707-2718

[48] S.H. Fu; T. Cheng; Q.C. Zhang; Q. Hu; P.T. Cao Two mechanisms for the normal and inverse behaviors of the critical strain for the Portevin–Le Chatelier effect, Acta Mater., Volume 60 (2012) no. 19, pp. 6650-6656

[49] M. Mazière; H. Dierke Investigations on the Portevin–Le Chatelier critical strain in an aluminum alloy, Comput. Mater. Sci., Volume 52 (2012) no. 1, pp. 68-72

[50] P. Verma; G.S. Rao; P. Chellapandi; G.S. Mahobia; K. Chattopadhyay; N.C. Srinivas; V. Singh Dynamic strain ageing, deformation, and fracture behavior of modified 9Cr–1Mo steel, Mater. Sci. Eng. A, Volume 621 (2015), pp. 39-51

[51] M. Mazière; S. Forest Strain gradient plasticity modeling and finite element simulation of Lüders band formation and propagation, Contin. Mech. Thermodyn., Volume 27 (2015)

[52] M. Mazière; C. Luis; A. Marais; S. Forest; M. Gaspérini Experimental and numerical analysis of the Lüders phenomenon in simple shear, Int. J. Solids Struct., Volume 106–107 (2017), pp. 305-314

[53] B. Max; B. Viguier; E. Andrieu; J.-M. Cloue A re-examination of the Portevin–Le Chatelier effect in alloy 718 in connection with oxidation-assisted intergranular cracking, Metall. Mater. Trans. A, Volume 45A (2014), pp. 5431-5441

[54] Y. Bréchet; Y. Estrin On a pseudo-Portevin–Le Chatelier effect, Scr. Metall. Mater., Volume 31 (1994), pp. 185-190

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