A finite strain elastic–viscoplastic self-consistent model for polycrystalline materials

Abstract A large strain elastic–viscoplastic self-consistent (EVPSC) model for polycrystalline materials is developed. At single crystal level, both the rate sensitive slip and twinning are included as the plastic deformation mechanisms, while elastic anisotropy is accounted for in the elastic moduli. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress–strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tome (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response due to lack of elastic deformation. It is also demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model.

[1]  John W. Hutchinson,et al.  Elastic-plastic behaviour of polycrystalline metals and composites , 1970, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  Studying grain fragmentation in ECAE by simulating simple shear , 2006 .

[3]  P. A. Turner,et al.  Self-consistent modeling of visco-elastic polycrystals: Application to irradiation creep and growth , 1993 .

[4]  A. Zaoui.  Continuum Micromechanics: Survey , 2002 .

[5]  Bjørn Clausen,et al.  Reorientation and stress relaxation due to twinning: Modeling and experimental characterization for Mg , 2008 .

[6]  Peter Mora,et al.  Macroscopic elastic properties of regular lattices , 2008 .

[7]  D. Brown,et al.  Investigation of Grain-Scale Stresses and Modeling of Tensile Deformation in a ZIRCALOY-4 Weldment , 2007 .

[8]  Alain Molinari,et al.  Homogenization of elastic-viscoplastic heterogeneous materials : Self-consistent and Mori-Tanaka schemes , 2009 .

[9]  R. Asaro,et al.  Overview no. 42 Texture development and strain hardening in rate dependent polycrystals , 1985 .

[10]  G. Weng.  A Self-Consistent Scheme for the Relaxation Behavior of Metals , 1981 .

[11]  Ricardo A. Lebensohn,et al.  Heterogeneous deformation and texture development in halite polycrystals: comparison of different modeling approaches and experimental data , 2003 .

[12]  George J. Weng,et al.  A self-consistent relation for the time-dependent creep of polycrystals , 1993 .

[13]  D. Lloyd,et al.  A mesoscopic approach for predicting sheet metal formability , 2004 .

[14]  S. Ahzi,et al.  A self consistent approach of the large deformation polycrystal viscoplasticity , 1987 .

[15]  Modelling damage of AlZnMg alloys , 1996 .

[16]  S. Macewen,et al.  Residual stresses in annealed zircaloy , 1989 .

[17]  S. Ahzi,et al.  Application of crystal plasticity theory for mechanically processed BSCCO superconductors , 1993 .

[18]  Said Ahzi,et al.  On the self-consistent modeling of elastic-plastic behavior of polycrystals , 1997 .

[19]  G. Weng,et al.  A unified approach from elasticity to viscoelasticity to viscoplasticity of particle-reinforced solids , 1998 .

[20]  Bernard Budiansky,et al.  THEORETICAL PREDICTION OF PLASTIC STRAINS OF POLYCRYSTALS , 1961 .

[21]  S. Harren.  The finite deformation of rate-dependent polycrystals—II: A comparison of the self-consistent and Taylor methods , 1991 .

[22]  M. Berveiller,et al.  Micromechanical modeling of the elastic-viscoplastic behavior of polycrystalline steels , 2001 .

[23]  T. Iwakuma,et al.  Finite elastic-plastic deformation of polycrystalline metals , 1984, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[24]  James R. Rice,et al.  Strain localization in ductile single crystals , 1977 .

[25]  E. van der Giessen,et al.  On crystal plasticity FLD analysis , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[26]  J. Hutchinson,et al.  Bounds and self-consistent estimates for creep of polycrystalline materials , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[27]  S. Nemat-Nasser,et al.  Rate-dependent, finite elasto-plastic deformation of polycrystals , 1986, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[28]  M. Yoo.  Slip, twinning, and fracture in hexagonal close-packed metals , 1981 .

[29]  Ricardo A. Lebensohn,et al.  A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals : application to zirconium alloys , 1993 .

[30]  Gwénaëlle Proust,et al.  Modeling the effect of twinning and detwinning during strain-path changes of magnesium alloy AZ31 , 2009 .

[31]  L. Anand,et al.  Inelastic deformation of polycrystalline face centered cubic materials by slip and twinning , 1998 .

[32]  E. Kröner.  Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls , 1958 .

[33]  M. Barnett,et al.  Investigation of deformation mechanisms involved in the plasticity of AZ31 Mg alloy: In situ neutron diffraction and EPSC modelling , 2008 .

[34]  P. A. Turner,et al.  A study of residual stresses in Zircaloy-2 with rod texture , 1994 .

[35]  R. Hill.  Generalized constitutive relations for incremental deformation of metal crystals by multislip , 1966 .

[36]  Lallit Anand,et al.  The process of shear band formation in plane strain compression of fcc metals: Effects of crystallographic texture , 1994 .

[37]  Lallit Anand,et al.  A constitutive model for hcp materials deforming by slip and twinning: application to magnesium alloy AZ31B , 2003 .

[38]  E. Kröner.  Zur plastischen verformung des vielkristalls , 1961 .

[39]  Rodney Hill,et al.  Continuum micro-mechanics of elastoplastic polycrystals , 1965 .

[40]  Ricardo A. Lebensohn,et al.  A self-consistent viscoplastic model: prediction of rolling textures of anisotropic polycrystals , 1994 .

[41]  Ricardo A. Lebensohn,et al.  A model for texture development dominated by deformation twinning: Application to zirconium alloys , 1991 .

[42]  Carlos N. Tomé,et al.  A dislocation-based constitutive law for pure Zr including temperature effects , 2008 .

[43]  S. Kalidindi.  Incorporation of deformation twinning in crystal plasticity models , 1998 .

[44]  T. Lin.  Analysis of elastic and plastic strains of a face-centred cubic crystal☆ , 1957 .

[45]  L. Walpole,et al.  On the overall elastic moduli of composite materials , 1969 .

[46]  S. Macewen,et al.  Residual grain-interaction stresses in zirconium alloys , 1990 .

[47]  S. Agnew,et al.  Plastic anisotropy and the role of non-basal slip in magnesium alloy AZ31B , 2005 .

[48]  John L. Bassani,et al.  Latent hardening in single crystals. II. Analytical characterization and predictions , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[49]  C. Tomé.  Self-consistent polycrystal models: a directional compliance criterion to describe grain interactions , 1999 .

[50]  C. Tomé,et al.  Application of texture simulation to understanding mechanical behavior of Mg and solid solution alloys containing Li or Y , 2001 .

[51]  André Zaoui,et al.  An extension of the self-consistent scheme to plastically-flowing polycrystals , 1978 .

[52]  C. Tomé,et al.  Validating a polycrystal model for the elastoplastic response of magnesium alloy AZ31 using in situ neutron diffraction , 2006 .

[53]  S. R. MacEwen,et al.  Advances in sheet metal forming analyses: dealing with mechanical anisotropy from crystallographic texture , 2003 .

[54]  P. A. Turner,et al.  Self-consistent modelling of nonlinear visco-elastic polycrystals: an approximate scheme , 1994 .

[55]  Michel Bornert,et al.  An affine formulation for the prediction of the effective properties of nonlinear composites and polycrystals , 2000 .

[56]  G. Weng,et al.  A secant-viscosity approach to the time-dependent creep of an elastic viscoplastic composite , 1997 .

[57]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[58]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[59]  Surya R. Kalidindi,et al.  Prediction of crystallographic texture evolution and anisotropic stress–strain curves during large plastic strains in high purity α-titanium using a Taylor-type crystal plasticity model , 2007 .

[60]  L. Anand,et al.  Crystallographic texture evolution in bulk deformation processing of FCC metals , 1992 .

[61]  G. Weng,et al.  Time-dependent creep of a dual-phase viscoplastic material with lamellar structure , 1998 .

[62]  Ricardo A. Lebensohn,et al.  A selfconsistent formulation for the prediction of the anisotropic behavior of viscoplastic polycrystals with voids , 2004 .

[63]  G. J. Weng,et al.  A Unified, Self-Consistent Theory for the Plastic-Creep Deformation of Metals , 1982 .

[64]  S. Agnew,et al.  Modeling the temperature dependent effect of twinning on the behavior of magnesium alloy AZ31B sheet , 2007 .

[65]  M. Jain,et al.  Effects of spatial grain orientation distribution and initial surface topography on sheet metal necking , 2007 .

[66]  J. Rice,et al.  Constitutive analysis of elastic-plastic crystals at arbitrary strain , 1972 .