A micromechanical constitutive model based on crystal plasticity for thermo-mechanical cyclic deformation of NiTi shape memory alloys

Abstract Based on crystal plasticity, a new micromechanical constitutive model is constructed to describe the cyclic deformation of polycrystalline NiTi shape memory alloy presented under different thermo-mechanical cyclic loading conditions. At the scale of single crystal, the phase transformation and transformation-induced plasticity of the NiTi shape memory alloys are considered to be related with the 24 martensite variants and the friction systems at austenite–martensite interfaces, respectively. Three kinds of internal variables are included in the single crystal model, i.e., the reversible martensite volume fraction, the residual martensite volume fraction, and the friction slip at austenite–martensite interfaces. The Helmholtz free energy for the representative volume element of NiTi single crystal is constructed and the thermodynamics driving forces for internal variables are obtained by corresponding dissipation inequalities, respectively. An explicit scale-transition rule is adopted to extend the proposed single crystal model to the polycrystalline version. Also, the initial crystallographic texture is addressed in order to reflect the anisotropic phase transformation behavior of the NiTi shape memory alloys presented in the tension and compression cases. The proposed model is firstly verified by comparing the simulations with the corresponding uniaxial cyclic deformation experiments of polycrystalline NiTi shape memory alloys, and then is discussed by describing the multiaxial cyclic deformation of the polycrystalline NiTi shape memory alloy under the strain-controlled and stress-controlled cyclic loading conditions with different multiaxial loading paths and predicting the recovery of residual martensite phase during the sequential heating. Finally, some details about the cyclic deformation of polycrystalline NiTi shape memory alloy in intra-granular scale are also addressed with the help of the proposed model.

[1]  Jan Van Humbeeck,et al.  Non-medical applications of shape memory alloys , 1999 .

[2]  Ferdinando Auricchio,et al.  Modelling of SMA materials: Training and two way memory effects , 2003 .

[3]  Wael Zaki,et al.  A 3D model of the cyclic thermomechanical behavior of shape memory alloys , 2007 .

[4]  S. Padula,et al.  A multi-axial, multimechanism based constitutive model for the comprehensive representation of the evolutionary response of SMAs under general thermomechanical loading conditions , 2011 .

[5]  T Prakash G. Thamburaja,et al.  Polycrystalline shape-memory materials: effect of crystallographic texture , 2001 .

[6]  D. Lagoudas,et al.  Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys , 2010 .

[7]  Yanzhong Zhang,et al.  Superelasticity decay of porous NiTi shape memory alloys under cyclic strain-controlled fatigue conditions , 2008 .

[8]  Dimitris C. Lagoudas,et al.  Shape memory alloys, Part II: Modeling of polycrystals , 2006 .

[9]  Wolfgang Predki,et al.  Cyclic torsional loading of pseudoelastic NiTi shape memory alloys: Damping and fatigue failure , 2006 .

[10]  David L. McDowell,et al.  The role of intergranular constraint on the stress-induced martensitic transformation in textured polycrystalline NiTi , 2000 .

[11]  G. Cailletaud,et al.  Utilisation de modèles polycristallins pour le calcul par éléments finis , 1994 .

[12]  G. Cailletaud,et al.  A polycrystalline model for the description of ratchetting : effect of intergranular and intragranular hardening , 2008 .

[13]  Dimitris C. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part I: theoretical derivations , 1999 .

[14]  Shuichi Miyazaki,et al.  Transformation pseudoelasticity and deformation behavior in a Ti-50.6at%Ni alloy , 1981 .

[15]  Franz Dieter Fischer,et al.  A micromechanical model for the kinetics of martensitic transformation , 1992 .

[16]  Neil Morgan,et al.  Medical shape memory alloy applications—the market and its products , 2004 .

[17]  Ken Gall,et al.  The role of texture in tension–compression asymmetry in polycrystalline NiTi , 1999 .

[18]  Zhufeng Yue,et al.  Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys , 2008 .

[19]  O. Bruhns,et al.  Cyclic polycrystalline visco-plastic model for ratchetting of 316L stainless steel , 2011 .

[20]  Lucas Delaey,et al.  Asymmetry of stress–strain curves under tension and compression for NiTi shape memory alloys , 1998 .

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

[22]  Lallit Anand,et al.  Thermal effects in the superelasticity of crystalline shape-memory materials , 2003 .

[23]  T Prakash G. Thamburaja,et al.  An isotropic-plasticity-based constitutive model for martensitic reorientation and shape-memory effect in shape-memory alloys , 2007 .

[24]  T Prakash G. Thamburaja,et al.  Thermo-mechanically coupled superelastic response of initially-textured Ti-Ni sheet , 2003 .

[25]  Y. Chemisky,et al.  Constitutive model for shape memory alloys including phase transformation, martensitic reorientation and twins accommodation , 2011 .

[26]  P. Šittner,et al.  Thermomechanical behavior of shape memory alloy under complex loading conditions , 1999 .

[27]  T. P. G. Thamburaja,et al.  The evolution of microstructure during twinning: Constitutive equations, finite-element simulations and experimental verification , 2009 .

[28]  Dimitris C. Lagoudas,et al.  Influence of cold work and heat treatment on the shape memory effect and plastic strain development of NiTi , 2001 .

[29]  E. Kröner,et al.  A simple formula for calculating the bounds and the self-consistent value of the shear modulus of a polycrystalline aggregate of cubic crystals , 1981 .

[30]  Shuichi Miyazaki,et al.  Effect of mechanical cycling on the pseudoelasticity characteristics of TiNi and TiNiCu alloys , 1995 .

[31]  T. P. G. Thamburaja.  Constitutive equations for martensitic reorientation and detwinning in shape-memory alloys , 2005 .

[32]  P. Ji,et al.  1-D constitutive model for evolution of stress-induced R-phase and localized Lüders-like stress-induced martensitic transformation of super-elastic NiTi wires , 2012 .

[33]  Eduard Oberaigner,et al.  TRANSFORMATION INDUCED PLASTICITY REVISED: AN UPDATED FORMULATION , 1998 .

[34]  Sylvain Calloch,et al.  A 3D super-elastic model for shape memory alloys taking into account progressive strain under cyclic loadings , 2009 .

[35]  T Prakash G. Thamburaja,et al.  Martensitic reorientation and shape-memory effect in initially textured polycrystalline Ti–Ni sheet , 2005 .

[36]  Bo Zhou.  A macroscopic constitutive model of shape memory alloy considering plasticity , 2012 .

[37]  Yong Qing Fu,et al.  TiNi-based thin films in MEMS applications: a review , 2004 .

[38]  X. Wang,et al.  An experimental study of the superelastic behavior in NiTi shape memory alloys under biaxial proportional and non-proportional cyclic loadings , 2010 .

[39]  Shuichi Miyazaki,et al.  Cyclic stress-strain characteristics of TiNi and TiNiCu shape memory alloys , 1995 .

[40]  H. Dai,et al.  Propagation stresses in phase transitions of an SMA wire: New analytical formulas based on an internal-variable model , 2013 .

[41]  Lakhdar Taleb,et al.  New investigations on transformation induced plasticity and its interaction with classical plasticity , 2006 .

[42]  Dimitris C. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part II : material characterization and experimental results for a stable transformation cycle , 1999 .

[43]  Sang-Joo Kim,et al.  Cyclic effects in shape-memory alloys: a one-dimensional continuum model , 1997 .

[44]  W. Zaki,et al.  A constitutive model for shape memory alloys accounting for thermomechanical coupling , 2011 .

[45]  Guozheng Kang,et al.  Ratchetting: Recent progresses in phenomenon observation, constitutive modeling and application , 2008 .

[46]  Guozheng Kang,et al.  Micromechanical constitutive model considering plasticity for super-elastic NiTi shape memory alloy , 2012 .

[47]  S. Nemat-Nasser,et al.  Superelastic and cyclic response of NiTi SMA at various strain rates and temperatures , 2006 .

[48]  Guozheng Kang,et al.  Ratchetting deformation of super-elastic and shape-memory NiTi alloys , 2009 .

[49]  Guozheng Kang,et al.  Constitutive model for uniaxial transformation ratchetting of super-elastic NiTi shape memory alloy at room temperature , 2010 .

[50]  L. G. Machado,et al.  Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys , 2012 .

[51]  Keh Chih Hwang,et al.  Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys. II: Study of the individual phenomena , 1993 .

[52]  Ken Gall,et al.  Cyclic deformation mechanisms in precipitated NiTi shape memory alloys , 2002 .

[53]  D. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part IV: modeling of minor hysteresis loops , 1999 .

[54]  Guozheng Kang,et al.  Whole-life transformation ratchetting and fatigue of super-elastic NiTi Alloy under uniaxial stress-controlled cyclic loading , 2012 .

[55]  F. Fischer,et al.  The influence of material anisotropy on transformation induced plasticity in steel subject to martensitic transformation , 1995 .

[56]  G. Bourbon,et al.  Thermodynamical model of cyclic behaviour of TiNi and CuZnAl shape memory alloys under isothermal undulated tensile tests , 1996 .

[57]  L. Brinson,et al.  Shape memory alloys, Part I: General properties and modeling of single crystals , 2006 .

[58]  Dimitris C. Lagoudas,et al.  Modeling of transformation-induced plasticity and its effect on the behavior of porous shape memory alloys. Part I: constitutive model for fully dense SMAs , 2004 .

[59]  Reza Naghdabadi,et al.  A finite strain kinematic hardening constitutive model based on Hencky strain: General framework, solution algorithm and application to shape memory alloys , 2011 .

[60]  D. McDowell,et al.  Mechanical behavior of an Ni-Ti shape memory alloy under axial-torsional proportional and , 1999 .

[61]  Z. Q. Li,et al.  The initiation and growth of macroscopic martensite band in nano-grained NiTi microtube under tension , 2002 .

[62]  Etienne Patoor,et al.  Micromechanical Modelling of Superelasticity in Shape Memory Alloys , 1996 .

[63]  G. Bourbon,et al.  The two way shape memory effect of shape memory alloys: an experimental study and a phenomenological model , 2000 .

[64]  W. Zaki.  An efficient implementation for a model of martensite reorientation in martensitic shape memory alloys under multiaxial nonproportional loading , 2012 .

[65]  Miinshiou Huang,et al.  A multivariant micromechanical model for SMAs Part 2. Polycrystal model , 2000 .

[66]  Qingping Sun,et al.  Micromechanics modelling for the constitutive behavior of polycrystalline shape memory alloys. I: Derivation of general relations , 1993 .

[67]  H. Tobushi,et al.  Phenomenological analysis on subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads , 1995 .

[68]  Wael Zaki,et al.  Thermomechanical coupling in shape memory alloys under cyclic loadings: Experimental analysis and constitutive modeling , 2011 .

[69]  Petr Šittner,et al.  Transmission electron microscopy investigation of dislocation slip during superelastic cycling of Ni-Ti wires , 2011 .

[70]  Alessandro Reali,et al.  A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity , 2007 .

[71]  Dimitris C. Lagoudas,et al.  Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part III: evolution of plastic strains and two-way shape memory effect , 1999 .

[72]  Miinshiou Huang,et al.  A multivariant micromechanical model for SMAs Part 1. Crystallographic issues for single crystal model , 2000 .

[73]  P. Anderson,et al.  Coupling between martensitic phase transformations and plasticity: A microstructure-based finite element model , 2010 .

[74]  Ken Gall,et al.  Cyclic deformation behavior of single crystal NiTi , 2001 .

[75]  T. P. G. Thamburaja,et al.  Superelastic behavior in tension–torsion of an initially-textured Ti–Ni shape-memory alloy , 2002 .

[76]  Stefanie Reese,et al.  Finite deformation pseudo-elasticity of shape memory alloys – Constitutive modelling and finite element implementation , 2008 .

[77]  B. Piotrowski,et al.  Modeling of niobium precipitates effect on the Ni47Ti44Nb9 Shape Memory Alloy behavior , 2012 .

[78]  Petr Šittner,et al.  Thermomechanical model for NiTi-based shape memory alloys including R-phase and material anisotropy under multi-axial loadings , 2012 .

[79]  Lakhdar Taleb,et al.  A micromechanical modeling of the Greenwood–Johnson mechanism in transformation induced plasticity , 2003 .

[80]  F. Fischer,et al.  A micromechanical approach to constitutive equations for phase changing materials , 1997 .