Three-dimensional thermomechanical modeling of pseudoelasticity in shape memory alloys with different elastic properties between austenite and martensite

In the present work, a three-dimensional micromechanical model has been developed based on Gall and Lim's expression for Gibbs free energy, which can reproduce the pseudoelastic behavior of NiTi shape memory alloys. The emphasis was put on the difference of elastic properties between austenite and martensite. The formulations for the evolution of volume fraction of the 24 martensite variants are derived. The discrete evolutionary equations are presented, with the expression of the mechanical Jacobian matrix. The model is implemented as User Material subroutine (UMAT) into ABAQUS. The model formulations and finite element method (UMAT) have been validated by numerical method. As an example, pseudoelastic response of a polycrystal NiTi shape memory alloy under uniaxial loading has been simulated. The distributions of the martensite and Mises stress are quite uniform. The Mises stresses are higher during loading than unloading, while the volume fractions during loading are lower than that during unloading at the same strain level. The results show that the model can predict experiments better than that without considering different elastic properties between austenite and martensite.

[1]  P. Papadopoulos,et al.  An experimental study of the superelastic effect in a shape-memory Nitinol alloy under biaxial loading , 2003 .

[2]  L. Brinson,et al.  A Simplified Multivariant SMA Model Based on Invariant Plane Nature of Martensitic Transformation , 2002 .

[3]  Ken Gall,et al.  On the mechanical behavior of single crystal NiTi shape memory alloys and related polycrystalline phenomenon , 2001 .

[4]  G. Eggeler,et al.  Martensitic phase transformation in Ni-rich NiTi single crystals with one family of Ni4Ti3 precipitates , 2004 .

[5]  Klaus Hackl,et al.  A micromechanical model for polycrystalline shape-memory alloys , 2004 .

[6]  Craig A. Rogers,et al.  One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials , 1990 .

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

[8]  Shigenori Kobayashi,et al.  Thermomechanics of Transformation Pseudoelasticity and Shape Memory Effect in Alloys , 1986 .

[9]  K. Tanaka,et al.  A phenomenological description on thermomechanical behavior of shape memory alloys , 1990 .

[10]  A. Tuissi,et al.  NiTiHf shape memory alloy: effect of aging and thermal cycling , 1999 .

[11]  E. Patoor,et al.  Determination of the interaction energy in the martensitic state , 2002 .

[12]  Yiu-Wing Mai,et al.  Effect of transformation volume contraction on the toughness of superelastic shape memory alloys , 2002 .

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

[14]  Ferdinando Auricchio,et al.  Shape-memory alloys: macromodelling and numerical simulations of the superelastic behavior , 1997 .

[15]  Marcelo A. Savi,et al.  On the Fremond’s constitutive model for shape memory alloys , 2004 .

[16]  E. Sacco,et al.  A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite , 1997 .

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

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

[19]  D. McDowell,et al.  Cyclic thermomechanical behavior of a polycrystalline pseudoelastic shape memory alloy , 2002 .

[20]  Yong Liu,et al.  Cyclic deformation of NiTi shape memory alloys , 1999 .

[21]  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 .

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

[23]  F. Auricchio,et al.  Generalized plasticity and shape-memory alloys , 1996 .

[24]  E. Sacco,et al.  Thermo-mechanical modelling of a superelastic shape-memory wire under cyclic stretching–bending loadings , 2001 .

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

[26]  S. Calloch,et al.  A phenomenological model for pseudoelasticity of shape memory alloys under multiaxial proportional and nonproportional loadings , 2004 .

[27]  G. Eggeler,et al.  Crack initiation and propagation in 50.9 at. pct Ni-Ti pseudoelastic shape-memory wires in bending-rotation fatigue , 2003 .

[28]  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 .

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

[30]  Sia Nemat-Nasser,et al.  Very high strain-rate response of a NiTi shape-memory alloy , 2005 .

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