On the Correspondence between Micromechanical Models for Isothermal Pseudoelastic Response of Shape Memory Alloys and the Preisach Model for Hysteresis

In this work, the authors derive the weighting functions of the Preisach model of hysteresis (used for real-time control applications) corresponding to the uniaxial isothermal psuedoelastic response of an SMA polycrystal. A uniform distribution of single crystals is taken to constitute the polycrystal. The assumed phase transformation criterion is based on the shear component of the traction vector on a habit plane reaching a threshold value. The derived weighting functions are correlated analytically to the isothermal transformation properties of the single crystals and through the orientation distribution function to the polycrystalline SMA. The purpose of the present work is to provide a point of departure from the traditional practice by which the weighting functions are being determined from experimental data on polycrystalline SMA actuators.

[1]  J. Shaw,et al.  Thermomechanical aspects of NiTi , 1995 .

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

[3]  Hisaaki Tobushi,et al.  Transformation start lines in TiNi and Fe-based shape memory alloys after incomplete transformations induced by mechanical and/or thermal loads , 1995 .

[4]  Scott R. White,et al.  Effect of training conditions and extended thermal cycling on nitinol two-way shape memory behavior , 1995 .

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

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

[7]  J. Mackenzie,et al.  The crystallography of martensite transformations II , 1954 .

[8]  J. Perkins,et al.  Shape Memory Effects in Alloys , 1975 .

[9]  Bernard D. Coleman,et al.  On a class of constitutive relations for ferromagnetic hysteresis , 1987 .

[10]  James K. Knowles,et al.  A continuum model of a thermoelastic solid capable of undergoing phase transitions , 1993 .

[11]  Robert V. Kohn,et al.  Symmetry, texture and the recoverable strain of shape-memory polycrystals , 1996 .

[12]  F. Falk,et al.  Pseudoelastic stress-strain curves of polycrystalline shape memory alloys calculated from single crystal data , 1989 .

[13]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[14]  D. Lagoudas,et al.  A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy , 1996 .

[15]  L. Brinson.  One-Dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-Constant Material Functions and Redefined Martensite Internal Variable , 1993 .

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

[17]  Toshinori Takagi,et al.  A Concept of Intelligent Materials , 1990 .

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

[19]  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.

[20]  Thomas J. Pence,et al.  A constitutive model for hysteretic phase transition behavior , 1994 .