On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material

Abstract A thermomechanical description of the martenstitic phase transformation and the associated shape memory effect in polycrystalline shape memory alloys (SMAs) is presented. The rate-independent constitutive relations are derived in the stress-temperature space using a Lagrangian formulation. The Kuhn–Tucker optimality conditions, constraints on evolution equations for transformations strain and shape of transformation function in thermodynamic force space are obtained naturally through the principle of maximum transformation dissipation. Various transformation functions are investigated and a generalized type transformation function is proposed. Numerical results of the model based on different transformation functions are compared with experimental results to determine their accuracy to predict SMA characteristics like tension–compression asymmetry, negative volumetric transformation strain and pressure dependence.

[1]  The strength-differential effect in plasticity , 1984 .

[2]  Friedrich K. Straub,et al.  Applications of torsional shape memory alloy actuators for active rotor blade control: opportunities and limitations , 1996, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[3]  Gordon S. G. Beveridge,et al.  Optimization: theory and practice , 1970 .

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

[5]  Mark Balzer,et al.  Effect of stress state on the stress-induced martensitic transformation in polycrystalline Ni-Ti alloy , 1996 .

[6]  Walter Noll,et al.  The thermodynamics of elastic materials with heat conduction and viscosity , 1963 .

[7]  James Casey,et al.  Approximate kinematical relations in plasticity , 1985 .

[8]  Shuichi Miyazaki,et al.  Superelastic Ni-Ti Alloys in Orthodontics , 1990 .

[9]  R. Lammering,et al.  Finite Element Analysis of the Behavior of Shape Memory Alloys and their Applications. , 1993 .

[10]  D. Lagoudas,et al.  Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms , 2000 .

[11]  Christopher A. Martin,et al.  Shape memory alloy TiNi actuators for twist control of smart wing designs , 1996, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[12]  P. M. Naghdi,et al.  A prescription for the identification of finite plastic strain , 1992 .

[13]  C. Liang,et al.  The multi-dimensional constitutive relations of shape memory alloys , 1991 .

[14]  T. W. Duerig,et al.  On the tensile and torsional properties of pseudoelastic NiTi , 1990 .

[15]  D. Lagoudas,et al.  A UNIFIED THERMODYNAMIC CONSTITUTIVE MODEL FOR SMA AND FINITE ELEMENT ANALYSIS OF ACTIVE METAL MATRIX COMPOSITES , 1996 .

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

[17]  E. Patoor,et al.  Calculation of Pseudoelastic Elements Using a Non-Symmetrical Thermomechanical Transformation Criterion and Associated Rule , 1998 .

[18]  Sanjay Govindjee,et al.  Computational aspects of solid-solid phase transformation modeling with a Gibbs function , 1999, Smart Structures.

[19]  P. Šittner,et al.  The stabilization of transformation pathway in stress induced martensite , 1995 .

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

[21]  Arun R. Srinivasa,et al.  Mechanics of the inelastic behavior of materials. Part II: inelastic response , 1998 .

[22]  Michael Ortiz,et al.  A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations , 1985 .

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

[24]  K. Gall,et al.  The influence of aging on critical transformation stress levels and martensite start temperatures , 1999 .

[25]  Dimitris C. Lagoudas,et al.  Material Characterization of SMA Actuators Under Nonproportional Thermomechanical Loading , 1999 .

[26]  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 .

[27]  K. Melton,et al.  Ni-Ti Based Shape Memory Alloys , 1990 .

[28]  Dirk Helm,et al.  Thermomechanical behavior of shape memory alloys , 2001, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[29]  P. Šittner,et al.  Calculation of mechanical behaviors of shape memory alloy under multi-axial loading conditions , 1998 .

[30]  Richard Von Mises,et al.  Mechanik der plastischen Formänderung von Kristallen , 1928 .

[31]  E. Patoor,et al.  Thermomechanical behaviour of shape memory alloys , 1988 .

[32]  Franz Dieter Fischer,et al.  Micromechanical modeling of martensitic transformation in random microstructures , 1998 .

[33]  D. Lagoudas,et al.  Thermomechanical Response of Shape Memory Composites , 1994 .

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

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

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

[37]  C. Liang,et al.  A multi-dimensional constitutive model for shape memory alloys , 1992 .

[38]  Victor Birman,et al.  Review of Mechanics of Shape Memory Alloy Structures , 1997 .

[39]  Chen Liang,et al.  Investigation of torsional shape memory alloy actuators , 1996, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[40]  K. Tanaka A THERMOMECHANICAL SKETCH OF SHAPE MEMORY EFFECT: ONE-DIMENSIONAL TENSILE BEHAVIOR , 1986 .

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

[42]  Rodney Hill,et al.  A VARIATIONAL PRINCIPLE OF MAXIMUM PLASTIC WORK IN CLASSICAL PLASTICITY , 1948 .

[43]  C. Lexcellent,et al.  Thermodynamics of isotropic pseudoelasticity in shape memory alloys , 1998 .

[44]  Arun R. Srinivasa,et al.  Mechanics of the inelastic behavior of materials—part 1, theoretical underpinnings , 1998 .

[45]  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 .

[46]  Elwood Spencer Buffa,et al.  Mathematical programming : an introduction to the design and application of optimal decision machines , 1970 .

[47]  T. W. Duerig,et al.  Engineering Aspects of Shape Memory Alloys , 1990 .