Model for resistance evolution in shape memory alloys including R-phase

The electrical resistance behavior of a shape memory alloy (SMA) wire can be used for sensing the state of an SMA device. Hence, this study investigates the resistance evolution in SMAs. A lumped parameter model with cosine kinetics to capture the resistance variation during the phase transformation is developed. Several SMA materials show the presence of trigonal or rhombohedral (R) phase as an intermediate phase, apart from the commonly recognized austenite and martensite phases. Most of the SMA models ignore the R-phase effect in their prediction of thermomechanical response. This may be acceptable since the changes in thermomechanical response associated with the R-phase are relatively less. However, the resistivity related effects are pronounced in the presence of the R-phase and its appearance introduces non-monotonicity in the resistivity evolution. This leads to additional complexities in the use of resistance signal for sensing and control. Hence, a lumped model is developed here for resistance evolution including the R-phase effects. A phase-diagram-based model is proposed for predicting electro-thermomechanical response. Both steady state hysteretic response and transient response are modeled. The model predictions are compared with the available test data. Numerical studies have shown that the model is able to capture all the essential features of the resistance evolution in SMAs in the presence of the R-phase.

[1]  A. Khandelwal,et al.  Phenomenological Modeling of Shape Memory Alloys , 2008 .

[2]  John A. Shaw,et al.  Shakedown response of conditioned shape memory alloy wire , 2008, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[3]  Michele Giordano,et al.  Electrical resistivity study and characterization during NiTi phase transformations , 2007 .

[4]  Gangbing Song,et al.  Position estimation and control of SMA actuators based on electrical resistance measurement , 2007 .

[5]  Shyi-Kaan Wu,et al.  Electrical resistivity of Ti–Ni binary and Ti–Ni–X (X = Fe, Cu) ternary shape memory alloys , 2006 .

[6]  L. Brinson,et al.  Use of electrical resistance testing to redefine the transformation kinetics and phase diagram for shape-memory alloys , 2006 .

[7]  F. Ghorbel,et al.  Differential hysteresis modeling of a shape memory alloy wire actuator , 2005, IEEE/ASME Transactions on Mechatronics.

[8]  H Meier,et al.  Numerical thermomechanical modelling of shape memory alloy wires , 2004 .

[9]  Gangbing Song,et al.  Position control of shape memory alloy actuators with internal electrical resistance feedback using neural networks , 2004 .

[10]  W Moussa,et al.  Effect of variable material properties and environmental conditions on thermomechanical phase transformations in shape memory alloy wires , 2003 .

[11]  K. K. Mahesh,et al.  Electrical resistivity and strain recovery studies on the effect of thermal cycling under constant stress on R-phase in NiTi shape memory alloy , 2002 .

[12]  M. Faulkner,et al.  Experimental characterization of free convection during thermal phase transformations in shape memory alloy wires , 2002 .

[13]  A. A. Movchan,et al.  Constitutive equations for two‐step thermoelastic phase transformations , 2001 .

[14]  M G Faulkner,et al.  Finite-element modeling of phase transformation in shape memory alloy wires with variable material properties , 2000 .

[15]  G. Guénin,et al.  Electro-thermomechanical behaviour of a Ti-45.0Ni-5.0Cu (at.%) alloy during shape memory cycling , 1999 .

[16]  Michele Pozzi,et al.  The electrical transport properties of shape memory alloys , 1999 .

[17]  L. C. Brinson,et al.  Phase diagram based description of the hysteresis behavior of shape memory alloys , 1998 .

[18]  Hisaaki Tobushi,et al.  Thermomechanical properties due to martensitic and R-phase transformations of TiNi shape memory alloy subjected to cyclic loadings , 1996, Smart Structures.

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

[20]  Koji Ikuta,et al.  Shape memory alloy servo actuator system with electric resistance feedback and application for active endoscope , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[21]  M. Ahmadian,et al.  On the Shortcomings of Shape Memory Alloy Phenomenological Models , 2004 .

[22]  P. Moreno.  Experimental identification of model parameters for SMA wires , 2003 .

[23]  Reg Dunlop,et al.  A Nitinol Wire Actuated Stewart Platform , 2002 .