Constitutive modeling of shape memory alloy wire with nonlocal rate kinetics
 Vikash K. Jha,
 D. Roy Mahapatra
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A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid–solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the nonlocal rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading–unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10^{6} for stressfree temperatureinduced transformation and 10^{4} for stressinduced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermomechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress–strain hysteresis loop is observed for mechanical loading with higher rates.
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 Title
 Constitutive modeling of shape memory alloy wire with nonlocal rate kinetics
 Journal

Continuum Mechanics and Thermodynamics
Volume 21, Issue 1 , pp 115
 Cover Date
 20090601
 DOI
 10.1007/s0016100900917
 Print ISSN
 09351175
 Online ISSN
 14320959
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Shape memory alloy
 Kinetics
 Free energy
 Microstructure
 Inhomogeneity
 64.60
 81.30
 83.10
 Industry Sectors
 Authors

 Vikash K. Jha ^{(1)}
 D. Roy Mahapatra ^{(1)}
 Author Affiliations

 1. Department of Aerospace Engineering, Indian Institute of Science, Bangalore, 560012, India