Characterization of NiTi shape memory alloys using dual kriging interpolation

A large number of industrial applications could benefit from the remarkable properties of shape memory alloys (SMA). The development of a general material law is the first important step before reliable design calculations of shape memory devices can be carried out. This paper presents a new phenomenological constitutive law based on dual kriging, which is a powerful mathematical tool used here as interpolation method to simulate the macroscopic mechanical behavior of shape memory alloys. From a set of experimental strain–temperature curves at constant loads, two deformation surfaces are constructed in the stress, strain and temperature space which describe the cooling and heating behaviors of the material for any stress. The response of a specimen subjected to complex thermomechanical loading can be calculated by dual kriging form a general 3-dimensional parametric solid constructed inside the hysteretic domain delimited by the main cooling and heating deformation surfaces. This approach presents the advantage of yielding immediately the explicit equation of any partial cycle inside the main hysteretic domain, thus yielding a general material law for shape memory alloys. Preliminary validation for a set of simple examples demonstrates the potential of this new model that includes in a single formulation superelasticity, rubber-like behavior and shape memory effect.