Modeling of niobium precipitates effect on the Ni47Ti44Nb9 Shape Memory Alloy behavior

Commercial Ni47Ti44Nb9 Shape Memory Alloy (SMA) is generally adopted for tightening applications thanks to its wide transformation hysteresis, compared with classical NiTi. Its sensibility to thermo-mechanical treatments allows it to be either martensitic or austenitic in a wide range of temperature, between −60 °C and 80 °C. A modeling of niobium precipitates effects on Ni47Ti44Nb9 SMA behavior is proposed. For this object, a two phase thermo-mechanical model is developed. It describes the global effective behavior of an elastoplastic inclusion (niobium precipitates) embedded within an SMA matrix. The constitutive law developed by and improved by is adopted to model the matrix shape memory behavior. The elastoplastic constitutive law for inclusion is the one proposed by Wilkins with Simo and Hughes’s radial return algorithm. The Mori–Tanaka scale transition scheme is considered for the determination of the effective constitutive equations. Obtained results highlight the effect of niobium precipitates on the thermomechanical behavior of Ni47Ti44Nb9, and particularly on the corresponding hysteresis size. It appears that the niobium plasticity increases this hysteresis size. The developed constitutive law has been implemented in the ABAQUS® Finite Element code and considered for the numerical prediction of the tightening pressure in a connection application.