One-dimensional constitutive model of stress-induced transitions between M_s and M_f in shape memory alloys

The mechanical constitutive relation of Shape Memory Alloy (SMA) materials during stress-induced transitions is discussed based on mixture theories. The twinned martensite variants and austenite parents are taken as two constituents with their own conversion or transition behavior when subjected to external loading. Corresponding internal variables for describing these transitions are newly defined. This model enables the numerical prediction of the overall mechanical behavior of SMA materials in the temperature range form M_s to M_f. Typical approaches of mixture theories; parallel and series models are applied in the formulation of the constitutive behavior of SMAs with the corresponding isostrain and isostress conditions. Tensile tests have been carried out with Ti-Ni specimens in a temperature range including martensitic transition temperatures. Numerical simulation based on the proposed model accurately predicted the mechanical behavior of stress-induced transitions in the concerned temperature range.