Mathematical modelling of pseudoelastic behaviour of tapered NiTi bars

Owing to their ability to exhibit the shape memory effect and pseudoelasticity, NiTi alloys have been used in many applications as actuators with temperature- or stress-controlling mechanisms. In some applications, it is necessary that the shape memory component act in a controllable range with respect to the controlling parameters, i.e., temperature for thermally induced actuation or stress for stress-induced actuation. However, in typical equiatomic NiTi the actuation range is narrow, which results in poor controllability of the system. This study proposes improved controllability of a typical NiTi component by tapering its structure and presents closed-form solution for load–displacement relation at different stages of loading cycle. The analytical solution is in good agreement with experimental data. The nominal stress–strain diagram shows gradient stress for stress-induced martensitic transformation. The nonlinear gradient can be controlled by geometrical designs and is influenced by elastic moduli of the austenite and martensite phases.

► Closed-form solution for nominal stress–strain behaviour of tapered NiTi bar is obtained which perfectly predicts the actual experiments.
► By tapering the SMA bar, nonlinear stress gradient is created over the stress plateau associated with the stress-induced martensitic transformation, which widen the controllable interval.
► The nonlinearity of the stress gradient is affected by material and geometrical properties.
► By reducing the radius ratio, the length and slope over stress plateau and its nonlinearity increases.