Analytical description of the bending behaviour of NiTi shape-memory alloys

Abstract

Shape-memory alloys (SMA) exhibit “super-elastic” deformation behaviour in both tensile and bending tests: linear-elastic and ideal-plastic sections occur alternately during a load/unload cycle. A new analytical model for the description of pure bending of SMA on the background of continuum mechanics is given. This model allows mathematical derivation of elasticity parameters needed for the characterization of SMA deformation. The parameter set consists of six elastic moduli and three strain limits, leading to a total of nine mechanical quantities necessary for analytically setting up the associated bending moment/bending angle diagram. The physical relevance of the elasticity parameters delivered by the model is checked by comparing experimental and theoretical (computed on the base of the parameter set) force systems on a T-shaped spring.