Anatomization of hysteresis loops in pure bending of ideal pseudoelastic SMA beams

Abstract

The results of qualitative analysis of the variation of stress and the phase content distribution in arbitrary symmetric cross-section of the beam are discussed for single bending cycle. The explicit analytical equations for the moment–curvature hysteresis loop are derived. The interrelation between formation of characteristic points on this diagram and movement of the beam planes separating the regions occupied by single phase (austenite or martensite) and their mixture (austenite and martensite) in the course of phase transitions is discussed. It is shown that at such mobile surfaces the gradient of macroscopic stress suffers jump discontinuity. The dimensionless bending diagrams (nomograms) for rectangular beams are constructed. They enable rough quantitative estimation of some basic design parameters without recourse to the computer-aided numerical calculations. One-dimensional Müller–Xu thermodynamic theory of ideal pseudoelasticity is used as the theoretical foundation for the analysis. The theory is briefly discussed and its generalization that accounts for the tension–compression asymmetry effect is presented.