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

The results of qualitative analysis of the variation of stress and the phas e 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 bea m planes separating the regions occupied by single phase (austenite or mart ensite) and their mixture (austenite and martensite) in the course of phase transitions is discussed. It is shown that at such mobile surfaces the gra dient of macroscopic stress suffers jump discontinuity, The dimensionless b ending diagrams (nomograms) for rectangular beams are constructed. They ena ble rough quantitative estimation of some basic design parameters without r ecourse to the computer-aided numerical calculations. One-dimensional Mulle r-Xu thermodynamic theory of ideal pseudoelasticity is used as the theoreti cal foundation for the analysis. The theory is briefly discussed and its ge neralization that accounts for the tension-compression asymmetry effect is presented. (C) 2001 Elsevier Science Ltd. All rights reserved.