Analytical study on stress-induced phase transitions in geometrically graded shape memory alloy layers. Part II: Analyses on geometrical shapes, loading procedures and boundary conditions

Abstract

Based on the asymptotic ODE system derived in part I of this series of papers, the mechanical behaviors of geometrically graded shape memory alloy (SMA) layers with different shapes, loading procedures and boundary conditions are studied in the current paper. First, for SMA layers with concave and convex shapes, the stress-strain curves during a full loading cycle are plotted based on the analytical solutions to the asymptotic ODE system, which can capture most of the experimental features. The effects of width ratio on the responses of the SMA layers are also discussed. Second, corresponding to the inner loops of the stress-strain curves, the configurations and phase states of the SMA layers with the different shapes are simulated. The underlying mechanisms responsible for the experimental features are also investigated. Third, the effects of boundary conditions are studied, where the free end boundary conditions, the mixed boundary conditions and the clamped boundary conditions are taken into account. The corresponding analytical solutions are derived and the responses of the SMA layers are simulated, which are compared with each other to reveal the effects of boundary conditions. The results obtained in the current paper further demonstrate the validity of the analytical approach for studying the phase transitions in geometrically graded SMA specimens.