Thermo-mechanical modelling of a superelastic shape-memory wire under cyclic stretching-bending loadings

Experimental investigations on superelastic shape-memory alloy wires show a significant dependency of the load-displacement response on the loading-un loading rate, coupled with a non-negligible oscillation of the wire tempera ture. Motivated by this observation, the present work proposes a thermo-mechanica l model, suitable to study the response of a superelastic shape-memory allo y wire under cyclic stretching-bending loadings. The model is based on the kinematical assumptions that sections which are p lane in the undeformed configuration remain plane also in the deformed conf iguration and that the wire shear deformation is negligible. As a consequen ce, we need to introduce only a one-dimensional constitutive stress-strain equation; this relation involves a scalar internal variable, representing t he martensite fraction, variable for which evolutionary equations are propo sed. The whole model is then thermo-mechanically coupled due to the presence of internal heat sources in the form of phase-transition latent heat and of me chanical dissipation. The paper also addresses a numerical scheme for the integration, in time, o f the model and the algorithmic solution of the corresponding time-discrete thermo-mechanical problem. Finally, results from numerical simulations are presented to show the response of a wire under cyclic stretching and bendi ng loading conditions imposed at different strain-rates. (C) 2001 Elsevier Science Ltd. All rights reserved.