On phase transformation models for thermo-mechanically coupled response of nitinol
The paper presents two constitutive models for the fully coupled thermomechanical behavior of shape-memory alloys. One of the models is based on a physically motivated multiplicative decomposition of the total deformation gradient at mesoscale. Another model constitutes an extension to the purely mechanical approach. That is, the first includes the effect of local rotations (at grain level) induced by the transformation strain, whereas the second neglects this effect altogether. First, the backgrounds on the kinematics and kinetics of phase transformation at the grain level are presented. The constitutive developments are stated using a Helmholtz free energy proposed for the phase transformation of nitinol by adding all relevant entropic, thermomechanical and chemical contributions. The study of the two models allows one to assess the significance of including the above-mentioned rotations in the prediction of stresses and temperatures during the phase transformation. A second alternative model is obtained by adding a thermomechanical, coupling and entropic terms to the Helmholtz free energy. Then an incremental method is proposed for the solution of the transformation equations subjected to constraints. Starting with a set of potentially active variants, this scheme uses a predictor-corrector approach which iteratively solves the constraint equations simultaneously with the transformation equations until both are exactly satisfied. The finite element formulation of the coupled thermomechanical problem is based on the use of the Galerkin method to solve the momentum and energy equations using a Newton-Raphson scheme. The evolution of temperature under mechanical loading at moderate strain rates and its effects on the constitutive response are investigated. Experiments on thin-walled tubes at different strain rates are used to estimate some material parameters and the heat transfer coefficient due to convection between the specimen and air. Finally, the finite element results are compared to a wider set of experiments for validation purposes.
scientific article; zbMATH DE number 5997846