Development and numerical implementation of one-dimensional phenomenological model for phase deformation in shape memory alloys

The paper is devoted to the development of a one-dimensional phenomenological model for phase and structural deformations in shape memory alloys. Phase deformation is reckoned as the length change in a chain of structural elements working in series: spherical austenitic and elongated martensitic elements. Martensitic elements are formed from the austenitic ones during the forward phase transition caused by cooling or loading and become the austenitic ones again after the reverse transition. A rotation angle of the martensitic element related to the longitudinal axis of the chain is determined by macroscopic stress acting at the moment of the element origination and characterizes the extent of the martensite orientation according to the acting stress. A remembering of a martensitic element rotation angle at the moment of its origination under forward transformation and its subsequent reproduction during reverse transformation allow taking into account the loading history and with the use of the universal approach describe several phenomena caused by martensitic transformation. Structural deformation is considered as a change in the rotation angle of the martensitic element due to the changed external stress. Total system deformation is determined by summing the elastic, phase and thermal components. A method of the model constants identification on the basis of macroscopic experimental data is suggested. The following experiments are needed for this purpose: forward transition under constant tension/compression load (several tests under different loads) and forward transition without any load (a dilatation expansion case). Several examples of the model numerical implementation for different cases are given: the shape memory effect, the forward transformation under a stepwise changing load, and reverse shape memory, taking into account the structural deformation occurring at the time of the load sign change. For some examples, a comparison with experimental data and with the results obtained by another model is given.