Phenomenological modeling of phase and structural deformations in shape memory alloys. One-dimensional case

The elements of construction made of shape memory alloys (SMA) during their exploitation are subjected to cooling and heating under varying stresses. This leads to simultaneous phase and structural transformations affecting each other and causing such accompanying phenomena as shape memory, cross-hardening, and martensitic inelasticity. Furthermore, stress variations provoke the shift of phase transformation temperatures and can predetermine forward and reverse phase transformations when the isothermal load increases or decreases (superelasticity phenomenon). This work presents a phenomenological model for describing, in the framework of the uniform approach, the listed phenomena because they have a significant effect on the stress-strain state of the structure. The model is based on the interconnection of forward transition and martensitic inelasticity diagrams which allows one to uniformly describe phase and structural deformations because both of them are related to the formation of the oriented martensite. We study a set of martensitic structural elements connected in series, each having a unique structural transformation factor (initial stress). The structural transformation factor is defined by the element emergence conditions at forward phase transformation and by the subsequent deformation behavior. This approach allows us to take into account, first, the mutual influence of the processes of phase and structural transformations, and second, the influence of the deformation history on further transition. The problem of joint deformation of the package of SMA rods is solved to illustrate the evolution of the stress-strain state of the system at simultaneous phase and structural transformations caused by the external thermomechanical effect.