On stability of elastic domain during isothermal solid-solid phase transformation in a tube configuration

Under isothermal quasi-static stretching the phase transition of a superelastic NiTi tube involves the formation (during loading) and vanishing (in unloading) of a high strain (martensite) domain. The two events are accompanied by a rapid stress drop/rise due to the formation/vanishing of domain fronts. From a thermodynamic point of view, both are instability phenomena that occur once the system reaches its critical state. This paper investigates the stability of a shrinking cylindrical domain in a tube configuration during unloading. The energetics and thermodynamic driving force of the cylindrical domain are quantified by using an elastic inclusion model. It is demonstrated that the two domain fronts exhibit strong interaction when they come close to each other, which brings a peak in the total energy and a sign change in the thermodynamic driving force. It is proved that such domain front interaction plays an important role in controlling the stability of the domain and in the occurrence of stress jumps during domain vanishing. It is also shown that the process is governed by two nondimensional length scales (the normalized tube length and normalized wall-thickness) and that the length scale dependence of the critical domain length and stress jump for the domain vanishing can be quantified by the elastic inclusion model