Mechanism of influence of nanocrystal sizes on the parameters of the curves of the pseudoelastic and thermoelastic deformations of alloys with the shape memory effect

The data available in the literature on the influence of the nanocrystal sizes of alloys with the shape memory effect on the parameters of the curves of their pseudoelastic and thermoelastic deformation are analyzed in the framework of the theory of diffuse martensitic transitions (DMT). The peculiarity of the DMT theory is that it is based on both thermodynamic and kinetic relationships that make it sensitive to the alloy structure on the mesoscopic scale. This enables one to state the functional dependence of the parameter of the martensitic deformation of the nanocrystals on the size of their cross section $D$. As a result of the analysis, it is found that the coefficient of the strain (martensitic) hardening and the hysteresis of the pseudoelastic strain curves of submicrocrystals of the Ni$_{54}$Fe$_{19}$Ga$_{27}$ are changed with $D$ by law $1/D^2$. The temperature range $(M_s-M_f)$ of the martensitic transition in TiNi alloy nanocrystals is changed by analogy law. These dependences are results of the constrained displacement of dislocations of the phase transformation by transverse sizes of the crystal. A kinetic mechanism of the appearance of the critical nanocrystal size $D_k$ is established; the transition of austenite to martensite does not occur at transverse crystal sizes smaller than the critical size.