Multiple bifurcations and local energy minimizers in thermoelastic martensitic transformations

Thermoelastic martensitic transformations in shape memory alloys can be modeled on the basis of nonlinear elastic theory.Microstructures of fine phase mixtures are local energy minimizers of the total energy.Using a one-dimensional effective model,we have shown that such microstructures are inhomogeneous solutions of the nonlinear Euler-Lagrange equation and can appear upon loading or unloading to certain critical conditions,the bifurcation conditions.A hybrid numerical method is utilized to calculate the inhomogeneous solutions with a large number of interfaces.The characteristics of the solutions are clarified by three parameters：the number of interfaces,the interface thickness,and the oscillating amplitude.Approximated analytical expressions are obtained for the interface and inhomogeneity energies through the numerical solutions.

Isothermal martensitic transformation in Ti-Ni-Cu-Co shape memory alloy:Insight from a thermally activated kinetic model

Recently the isothermal martensitic transformation in shape memory alloys(SMAs)has been reported in many literatures,and several models have been proposed to interpret the isothermal and athermal kinet-ics.However,the underlying mechanisms remain inadequately understood.In this work,the isothermal transformation from B2 to B19 is confirmed in Ti-Ni-Cu-Co melt-spun ribbons at the temperature range between M s and M f.It reaches a saturation point at every isothermal temperature T iso,and the saturation points correspond to the f−T curve at the cooling rate of 0.5 K/min.The experimental results indicate that the isothermal accumulation of martensite is a relaxation process from the transient state to the thermoelastic balance one.A thermally activated kinetic model is developed in this study to characterize the isothermal and athermal kinetics.The model is able to estimate the evolution of martensite volume fraction under any temperature path T(t)and it agrees with the experimental results well.According to the model,the effects of elastic energy,nucleation density,and activation energy on the kinetics are in-vestigated.Among those,a small nucleation density n i as well as a large activation energy Qwill result in a significant isothermal transition.In this work,the slighter isothermal effects originate from the higher value of n i.As for the non-stoichiometric SMAs,the higher value of Qis responsible for the accumula-tion of martensite at the isothermal process.Accordingly,the present work provides a novel view from a kinetic model to understand the isothermal martensitic transformation in SMAs.

Irreversibility and transformation randomness of thermoelastic martensitic transformation in Ni–Ti alloys

In this work, the in situ optical observation was carried out in complete and incomplete transformation cycles of Ni–Ti alloys. In complete transformation cycles, initial martensite plates nucleate randomly in austenite. However, in a partial transformation cycle, the existing martensite plates have an influence on guiding the formation of subsequent martensite plates. And the randomness decreases with the decrease in transformation volume involved in the partial cycle. It is suggested that the randomness of transformations contributes to the introduction of defects, and the irreversibility associates with transformation randomness of martensite plates. For instance, a higher randomness in transformations could introduce more defects and more obvious irreversibility. On the other hand, defects generated in thermoelastic martensitic transformation are responsible for the hysteresis of transformations. Therefore, the randomness of transformations also contributes to the transformation hysteresis. These results could help further understanding on some martensitic transformation phenomena of shape memory alloys, such as the nonlinear and history-dependent characteristic.