Phase Field Study Of Ni₄Ti₃ Precipitation Behavior In NiTi Shape Memory Alloys

The near-equiatomic NiTi alloys have become one of the most valuable metallic intelligent materials due to their unique shape memory effect, superelasticity as well as excellent biocompatibility. These unique properties are associated with the phase transformations in NiTi shape memory alloys (SMAs), which typically include B2-R transformation and B2-B19′transition. Moreover, as is generally recognized the Ni₄Ti₃ precipitates in NiTi alloys have a significant influence on the above transformation behaviors by introducing multiple-step martensitic transformations. Thus, an in-depth study on the Ni₄Ti₃ precipitatation will deepen our fundamental understanding of the effect of diverse transformations on the excellent properties of NiTi SMAs. However, due to the complexity, high cost and time-consuming operation of experimental research on these topics, computer simulation has become a powful tool and an effective alternative.In this thesis, a phase field model was developed to simulate the B2-R and B2-B19′martensitic phase transformations in dense and porous NiTi alloys, in particular for describing the microstructure evolution of B2-R transition in three-dimension and two-dimension, respectively. Based on the above simulation, the phase field model was then extended to study the B2-R transformation in porous NiTi alloy, and the effects of porosity ratio and pore size of the porous alloy on the growth kinetics of R-phase have been studied. In addition, a phase field model applicable for B2-B19′transition was used to predict the twining mode in B2-B19′phase transformation. Furtheremore, in this study the focus has also been placed on simulating the microstructure evolution and growth kinetics of Ni₄Ti₃ precipitates in both dense and porous NiTi alloys, in particular, the effects of the external applied stress on the microstructure evolution and growth kinetics of Ni₄Ti₃ precipitates were characterized. Based on the above studies, precipitation behavior of Ni₄Ti₃ particles in bi-crystalline NiTi alloys were characterized, in which the attention was paid to clarify the effect of initial Ni concentration (atomic weight), grain boundary and the external stress on Ni₄Ti₃ precipitation behavior in the bi-crystalline system. Moreover, the Ni₄Ti₃ precipitation behaviors in porous NiTi alloys containing both nano-sized and micro-sized pores were studied in more details. The effects of the applied stress and its direction as well as the pore size on the Ni₄Ti₃ precipitation were clarified. A method of"volume element"was proposed to study the microstructural feature of Ni₄Ti₃ variants in different volume elements. In addition, the time dependences of variant area fraction, variant size as well as the size distribution were obtained.The simulation results show that the R-phase variants can form three-dimensional banded structure and two-dimensional herring-bone microstructure through self-accommodation between R-phase variants. The R-phase variants nucleate preferentially around the pores, and there are more R-phase variants to nucleate around the large pores than the smaller ones. Two types of twinning planes are found, which are {101}_B2 and {001}_B2 respectively, and four variants meet at <010>_B2. It has been shown that the average size of R-phase variants decreases with increasing porosity ratio, while increasing with increasing pore size. The size uniformity of R-phase variants increases with increasing porosity ratio but shows no dependency on pore size. It is also shown that the B2-R transformation can generate uniform and fine R-phase microstructure only when the NiTi matrix contains a large number of small size pores. In the simulation of B2-B19′phase transformation, it is indicated that by taking into account the transformation induced elastic strain, the martensitic variants are self-accommodated and the present phase field model can predict the Type I twinning mode in B2-B19′phase transitions with good precision and visualization.Through the phase field study of Ni₄Ti₃ precipitation in single crystalline NiTi alloys, it is suggested that the time dependences of length, width and area fraction of Ni₄Ti₃ precipitate obey a power law, a linear and a logarithmic equation, respectively. The length-to-width ratio of the precipitate is not a constant value, but increases rapidly in the early stage of precipitation and slows down in later stage, and this is corresponding to formation of the precipitate with plate- or lenticular-shaped morphology and coincident with the experimental observations reported.The phase field study of the effects of the applied stress on the microstructure and growth kinetics of Ni₄Ti₃ precipitates suggests that during stress-free aging, four groups of the variants precipitate along the corresponding (111)_B2 habit plane; when the NiTi matrix is under [111]_B2 compressive stress-assisted aging, there is only one group of the variants with the normal lines parallel to [111]_B2 to precipitate. Although the uniaxial compressive stress apparently promotes the nucleation and slightly accelerates the growth of Ni₄Ti₃ variants in each group, the trends of aging time dependences of the area fraction, variant length, variant width and length-width ratio seem unchanged. The higher level of stresses can cause length and width of the variant slightly larger, but the area fraction of the Ni₄Ti₃ particles increases with increasing stress level. The simulation results are in good coincidence with the experimental results available.In the bi-crystalline NiTi alloys, the phase field simulation results indicate that during stress-free aging of the bi-crystalline NiTi alloy with a low supersaturation of Ni concentration (i.e., Ti-51.5at.%Ni), the Ni₄Ti₃ precipitates exhibit a heterogeneous distribution with a high concentration of particles at the grain boundary, leaving most part the grain interior precipitates free; while for the NiTi alloy with a high supersaturation of Ni concentration (i.e., Ti-52.5at.%Ni) the Ni₄Ti₃ precipitates show a homogeneous distribution across the entire simulation system. The stress-assisted aging can give rise to homogeneous distribution of the precipitates, regardless of initial Ni-content; however, the distribution of the variant type within the two grains is heterogeneous. These findings indicate that the grain boundary plays a necessary but insufficient role for heterogeneous distribution of Ni₄Ti₃ precipitates, since the grain boundary effect is composition and stress dependent. Moreover, it has been shown that the precipitation behavior in the bi-crystalline NiTi alloy can be changed by the initial supersaturation level of Ni-content and the external compressive stress which becomes more sensitive in the NiTi alloy with the relatively low supersaturation of Ni.In the study of Ni₄Ti₃ precipitation behavior in porous NiTi SMAs, two types of pores with the size in both nanoscale and microscale have been considered. The simulation results present that in the system containing nano-sized pores, under a high applied stress, more Ni₄Ti₃ particles precipitate around pores than that under a low stress, regardless of pore size; also the larger pores can attract more precipitates while less particles precipitating around smaller pores. Moreover, the precipitation of Ni₄Ti₃ particles exhibits different regional preferences near pores. The applied stress along [100]_B2 direction can cause most particles to precipitate in near-pore region along [010]_B2, while [010]_B2 stress along [100]_B2. The uniaxial compressive stress can result in inhomogeneous Ni₄Ti₃ precipitation around pores. However, for the system containing micro-sized pores, it is found that during stress-assisted aging of porous NiTi SMAs, the morphologies of Ni₄Ti₃ precipitation in different regions near the pores appear in different patterns, while a gradient microstructure including total precipitate density gradient and individual variant density gradient may occur. The relationship between the average length and aging time is independent of position near the pore, but the average length in a given aging time is position related. Finally, it has been shown that the uniformity of variant size distribution decreases with aging time and the applied stress level. In the direction normal to the applied stress, the uniformity of variant size distribution is relatively worse than that in the direction along the applied stress.