Three-dimensional phase field simulation of the morphology and growth kinetics of Ni₄Ti₃precipitates in a NiTi alloy

Abstract

A three-dimensional phase field model is applied to study the morphology and growth kinetics of Ni4Ti3 precipitates, as well as the Ni concentration distribution feature, during the aging of a NiTi alloy. The model can reproduce well the multiple-variants morphology of Ni4Ti3 precipitates. The diameter-to-thickness ratio of lenticular Ni4Ti3 precipitates in the equilibrium shape is 4.2. Simulation results show that the Ni depletion region near the face of Ni4Ti3 precipitates is broader than that near the edge of the precipitates, and both the depletion level of Ni concentration and the length of the Ni depletion region adjacent to the precipitates increase with the aging time. The growth of the precipitate diameter and thickness can be described by the power-law fitting equation, with growth exponent m = 0.47 for the diameter and m = 0.46 for the thickness, which are in good agreement with those obtained in previous experimental and analytical studies.

Phase field modeling of Ni-concentration distribution behavior around Ni4Ti3 precipitates in NiTi alloys

“…The edge-face configuration of Ni 4 Ti 3 precipitates with different variant types are commonly observed in many experimental studies [5,[20][21][22] and the Ni-concentration distributions surrounding the precipitates are thought to be different from those observed around a single precipitate [13,19]. Morphology of two precipitates with the edge-face configuration evolved from two equal-sized nuclei embedded in the B2 matrix is shown in Fig.…”

“…The elastic strain energy is a function of both concentration and SFTS, thus, the change of elastic energy contribution by employing the scaling technique will result in a shift of c e B2 , which will be addressed in the following section. In the present study, the value of c e B2 ¼ 0:501 in the reference state is adopted [13,19]. The concentration relaxation process is stopped when the following criterion is reached:…”

“…The simulation is firstly carried out with an ellipsoidal-shaped Ni 4 Ti 3 disk embedded in a computational domain with 100 Â 100 Â 100 grid points, which has the disk diameter-to-thickness ratio of 3.6 [19]. Different initial disk diameters of D = 20, 40, 50 l eff 0 are used to study the effect of precipitate size (after undergoing the same aging time) on the Ni-concentration variation in the matrix surrounding a precipitate.…”

“…Hence, it would be useful to launch further studies to check the effects of physical parameters entering in the model, such as interfacial energy, scaling factor and domain size, on the Ni-concentration profile surrounding the precipitates. Previous study was performed to study the effect of the abovementioned parameters on the Ni-concentration distributions surrounding a single precipitate [19]. In this study, we consider the system containing a two-precipitate pair with certain spacing.…”

Computational Thermodynamics and Kinetics-Based ICME Framework for High-Temperature Shape Memory Alloys

“…Over the last decade, there have been a large number of works on the use of phase field models to describe the microstructural evolution in shape memory alloys. The works have ranged from microstructural evolution simulations in polycrystalline SMAs [115,116]; domain evolution in ferromagnetic SMAs where magneto-thermoelastic coupling is explicitly considered [117,118]; to simulations of complex microstructural evolution in which [14,[119][120][121][122]. In this work, we will focus on the latter examples as the use of PFM to investigate martensite domain structure in SMAs is outside the scope of the work and has been covered extensively elsewhere [123].…”