Modeling of static coarsening of two-phase titanium alloy in the α+β two-phase region at different temperature by a cellular automata method

Abstract

A cellular automata (CA) method was employed to model static coarsening controlled by diffusion along grain boundaries at 1173 K and through the bulk at 1213 and 1243 K for a two-phase titanium alloy. In the CA model, the coarsening rate was inversely proportional to the 3rd power of the average grain radius for coarsening controlled by diffusion along grain boundaries, and inversely proportional to the 2nd power of the average grain radius for coarsening controlled by diffusion through the bulk. The CA model was used to predict the morphological evolution, average grain size, topological characteristics, and the coarsening kinetics of the Ti-6Al-2Zr-1Mo-1V (TA15) alloy during static coarsening. The predicted results were found to be in good agreement with the corresponding experimental results. In addition, the effects of the volume fraction of the  phase (V f ) and the initial grain size on the coarsening were discussed. It was found that the predicted coarsening kinetic constant increased with V f and that a larger initial grain size led to slower coarsening. Two-phase titanium alloys have been widely used in the aerospace industry because of their excellent moderate room-temperature and high-temperature strength [1][2][3]. For these types of alloys, static coarsening occurs easily during their application at higher temperatures, which usually has a large effect on the grain size, morphology, and phase volume fraction and, in turn, on the mechanical properties of the final parts. Therefore, investigation of the coarsening mechanism of such alloys at high temperatures is necessary for microstructure design and process control. Over the years, many researchers have carried out experiments to study the static coarsening of two-phase titanium alloys in the single phase field or the  two-phase field. It is generally believed that the static coarsening process can be expressed as a power law as a function of aver-where d is the average grain diameter during coarsening, d 0 is the initial value at time t 0 , K is the coarsening rate constant, and n is the coarsening exponent. Different values of n represent different coarsening mechanisms. Gil and Planell [4], Semiatin et al. [5], and Ivasishin et al. [6] investigated the static coarsening behavior of Ti-6Al-4V alloy in the  single phase field, and found that the value of n deviated from the theoretical value of 2 for pure metals under all temperatures tested. The authors attributed this difference to the effect of solute atoms, precipitates, or impurities [7]. However, for two-phase titanium alloys the coarsening mechanism in the  two-phase field is much more complicated than that in the  single phase field. Some authors, including Hu and Rath [8] and Grewal and Ankem [9,10],

Coarsening of (αTi) + (βTi) Microstructure in the Ti–Al–V Alloy at Constant Temperature

“…In this case, the characteristic lengths of the diffusion pathways are much larger than the size of the grains . According to the experimental studies and numerical simulations, the obtained value n ≈ 4 corresponds to the grain growth in (αTi) and (βTi), which is controlled by diffusion along grain and/or interphase boundaries. Note that similar result was obtained theoretically in ref .…”

“…These images also indicate the simultaneous growth of (αTi) and (βTi) grains. Numerical modeling of the growth of grains in two‐phase polycrystal shows that the growth law with n = 3 corresponds to a process of coarsening of grains, controlled by the bulk diffusion . The authors of ref .…”

Cellular Automaton Simulation of Microstructure Evolution for Friction Stir Blind Riveting

“…Cellular automaton (CA) has provided the capability to simulate and predict the evolution of microstructure during metal forming processes [23][24][25][26]. In particular, CA methods have been developed to simulate the microstructure evolution governed by DRX during hot forming processes of various metals such as steels [23,[27][28][29][30][31][32][33], copper [24,25,[34][35][36][37], magnesium alloys [26,38,39], and titanium alloy [40,41]. These previous works demonstrated that the CA method is a computation-efficient numerical approach to simulate microstructure evolution.…”

A review on the modeling and simulations of solid-state diffusional phase transformations in metals and alloys

“…Since Hesselbarth [123] et al used the cellular automaton approach for the simulation of recrystallization, in the past several decades, it gradually becomes very promising and popular for simulating the microstructure evolution due to its computation efficiency, flexibility in multi-scale bridging, and physical consistency. Cellular automaton method has been successfully performed in two-or three-dimensional modeling and simulations of dynamic and static recrystallization [124,125], grain coarsening [126], solidification [126], solid-state phase transformation [127], micro-shear band and shear band propagation [128], cracks propagation [129], etc. It provides a deeper insight into the mechanism and morphological complexity of them without timeconsuming solution of complicated partial differential equations.…”