Static coarsening of titanium alloys in single field by cellular automaton model considering solute drag and anisotropic mobility of grain boundaries

Abstract

Static coarsening is an important physical phenomenon that influences microstructural evolution and mechanical properties. How to simulate this process effectively has become an important topic which needs to be dealt with. In this paper, a new cellular automaton (CA) model, which considers the effect of solute drag and anisotropic mobility of grain boundaries, was developed to simulate static grain coarsening of titanium alloys in the beta-phase field. To describe the effect of the drag caused by different solute atoms on coarsening, their diffusion velocities in beta titanium were estimated relative to that of titanium atoms (Ti). A formula was proposed to quantitatively describe the relationship of the diffusion velocity of Ti to that of solute atoms; factors influencing the diffusion velocity such as solute atom radius, mass, and lattice type were considered. The anisotropic mobility of grain boundaries was represented by the parameter c 0 , which was set to 1 for a fully anisotropic effect. These equations were then implemented into the CA scheme to model the static coarsening of titanium alloys Ti-6Al-4V, Ti17 (Ti-5Al-4Mo-4Cr-2Sn-2Zr, wt%), TG6 (Ti-5.8Al-4.0Sn-4.0Zr-0.7Nb-1.5Ta-0.4Si-0.06C, wt%) and TA15 (Ti-6Al-2Zr-1Mo-1V, wt%) in the beta field. The predicted results, including coarsening kinetics and microstructural evolution, were in good agreement with experimental results. Finally, the effects of time, temperature, and chemical composition on grain coarsening and the limitations of the model were discussed. The mechanical properties of titanium alloys such as the creep resistance, fracture toughness and crack propagation resistance are determined by their grain sizes in the beta phase field [1,2]. However, the grains are prone to static coarsening when held in the beta phase field because of the structural characteristics of beta-titanium and relatively high stacking fault energy at high temperatures [3]; this results in a marked decrease in the mechanical properties of final products. Therefore, it is necessary to understand and to control static coarsening of titanium alloys in a single phase field to obtain the expected mechanical properties. Previously, many experimental investigations have focused on the static coarsening behaviors of titanium alloys in the beta phase field. Ivasishin et al. [4,5] investigated the effect of texture evolution on the values of the static coarsening exponent n and activation energy for Ti-6Al-4V alloy in the beta field. They found values of n ranging from 0.22 to 0.31 at different temperatures, but there were marked deviations attributed to different materials and experiments when the results were compared with those of others. Recently, Semiatin et al. [6][7][8] investigated the static grain coarsening of Ti-6Al-4V alloy via a series of heat treatments at typical temperatures. They found that the coarsening process of primary alpha particles was controlled by the volume diffusion of solute elements at lower temperatures and the growth exponent was equal to 0.33.

Effect of Al Content on the Microstructural and Grain Growth Kinetics of Magnesium Alloys

“…This is particularly obvious at lower temperatures, while the grain growth curves appear more parabolic as the temperature increases, particularly in AZ61 and AZ91 Mg alloys. The linear fits suggest that the process is indeed thermally activated, and the activation energy Q is 204.1 KJ/mol, 166.1 KJ/mol, and 215.6 KJ/mol, which is larger than the grain boundary diffusion energy (92 KJ/mol) and bulk diffusion energy (135 kJ/mol) in Mg [14]. The range of values obtained for these Mg alloys suggests that the activation energy may depend upon the composition (impurity levels) and the initial conditions (microstructure, vacancy content, etc.).…”

“…The diffusion velocity of solute atoms in the matrix is controlled by their radius, mass, and lattice type. For Mg with a hcp crystal structure (c/a ratio = 1.6236), the diffusion of solute atoms in the hcp-Mg matrix is anisotropic [14,36]. This means that the diffusion coefficients (D diff ) of solute atoms along or perpendicular to the c-axis are different.…”

Review on globularization of titanium alloy with lamellar colony

“…Secondly, with aggravation of deformation degree, due to the differences in solute concentration gradient, solute atom passes the dislocation channel and crosses interface, triggering the formation of thermal grooving. Thirdly, the diffusion rate and path of solute element is affected by curvature effect, solute atom's dragging effect [42] and solute concentration gradient. The alpha stable solute atom Al in the interface near the thermal grooving are concentrated and the concentration of beta stable solute atom Mo is lower.…”

“…However, the effect of the alpha/beta interface on the diffusion of solute atom during globularization is scarce. The diffusion of the solute atoms especially the Mo and V atoms are affected by the solute concentration gradient [33,40], solute atom's dragging effect [42] on the interface migration and the lose coherency of alpha/beta interface. Although literature [75] suggested the loss of coherency increased the rate of diffusion along the interphase boundaries resulting in an acceleration of the rate of globularization of the two phases, specific experimental research and quantitative analysis are needed.…”

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

“…Subsequently, Raghavan and Sahay [22,23], and Kugler and Turk [24] simulated topological characteristics during the coarsening of polycrystalline materials in the single phase field. Recently, Wu et al [25] studied the effects of solute drag on the coarsening kinetics of a near- titanium alloy in the  single field by the CA method.…”