Finite element modeling of the morphology of β to α phase transformation in Ti-6Al-4V alloy

In the present work, a mathematical model and computer programs were developed for numerical simulation of the processes of nucleation and growth of the α-phase Widmanstätten plates during the course of the β ⇒ α phase transformation in a Ti-6Al-4V alloy. The α-phase appearance at the grain boundary of β phase is described by a numerical procedure for random nucleation as a function of the vanadium concentration and the temperature. The rate at which an interface moves depends both on the intrinsic mobility and on the rate at which diffusion can remove the excess of vanadium atoms ahead of the interface. The finite-element method (FEM) was used for solving the diffusion equation on the domain occupied by β phase. The elements chosen have dimensions in both space and time. A computer code based on the finite-element modeling and the volume of fluids method was developed to trace the movement of the α/β interface. The influences of the cooling rate and the temperature of isothermal exposure on the Widmanstätten morphology were simulated and analyzed. The developed models and program packages are capable of one-dimensional (1-D) and two-dimensional (2-D) simulations of the morphology of the β ⇒ α phase transformation in Ti-6Al-4V alloy for continuous cooling with any cooling path and for an arbitrary combination between continuous cooling and isothermal exposure.