Introduction to the level-set full field modeling of laths spheroidization phenomenon in α/β titanium alloys

Abstract

Abstract. Fragmentation of α lamellae and subsequent spheroidization of α laths in α/β titanium alloys occurring during and after deformation are well known phenomena. We will illustrate the development of a new finite element methodology to model them. This new methodology is based on a level set framework to model the deformation and the ad hoc simultaneous and/or subsequent interfaces kinetics. We will focus, at yet, on the modeling of the surface diffusion at the α/β phase interfaces and the motion by mean curvature at the α/α grain interfaces.

Full field model describing phase front propagation, transformation strains, chemical partitioning and diffusion in solid-solid phase transformations

“…To check that the numerical method provided correct result, the numerical elastostatic solution was compared to the analytical solution given by Eq. ( 26) and (27). When plotted along a line, which passes through the center of the cylindrical region, and is directed along the x-direction, σ xx = σ rr .…”

“…This allows for comparison of the numerical result against the analytical solution given by Eqs. ( 26) and (27). Continuity of the stress field and the stress near the simulation region boundaries were used to determine the constants C 1 and C 2 in Eq.…”

“…A function representing singed distance from the interface is usually applied as the propagating field, and the movement of the interface is calculated with a level-set equation. The phase propagation speed is used as an input of the model, hence the physics affecting the interface propagation can be implemented in the model, when the propagation speed can be calculated based on them [26,27].…”

“…Figure 3: Comparison between the numerical elastostatic solution and the analytical solution for the stress σ xx in a system containing enlarged cylindrical region, described by Eq. (26) and(27).…”