Diffusion models for evaporation losses during electron-beam melting of alpha/beta-titanium alloys

Abstract

An analysis of the evaporation of aluminum during electron-beam melting (EBM) of alpha/beta-titanium alloys was performed. The analysis was based on the solution of the one-dimensional diffusion equation for the solute-concentration gradient in the melt pool subject to the flux boundary condition for the evaporation rate at the melt surface quantified using the Langmuir equation. The effect of process parameters and material coefficients (e.g., the diffusivity and solute activity in the melt) on predicted concentration gradients and melt losses under steady-state melting conditions was established for both the finite-domain and the semi-infinite-domain diffusion problems. The accuracy of the modeling approach was validated by comparison to previous measurements for the EBM of alloys with a nominal Ti-6Al-4V composition.

The prospects for additive manufacturing of bulk TiAl alloy

“…By using high power and high scanning speed, the cooling rate is fast enough to largely suppress α to α 2 phase transformation and promote a microstructure with the hard ordered B2 phase. On the other hand, a decreased scanning speed induces higher local superheat, thereby increasing the evaporation of aluminium 18 . Ge et al also reported the strong influence of energy input on Al evaporation for Ti-47Al-2Cr-2Nb powders 19 .…”

The role of modeling in the development of advanced processes for metallic aerospace alloys

“…Based on the solution of the one-dimensional diffusion equation, several very recent investigations have provided an alternate method to describe the competition between diffu sion of solutes to the melt surface and subsequent evapora tion [14,17]. For example, Semiatin et al [17] used a solution from Carslaw and Jaeger [18] to estimate the total solute loss from a melt pool of depth d, surface area A, and initial solute composition Co (in kg/m 3 ), i.e., Total Flux = AdCo×…”

“…For example, Semiatin et al [17] used a solution from Carslaw and Jaeger [18] to estimate the total solute loss from a melt pool of depth d, surface area A, and initial solute composition Co (in kg/m 3 ), i.e., Total Flux = AdCo×…”

“…2 for predicting aluminum losses in titanium alloys are values of the activity coefficient γAl and diffusivity DAl. In Reference [17], activity coefficients estimated from a ther modynamic database [14] were used. The diffusivity of alu- 3.…”

“…Additional work would also be useful to validate the basic assumptions of the diffusion model; i.e., laminar flow of the melt through the refining hearth with limited mixing across the melt-pool depth. In this regard, estimates of the temperature profile across the depth suggest that mixing associated with buoyancy and Marangoni shear may be limited [17], as is required for the model to be valid.…”