# Mathematical modeling of electron beam cold hearth casting of titanium alloy ingots

## Abstract

The electron beam cold hearth remelting (EBCHR) process is used extensively for the refining of titanium alloys and casting of ingots. The main challenges associated with the final phase of the casting process are the formation of macroscopic shrinkage voids and evaporative losses of alloying elements in the top portion of the ingots. The purpose of the current work is to better understand the casting process and to give a theoretical foundation for addressing the issues of shrinkage void formation and evaporative losses. To this end, a mathematical model has been developed to describe the EBCHR casting of a Ti-6AI-4V ingot. The model characterizes the mass, momentum, and heat transports together with their interactions, by solving the coupled thermal-fluid flow fields inside the ingot. The formation of shrinkage voids is predicted using the Niyama criterion calculated with the results of the model. Industrial experiments have been conducted to provide data for formulation of the model’s boundary conditions and validation of its predictions. An overall heat balance analysis has been conducted on the domain used in the model at steady state. The results indicate that the primary energy input to the ingot is from the enthalpy of the inlet titanium, which accounts for approximately 65% of the total heat. The electron beams account for the balance or approximately 35%. The major energy losses from the domain are from the bottom and from the top surface, 24% and 31% respectively, and the mould, 29%, with the balance lost to the below mould environment, 16%. The model has also been used to examine the effects of ramping the casting speed near the end of the casting process and adjusting the beam power and pattern during the final stage of casting. Casting speed appears to be effective in raising the location of the final void, and thus may be effective in reducing size of the cropped prior to rolling. The latter appears to be effective in reducing the surface area of the liquid pool during the final solidification and therefore may be useful in reducing the evaporation losses. Judicious use of the two in combination may yield an optimum termination strategy.Applied Science, Faculty ofMaterials Engineering, Department ofGraduat

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Last time updated on 14/12/2019

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