Mathematical modeling of aluminum evaporation during electron-beam cold-hearth melting of Ti-6Al-4V ingots

Akhonin, S.V.; Trigub, N. P.; Zamkov, V. N.; Semiatin, S. L.

doi:10.1007/s11663-003-0071-4

Cited by 52 publications

(36 citation statements)

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“…Similar measurements of evaporation losses have been made at the Paton Institute in Kiev, [4] a leader in the production of higher than those measured. The existence of an oxide film on the melt surface might reduce the relative rates of evaporation.…”

supporting

confidence: 72%

“…[20] at y ϭ 0 is [6] [21] C Al /C [4] ). Assuming that Al ϭ 2700 kg/m 3 , ϭ 1527 Pa, ␥ Al ϭ 0.30 (average value for 0 Ͻ X Al Ͻ 0.125), and D (2100 K) ϭ 3.74 ϫ 10 Ϫ8 m 2 /s, the flux coefficients were determined to be ␤ ϭ 8.755 10 Ϫ5 m/s and h ϭ 2340.9 m Ϫ1 .…”

Section: [17]mentioning

confidence: 99%

“…The activity coefficients of the components, ␥ i , may be expressed through the partial excess Gibbs energy ; i.e., [4] …”

mentioning

confidence: 99%

“…pct V. Using these estimates of and Eqs. [1] through [4], the corresponding activity coefficients, vapor pressures of the components, and evaporation rates for liquid solutions of Ti-6Al-4V (Ti-10.2Al-3.6V, at. pct) have been calculated.…”

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confidence: 99%

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Evaluation of evaporation losses during electron-beam melting of Ti-Al-V alloys

Ivanchenko

Ивасишин

Semiatin

2003

Metall Mater Trans B

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Electron-beam cold-hearth melting (EBCHM) is finding increasing application for the production of titanium alloys due to its ability to dissolve or eliminate inclusions with high melting temperatures. However, the melting of titanium alloys under vacuum results in the marked vaporization of volatile alloying elements, such as aluminum, having vapor pressures exceeding that of titanium. In this article, the evaporation rates of Al, Ti, and V from Ti-rich Ti-Al-V melts, in particular, Ti-6Al-4V, are evaluated on the basis of the thermodynamics of liquid solutions of the melt components. First, the ideal evaporation rate is estimated based on Langmuir's equation and thermodynamic calculations of the activity of the alloying elements. Second, the rate-limiting influence of diffusion of aluminum to the surface of the melt on the evaporation kinetics is considered.The rate of ideal evaporation of component i into vacuum (W i ) varies with temperature according to Langmuir's equation:[1] [2] in which X i , ␥ i , and M i are the molar fraction, activity coefficient, and molar mass of the evaporating species, respectively; P i is the partial pressure of vapor of component i over the multicomponent melt; R is the gas constant; T is the absolute temperature; and is the vapor pressure above the melt of pure element i. The vapor pressures of pure Al, Ti, and V can be estimated using the Clausius-Clapeyron equation:The constants A, B, and C in Eq.[3] are listed in Table I for Al, Ti, and V.The activity coefficients of the components, ␥ i , may be expressed through the partial excess Gibbs energy ; i.e.,In turn, the values of ⌬G -i ex are related to the integral thermodynamic functions ⌬G ex , which are as follows for a ternary system (with components 1, 2, and 3):If the Redlich-Kister equation is used to express the excess Gibbs energy of the Al-Ti, Al-V, and Ti-V binary systems, ⌬G ex of the Al-Ti-V ternary solution can be expressed for the general case as [6] in which X Al , X V , and X Ti denote the mole fractions of components in the melt; ␣ 1 , ␣ 2 , and ␣ 3 are interaction parameters for the ternary solution; and the terms for binary A-B systems are temperature-dependent model parameters; viz.[7]In practice, the maximum number n in the series expansions for ⌬G rarely exceeds 3, and the number of terms in Eq. [7] is taken less than that indicated. The thermodynamic properties of the Ti-Al, Al-V, and Ti-V binary liquid solutions are known and presented in Reference 2. The corresponding model parameters for Ti-Al, Al-V, and Ti-V systems are given in Table II.In view of the typical absence of experimental information on the thermodynamic properties of ternary solutions, the corresponding interaction parameters are usually put to zero, and the extra terms are omitted in Eq. [6]. Such thermodynamic evaluations were performed in Reference 2 for the Al-Nb-Ti, Al-Ta-Ti, and Al-Ti-W ternary systems. In the case of the Al-Ti-V ternary system, the same approximation was used in the present work, taking into account the fact that the...

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supporting

confidence: 72%

Section: [17]mentioning

confidence: 99%

“…The activity coefficients of the components, ␥ i , may be expressed through the partial excess Gibbs energy ; i.e., [4] …”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Evaluation of evaporation losses during electron-beam melting of Ti-Al-V alloys

Ivanchenko

Ивасишин

Semiatin

2003

Metall Mater Trans B

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“…In several efforts [15,16], the com position was assumed to be uniform across most of the meltpool depth, but was taken to be substantially less within a thin 'boundary layer' at the surface through which solute must diffuse prior to evaporating from the melt. In the sim plest of such approaches, a mass-transfer coefficient, which is essentially also a fitting parameter, was utilized to describe the surface phenomena.…”

Section: Models For Ebchm Ingot Compositionmentioning

confidence: 99%

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

et al. 2004

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The application of various modeling techniques in the design and control of a number of emerging processes for aerospace alloys is summarized. These techniques include those that are based on melting and solidification (electron-beam cold-hearth melting, laser deposition), deformation (severe-plastic deformation), rapid heat treat ment (dual-microstructure processing), and metal removal (distortion-free machining, high-speed machining). The models that have been developed and applied to these processes include those that are largely phe nomenological (e.g., continuum FEM codes) or mechanism based. The key elements of models for various processes, important analytical/numerical results, and how these results are or can be used for manufacturing design are summarized. Challenges for the further development and application of the models for industrial processes are also described. These include refinement of the physics-based understanding of the processes and measurement of various material properties that are needed to apply the models in a real-world man ufacturing environment.

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