Abstract: The vacuum arc remelting process model software (BMPS-VAR) was used to numerically simulate the shape of the melt pool, temperature field, and elemental composition distribution at different stages of the vacuum consumable melting process of a φ 760 mm TC11 titanium alloy ingot. The same process as the melting simulation was used for experimental verification. The results show that the measured shrinkage depth of the ingot is 112 mm, which is basically consistent with the simulation results. The numerical simulation of VAR process provides effective result prediction and technical support for establishing TC11 titanium alloy vacuum self consumption melting model and solving practical smelting problems.
Keywords: TC11 titanium alloy; Vacuum consumable melting; Numerical simulation; Shape of the molten pool; Element distribution
TC11 titanium alloy (nominal chemical composition Ti-6.5Al-3.5Mo-1.5Zr-0.3Si) is a type of α - β titanium alloy material with excellent comprehensive performance [1]. It has excellent thermal strength at 500 ℃, high room temperature strength, and good thermal processing technology. It is widely used in the components of aviation engine compressors [2], such as blades, shafts, drums, etc. The industrial production of high-quality aviation titanium alloy ingots mainly relies on vacuum consumable arc melting (VAR), but due to uneven temperature distribution during melting and solidification processes, the ingots are prone to defects such as uneven elemental composition and microstructure. Segregation of TC11 titanium alloy elements may lead to defects such as low magnification white spots in forged bars [4], thereby affecting the performance of forgings. Obtaining ingots with accurate composition, low segregation, and uniform structure requires appropriate melting processes to ensure [5]. Industrial grade vacuum consumable melting is a process in which multiple physical fields such as electromagnetic field, flow field, and temperature field interact with each other. The shape, depth, temperature field, and elemental composition distribution of the molten pool during the melting process are key factors affecting the quality of the ingot. However, in the actual production process, the visualization level of melting is low and cannot be predicted. If traditional trial and error methods are used for research, there are problems of high production costs and long cycles.
Using numerical simulation technology to model and simulate the vacuum consumable arc melting process can intuitively observe the melting process, effectively predict the influence of process parameters on ingot quality, greatly reduce the number of experiments, shorten the research and development cycle, reduce research and development costs, and provide important guidance for practical production. In recent years, scholars at home and abroad have mostly used numerical simulation methods to study the effects of temperature field and electromagnetic field in VAR process on ingots [6-7]. Yang Zhijun et al. [8] used numerical simulation to study the electromagnetic field, temperature field, and flow field distribution of Ti-1023 alloy ingots under different parameters. KARIMI-SIBAKI et al. [9] simulated the distribution of electromagnetic and temperature fields, as well as the evolution of molten pool shape during vacuum self consumption process. However, there are few reports on the simulation and experimental verification of temperature field and element concentration field distribution during the melting process of TC11 titanium alloy.
In response to the above issues, this article uses the special melting simulation software (BMPS-VAR and BMPS-ESR) independently developed by Baosteel Central Research Institute [10] to study the vacuum consumable arc melting process of TC11 titanium alloy ingots with a diameter of 760 mm. Different melting stages, melt pool shapes, and element composition distributions are explored, and the reliability of the relevant simulation results is verified by actual melting ingots. This provides a reference for the industrial production of large-scale TC11 titanium alloy ingots with vacuum consumable melting and the development of melting processes.
1. Mathematical and physical models for simulation
The basic physical parameters of the TC11 titanium alloy material used in the calculation are shown in Table 1, the solidification equilibrium distribution coefficients of the main elements are shown in Table 2, and the parameters related to the VAR process are shown in Table 3. The dynamic parameter curve of the melting current over time used in the simulation process is shown in Figure 1. This curve is specifically designed for this experiment and is not an industrial production parameter. The magnitude of the melting current during VAR melting can cause changes in the flow within the melt pool and affect the temperature field [11-12].

　Table 2 Distribution coefficient K of solidification equilibrium of main elements
Table 2 Partition coefficient k of main elements

　　Table 3 VAR Melting Process Parameters
Table 3 VAR process parameters

　　2. Simulation result analysis
2.1 Simulation results of temperature field in different melting stages
Figure 2 shows the temperature field distribution changes of TC11 titanium alloy at different stages of VAR process. Figure 2 (a) shows the simulation results of the temperature field at t=80 min. At this time, there is less melted metal, and the melt at the bottom of the crucible solidifies, resulting in a decrease in temperature. When the melting process reaches 160 minutes (Figure 2 (b)), the height of the ingot increases, and the temperature in the high-temperature zone at the top of the melt pool can reach 2000 ℃. Under the action of cooling water, the temperature at the bottom of the crucible gradually decreases. Compared with the time at t=80 minutes, the temperature field has undergone significant changes at this time. Due to the distance between the middle of the melt pool and the crystallizer wall, heat accumulation * is significant, resulting in a higher temperature at the center than at the edges within the same cross-section. During the subsequent melting process, the contact area between the liquid metal and the crystallizer wall gradually increases, and heat is carried away by the cooling water. Figure 2 (c) shows that at t=320 min, a large amount of heat is dissipated through the crucible wall, the solidification process enters a stable state, and the temperature of the ingot decreases. At t=490 min (Figure 2 (d)), the vacuum self consumption melting is completed, and the ingot enters the vacuum cooling stage, with the ingot temperature gradually decreasing.

　　Figure 2 Temperature Field Calculation Results of TC11 Titanium Alloy VAR at Different Stages
Fig.2 Simulation results of temperature fields at different stages during VAR process
2.2 Simulation results of molten pool shape
Figure 3 shows the calculation results of the volume fraction distribution of the liquid phase during the VAR process of TC11 titanium alloy. The red area represents the liquid phase zone, and the blue area represents the solidification zone. The shape of the liquid phase zone reflects the shape of the molten pool during the VAR process. Combined with Figure 2 analysis, it can be seen that the morphology of the molten pool changes dynamically with the temperature field. Figure 3 (a) (t=80 min) shows the establishment period of the melt pool, forming a shallow "bowl" shaped melt pool. When the melting time is 160 minutes (Figure 3 (b)), the heat emitted through the crucible is still less than the heat released during the solidification of the metal liquid. The accumulation of heat increases the depth of the molten pool to 800 mm, and the molten pool forms a "U" shape. Due to the significant accumulation of heat in the middle of the molten pool, the depth increases rapidly in the direction of the central axis, and the shape of the molten pool gradually changes from a "U" shape to a "V" shape, as shown in Figure 3 (c) (t=240 min). The depth of the molten pool is about 1000 mm. At t=320 min, the ingot has entered the shrinkage stage (Figure 3 (d)), where the longitudinal length of the liquid phase zone shortens, the melting current decreases, and the melting rate gradually decreases. The volume of the metal melt pool gradually shrinks, which may result in shrinkage porosity. Therefore, controlling the depth of the melt pool through the melting process is particularly important. When the hot sealing stage of the melt pool is completed, the ingot has solidified into shape, but there is still a small amount of alloy melt pool that has not completely solidified. At t=490 min (Figure 3 (e)), the ingot enters the cooling stage, and the longitudinal length of the liquid phase zone gradually shortens. At t=520 min, the liquid phase zone of the ingot disappears (Figure 3 (f)).

　　Figure 3 Simulation results of melt pool shape at different stages during VAR process of TC11 titanium alloy
Fig.3 Simulation results of the shape of the mold pool in the ingot at different stages during VAR process for TC11 titanium alloy
2.3 Simulation results of element composition distribution
Figure 4 shows the simulation results of the element composition (mass fraction) distribution of the vacuum consumable melting of the φ 760 mm TC11 titanium alloy ingot. The distribution pattern of its elemental composition is shown in the figure. Figure 4 (a) shows that the content of Al element (K=1.070, as shown in Table 2) is higher at the edges and bottom, and lower at the longitudinal center, exhibiting a negative segregation pattern; The Mo element exhibits the same negative segregation pattern (Figure 4 (b)); Figure 4 (c) shows a slightly negative segregation distribution of O element, with small differences in the mass fractions of its components at different positions; The distribution of Fe element (Figure 4 (d)) is opposite to that of Al element, showing a positive segregation pattern. The mass fraction at the edge of the ingot is 0.142% to 0.148%, and at the longitudinal center it is 0.160% to 0.162%. This means that the content is low at the edge and bottom, and high at the center; Si and Zr elements also exhibit positive segregation patterns, as shown in Figures 4 (e) to (f), respectively. The segregation zone of each element at the top of the ingot is shaped like a bowl, with a longitudinal center length of approximately 110 mm. The difference between the * value and the * minimum value of the element in the cross-sectional distribution of the ingot is used to characterize the uniformity of element melting. A small difference indicates that the melting process has good control over segregation. The ratio of element difference to the design composition of the element indicates the ease of control of the element during melting. The calculation results are shown in Figure 5. The difference ratio of Fe and Si is relatively large, 0.203 and 0.144 respectively, which are the two elements that are prone to segregation in TC11 titanium alloy. The segregation of Al and O elements in TC11 titanium alloy is prone to brittle fracture during tensile and impact testing [13]. According to the equilibrium distribution coefficient and melting simulation results, the segregation tendency of Al and O elements is relatively low.

　　Figure 4: Calculation Results of TC11 Element Composition Distribution
Fig.4 Simulation results of element distribution for TC11 titanium alloy

　　Figure 5 Calculation results of the difference ratio of various elements in TC11 titanium alloy
Fig.5 Simulation results of difference ratios of elements in TC11 titanium alloy
3. Experimental verification
Based on the VAR numerical simulation results, the depth of the molten pool and the concentrated distribution of segregation elements at the top of the ingot before the end of the melting process are used as reference data for the cutting position of the φ 760 mm ingot. Taking into account the yield of the ingot, it is recommended that the cutting depth be 110 mm. To verify the reliability of the VAR process simulation results, vacuum consumable arc smelting tests were conducted on TC11 titanium alloy ingots with a diameter of 760 mm using the same process as the smelting simulation process. The results showed that the appearance quality of the ingots was good. Cut longitudinally along the center of the ingot and observe the internal quality of the ingot (Figure 6). It can be seen from the figure that a shrinkage cavity is generated at the 112mm position at the head of the ingot. It can be seen that the measured results are basically consistent with the simulated results, indicating that this numerical model can provide result prediction and theoretical support for TC11 titanium alloy melting.

　　Figure 6 Longitudinal sectional view of TC11 titanium alloy ingot with a diameter of 760 mm
Figure 6: The longitudinal section picture of TC11 titanium alloy ingot (diameter 760 mm)
4. Conclusion
(1) Using BMPS-VAR simulation software to simulate the temperature field of TC11 titanium alloy VAR process at different stages. The melting current, voltage, and other parameters of vacuum consumable melting affect the temperature gradient of the molten pool, which in turn affects the shape of the metal molten pool. The shape of the molten pool changes from an initial "bowl" shape to a mid-term "U" shape, and then to a "V" shape.
(2) The element segregation during the VAR process of TC11 titanium alloy can be predicted through melting simulation. From the distribution pattern of composition, the content of Al, Mo, and O elements is higher at the edge and bottom of the ingot, and lower at the longitudinal center, showing a negative segregation pattern; The content of Fe, Si, and Zr elements is low at the edges and bottom, and high at the longitudinal center, showing a positive segregation pattern.
(3) The accuracy of the smelting simulation was verified by comparing the simulation and experimental verification results. This vacuum consumable melting simulation technology can be applied in the fields of predicting the cutting distance of finished ingots, predicting the depth of the ingot melt pool, and predicting the distribution of easily segregated elements in ingots, providing theoretical support for improving the quality of industrial grade large ingots, optimizing process parameters, and predicting element segregation in vacuum consumable melting.