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Control of the floating zone stability during electron beam melting process of Ni-25%Si alloy
Journal of Manufacturing Processes 45 (2019) 702–709
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Technical Paper
Control of the floating zone stability during electron beam melting process of Ni-25%Si alloy
T
⁎
Xiaopeng Lia,b, Binggang Zhanga, , Houqin Wanga, Tao Yua a b
State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin 150001, China College of Material Science and Engineering, Nanjing University of Science and Technology, Nanjjing 210094, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Electron beam floating zone method Ni-25at%Si alloy Finite element method Heat Beam attenuation
In this study, the Ni-25at%Si alloy was fabricated by electron beam floating zone (EBFZ) method. The finite element method was used to calculate the temperature field of electron beam refining process. The electron beam refining process was controlled based on the temperature distribution which was varied with the process parameters. The electron beam refining process of Ni-25at%Si can be divided into 2 stages. The first stage featured the forming of a stable floating zone and the second stage featured the moving of the stable floating zone. The experimental results showed that it was difficult to balance the surface tension and gravity during the melting process due to the low surface tension of Ni-25at% Si alloy. The heat capacity of Ni-25at%Si alloy bar was limited, which easily led to the heat accumulation inside the melting zone during the refining process, resulting in the dynamically changing of surface tension and decreasing the stability of the refining process. Based on the inherent relationship among temperature, surface tension and the stability of the melt zone, the temperature field of the floating zone was quantitatively analyzed by numerical simulation and the process parameters for maintaining the stability of the floating zone were obtained. Then the "beam attenuation" technique was put forward to eliminate the heat accumulation during the refining process and a stable refining process was finally obtained.
1. Introduction The Ni-25at%Si alloy, which is characterized by excellent high temperature oxidation resistance at elevated temperature, has wined great interest in the aerospace field [1–3]. However, the brittleness of Ni-25at%Si alloy, which is not conducive to machining, restricts its application [4–6]. Improving the toughness of Ni-25at%Si alloy will promote its application in the future. R Ahmad et al [7] found that lamellar αNi-γ (Ni31Si12) eutectic structures could form from Ni-25at% Si alloy and the αNi would be the toughening phase to improve the room temperature toughness of Ni-25at% Si. Additionally, many studies [8–10] have obtained unidirectional full lamellar in situ eutectic composites with improved toughness by directional solidification. Thus, it is feasible to prepare unidirectional full lamellar αNi-γ (Ni31Si12) eutectic structures with improved toughness at the composition of Ni-25at%Si by directional solidification. The EBFZ method is one of directional solidification methods which is characterized as high energy density, high vacuum degree, high temperature gradient and no crucible pollution. It is widely used in refining and purifying refractory metals [11] and superalloys [12,13].
⁎
Thus, EBFZ of Ni-25%Si was carried out in this work. The key point to refine Ni-25%Si alloy successfully was to keep the floating zone stable as a free surface without any support would form during EBFZ process. However, most of former research only focused on the changing of microstructures and composition after EBFZ process and little attention has been paid on the influence of the particularity of EBFZ, namely crucibleless, on the refining process. It is reasonable to ignore this part in EBFZ processing of refractory metals as it is much easier to keep floating zone stable because of their relative large surface tension. While for the alloys with small surface tension, such as Ni-25%Si alloy, it is very difficult to keep the floating zone stable. In the present paper, the influence of the process parameters on the stability of floating zone were investigated using the finite element method. Meanwhile, the refining process was collected by a charge-coupled device (CCD) visual system. The calculated results were verified by experimental results. Finally, the processing parameters for producing stable floating zone in EBFZ were given out.
Corresponding author at: No. 92, Xidazhi Street, Nangang District, Harbin City, Heilongjiang Province 150001, China. E-mail address: [email protected] (B. Zhang).
https://doi.org/10.1016/j.jmapro.2019.08.008 Received 3 September 2018; Received in revised form 12 June 2019; Accepted 5 August 2019 Available online 19 August 2019 1526-6125/ © 2019 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
Journal of Manufacturing Processes 45 (2019) 702–709
X. Li, et al.
Fig. 3. The circular Gauss surface heat source.
Fig. 1. The schematic illustration of the EBFZ processes.
materials are isotropic continuum; 2) The initial temperature is 20 °C; 3) EBFZ process is a quasi-steady process; 4) The transport of heat by convection is disregarded because of Pr < < 1 for Ni-25%Si alloy; 5) The heat transfer coefficient is 40 W/m2·K; 6) The mechanical boundary is omitted as the calculation only focus on the temperature field of EBFZ process.
2. Numerical and experimental procedure Fig. 1 shows the schematic illustration of the EBFZ processes. The cathode in Fig.1 can move up and down at different speed and the specimen will rotate during the EBFZ process to uniform the heating distribution circumferentially along the specimen. Thus, we only considered the moving of heat source in the simulation procedure and the rotation of specimen was ignored.
2.2. Heat source The EBFZ equipment contains an annular cathode and no focusing coils to focus the electron beam. Hence, the electron beam was in defocusing state and the electron beam performed in heat conduction mode without keyhole phenomenon during EBFZ process. Based on the heating characteristic, an annular heat source was built in the present study. The annular heat source was treated as Gaussian plane heat source, namely, the energy distributed as Gaussian function along the z direction while the energy distributed uniformly along the circumference of specimen as shown in Fig. 3. Hence, the Gaussian plane heat source can be written as:
2.1. Mesh generation and calculation conditions The 3-D finite element model (FEM) is employed to analyze the thermal fields of EBFZ process in this study. The material used here is Ni-25%Si alloy with dimensions of φ10 mm × 100 mm. Non-uniform mesh is adopted to build the model of the specimen. Finite element mesh used in the work is shown in Fig. 2. There are total 22,000 units and 24,745 nodes in this model. For the calculation, the following conditions are assumed: 1) The
Fig. 2. Finite element mesh generation. 703
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q (z ) = qm exp(−kz 2)
(1)
Table 1 Nomenclature used in the simulation.
The total heat input during the EBFZ process was determined as:
Q0 =
+∞
∫−∞
q (z )2πr dz =
+∞
∫−∞
qm exp(−kz 2)2πr dz
(2)
Then the maximum heat flux in the Gaussian plane heat source was obtained:
qm =
Q0 k1/2 2r π3/2
(3)
Based on the assumption that 95% of the total thermal energy would locate in small region, namely the heated region, the following relationship can be deduced:
95%Q0 =
+z h
∫−z
q (z )2πr dz =
h
+z h
∫−z
h
qm exp(−kz 2)2πr dz
1.92 z h2
Prandtl number The maximum heat density Constant The radius of the Ni-25%Si sample Heat density Width of heated region The total heat input during the EBFZ process
Parameters
Beam current (mA)
Moving rate of floating zone (mm/h)
Accelerating voltage (kV)
Values
15, 16, 17
50
9
3. Results and discussions
(5)
1.386Q0 1.92 exp(− 2 z 2) z h⋅2r π3/2 zh
Pr qm k r q(z) 2zh Q0
(4)
3.1. EBFZ melting process and FEM verification
Substituting Eq. (3) and (5) into Eq. (1), the heat density distribution in heated region could be written as:
q (z ) =
Nomenclature
Table 2 The specific values of the parameters of EBFZ process.
Thus, the following relationship between k and zh can be obtained:
k=
Symbol
Fig.5 and Fig.7 shows the two typical stages of EBFZ process which were collected by the CCD visual system. The first stage featured the forming of a stable floating zone. With the increase of beam current, the width of the melted surface increased gradually and a floating zone was obtained when the width of the melted surface reached to 10.25 mm as shown in Fig.5a. This stage was used to verify the accuracy of the FEM. As shown in Fig. 5b, the width of the melted surface obtained by FEM well matched with the corresponding experimental results in the first stage. To further verify the accuracy of the FEM, the sectional morphology of the FEM result obtained at 840 s was compared with the experimental result as shown in Fig. 6. The calculated morphology was closed to that obtained experimentally which confirmed that the proposed heat source model was suitable for the simulation of the EBFZ process. It was also can be seen in Fig.6 that the solid/liquid interface appears curved shape which would not produce unidirectional temperature gradient. The calculated results of EBFZ process showed that the solid/liquid interface would be planar after 45 s (Fig. 6b). Thus, another 45 s were spent after the initial stages of the EBFZ process to ensure that the unidirectional temperature gradient was produced and the floating zone was overheated. Hereafter, a stable floating zone (Fig.7a) with planar solid/liquid interface (Fig.7b) was produced and then it moved at a certain rate in the second stage of EBFZ process.
(6)
2.3. Thermo-physical properties of Ni-25%Si The temperature-dependent thermo-physical properties of the Ni25%Si alloy were measured by NETZSCH LFA and the specific values are shown in Fig. 4. As the melting process of EBFZ is only related to thermo-physical parameters of Ni-25%Si alloy, the mechanical properties of Ni-25%Si alloy are not considered here. (Table 1) 2.4. Experimental process In this study, the Ni-25at%Si alloy with the size of 10 mm in diameter and 100 mm in length was remelted by EBFZ with different beam current and moving rate of the molten zone. The specific values of the parameters are shown in Table 2. The high voltage of EBFZ equipment was 9 kV. The increment of beam current was 2 mA/min during the beam current loading process. The EBFZ process was collected by CCD visual system. Before the process, the oxide layer was removed by grinding, cleaning and drying.
Fig. 4. The relationship between thermophysical properties and temperature a) Specific heat; b) Thermal conductivity. 704
Journal of Manufacturing Processes 45 (2019) 702–709
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Fig. 5. The formation of the floating zone in first stage of EBFZ process under 16 mA. (a)The experimental results, (b) the simulation results.
Fig. 6. The longitudinal section morphology of melting zone obtained by 16 mA at 840 s. a) Numerical simulation result; b) Experimental result.
Fig. 7. The longitudinal section morphology of melting zone obtained by 16 mA at 885 s. a) Numerical simulation result; b) Experimental result.
3.2. Controlling of the first stage of EBFZ process
Further examination revealed that with increase of beam current, the height of floating zone decreased gradually. The FEM was used to explain this phenomenon. Fig. 9 shows the simulation results of the EBFZ process under different beam current. Due to the small heat flux at 15 mA, it would spend 1017s to form a floating zone with planar liquid/ solid boundary as shown in Fig9a. Heating for a long time resulted in a large floating zone of 13.6 mm with small temperature gradient and
Fig. 8 showed the morphologies of floating zone obtained by different beam current. All the three floating zones showed conical shape with melts accumulation at the bottom. The floating zone obtained at 15 mA and 17 mA showed more unevenly than that of 16 mA which means that floating zone obtained at 16 mA is the most stable one. 705
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Fig. 8. The different floating zone morphologies obtained by different beam current. (a) 15 mA, (b) 16 mA and (c)17 mA.
Fig. 9. The thermal field and temperature distribution obtained by different beam current. a)15 mA; b) 16 mA; c) 17 mA; d) Temperature distribution of melted zone. Table 3 The distribution of temperature and surface tension of the molten zone and the corresponding maximum zone height.
Table 4 The distribution of temperature and surface tension of the molten zone and the corresponding maximum zone height.
Ranges
Average temperature/ ℃
Surface tension/(mN/ m)
Lmax(i) /m
Lmax/mm
Ranges
Average temperature/ ℃
Surface tension/(mN/ m)
Lmax(i) /m
Lmax/mm
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1257.925 1296.955 1340.80 1387.085 1414.825 1407.095 1380.670 1356.205 1336.00 1317.745 1300.495 1283.895 1267.775 1252.050
1842.743 1826.243 1807.709 1788.142 1776.415 1779.683 1790.854 1801.196 1809.738 1817.455 1824.747 1831.764 1838.579 1845.227
0.012987 0.012929 0.012863 0.012793 0.012751 0.012763 0.012803 0.012840 0.012870 0.012897 0.012923 0.012948 0.012972 0.012996
12.881
1 2 3 4 5 6 7 8 9 10 11 12
1272 1311 1354 1384 1382 1360 1338 1321 1305 1290 1276 1262
1836.793 1820.306 1802.128 1789.446 1790.292 1799.592 1808.892 1816.079 1822.843 1829.184 1835.102 1841.020
0.013013 0.012955 0.012890 0.012845 0.012848 0.012881 0.012914 0.012940 0.012964 0.012987 0.013008 0.013028
12.939
floating zone. To calculate the Lmax accurately, we assumed that the temperature between the two nodes of the finite model was constant and equaled to the average temperature. Thus, the Lmax(i) between every two nodes could be calculated and the critical size of melting zone could be obtained by Lmax =ΣLmax(i)/ i. Based on the assumption above, the critical size of melting zones obtained by different parameters could by calculated as Table 3–5. As shown in Table 3–5, the maximum height of the floating zones obtained by 15 mA、16 mA and 17 mA was 12.881mm、12.939 mm and 12.904 mm, respectively. While the experimental results showed that the maximum height of the floating zones obtained by 15 mA、 16 mA and 17 mA was 13.6 mm, 12.4 mm and 12.0 mm. Thus, based on the theory of Heywang [14], the floating zone of 15 mA was unstable. Interestingly, the calculated results showed that the floating zones obtained by 17 mA was stable theoretically, while the experimental results
peak temperature as shown in Fig. 9d. The floating zone of 17 mA in Fig. 9c is also unstable although its height (12.0 mm) is smaller than that of 16 mA (12.4 mm). Researches of Heywang [14] showed that only the height of the floating zone less than a certain value can it keep stable. The maximum height of the floating zone can be calculated as following:
L max = 2.62
γlv ρ ⋅g
(7)
where γlv is the surface tension of the melts which varies with temperature, ρ the density of the melt and g the acceleration due to gravity. It was hard to calculate the critical size of floating zone directly by Eq. 1 as the surface tension and temperature varying with the positions in the 706
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To quantitatively analyze the reason why the floating zone transferred to unstable state during the refining process, the temperature field of the process was calculated by FEM and the results were shown in Fig.11. The size of floating zone kept increasing with the experiment procedure if nothing was done. Fig.12 showed the relationship between the floating zone height and time. The initial height of the floating zone in Fig. 12 was that of the stable floating zone in first stage. Thus, the extra size in Fig. 12, namely Eq. (8) for that of 16 mA at 50 mm/h, caused by heat accumulation would lead to the instability of floating zone and some essential measures must be adopted to eliminate the influence of heat accumulation. The beam current, which was the unique energy-related factor in EBWZ process, was selected as the controlled variable to eliminate the influence of heat accumulation.
Table 5 The distribution of temperature and surface tension of the molten zone and the corresponding maximum zone height. Ranges
Average temperature/ ℃
Surface tension/(mN/ m)
Lmax(i) /m
Lmax/mm
1 2 3 4 5 6 7 8 9 10 11
1266.615 1312.95 1366.67 1415.97 1428.365 1401.715 1367.975 1340.93 1317.765 1296.375 1276.06
1839.069 1819.482 1796.772 1775.931 1770.692 1781.958 1796.221 1807.654 1817.446 1826.489 1835.077
0.013022 0.012952 0.012871 0.012796 0.012777 0.012818 0.012869 0.012910 0.012945 0.012977 0.013007
12.904
ΔL = L (t ) − 12.4 mm
(8)
The relation between L(t) and t was obtained by using nonlinear curve fitting as shown in Fig.12. Based on the assumption that the heat transfer coefficient was constant during the EBFZ process under different beam currents, the extra beam current resulting in the extra size of floating zone was calculated. According to the energy calculation formula (Eq.9), the relationship between the extra beam current and the extra size of floating zone were calculated as following.
showed an unstable morphology. It might because of the large heating flux of 17 mA that results in a relatively high temperature gradient and peak temperature in the melting process. Thus, the floating zone was susceptible to the external disturbance during the melting process. As for the floating zone obtained by 16 mA, the appropriate temperature gradient and peak temperature, which lead to moderate surface tension, resulted in a stable floating zone with the simulated and experimental height of 12.939 mm and 12.4 mm, respectively. Accordingly, the beam current of 16 mA was optimized parameter to form a stable floating zone in the first stage of EBFZ and it was used in the following experiment.
ΔQ = cmΔT
(9)
where c is the specific heat capacity; ΔT is the temperature differential between initial temperature (20℃) and the final temperature；The ΔQ in Eq.9 is the Joule heat energy used to melt the extra floating zone which can be calculated by Eq. 10.
ΔQ = UΔI (t ) t
3.3. Controlling the second stage of EBFZ process
(10)
where U is the accelerating voltage; ΔI(t) is the beam current; t is the time. m is the mass of the floating zone which is defined as Eq. 11.
Based on the previous analyses, the beam current of 16 mA was used to refining the Ni-25%Si alloys. Fig.10 showed the typical morphologies of the floating zone and refined specimen under the beam current of 50 mA. It can be seen in Fig.10 that the unstable floating zone was necking (Fig.10a) during the EBFZ process and the melt accumulated at the bottom of the floating zone which lead to the coarsening of the refined part of the specimen (Fig.10b). Finally, the unstable floating zone was break and the refining process terminated. It was the heat accumulation that resulting in the interruption of the EBFZ process as the heat capacity of the refine specimen was limited.
m = ρV = ρπr 2ΔL (t )
(11)
where ρ is the density of Ni-25%Si alloys; r is radius of the specimen. Thus, the Eq.9 can be written by Eq.12：
ΔI (t ) =
cρπr 2ΔL (t ) ΔT Ut
(12)
where the relationship between ΔT and t can be extracted from the simulation results as shown in Fig.13. Thus, the temperature difference
Fig. 10. The morphology of molten zone and the refined specimen obtained by 17 mA/50 mm/h. a) Morphology of molten zone; b) Morphology of refined specimen. 707
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Fig. 11. The simulation results of electron beam floating zone process under the condition of 16 mA/50 mm/h.
Fig. 12. The non-linear fitting curve between floating zone size and time.
Fig. 14. The typical morphology of floating zone and the refined specimen after controlling the beam current a) Morphology of molten zone; b) Morphology of refined specimen.
Table 6 Nomenclature used in the analytical calculation.
Fig. 13. The non-linear fitting curve between temperature and time.
ΔT induced by heat accumulation can be expressed as Eq.13. Table 6 summarized the physical data used for the calculations. Finally, the governing equation of extra beam current is obtained as Eq.14. ΔT=T-20 = 1152.5 + 0.226t
ΔI (t ) = [
11.74 −
t 28.9e− 980
t
Symbol
Unit
Value
Average surface tension
γlv
mN/m
Density of the melt Average specific heat capacity Accelerating voltage Radius of the specimen
ρ c
g/cm J/g/K
1836.785(Obtained by JMatPro) 7.5 2.99 (Tested)
U r
kV mm
9 5
3
current should vary as Eq.9 to make the floating zone stable during the second stage of EBFZ process. Fig.14 showed the verifying experiments with the growth rate of 50 mm/h and the beam current varying with Eq.15. It could be seen that the floating zone was more stable than that of Fig.10 and the finally radius of the specimen after refining was more uniform than that of Fig.10b. (Table 6)
(13) t
+ 0.0023 − 0.0057e− 980 ] × 103mA
Property
(14)
From the equations above, it could be calculated that the beam 708
Journal of Manufacturing Processes 45 (2019) 702–709
X. Li, et al. t
I (t ) = 16 − [
t 11.74 − 28.9e− 980 + 0.0023 − 0.0057e− 980 ] × 103mA t
oxygen embrittlement and its remedies. Intermetallics 2002;10(4):309–16. [2] Yiping L, Ning L, Ting S, Weida L. Microstructure and hardness of undercooled Ni 78.6 Si 21.4 eutectic alloy. J Alloys Compd 2010;490(1):1–4. [3] Fan K, Liu F, Yang G, Yaohe Z. Precipitation in as-solidified undercooled Ni–Si hypoeutectic alloy: effect of non-equilibrium solidification. Mat Sci Eng A-Struc 2011;528(22):6844–54. [4] Baker I, Padgett RA, Schulson EM. Auger electron spectroscopy study of Ni3Si. Scr Metall Mater 1989;23(11):1969–73. [5] Takasugi T, Yoshida M. Mechanical properties of the Ni3(Si, Ti) alloys doped with carbon and beryllium. J Mater Sci 1991;26(11):3032–40. [6] Takasugi T, Kawai H, Kaneno Y. Mechanical and chemical properties of Ni3Si and Ni3(Si, Ti) alloys multiphased by chromium addition. Mater Sci Tech 2001;17(6):671–80. [7] Ahmad R, Cochrane RF, Mullis AM. The formation of regular αNi-γ (Ni31Si12) eutectic structures from undercooled Ni–25at% Si melts. Intermetallics 2012;22:55–61. [8] Fujiwara H, Kawabata T, Miyamoto H, Ameyama K. Mechanical properties of harmonic structured composite with pure titanium and Ti–48 at% Al alloy by MM/SPS process. Mater Trans 2013;54(9):1619–23. [9] Sun Y, Chen J, Ma F, Ameyama K, Wenlong X. Tensile and flexural properties of multilayered metal/intermetallics composites. Mater Charact 2015;102:165–72. [10] Rodriguez-Suarez T, Bartolomé JF, Moya JS. Mechanical and tribological properties of ceramic/metal composites: a review of phenomena spanning from the nanometer to the micrometer length scale. J Eur Ceram Soc 2012;32(15):3887–98. [11] Cortenraad R, Ermolov SN, Semenov VN, Ermolov SN, Denier AW. Electron-beam growing and purification of W crystals. Vacuum 2001;62(2):181–8. [12] Cui C, Zhang J, Wu K, Youping M, Dening Z. Directional solidification of Ni–Ni3Si eutectic in situ composites by electron beam floating zone melting. Physica B 2013;412:70–3. [13] Cui C, Zhang J, Jia Z, Lin L, Zhiwei J. Microstructure and field emission properties of the Si–TaSi2 eutectic in situ composites by electron beam floating zone melting technique. J Cryst Growth 2008;310(1):71–7. [14] Lüdge A, Riemann H, Wünscher M, Riemann H, Michael W, Behr G. Floating zone crystal growth[M]. Chichester, UK: John Wiley and Sons; 2010.
(15) 4. Conclusions (1) The stability of floating zone during the first stage was affected by electron beam current. The floating zone obtained at 16 mA with appropriate temperature gradient and peak temperature was the most stable one as the calculate critical size(12.939 mm) of floating zone was larger than that of the experimental results. (2) The heat accumulation results in the interruption of the EBFZ process during the second stage. The "beam attenuation" model was developed to eliminate the effect of heat accumulation in EBFZ process and improve the stability of floating zone. When the refine velocity speed is 50 mm/h, the decay curves of beam current can be depicted as following equation. t
I (t ) = 16 − [
t 11.74 − 28.9e− 980 + 0.0023 − 0.0057e− 980 ] × 103mA t
Acknowledgements This work was supported by State Key Lab of Advanced Welding and Joining, Harbin Institute of Technology. References [1] Zhu JH, Liu CT. Intermediate-temperature mechanical properties of Ni–Si alloys:
709
Contents lists available at ScienceDirect
Journal of Manufacturing Processes journal homepage: www.elsevier.com/locate/manpro
Technical Paper
Control of the floating zone stability during electron beam melting process of Ni-25%Si alloy
T
⁎
Xiaopeng Lia,b, Binggang Zhanga, , Houqin Wanga, Tao Yua a b
State Key Laboratory of Advanced Welding and Joining, Harbin Institute of Technology, Harbin 150001, China College of Material Science and Engineering, Nanjing University of Science and Technology, Nanjjing 210094, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Electron beam floating zone method Ni-25at%Si alloy Finite element method Heat Beam attenuation
In this study, the Ni-25at%Si alloy was fabricated by electron beam floating zone (EBFZ) method. The finite element method was used to calculate the temperature field of electron beam refining process. The electron beam refining process was controlled based on the temperature distribution which was varied with the process parameters. The electron beam refining process of Ni-25at%Si can be divided into 2 stages. The first stage featured the forming of a stable floating zone and the second stage featured the moving of the stable floating zone. The experimental results showed that it was difficult to balance the surface tension and gravity during the melting process due to the low surface tension of Ni-25at% Si alloy. The heat capacity of Ni-25at%Si alloy bar was limited, which easily led to the heat accumulation inside the melting zone during the refining process, resulting in the dynamically changing of surface tension and decreasing the stability of the refining process. Based on the inherent relationship among temperature, surface tension and the stability of the melt zone, the temperature field of the floating zone was quantitatively analyzed by numerical simulation and the process parameters for maintaining the stability of the floating zone were obtained. Then the "beam attenuation" technique was put forward to eliminate the heat accumulation during the refining process and a stable refining process was finally obtained.
1. Introduction The Ni-25at%Si alloy, which is characterized by excellent high temperature oxidation resistance at elevated temperature, has wined great interest in the aerospace field [1–3]. However, the brittleness of Ni-25at%Si alloy, which is not conducive to machining, restricts its application [4–6]. Improving the toughness of Ni-25at%Si alloy will promote its application in the future. R Ahmad et al [7] found that lamellar αNi-γ (Ni31Si12) eutectic structures could form from Ni-25at% Si alloy and the αNi would be the toughening phase to improve the room temperature toughness of Ni-25at% Si. Additionally, many studies [8–10] have obtained unidirectional full lamellar in situ eutectic composites with improved toughness by directional solidification. Thus, it is feasible to prepare unidirectional full lamellar αNi-γ (Ni31Si12) eutectic structures with improved toughness at the composition of Ni-25at%Si by directional solidification. The EBFZ method is one of directional solidification methods which is characterized as high energy density, high vacuum degree, high temperature gradient and no crucible pollution. It is widely used in refining and purifying refractory metals [11] and superalloys [12,13].
⁎
Thus, EBFZ of Ni-25%Si was carried out in this work. The key point to refine Ni-25%Si alloy successfully was to keep the floating zone stable as a free surface without any support would form during EBFZ process. However, most of former research only focused on the changing of microstructures and composition after EBFZ process and little attention has been paid on the influence of the particularity of EBFZ, namely crucibleless, on the refining process. It is reasonable to ignore this part in EBFZ processing of refractory metals as it is much easier to keep floating zone stable because of their relative large surface tension. While for the alloys with small surface tension, such as Ni-25%Si alloy, it is very difficult to keep the floating zone stable. In the present paper, the influence of the process parameters on the stability of floating zone were investigated using the finite element method. Meanwhile, the refining process was collected by a charge-coupled device (CCD) visual system. The calculated results were verified by experimental results. Finally, the processing parameters for producing stable floating zone in EBFZ were given out.
Corresponding author at: No. 92, Xidazhi Street, Nangang District, Harbin City, Heilongjiang Province 150001, China. E-mail address: [email protected] (B. Zhang).
https://doi.org/10.1016/j.jmapro.2019.08.008 Received 3 September 2018; Received in revised form 12 June 2019; Accepted 5 August 2019 Available online 19 August 2019 1526-6125/ © 2019 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
Journal of Manufacturing Processes 45 (2019) 702–709
X. Li, et al.
Fig. 3. The circular Gauss surface heat source.
Fig. 1. The schematic illustration of the EBFZ processes.
materials are isotropic continuum; 2) The initial temperature is 20 °C; 3) EBFZ process is a quasi-steady process; 4) The transport of heat by convection is disregarded because of Pr < < 1 for Ni-25%Si alloy; 5) The heat transfer coefficient is 40 W/m2·K; 6) The mechanical boundary is omitted as the calculation only focus on the temperature field of EBFZ process.
2. Numerical and experimental procedure Fig. 1 shows the schematic illustration of the EBFZ processes. The cathode in Fig.1 can move up and down at different speed and the specimen will rotate during the EBFZ process to uniform the heating distribution circumferentially along the specimen. Thus, we only considered the moving of heat source in the simulation procedure and the rotation of specimen was ignored.
2.2. Heat source The EBFZ equipment contains an annular cathode and no focusing coils to focus the electron beam. Hence, the electron beam was in defocusing state and the electron beam performed in heat conduction mode without keyhole phenomenon during EBFZ process. Based on the heating characteristic, an annular heat source was built in the present study. The annular heat source was treated as Gaussian plane heat source, namely, the energy distributed as Gaussian function along the z direction while the energy distributed uniformly along the circumference of specimen as shown in Fig. 3. Hence, the Gaussian plane heat source can be written as:
2.1. Mesh generation and calculation conditions The 3-D finite element model (FEM) is employed to analyze the thermal fields of EBFZ process in this study. The material used here is Ni-25%Si alloy with dimensions of φ10 mm × 100 mm. Non-uniform mesh is adopted to build the model of the specimen. Finite element mesh used in the work is shown in Fig. 2. There are total 22,000 units and 24,745 nodes in this model. For the calculation, the following conditions are assumed: 1) The
Fig. 2. Finite element mesh generation. 703
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q (z ) = qm exp(−kz 2)
(1)
Table 1 Nomenclature used in the simulation.
The total heat input during the EBFZ process was determined as:
Q0 =
+∞
∫−∞
q (z )2πr dz =
+∞
∫−∞
qm exp(−kz 2)2πr dz
(2)
Then the maximum heat flux in the Gaussian plane heat source was obtained:
qm =
Q0 k1/2 2r π3/2
(3)
Based on the assumption that 95% of the total thermal energy would locate in small region, namely the heated region, the following relationship can be deduced:
95%Q0 =
+z h
∫−z
q (z )2πr dz =
h
+z h
∫−z
h
qm exp(−kz 2)2πr dz
1.92 z h2
Prandtl number The maximum heat density Constant The radius of the Ni-25%Si sample Heat density Width of heated region The total heat input during the EBFZ process
Parameters
Beam current (mA)
Moving rate of floating zone (mm/h)
Accelerating voltage (kV)
Values
15, 16, 17
50
9
3. Results and discussions
(5)
1.386Q0 1.92 exp(− 2 z 2) z h⋅2r π3/2 zh
Pr qm k r q(z) 2zh Q0
(4)
3.1. EBFZ melting process and FEM verification
Substituting Eq. (3) and (5) into Eq. (1), the heat density distribution in heated region could be written as:
q (z ) =
Nomenclature
Table 2 The specific values of the parameters of EBFZ process.
Thus, the following relationship between k and zh can be obtained:
k=
Symbol
Fig.5 and Fig.7 shows the two typical stages of EBFZ process which were collected by the CCD visual system. The first stage featured the forming of a stable floating zone. With the increase of beam current, the width of the melted surface increased gradually and a floating zone was obtained when the width of the melted surface reached to 10.25 mm as shown in Fig.5a. This stage was used to verify the accuracy of the FEM. As shown in Fig. 5b, the width of the melted surface obtained by FEM well matched with the corresponding experimental results in the first stage. To further verify the accuracy of the FEM, the sectional morphology of the FEM result obtained at 840 s was compared with the experimental result as shown in Fig. 6. The calculated morphology was closed to that obtained experimentally which confirmed that the proposed heat source model was suitable for the simulation of the EBFZ process. It was also can be seen in Fig.6 that the solid/liquid interface appears curved shape which would not produce unidirectional temperature gradient. The calculated results of EBFZ process showed that the solid/liquid interface would be planar after 45 s (Fig. 6b). Thus, another 45 s were spent after the initial stages of the EBFZ process to ensure that the unidirectional temperature gradient was produced and the floating zone was overheated. Hereafter, a stable floating zone (Fig.7a) with planar solid/liquid interface (Fig.7b) was produced and then it moved at a certain rate in the second stage of EBFZ process.
(6)
2.3. Thermo-physical properties of Ni-25%Si The temperature-dependent thermo-physical properties of the Ni25%Si alloy were measured by NETZSCH LFA and the specific values are shown in Fig. 4. As the melting process of EBFZ is only related to thermo-physical parameters of Ni-25%Si alloy, the mechanical properties of Ni-25%Si alloy are not considered here. (Table 1) 2.4. Experimental process In this study, the Ni-25at%Si alloy with the size of 10 mm in diameter and 100 mm in length was remelted by EBFZ with different beam current and moving rate of the molten zone. The specific values of the parameters are shown in Table 2. The high voltage of EBFZ equipment was 9 kV. The increment of beam current was 2 mA/min during the beam current loading process. The EBFZ process was collected by CCD visual system. Before the process, the oxide layer was removed by grinding, cleaning and drying.
Fig. 4. The relationship between thermophysical properties and temperature a) Specific heat; b) Thermal conductivity. 704
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Fig. 5. The formation of the floating zone in first stage of EBFZ process under 16 mA. (a)The experimental results, (b) the simulation results.
Fig. 6. The longitudinal section morphology of melting zone obtained by 16 mA at 840 s. a) Numerical simulation result; b) Experimental result.
Fig. 7. The longitudinal section morphology of melting zone obtained by 16 mA at 885 s. a) Numerical simulation result; b) Experimental result.
3.2. Controlling of the first stage of EBFZ process
Further examination revealed that with increase of beam current, the height of floating zone decreased gradually. The FEM was used to explain this phenomenon. Fig. 9 shows the simulation results of the EBFZ process under different beam current. Due to the small heat flux at 15 mA, it would spend 1017s to form a floating zone with planar liquid/ solid boundary as shown in Fig9a. Heating for a long time resulted in a large floating zone of 13.6 mm with small temperature gradient and
Fig. 8 showed the morphologies of floating zone obtained by different beam current. All the three floating zones showed conical shape with melts accumulation at the bottom. The floating zone obtained at 15 mA and 17 mA showed more unevenly than that of 16 mA which means that floating zone obtained at 16 mA is the most stable one. 705
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Fig. 8. The different floating zone morphologies obtained by different beam current. (a) 15 mA, (b) 16 mA and (c)17 mA.
Fig. 9. The thermal field and temperature distribution obtained by different beam current. a)15 mA; b) 16 mA; c) 17 mA; d) Temperature distribution of melted zone. Table 3 The distribution of temperature and surface tension of the molten zone and the corresponding maximum zone height.
Table 4 The distribution of temperature and surface tension of the molten zone and the corresponding maximum zone height.
Ranges
Average temperature/ ℃
Surface tension/(mN/ m)
Lmax(i) /m
Lmax/mm
Ranges
Average temperature/ ℃
Surface tension/(mN/ m)
Lmax(i) /m
Lmax/mm
1 2 3 4 5 6 7 8 9 10 11 12 13 14
1257.925 1296.955 1340.80 1387.085 1414.825 1407.095 1380.670 1356.205 1336.00 1317.745 1300.495 1283.895 1267.775 1252.050
1842.743 1826.243 1807.709 1788.142 1776.415 1779.683 1790.854 1801.196 1809.738 1817.455 1824.747 1831.764 1838.579 1845.227
0.012987 0.012929 0.012863 0.012793 0.012751 0.012763 0.012803 0.012840 0.012870 0.012897 0.012923 0.012948 0.012972 0.012996
12.881
1 2 3 4 5 6 7 8 9 10 11 12
1272 1311 1354 1384 1382 1360 1338 1321 1305 1290 1276 1262
1836.793 1820.306 1802.128 1789.446 1790.292 1799.592 1808.892 1816.079 1822.843 1829.184 1835.102 1841.020
0.013013 0.012955 0.012890 0.012845 0.012848 0.012881 0.012914 0.012940 0.012964 0.012987 0.013008 0.013028
12.939
floating zone. To calculate the Lmax accurately, we assumed that the temperature between the two nodes of the finite model was constant and equaled to the average temperature. Thus, the Lmax(i) between every two nodes could be calculated and the critical size of melting zone could be obtained by Lmax =ΣLmax(i)/ i. Based on the assumption above, the critical size of melting zones obtained by different parameters could by calculated as Table 3–5. As shown in Table 3–5, the maximum height of the floating zones obtained by 15 mA、16 mA and 17 mA was 12.881mm、12.939 mm and 12.904 mm, respectively. While the experimental results showed that the maximum height of the floating zones obtained by 15 mA、 16 mA and 17 mA was 13.6 mm, 12.4 mm and 12.0 mm. Thus, based on the theory of Heywang [14], the floating zone of 15 mA was unstable. Interestingly, the calculated results showed that the floating zones obtained by 17 mA was stable theoretically, while the experimental results
peak temperature as shown in Fig. 9d. The floating zone of 17 mA in Fig. 9c is also unstable although its height (12.0 mm) is smaller than that of 16 mA (12.4 mm). Researches of Heywang [14] showed that only the height of the floating zone less than a certain value can it keep stable. The maximum height of the floating zone can be calculated as following:
L max = 2.62
γlv ρ ⋅g
(7)
where γlv is the surface tension of the melts which varies with temperature, ρ the density of the melt and g the acceleration due to gravity. It was hard to calculate the critical size of floating zone directly by Eq. 1 as the surface tension and temperature varying with the positions in the 706
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To quantitatively analyze the reason why the floating zone transferred to unstable state during the refining process, the temperature field of the process was calculated by FEM and the results were shown in Fig.11. The size of floating zone kept increasing with the experiment procedure if nothing was done. Fig.12 showed the relationship between the floating zone height and time. The initial height of the floating zone in Fig. 12 was that of the stable floating zone in first stage. Thus, the extra size in Fig. 12, namely Eq. (8) for that of 16 mA at 50 mm/h, caused by heat accumulation would lead to the instability of floating zone and some essential measures must be adopted to eliminate the influence of heat accumulation. The beam current, which was the unique energy-related factor in EBWZ process, was selected as the controlled variable to eliminate the influence of heat accumulation.
Table 5 The distribution of temperature and surface tension of the molten zone and the corresponding maximum zone height. Ranges
Average temperature/ ℃
Surface tension/(mN/ m)
Lmax(i) /m
Lmax/mm
1 2 3 4 5 6 7 8 9 10 11
1266.615 1312.95 1366.67 1415.97 1428.365 1401.715 1367.975 1340.93 1317.765 1296.375 1276.06
1839.069 1819.482 1796.772 1775.931 1770.692 1781.958 1796.221 1807.654 1817.446 1826.489 1835.077
0.013022 0.012952 0.012871 0.012796 0.012777 0.012818 0.012869 0.012910 0.012945 0.012977 0.013007
12.904
ΔL = L (t ) − 12.4 mm
(8)
The relation between L(t) and t was obtained by using nonlinear curve fitting as shown in Fig.12. Based on the assumption that the heat transfer coefficient was constant during the EBFZ process under different beam currents, the extra beam current resulting in the extra size of floating zone was calculated. According to the energy calculation formula (Eq.9), the relationship between the extra beam current and the extra size of floating zone were calculated as following.
showed an unstable morphology. It might because of the large heating flux of 17 mA that results in a relatively high temperature gradient and peak temperature in the melting process. Thus, the floating zone was susceptible to the external disturbance during the melting process. As for the floating zone obtained by 16 mA, the appropriate temperature gradient and peak temperature, which lead to moderate surface tension, resulted in a stable floating zone with the simulated and experimental height of 12.939 mm and 12.4 mm, respectively. Accordingly, the beam current of 16 mA was optimized parameter to form a stable floating zone in the first stage of EBFZ and it was used in the following experiment.
ΔQ = cmΔT
(9)
where c is the specific heat capacity; ΔT is the temperature differential between initial temperature (20℃) and the final temperature；The ΔQ in Eq.9 is the Joule heat energy used to melt the extra floating zone which can be calculated by Eq. 10.
ΔQ = UΔI (t ) t
3.3. Controlling the second stage of EBFZ process
(10)
where U is the accelerating voltage; ΔI(t) is the beam current; t is the time. m is the mass of the floating zone which is defined as Eq. 11.
Based on the previous analyses, the beam current of 16 mA was used to refining the Ni-25%Si alloys. Fig.10 showed the typical morphologies of the floating zone and refined specimen under the beam current of 50 mA. It can be seen in Fig.10 that the unstable floating zone was necking (Fig.10a) during the EBFZ process and the melt accumulated at the bottom of the floating zone which lead to the coarsening of the refined part of the specimen (Fig.10b). Finally, the unstable floating zone was break and the refining process terminated. It was the heat accumulation that resulting in the interruption of the EBFZ process as the heat capacity of the refine specimen was limited.
m = ρV = ρπr 2ΔL (t )
(11)
where ρ is the density of Ni-25%Si alloys; r is radius of the specimen. Thus, the Eq.9 can be written by Eq.12：
ΔI (t ) =
cρπr 2ΔL (t ) ΔT Ut
(12)
where the relationship between ΔT and t can be extracted from the simulation results as shown in Fig.13. Thus, the temperature difference
Fig. 10. The morphology of molten zone and the refined specimen obtained by 17 mA/50 mm/h. a) Morphology of molten zone; b) Morphology of refined specimen. 707
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Fig. 11. The simulation results of electron beam floating zone process under the condition of 16 mA/50 mm/h.
Fig. 12. The non-linear fitting curve between floating zone size and time.
Fig. 14. The typical morphology of floating zone and the refined specimen after controlling the beam current a) Morphology of molten zone; b) Morphology of refined specimen.
Table 6 Nomenclature used in the analytical calculation.
Fig. 13. The non-linear fitting curve between temperature and time.
ΔT induced by heat accumulation can be expressed as Eq.13. Table 6 summarized the physical data used for the calculations. Finally, the governing equation of extra beam current is obtained as Eq.14. ΔT=T-20 = 1152.5 + 0.226t
ΔI (t ) = [
11.74 −
t 28.9e− 980
t
Symbol
Unit
Value
Average surface tension
γlv
mN/m
Density of the melt Average specific heat capacity Accelerating voltage Radius of the specimen
ρ c
g/cm J/g/K
1836.785(Obtained by JMatPro) 7.5 2.99 (Tested)
U r
kV mm
9 5
3
current should vary as Eq.9 to make the floating zone stable during the second stage of EBFZ process. Fig.14 showed the verifying experiments with the growth rate of 50 mm/h and the beam current varying with Eq.15. It could be seen that the floating zone was more stable than that of Fig.10 and the finally radius of the specimen after refining was more uniform than that of Fig.10b. (Table 6)
(13) t
+ 0.0023 − 0.0057e− 980 ] × 103mA
Property
(14)
From the equations above, it could be calculated that the beam 708
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I (t ) = 16 − [
t 11.74 − 28.9e− 980 + 0.0023 − 0.0057e− 980 ] × 103mA t
oxygen embrittlement and its remedies. Intermetallics 2002;10(4):309–16. [2] Yiping L, Ning L, Ting S, Weida L. Microstructure and hardness of undercooled Ni 78.6 Si 21.4 eutectic alloy. J Alloys Compd 2010;490(1):1–4. [3] Fan K, Liu F, Yang G, Yaohe Z. Precipitation in as-solidified undercooled Ni–Si hypoeutectic alloy: effect of non-equilibrium solidification. Mat Sci Eng A-Struc 2011;528(22):6844–54. [4] Baker I, Padgett RA, Schulson EM. Auger electron spectroscopy study of Ni3Si. Scr Metall Mater 1989;23(11):1969–73. [5] Takasugi T, Yoshida M. Mechanical properties of the Ni3(Si, Ti) alloys doped with carbon and beryllium. J Mater Sci 1991;26(11):3032–40. [6] Takasugi T, Kawai H, Kaneno Y. Mechanical and chemical properties of Ni3Si and Ni3(Si, Ti) alloys multiphased by chromium addition. Mater Sci Tech 2001;17(6):671–80. [7] Ahmad R, Cochrane RF, Mullis AM. The formation of regular αNi-γ (Ni31Si12) eutectic structures from undercooled Ni–25at% Si melts. Intermetallics 2012;22:55–61. [8] Fujiwara H, Kawabata T, Miyamoto H, Ameyama K. Mechanical properties of harmonic structured composite with pure titanium and Ti–48 at% Al alloy by MM/SPS process. Mater Trans 2013;54(9):1619–23. [9] Sun Y, Chen J, Ma F, Ameyama K, Wenlong X. Tensile and flexural properties of multilayered metal/intermetallics composites. Mater Charact 2015;102:165–72. [10] Rodriguez-Suarez T, Bartolomé JF, Moya JS. Mechanical and tribological properties of ceramic/metal composites: a review of phenomena spanning from the nanometer to the micrometer length scale. J Eur Ceram Soc 2012;32(15):3887–98. [11] Cortenraad R, Ermolov SN, Semenov VN, Ermolov SN, Denier AW. Electron-beam growing and purification of W crystals. Vacuum 2001;62(2):181–8. [12] Cui C, Zhang J, Wu K, Youping M, Dening Z. Directional solidification of Ni–Ni3Si eutectic in situ composites by electron beam floating zone melting. Physica B 2013;412:70–3. [13] Cui C, Zhang J, Jia Z, Lin L, Zhiwei J. Microstructure and field emission properties of the Si–TaSi2 eutectic in situ composites by electron beam floating zone melting technique. J Cryst Growth 2008;310(1):71–7. [14] Lüdge A, Riemann H, Wünscher M, Riemann H, Michael W, Behr G. Floating zone crystal growth[M]. Chichester, UK: John Wiley and Sons; 2010.
(15) 4. Conclusions (1) The stability of floating zone during the first stage was affected by electron beam current. The floating zone obtained at 16 mA with appropriate temperature gradient and peak temperature was the most stable one as the calculate critical size(12.939 mm) of floating zone was larger than that of the experimental results. (2) The heat accumulation results in the interruption of the EBFZ process during the second stage. The "beam attenuation" model was developed to eliminate the effect of heat accumulation in EBFZ process and improve the stability of floating zone. When the refine velocity speed is 50 mm/h, the decay curves of beam current can be depicted as following equation. t
I (t ) = 16 − [
t 11.74 − 28.9e− 980 + 0.0023 − 0.0057e− 980 ] × 103mA t
Acknowledgements This work was supported by State Key Lab of Advanced Welding and Joining, Harbin Institute of Technology. References [1] Zhu JH, Liu CT. Intermediate-temperature mechanical properties of Ni–Si alloys:
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