2020 年 61 巻 7 号 p. 1230-1238
Microstructure evolution of Ag–28Cu–1Ni alloy during the continuous casting process was simulated based on 3D-CAFE method, and the effect of the mean nucleation undercooling and the distance from the bottom of the ingot to the cross section on the solidification structure were studied. Furthermore, the effects of pouring temperature, heat transfer coefficient and pulling speed on solidification structure were also investigated. The results show that the simulated results are in agreement with the experimental results. The solidification structure consists of four parts, including region of surface fine grain, zone of columnar grain, transition zone of CET (columnar to equiaxed grain transition) and region of center equiaxed grain. The higher the mean undercooling, the larger the columnar dendrite zone. The ΔTv,max = 5 K is determined as an important simulation parameter to simulate the microstructure evolution. As the cross-section increases from the bottom of the ingot, the columnar crystal regions gradually expand. Moreover, lowering the pouring temperature, increasing the heat transfer coefficient or improving the pulling speed have the beneficial effect on grain refinement. Under the optimal process conditions, the largest proportion of equiaxed grains and the finer grain size is present in the solidified structure.
The proportion of columnar grains to equiaxed grains during solidification processes can reflect the distribution uniformity degree of solute elements in solidification microstructure. And the solidification structure of the casting determines the mechanical properties and forming quality of the casting.1,2) Therefore, it is of actual significance to study the solidification microstructure.
Cellular Automation-Finite Element model (CAFE) is the first computational model of solidification structure that combines macroscopic heat flow calculation with microscopic grain growth.3,4) Based on the theory of grain nucleation, the dynamics theory of dendrite growth, CET transformation criterion and other crystallographic theory. The process of nucleation, growth and evolution of grains were simulated by establishing the models of grain nucleation and growth. Finally, an accurate evaluation on the microstructure and mechanical properties of different parts for the workpiece is achieved.5,6) Gandin and Rappaz proposed three-dimensional CAFE algorithm in 1999.6) The CAFE method belongs to a deterministic method that can calculate the temperature field, flow field and solute field of the solidification process.7–9) Besides, it can also be used to simulate the competitive growth of dendrites, the morphological changes of columnar crystals and equiaxed crystals, the segregation and the transformation of columnar crystals to equiaxed grains (CET).10–12) Gandin et al.13,14) coupled the cellular automaton method (CA) with the finite element method (FE) to simulate the evolution process of the solidification structure for the AlSi alloy and predict the preferred growth of the columnar crystals in the outer equiaxed grains of ingot, the competitive growth between columnar crystals, and the transformation of columnar crystal to equiaxed crystal, the simulation results agree with the experimental observation. Bu et al.15) used the CAFE model combined with finite element and cellular automata to simulate and predict the solidification structure of Al–Cu alloy by adding the solid-phase diffusion coefficient of vacancy formation energy. The results can accurately reflect the distribution, proportion and size of equiaxed and columnar crystals. There are few reports on the simulation of solidification structure about precious metals. However, solidification simulation for precious metals can significantly reduce the cost of experiments and quickly obtain the optimal process parameters.
Ag–28Cu–1Ni alloy is one of the most widely used electronic filler metals due to its excellent fluidity, permeability and brazing properties.16–18) In the process of continuous casting, the process parameters (such as pouring temperature, heat transfer coefficient, pulling speed, etc.) have great influence on the quality of the casting blank, and it is costly to find the best process parameters through the experiment. The computational simulation provides a low-cost, high-efficiency approach for the improvement and research of the process.19) Furthermore, the Gaussian distribution parameters directly affect grain size, and the proportion of columnar grains to equiaxed grains during the simulation. In addition, Gaussian distribution parameters are interactive and vary with casting shape and size, casting temperature, and cooling conditions. Thus, it is necessary to study the influence of Gaussian distribution parameters on solidification simulation, which is beneficial to the simulation of 3D microstructure more quickly and accurately.20)
Therefore, the solidification structure of Ag–28Cu–1Ni alloy was simulated by the 3D CAFE program in Procast software, and the effects of the pouring temperature, the heat transfer coefficient, the pulling speed and the mean nucleation undercooling (Gauss distribution parameter) on the solidification structure are analyzed, and the optimal technological parameters are obtained, which can provide practical value for industrial production.
The stage of solidification nucleation adopts Rappaz’s the deterministic nucleation model based on gaussian distribution.21) The model holds that the characteristics of the nucleation should be a continuous curve rather than a discrete distribution, and the nucleation position is described by a continuous distribution function (ΔT);
| \begin{equation} n(\varDelta T) = \frac{n_{\text{max}}}{\varDelta T_{\sigma}\sqrt{2\pi}}\int_{0}^{\varDelta T}\exp\left[\frac{(\varDelta T - \varDelta T_{\text{max}})^{2}}{2\varDelta T_{\sigma}^{2}}\right] d(\varDelta T) \end{equation} | (1) |
Where n(ΔT) is the grain density when the undercooling is ΔT, nmax is the maximum nucleation density obtained from the integration of normal distribution from 0 to infinity, ΔTmax is the maximum nucleation undercooling, ΔTσ is the standard deviation of nucleation undercooling.
2.1.2 Growth kinetics model of dendrite tipDuring the solidification process, grain growth is affected not only by the dynamic undercooling but also by the composition undercooling. The total undercooling of the dendrite tip is described by the following equation:22)
| \begin{equation} \Delta T = \Delta T_{\text{c}} + \Delta T_{t} + \Delta T_{\text{k}} + \Delta T_{r} \end{equation} | (2) |
| \begin{equation} v(\Delta T) = a_{2}\Delta T^{2} + a_{3}\Delta T^{3} \end{equation} | (3) |
Where a2 and a3 are the coefficients of the polynomial of dendrite tip growth rate, ΔT is the total undercooling of the dendrite tip.
2.2 Macroscopic model 2.2.1 Calculation of thermophysical propertiesThe parameters of thermophysical properties include density, specific heat, enthalpy, latent heat, heat transfer coefficient, liquid viscosity and so on,25) which are usually calculated by a simple two-hybrid model:26)
| \begin{equation} p = \sum\nolimits_{i}x_{i}p_{i} + \sum\nolimits_{i}\sum\nolimits_{j > i}x_{i}x_{j}\sum\nolimits_{v}\varOmega_{ij}^{v}(x_{i} - x_{j})^{v} \end{equation} | (4) |
Where P is the characteristic of phase; Pi is the characteristic of pure elements in the phase; $\varOmega _{ij}^{v}$ is a binary interaction parameter; xi, xj is the mole fraction of the element in the phase, mol/L; v is a variable for determining the binary interaction parameters $\varOmega _{ij}^{v}$, 0 ≤ v ≤ 2.
2.2.2 The governing equationConsidering the three-dimensional transient flow and heat transfer of molten metal, a governing equation based on mass, momentum and energy balance is established. At the same time, considering the influence of gravity, the gravity term is added to the momentum equation so that the equation can be applied to the mushy region and the solid phase region.27,28) Its governing equation is as follows:(1) Mass conservation equation
| \begin{equation} \frac{\partial\rho}{\partial t} + \frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z} = 0 \end{equation} | (5) |
| \begin{align} &\frac{\rho}{f_{1}}\frac{\partial u}{\partial t} + \frac{\rho}{f_{1}^{2}}\left(u\frac{\partial u}{\partial x} + v\frac{\partial v}{\partial y} + w\frac{\partial w}{\partial z}\right)\\ &\quad =- \frac{\partial P}{\partial x} + \rho gx + \frac{\partial}{\partial x}\left(\frac{u}{f_{1}}\frac{\partial u}{\partial x}\right) + \frac{\partial}{\partial y}\left(\frac{u}{f_{1}}\frac{\partial u}{\partial y}\right) \\ &\qquad + \frac{\partial}{\partial z}\left(\frac{u}{f_{1}}\frac{\partial u}{\partial z}\right) - \left(\frac{u}{K}\right)U \end{align} | (6) |
| \begin{align} &\rho\frac{\partial H}{\partial t} + \rho \frac{\partial H}{\partial T}\left(u\frac{\partial T}{\partial x} + v\frac{\partial T}{\partial y} + w\frac{\partial T}{\partial z}\right) \\ &\quad =\frac{\partial}{\partial x}\left(k_{T}\frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(k_{T}\frac{\partial T}{\partial y}\right) + \frac{\partial}{\partial z}\left(k_{T}\frac{\partial T}{\partial z}\right) \end{align} | (7) |
| \begin{equation} H(T) = \int_{0}^{T} C_{p}(T)dT + L(1 - f_{s}) \end{equation} | (8) |
Where ρ for density, kg/m3; t for time, s; u, v and w represent the velocity vectors of x, y and z respectively, m/s; $K = K_{0}[\varphi _{1}^{3}/(1 - \varphi _{1})^{2}]$, (K is the permeability of the solid-liquid two-phase region, m2, φ1 is the volume fraction of the liquid phase and Ko is the parameter related to the dendrite size of the two-phase region); f1 for the liquid fraction; fs for the for the solid fraction; P for pressure, Pa; U for the absolute viscosity, Pa·S; gx is the gravity component of x, m/s2; KT represents the thermal conductivity, W/(m·K); H for enthalpy, J/kg; L for solidifying latent heat, J/kg; T represents the node temperature, K; Cp is specific heat capacity, J/(kg·K).
2.3 Coupling the FE and CA modelThe aim of this work is to combine the FE and CA calculations in a single model to predict simultaneously the effects of the latent heat release on the calculated thermal history and the microstructure evolution (as a function of the thermal field). For this purpose, interpolation coefficients are defined between nodal points of FE mesh and CA cells as illustrated in Fig. 1. The CA cell, ω, with its centre infinite element I, has non-zero interpolation coefficients Pωi, Pωj, and Pωk with FE nodes i, j, and k, respectively. Combined with the known FE nodes and interpolation coefficients, the temperature of the CA cells in the grid can be determined. The same interpolation coefficients are used to sum up, at nodal points, the latent heat released by nucleation and growth, and the thickening of the dendritic microstructures calculated at the scale of CA cells.
Relation between FE mesh and CA cells.29)
In order to calculate the extended process of the simulated crystalline region over time, the Mile (mix Lagrangian and Eulerian algorithm) method was used to calculate the temperature distribution at the starting stage of the Ag–28Cu–1Ni ingot during continuous casting. The principle of the Mile method is illustrated in Fig. 2.
The principle of Mile method.
First of all, the casting region is divided into region 1 and region 2, and a number of zero-thickness foldable units are placed between the contact interfaces of the two regions. As the continuous casting process starts, the position of the region 1 stays at initial position, and the region 2 moves down at a set traction speed. In order to maintain the continuity of temperature and velocities between two regions, a number of unit layers with an initial zero thickness are given, and it is assumed that each unit layer can reach a certain thickness value. When the ingot moves down to the set thickness, a new element layer is unfolded, the layers are gradually “unfolded”, similar to the unfolding of an accordion, and finally forming the whole ingot. In the fixed area 1, the Eulerian algorithm is used to calculate the flow and heat transfer of the liquid metal, and the thermo-mechanical coupling of moving region 2 and 3 are calculated by the Lagrangian algorithm.30,31)
The calculation model in this paper is depicted in Fig. 3. Parts I, II, III and V correspond to parts 1, 2, 3 and 5 in Fig. 2. Between the II and III sections, the number for the foldable layers of elements is defined as 40, and the thickness of each layer after the expansion is set to 0.2 mm. The mesh of the casting area III in the model is a dynamic mesh, and the other areas is a fixed mesh, as shown in Fig. 3(b). The diameter of the ingot is 30 mm, and the crystallizer V is made of pure copper and the pull rod IV is made of 45# steel (carbon steel). In order to reduce the computation time and improve the calculation precision, the parameters of the mesh are as follows: the total number of nodes is 83176, and the number of tetrahedral elements is 543187.
Meshing of computational domain ((a) original mesh, (b) stretching mesh).
As shown in Fig. 3(a):
In the crystallizer, the average heat flux density is used to indicate the intensity of convective heat transfer:32)
| \begin{equation} q = \frac{\rho_{w}c_{w}W\Delta T}{S} \end{equation} | (9) |
The heat transfer coefficient and average heat flux density have the following relationship:
| \begin{equation} h = \frac{q}{T_{s} - T_{w}} \end{equation} | (10) |
q is the average heat flux density of the crystallizer, W/m2; ρw is the density of cooling water, kg/m3; cw is the heat capacity of cooling water, J/(kg·k); W is the flow of cooling water, m3/s; ΔT is the water temperature difference in the import and export of the crystallizer, K; S is the effective contact area of liquid metal and crystallizer, m2.
3.3 The determination of simulation parametersThe General Research for Nonferrous Metals provides pure silver (99.99 mass%), pure nickel (99.9 mass%) and electrolytic copper (99.9 mass%) as raw materials for experiment. An Ag–28Cu–1Ni (mass%) ingot with dimension of Φ30 mm prepared by continuous casting process, and the schematic diagram of the directional solidification apparatus is shown in Fig. 4. The melting temperature range of the directional solidification process in vacuum environment is 1113∼1173 K, the holding time is 15 min, the pulling speed interval is 1 × 10−2∼2.5 × 10−2 m/s, the cooling water flow is 200∼500 L/h, and the cooling water temperature is 22°C. The experimental and simulated samples were taken along a cross section of 800 mm from the bottom of the ingot. The cross section of the alloy are ground and polished, and then eroded by an etching agent (volume ratio NH3·HO2:H2O2:HO2 = 1:1:1) to obtain the metallographic structure.
Schematic diagram of continuous casting device.
During solidification simulation, the pouring temperature, heat transfer coefficient and pulling speed were obtained through actual measurement, and the simulation conditions were consistent with the actual experimental conditions. The cooling condition is the water cooling mode in the crystallizer, and the heat transfer coefficient varies with the change of the water flow rate. The process conditions of casting temperature, heat transfer coefficient and pulling speed on the microstructure evolution of Ag–28Cu–1Ni ingots are listed in Table 1.
In addition, the physical parameters used in the numerical simulation of Procast software are shown in Table 2. Most of the physical parameters are calculated by JmatPro software, and a small part is obtained through the literature.33–35) The kinetic parameters of dendritic tip growth are defined a2 = 2.13716 × 10−6 m/(s·K3) and a3 = 1.11035 × 10−7 m/(s·K3), which are calculated by liquidus slope, equilibrium partition coefficient, liquid phase diffusion coefficient and Gibbs-Thomson coefficient.
The microstructure of the continuous casting Ag–28Cu–1Ni alloy is shown in Fig. 5. The microstructure of the Ag–28Cu–1Ni ingot is a typical solidified structure, including a chill crystal region composed of fine equiaxed grains, a columnar crystal region, and a central equiaxed crystal region. The diameter of equiaxed grain is in the range of 0.5∼1.5 mm, and the closer to the center of the casting, the larger the equiaxed grains. There are a large number of columnar crystals around the casting. The width of the columnar crystal is less than 1 mm and the length is between 0.5 and 3 mm. Figure 6 is a local macroscopic structure of an Ag–28Cu–1Ni ingot. According to the American Society for Testing and Materials standards, $N_{V} = 0.8N_{A}^{3/2} = 0.5659N_{L}^{3}$ (NV is the number of grain per unit volume, NA is the number of grain per unit area, and NL is the number of grain on the unit measuring line). From the Fig. 5, the nucleation density nv,max = 1.5 × 108 m−3 in the bulk of the liquid and nucleation density ns,max = 1.8 × 105 m−2 at the mold wall are calculated.
Experimental results of Ag–28Cu–1Ni ingot during continuous casting.
Local macroscopic structure of Ag–28Cu–1Ni ingot in Fig. 5.
The above three-dimensional mathematical model (CAFE) was applied to the continuous casting of Ag–28Cu–1Ni ingots, which considered non-uniform nucleation and grain growth of the crystallizer surface and in the bulk of the melt. In the process of microstructure simulation, Gaussian distribution parameters have critical effects on the solidified structure. The Gaussian distribution parameters (nv(s),max, ΔTv(s),max and ΔTv(s),σ) can be gained by the experiments, but the errors of these parameters available are always inevitable in testing of practical castings. Thus, it’s absolutely necessary to investigate the effects of Gaussian distribution parameters on solidified structure, in order to find the appropriate Gaussian distribution parameters for calculation, which helps to improve the accuracy of the simulation results. Gaussian distribution function both in the bulk and at the surface of the ingot are described in Fig. 7, the maximum nucleation density (nv(s),max), the standard deviation of nucleation undercooling (ΔTv(s),σ) and the mean nucleation undercooling (ΔTv(s),max) were used to represent the undercooling. The value of nv(s),max stands for the maximum number of heterogeneous nuclei, which can be easily obtained from the macroscopic morphology of the solidified structure. The value of ΔTv(s),σ only determines the rate at which the heterogeneous nucleation reaches the maximum density of grains. ΔTv(s),max is the undercooling required for the nucleation of the heterogeneous nucleus. When the undercooling required for nucleation of the heterogeneous nucleus is reached, the nucleus are activated and begin to nucleate and grow. Furthermore, it is difficult to adjust six nucleation parameters to match each other in microstructure simulation. Consequently, in this study, we focus on the study of the mean nucleation undercooling parameter and assume that the other two Gaussian parameters are specific empirical values. Table 3 lists the different Gaussian distribution parameters in the CAFE model. The mean nucleation undercooling (ΔTv,max) is a single variable and other nucleation parameters are assigned constant. The effect of mean bulk undercooling on the microstructure of the Ag–28Cu–1Ni alloy are presented in Fig. 8 so as to determine the mean nucleation undercooling in the bulk of the molten metal. The simulation using the different process parameters with the pouring temperature, heat transfer coefficient and the pulling speed for this simulation are defined as 1173 K, 4000 W/(m·K) and 2 × 10−2 m/s, respectively. Moreover, the above-mentioned simulated microstructure of the cross-section is 800 mm distant from the bottom of the ingot.
Nucleation site distributions for nuclei formed at the mould wall (indexed as “s”) and in the bulk of the liquid (indexed as “v”).36)
Simulation results of Ag–28Cu–1Ni ingot with the different mean nucleation undercooling in the bulk of the liquid: 1.5 K (a); 5 K (b) and 10 K (c).
In the Fig. 8, the different colors represent different crystallographic orientations, and the contact surfaces with color and gray areas on the ingot represent the solidification interface. The grain size and the growth direction of columnar grains are also presented in Fig. 8. Furthermore, the formation of crystalline regions corresponds to different mean nucleation undercooling. In Fig. 8(a), a large amount of equiaxed grains nucleate in the bulk of the liquid metal. In Fig. 8(b), the microstructure of the Ag–28Cu–1Ni ingot consists of four different crystalline zones, including region of surface fine grain, zone of columnar grain, transition zone of CET and region of center equiaxed crystal. When the mean nucleation undercooling is increased to 10 K, the columnar grains which originate from nuclei of the periphery at the chill zone can develop up to the center of the Ag–28Cu–1Ni ingot, as can be seen in Fig. 8(c). Therefore, the nucleation parameter has significant effect on the crystalline zones. Obviously, the higher the mean nucleation undercooling, the larger the columnar grain zone.
The above phenomena can be explained as follows: the nuclei are activated to nucleate and grow as the undercooling required for heterogeneous nucleation is reached. The lower the nucleation undercooling, the stronger the nucleation ability of the heterogeneous particles, and the more grains appear in the solidified structure. Therefore, the ability of heterogeneous nucleation will be weakened and the number of grains will be reduced with the increase of the mean nucleation undercooling, which is beneficial to the weakening the growth of equiaxed grain as well as the CET transformation, resulting the enhancement of the nucleation and growth ability of columnar crystal.
The results show that when the mean undercooling is 5 k, the simulation results are in good agreement with the actual experimental results. The diameter of the equiaxed grain is in the range of 0.5∼2 mm, the width of columnar crystal is less than 1 mm, and the length is in the range of 0.5∼3.5 mm. The quantitative results of simulated grain size approximate the experimental results. Accordingly, the mean bulk undercooling, ΔTv,max = 5 K, as the determined nucleation parameter to predict and analyze the microstructure evolution under different casting conditions, which extends the ability to control the solidified structure by controlling pouring temperature, heat transfer coefficient and pulling speed of Ag–28Cu–1Ni ingot during continuous casting.
4.3 The crystallization process and the simulated microstructure of Ag–28Cu–1Ni ingot at different distance from the bottom surface of ingotThe crystallization process of Ag–28Cu–1Ni alloy is shown in Fig. 9(a)–(e). In the initial stage of the solidification simulation, the molten metal on the periphery of the ingot is in contact with the water-cooled crystallizer, resulting in an increase at the undercooling. The greater undercooling causes more grains are clearly nucleated on the wall of the casting, these equiaxed grains are small in size and have a random orientation. In Fig. 9(d)–(e), the columnar crystals are epitaxial from the opposite direction of heat flow, and the growth direction is perpendicular to the isothermal lines in the liquid. Hence, the columnar grains on the surface of the ingot tend to be perpendicular to the surface of the mold. Furthermore, the “columnar to equiaxed” transition (CET) can be clearly seen in Fig. 9, which is attributable to the following reasons: the equiaxed grains begin to nucleate and grow at the expense of columnar grains as the undercooling in the residual liquid becomes small, thus leading to the transition from columnar grains to equiaxed grains. In the final stage of solidification, the temperature gradient at the center of the ingot is reduced, which is not conducive to the formation of columnar crystals, thereby obtaining the equiaxed crystals.
The crystallization process of Ag–28Cu–1Ni ingot during continuous casting at pouring temperature, heat transfer coefficient and pulling speed was determined to be 1173 K, 4000 W/(m·K) and 2 × 10−2 m/s, respectively. Simulated solidification time: (a) 0.3124 s (b) 1.1341 s (c) 1.2969 s (d) 1.7224 s (e) 2.4912 s.
In addition, we also observed the simulated microstructure of the cross sections at different distances from the bottom of the ingot, and the simulation results are showed in Fig. 10. It can be observed from Fig. 10(a) that equiaxed grains occupy the entire area, owing to the cross section is closer to the water-cooled dummy bar, the undercooling of this cross section greater than the mean undercooling on the other cross section (500 mm, 1000 mm). Eventually, the number of grains nucleated in the Ag–28Cu–1Ni ingot is rapidly increased. Hence, the undercooling decreases as the distance between the ingot and the bottom of the ingot increases. Moreover, it can be concluded from Fig. 10 that the columnar crystal region gradually expands as the distance from the bottom of the ingot increases.
Simulation results show that in different cross sections: the distance from the bottom of the ingot is 100 mm (a), 500 mm (b) and 1000 mm (c).
When the cross section is 800 mm from the bottom of the ingot, the microstructure simulation of Ag–28Cu–1Ni ingot at different pouring temperatures (1113, 1173, 1233 and 1293 K) with the identical heat transfer coefficient 4000 W/(m·K) and pulling speed of 2 × 10−2 m/s was carried out, and the result is shown in Fig. 11. The chilling zone composed of fine equiaxed grains is the largest at the lower pouring temperature, and the thickness of the chilling layer decreases with the increase of pouring temperature. However, the percentage of the columnar grains in the entire region increases with the increase of pouring temperature. The statistical simulation results of Ag–28Cu–1Ni alloy within the identical cross section at different casting conditions are described in Table 4. As can be seen from Table 4, the average grain radius increases from 5.79 × 10−7 to 8.26 × 10−7 mm, and the number of the grains decreases from 1262 to 757 as the pouring temperature increasing from 1113 to 1293 K.
The solidified structures under the identical casting conditions at different casting temperatures: 1113 K (a); 1173 K (b), 1233 K (c) and 1293 K (d).
When the casting temperature is 1113 K (superheat is 45 K), the smaller temperature gradient of melt is conducive to the retention of free grains formed from the casting wall, resulting the increase of the nucleus for heterogeneous nucleation. Thus, the proportion of equiaxed grains is larger. In addition, the smaller temperature gradient of melt will result in the actual undercooling of molten metal is greater than that of the nucleation undercooling, which leads to the increase of preserved nuclei at the frontier of columnar dendritic. Eventually, the CET transformation occurred and the proportion of equiaxed grains was also improved. The transition extent of CET under low superheat is greater than that under high superheat. Furthermore, when the pouring temperature is 1113 K, the constitutional undercooling at the frontier of solid-liquid interface reaches the maximum, which is much greater than that of the undercooling required for heterogeneous nucleation. All nuclei grow almost simultaneously, thus the grain size of the central equiaxed grains is more uniform than that of the high superheat conditions.
When the casting temperature is 1293 K (superheat is 225 K), the possibilities of remelting and disappearing for the free grains from the chilled layer have been improved, reducing the number of nuclei in the melt and restraining the growth of equiaxed grains. The increase of the superheat results in the increase of the thermal gradient, which promotes the growth of the columnar dendrites and the decrease in nucleation rate.
Therefore, in the continuous casting process, lowering the pouring temperature is the most effective way to refine the grain size and improve the amount of equiaxed grains for Ag–28Cu–1Ni ingot.
In addition, the transformation position of CET is moved to the peripheral direction of the casting as the decrease of superheat. Due to the decrease of superheat, the formation time of the stable chilled layer is prolonged, which is conducive to the separation of more grains from the cast wall. These grains move toward the front of columnar dendrite, resulting in an increase in the number of retained nuclei at the front of columnar dendrite. These nuclei have been stably grown before the columnar grains grow, and the CET transformation is ahead of schedule.
4.4.2 Effect of heat transfer coefficient on solidification structureFigures 12(a)–(d) show the solidification structure of the simulated Ag–28Cu–1Ni alloy under different heat transfer coefficients. When the heat transfer coefficient is 2000 W/(m·K), the solidified structure is occupied by the columnar grain between the surface of casting and 2.5 mm away from the surface of casting, and the remaining area of the casting consists of equiaxed grains. When the heat transfer coefficient increases from 2000 to 5000 W/(m·K), the columnar grains can be observed from the surface of casting to the 9 mm away from the casting surface. Moreover, the proportion of columnar grain region increases but the proportion of equiaxed crystal region decreases with the increase of heat transfer coefficient. Further, as shown in Table 4, the average grain radius increases from 6.13 × 10−7 to 7.32 × 10−7 mm, and the number of the grains decreases from 1264 to 825 as the heat transfer coefficient increasing from 2000 to 5000 W/(m·K).
The solidified structures of Ag–28Cu–1Ni alloy under the identical casting conditions at different heat transfer coefficient: 2000 W/(m·K) (a); 3000 W/(m·K) (b); 4000 W/(m·K) (c) and 5000 W/(m·K) (d).
The temperature field and flow field during solidification determine the solidification structure, and the temperature gradient of the solidification front is much larger than the temperature gradient of the low heat transfer coefficient when the heat transfer coefficient is large. The greater the temperature gradient, the more favorable the growth of columnar grains. Besides, in terms of the flow rate of fluid at the front of liquidus, the flow rate under the condition of large heat transfer coefficient is much smaller than that of the low heat transfer coefficient. The smaller the flow rate of the fluids, the less the generation of dendritic fragments and the transport of the solute, which is unfavorable to the formation of the undercooled zone and the equiaxed grains. Therefore, the solidification structure is composed of coarse columnar grains under the condition of large heat transfer coefficient.
In terms of solid-liquid phase zone, the low heat transfer coefficient is wider than the high heat transfer coefficient. The wider the solid-liquid phase zone, the more favorable for the retention and development of free grains separated from the casting wall, which leads to the increase at the number of nuclei. In addition, in the case where the heat transfer coefficient is low, the smaller the temperature gradient at front of the liquidus line, the more favorable for the formation of equiaxed grains. Moreover, the flow rate of the fluid at the front of the liquidus line increases with the solidification process under the low heat transfer coefficient. The greater the flow rate of the fluid in the front of the liquidus, the more beneficial to the removal of heat from the melt and the formation of the undercooled zone. Therefore, under the condition of low heat transfer coefficient, large undercooling can be obtained in the casting, and the smaller temperature gradient is beneficial to the formation of equiaxed grains. Consequently, when the heat transfer coefficient is small, the proportion of the equiaxed grains in the solidification structure of the castings is higher.
4.4.3 Effect of the pulling speed on solidification structureThe effects of pulling speed on the solidified structures of Ag–28Cu–1Ni ingots are shown in Fig. 13. In this case, the microstructure simulation are implemented at different pulling speeds (1 × 10−2, 1.5 × 10−2, 2 × 10−2 and 2.5 × 10−2 m/s) with the identical pouring temperature 1173 K and the same heat transfer coefficient 4000 W/(m·K). The columnar dendrite zones expand with the increase of pulling speed. Furthermore, the statistical simulated results of Table 4 shows the relationship between the number of grains and the average grain radius with the pulling speed. It can be found from the Table 4 that the average grain radius increases from 5.47 × 10−7 to 8.05 × 10−7 mm, and the number of the grains decreases from 1289 to 771 as the pulling speed increases from 1 × 10−2 to 2.5 × 10−2 m/s. The higher pulling speed leads to lower cooling rate for the fixed cooling capacity of the crystallizer, resulting in the increasing of the liquid undercooling. The above factors will induce much more grains nucleate on the Ag–28Cu–1Ni ingot, which weakens the growth of columnar grains and leads to grain refinement. Therefore, in order to refine grains and improve the proportion of fine equiaxed crystals, the pulling speed should be properly reduced for the Ag–28Cu–1Ni ingot during continuous casting.
The solidified structures of Ag–28Cu–1Ni alloy within the identical casting conditions at different pulling speeds: 1 × 10−2 m/s (a); 1.5 × 10−2 m/s (b); 2 × 10−2 m/s (c) and 2.5 × 10−2 m/s (d).
As can be seen from Fig. 14, the effect of process parameters on distribution of grain size is different. The heat transfer coefficient has a great influence on the grain size distribution, the number of small grains increases and the distribution range of grain size becomes wider as the increase of heat transfer coefficient. The distribution range of grain size is also increased with increasing of pouring temperature, but the amplitude variation is less affected than the heat transfer coefficient. With the increase of the pulling speed, the distribution range of grain size decreased initially and then increased, and the fluctuation range of the grain size was bigger than that of the first two cases.
The distribution of grain size for Ag–28Cu–1Ni ingot at different heat transfer coefficient (a), pouring temperature (b) and pulling speed (c).
The microstructure evolution of Ag–28Cu–1Ni ingot during the continuous casting process was simulated based on CAFE method. For the determined parameters, the simulated results are agreement with experimental result. The solidified structure consists of four parts, including region of surface fine grain, zone of columnar grain, transition zone of CET and region of central equiaxed crystal. In the modele of microstructure evolution for the Ag–28Cu–1Ni ingot, the nucleation parameters have a significant influence on the crystalline zones. Obviously, the higher the mean nucleation undercooling, the larger the columnar crystal zone. Besides, the columnar grain regions expands with the distance from the bottom of the ingot increasing. The effects of pouring temperature, heat transfer coefficient and pulling speed on the microstructure of Ag–28Cu–1Ni ingot under the steady-state solidification were obtained. The results show that with the pouring temperature increasing, the average grain radius increases. Therefore, the reduction of superheat is the most effective way to refine the grain size and improve the amount of equiaxed grains. With the increase of heat transfer coefficient, the proportion of columnar crystal regions increases and the proportion of equiaxed crystal regions decreases. Furthermore, the average grain area and the average grain radius decrease. With the pulling speed increasing, the columnar zone expands and the number of grains decreases, whereas the mean radius of grains increases. Therefore, in order to refine grains and improve productivity, the pulling speed should be appropriately reduced. Furthermore, under the same process parameters, the pulling speed has the greatest effect on the distribution of grain size. Comparison of solidification simulation results under various process conditions, the optimum process conditions obtained are as follows: the heat transfer coefficient is 2000 W/(m·K), the pouring temperature is 1113 K, and the pulling speed is 1 × 10−2 m/s.
This work was supported by the National Key Research and Development Program of China [Project No. 2017YFB0305700], National Natural Science Foundation of China [Project No. U1602271 and U1602275], Major Science and Technology Projects in Yunnan Province [Project No. 2018ZE011, 2018ZE012, 2018ZE022, 2018ZE026 and 2018ZE020] and Yunnan Basic Applied Research Program [Project No. 2018FB088].
