Experimental study and cellular automaton simulation on solidification microstructure of Mg-Gd-Y-Zr alloy
School of Materials Science and Engineering,Tsinghua University
Key Laboratory for Advanced Materials Processing Technology Ministry of Education,Tsinghua University
Shanghai Spaceflight Precision Machinery Institute
作者简介:Zhi-Qiang Han e-mail:zqhan@tsinghua.edu.cn;
收稿日期:2 November 2018
基金:financially supported by the National Key Research and Development Program of China (No. 2016YFB0701204);the National Science and Technology Major Project of China (No.2017ZX04006001);the National Natural Science Foundation of China (No.U1737208);
Experimental study and cellular automaton simulation on solidification microstructure of Mg-Gd-Y-Zr alloy
Xu-Yang Wang Fei-Fan Wang Ke-Yan Wu Xian-Fei Wang Lv Xiao Zhong-Quan Li Zhi-Qiang Han
School of Materials Science and Engineering,Tsinghua University
Key Laboratory for Advanced Materials Processing Technology Ministry of Education,Tsinghua University
Shanghai Spaceflight Precision Machinery Institute
Abstract:
The solidification microstructure of Mg-Gd-YZr alloy was investigated via an experimental study and cellular automaton(CA) simulation.In this study,stepshaped castings were produced,and the temperature variation inside the casting was recorded using thermocouples during the solidification process.The effects of the cooling rate and Zr content on the grain size of the Mg-Gd-Y-Zr alloy were studied.The results showed that the grain size decreased with an increase in the cooling rate and Zr content.Based on the experimental data,a quantitative model for calculating the heterogeneous nucleation rate was developed,and the model parameters were determined.The evolution of the solidification microstructure was simulated using the CA method,where the quantitative nucleation model was used and a solute partition ceoefficient was introduced to deal with the solute trapping in front of the solid-liquid(S/L) interface.The simulation results of the grain size were in good agreement with the experimental data.The simulation also showed that the fraction of the eutectics decreased with an increasing cooling rate in the range of 2.6-11.0℃·s-1,which was verified indirectly by the experimental data.
Keyword:
Solidification microstructure; Mg-Gd-Y-Zr alloy; Cooling rate; Zr content; Nucleation; Cellular automaton;
Received: 2 November 2018
1 Introduction
Lightweight materials and processing technology have attracted considerable interest due to the need for energy conservation,emission reduction and environmental protection.As a lightweight structural material,magnesium alloy is widely used in automotive,aerospace and electronics industries
The characteristics of the castings in the aerospace field,such as a complex shape,large size and non-uniform thickness,lead to different cooling rates during the casting process.The cooling rate influences the solidification micro structure of the castings.Numerous studies have investigated the effect of the cooling rate on the solidification microstructure of Mg-Gd-Y-Zr alloy
Recently,with the development of computer technology and numerical simulation techniques,cellular automaton(CA) and phase field (PF) have become important and effective methods for simulating microstructure evolution in materials processing
In engineering practices,there is a strong demand for engineers to predict the characteristics of the microstructure,such as the grain size and content of the secondary phase.However,the models or simulation tools for predicting the grain size and content of the secondary phase have not been established for the Mg-Gd-Y-Zr alloy.In this study,the effects of the cooling rate and Zr content on the grain size were studied experimentally.A quantitative model for calculating the heterogeneous nucleation rate of the Mg-Gd-Y-Zr alloy was developed based on the experimental data.The microstructure of the alloy was simulated using the CA method,where the nucleation model was used,and a solute partition coefficient was introduced to deal with the solute trapping in front of the S/L interface.
2 Experimental
2.1 Experiment procedure
The Mg-Gd-Y-Zr alloy was prepared using high-purity Mg (99.95 wt%) and master alloys,including Mg-25 wt%Gd,Mg-25 wt%Y and Mg-30 wt%Zr.The melting process was conducted in an electric resistance furnace under the mixed atmosphere of 1 vol%SF6+99 vol%CO2.The melt was refined at 750℃for 5 min,cooled to730℃and poured into a permanent mold.Castings with five steps were produced,and thermocouples were used to record the temperature variation inside the castings during the solidification process.The geometry of the casting is shown in a previous study
2.2 Nucleation model
The aim of this section is to build a model which is capable of describing the heterogeneous nucleation during the solidification of the Mg-Gd-Y-Zr alloy based on the classical nucleation theory.A quantitative description of the nucleation process,incorporating the effects of the cooling rate and Zr content,is developed by determining the model parameters based on the experimental data.Christian
where kB is the Boltzmann constant;h is the Planck constant;T is the absolute temperature;ΔGmo is the activation energy for diffusion;Nhe is the number of atoms on the effective nucleus surface;and
where
The reasonable values of N and
Based on the assumption that the nucleation only occurs before the recalescence phenomenon in the solidification process,the grain density (nv) can be obtained by the following equation:
whereΔTmax is the maximum undercooling,and Rc is the cooling rate.The nucleation rate is assumed to be a linear function of undercooling.Thus,Eq.(6) can be written as:
where is the heterogeneous nucleation rate when the undercooling increases toΔTmax.
The following equation is deduced by correlating Eqs.(5) and (7).
In the above equation,the proportion coefficient 0.5 can be incorporated into the heterogeneous nucleation coefficient (Khe),which is associated with Zr content in the Mg-Gd-Y-Zr alloy.Here,AGmo and Aθare assumed to be constants for the particular nucleation agent (Zr) in the Mg-Gd-Y-Zr alloy.The model parameters Khe,AGmo and Aθare determined by using the experimental data of nv,ATmax and Rc.
2.3 Solute partition coefficient
In our previous study
where ke is the equilibrium partition coefficient;δi is the atomic jump distance;Di is the interfacial diffusion coefficient;and V is the solidification velocity.For V=0,k*=ke,and for largeδiV/Di,k*=1.It is difficult to acquire the values of Di andδi;therefore,the diffusion coefficient in the liquid phase (DL) and the thickness of the diffusion layer in the liquid phase (δL) are used in Eq.(9).
3 Results and discussion
3.1 Experimental results
The castings of the Mg-10Gd-3Y-Zr alloys with Zr contents of 0.58 wt%,1.26 wt%and 1.94 wt%were produced.In the solidification process,the cooling curves were recorded by thermocouples.The transient cooling rate,which is the first-order derivative of the cooling curve,varies with time.The transient cooling rate curve of the alloy can be pided into four stages.The first stage describes the cooling process of the liquid phase,in which the temperature of the melt decreases sharply.The second and third stages correspond to the solidification of the primary phase and the formation of the eutectics,respectively.In these two stages,the release of latent heat reduces the transient cooling rate.The transient cooling rate begins to increase after the melt has solidified completely in the last stage.Based on the above-mentioned characteristics,some parameters of solidification can be identified,as shown in Fig.1.The parameter Ts is the starting temperature of nucleation of the primary phase,and ts is the time corresponding to Ts.The parameter T1 is the temperature immediately before recalescence,at which nucleation of the primary phase is assumed finished.Tes is the starting temperature of the eutectics;Te is the ending temperature of solidification;and te is the time corresponding to Te.The average cooling rate in the solidification process,which is denoted by Rc,was calculated using Eq.(10).Here,Rc is a unique parameter corresponding to a particular cooling curve or dT/dt curve.The cooling rate mentioned later in this paper represents the average cooling rate Rc.
The maximum undercooling (ΔTmax) was calculated by Eq.(11).
Fig.1 Cooling curve and transient cooling rate curve (dT/dt) of Mg-Gd-Y-Zr alloy with 0.58 wt%Zr (when averaged cooling rate in solidification process being 2.6℃·s-1)
The maximum undercooling increases from 1.0 to9.3℃when the cooling rate increases from 2.6 to11.0℃·s-1,according to Fig.2,and the mathematic relation between the maximum undercooling and cooling rate can be expressed by the following equation.
The OM images of the Mg-Gd-Y-Zr alloy with0.58 wt%Zr at different cooling rates are shown in Fig.3.Figure 4 shows the grain sizes of the Mg-Gd-Y-Zr alloys with various Zr contents at different cooling rates.The grain size of the Mg-GdY-Zr alloy decreases with an increase in Zr content at the same cooling rate.When Zr content is 0.58 wt%,the grain size decreases from 73.94 to50.10μm as the cooling rate changes from 2.6 to6.7℃·s-1.A further increase in the cooling rate has little effect on the grain size.When the cooling rate increases from 3.0 to 8.8℃-s-1,the grain size of the MgGd-Y-Zr alloy with 1.26 wt%Zr decreases from 49.04 to42.26μm.The grain size of the alloy with 1.94 wt%Zr decreases from 41.71 to 35.00μm with an increase in the cooling rate from 2.6 to 7.8℃·s-1.
3.2 Determination of parameters in nucleation model
The grain density was determined using the procedure provided in a previous study referenced by ASTM Standard E 112-85,where the grain size (l) is related to the grain density (nv) as nv=0.566l-3.The model parameters Khe,AGmo and AB were determined by substituting the experimental data of nv,ΔTmax and Rc into Eq.(8),as listed in Table 1.Figure 5 shows the experimental results and the fitting results of the grain density.When the maximum undercooling increases,the grain density increases,and its increasing rate decreases.At the same maximum undercooling,the grain density of the Mg-Gd-Y-Zr alloy with a high Zr content is higher than that of the alloy with a low Zr content.When the maximum undercooling changes from 3 to 6℃,the increment of the grain density increases with an increase in Zr content.
Fig.2 Relationship between maximum undercooling (ATmax) and cooling rate (Rc) of Mg-Gd-Y-Zr alloy with 0.58 wt%Zr
Fig.3 OM images of Mg-Gd-Y-Zr alloy with 0.58 wt%Zr at various cooling rates:a 2.6℃·s-1,b 3.3℃·s-1,c 6.1℃·s-1 and d 11.0℃·s-1
Fig.4 Grain sizes of Mg-Gd-Y-Zr alloys with various Zr contents at different cooling rates
3.3 Quantitative value of solute partition coefficient
During solidification of Mg-GdY-Zr alloy,the primary phase precipitates from the liquid phase,which is followed by the eutectic reaction.In the Mg-10Gd-3Y-Zr(0.58 wt%,1.26 wt%,and 1.94 wt%) alloys,the contents of the main solute elements (Gd and Y) are higher than the nucleation agent (Zr).Wu et al.
In the CA program,some parameters of the Gd atom for calculating the partition coefficient are listed in Table 2,and the solute partition coefficient of Gd can be calculated by Eq.(9).The solidification velocity was calculated by
3.4 Simulation results
The quantitative nucleation model that considered the effects of the cooling rate and Zr content on the grain size and the solute partition coefficient dealing with the solute trapping in the Mg-Gd-Y-Zr alloy was used in the CA simulation.Figure 6 shows the simulation results for the solidification microstructure of the Mg-Gd-Y-Zr alloy with 0.58 wt%Zr at various cooling rates.The average size of the secondary phase and the grain size decrease when the cooling rate increases from 2.6 to 6.1℃·s-1.The solute partition coefficient increases with an increase in the cooling rate;therefore,the distribution of the Gd content in the primary phase tends to be more homogeneous.Figure 7a,b shows the OM images which were also shown in our previous study
Table 1 Parameters in nucleation model
Fig.5 Effects of maximum undercooling (ΔTmax) and Zr content on grain density (nv)
Table 2 Parameters of Gd atom for calculating partition coefficient
Table 3 Solidification velocity and partition coefficient at different cooling rates
Figure 8 shows the simulation results on the content of the eutectics in the Mg-GdY-Zr alloy with 0.58 wt%Zr.The content of the eutectics calculated by CA method decreases with an increase in the cooling rate from 2.6 to11.0℃·s-1.As shown in our previous study
Fig.6 Simulation results of Mg-Gd-Y-Zr alloy with 0.58 wt%Zr at various cooling rates:a 2.6℃·s-1,b 3.3℃·s-1,c 4.4℃·s-1 and d 6.1℃·s-1
Fig.7 OM images and simulation results of Mg-Gd-Y-Zr alloy with 0.58 wt%Zr at different cooling rates:a experimental result at11.0℃·s-1
Fig.8 Simulation results on fraction of eutectics
4 Conclusion
In this study,the solidification microstructure of the MgGd-Y-Zr alloy was investigated via an experimental study and a CA simulation.The grain size of the Mg-GdY-Zr alloy decreases with an increasing Zr content at the same cooling rate.When the cooling rate increases from2.6 to 6.7℃·s-1,the grain size of the Mg-Gd-Y-Zr alloy with 0.58 wt%Zr decreases from 73.94 to50.10μm.When the cooling rate increases from 3.0 to8.8℃·s-1,the grain size of the alloy with 1.26 wt%Zr decreases from 49.04 to 42.26μm.When the cooling rate increases from 2.6 to 7.8℃·s-1,the grain size of the alloy with 1.94 wt%Zr decreases from 41.71 to35.00μm.Based on the experimental data,a quantitative nucleation model describing the effects of the cooling rate and Zr content on the heterogeneous nucleation rate of the Mg-Gd-Y-Zr alloys was developed and the model parameters were determined.The solidification microstructure was simulated using the CA method,where the nucleation model was used and a solute partition coefficient was introduced to deal with solute trapping in front of the S/L interface.The simulation results of the grain size were in a good agreement with the experimental data.The simulation also shows that the fraction of the eutectics decreases with an increasing cooling rate in the range of 2.6-11.0℃·s-1,which is verified indirectly by the experimental data.
参考文献