Phase-field-lattice Boltzmann study for lamellar eutectic growth in a natural convection melt

In the present study, the influence of natural convection on the lamellar eutectic growth is determined by a phase-field-lattice Boltzmann study for Al-Cu eutectic alloy. The mass difference resulting from concentration difference led to the fluid flow, and a robust parallel and adaptive mesh refinement algorithm was employed to improve the computational efficiency without any compromising accuracy. Results show that the existence of natural convection would affect the growth undercooling and thus control the interface shape by adjusting the lamellar width. In particular, by alternating the magnitude of the solute expansion coefficient, the strength of the natural convection is changed. Corresponding microstructure patterns are discussed and compared with those under no-convection conditions.     

Numerical simulation of dendrite growth in Ni-based superalloy casting during directional solidification process

An understanding of dendrite growth is required in order to improve the properties of castings. For this reason, cellular automaton?finite difference (CA?FD) method was used to investigate the dendrite growth during directional solidification (DS) process. The solute diffusion model combined with macro temperature field model was established for predicting the dendrite growth behavior. Model validation was performed by the DS experiment, and the cooling curves and grain structures obtained by the experiment presented a reasonable agreement with the simulation results. The competitive growth of dendrites was also simulated by the proposed model, and the competitive behavior of dendrites with different misalignment angles was also discussed in detail. Subsequently, 3D dendrites growth was also investigated by experiment and simulation, and both were in good accordance. The influence on dendrites growth of initial nucleus was investigated by three simulation cases, and the results showed that the initial nuclei just had an effect on the initial growth stage of columnar dendrites, but had little influence on the final dendritic morphology and the primary dendrite arm spacing.     

Phase field simulation of dendrite growth under convection

The phase-field model coupled with a flow field was used to simulate the solidification of pure materials by the finite difference method. The effects of initial crystal radius, the space step and the interface thickness on the dendrite growth were studied. Results indicate that the grain grows into an equiaxial dendrite during free flow and into a typical branched structure under forced flow. The radius of an initial crystal can affect the growth of side-branches but not the stability of the dendrite's tip when an appropriate value is assigned to it. With an increase in space steps, side-branches appear at the upstream of the longitudinal principal branch and they grow rapidly. With an increase in the interface thickness, the trunk of the longitudinal upstream and lateral principal branches grow longer and become more slender while the number of secondary branches increases.     

Phase-field simulation of secondary dendrite growth in directional solidification of binary alloys

Phase field method was used to simulate the effect of grains orientation angle θ_(11) and azimuth θ_A of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites. In the simulation process, two single-factor influence experiments were designed for columnar crystal structures. The simulation results showed that, when θ_(11) 45o and θ_A 45o, as θ_(11) was enlarged, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging grain boundary(GB) presented an increasing inclination to that of preferentially growing dendrites; with increasing θ_A, the growth direction of the secondary dendrites on the preferentially growing dendrites at the converging GB exhibited greater deflection,and the secondary dendrites grew with branches; the secondary dendrites on the preferentially growing dendrites at diverging GBs grew along a direction vertical to the growth direction of the preferentially growing dendrites.When θ_A = 45o and θ_(11) = 45o, the secondary dendrites grew in a direction vertical to the growth direction of preferentially growing dendrites. The morphologies of the dendrites obtained through simulation can also be found in metallographs of practical solidification experiments. This implies that the effect of a grain's orientation angle and azimuth of non-preferentially growing dendrites on the secondary dendrites of preferentially growing dendrites does exist and frequently appears in the practical solidification process.     

Modelling dendrite evolution under rapid solidification conditions

Abstract

The evolution of a single dendrite is simulated by the cellular automaton (CA) method, in which the influences of interface velocity on the solute partition coefficient ahead of the interface and liquidus slope are investigated under rapid solidification conditions. Furthermore, the kinetic undercooling ahead of the interface is also taken into account, which is neglected under normal solidification conditions. The simulated dendrite morphology is compared with that of the equilibrium conditions and it is shown that the interface easily loses stability around the dendritic tip causing more and more secondary dendrite arms to appear. In addition, the solute partition coefficient increases when the interface velocity increases, which leads to a decrease in solute microsegregation.     

Phase field modeling of multiple dendrite growth of AI-Si binary alloy under isothermal solidification

Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems. In this study, the growth process of multiple dendrites in AI-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model. The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification. With the increase of growing time, the grains begin to coalesce and impinge the adjacent grains. When the dendrites start to impinge, the dendrite growth is obviously inhibited.     

Numerical simulation of solidification for aluminum-base multicomponent alloy

Solidification simulation of an aluminum-base multicomponent alloy was carried out by a method combining thermodynamic analysis using Thermo-Calc and heat-transfer calculation. An Al-9.5% Si-3% Cu-1% Mg-0.8% Fe (all mass%) aluminum-base multicomponent alloy was used for the simulation. The effect of latent heat on the heat-transfer calculation was considered by using an enthalpy method. The temperature-enthalpy curves for both an equilibrium state and nonequilibrium state with assumptions of no diffusion in the solid were calculated by using Thermo-Calc. A small casting with a cylindrical shape was used for the heat-transfer simulation. The vertical cross section of the casting was divided into rectangular grids, and the enthalpy change of each grid was numerically calculated. The calculated enthalpies in the grids were converted for each time-step into temperatures by using the temperature-enthalpy curve. A casting experiment was carried out under the same conditions as those of the simulation, and the calculated cooling curves obtained under the nonequilibrium condition agreed with the experimental ones.     

Numerical simulation of solidification for aluminum-base multicomponent alloy

Solidification simulation of an aluminum-base multicomponent alloy was carried out by a method combining thermodynamic analysis using Thermo-Calc and heat-transfer calculation. An Al-9.5% Si-3% Cu-1% Mg-0.8% Fe (all mass%) aluminum-base multicomponent alloy was used for the simulation. The effect of latent heat on the heat-transfer calculation was considered by using an enthalpy method. The temperature-enthalpy curves for both an equilibrium state and nonequilibrium state with assumptions of no diffusion in the solid were calculated by using Thermo-Calc. A small casting with a cylindrical shape was used for the heat-transfer simulation. The vertical cross section of the casting was divided into rectangular grids, and the enthalpy change of each grid was numerically calculated. The calculated enthalpies in the grids were converted for each time-step into temperatures by using the temperature-enthalpy curve. A casting experiment was carried out under the same conditions as those of the simulation, and the calculated cooling curves obtained under the nonequilibrium condition agreed with the experimental ones.     

Numerical simulation of facet dendrite growth

Numerical simulation based on phase field method was performed to describe the solidification of silicon. The effect of anisotropy, undercooling and coupling parameter on dendrite growth shape was investigated. It is indicated that the entire facet dendrite shapes are obtained by using regularized phase field model. Steady state tip velocity of dendrite drives to a fixed value when γ≤0.13. With further increasing the anisotropy value, steady state tip velocity decreases and the size is smaller. With the increase in the undercooling and coupling parameter, crystal grows from facet to facet dendrite. In addition, with increasing coupling parameter, the facet part of facet dendrite decreases gradually, which is in good agreement with Wulfftheory.     

Influence of directional solidification variables on primary dendrite arm spacing of Ni-based superalloy DZ125

The primary dendrite morphology and spacing of DZ125 superalloy have been observed during directional solidification under high thermal gradient about 500 K/cm. The results reveal that the primary dendrite arm spacing decreases from 94 μm to 35.8 μm with the increase of directional solidification cooling rate from 2.525 K/s to 36.4 K/s. The regression equation of the primary dendrite arm spacings λ1 versus cooling rate is λ1=0.013(GV)-0.32. The predictions of Kurz/Fisher model and Hunt/Lu model accord reasonably well with the experimental data. The influence of directional solidification rate under variable thermal gradient on the primary dendrite arm spacing has also been investigated.     

自然对流作用下Al-Si合金凝固过程的组织演变模拟

通过实验观察Al-Si合金的凝固组织,测量枝晶组织的二次枝晶臂间距,并分析温度对凝固组织的影响。在相场模型中引入重力引起的自然对流以预测实验条件下Al-Si合金凝固组织的演变。模拟结果与实验结果吻合良好,验证了本文中提出的模拟方法的可靠性。基于本文的耦合模型,开展一系列不同溶质含量合金柱状晶和等轴晶组织生长的二维和三维模拟,发现合金中溶质含量对凝固组织的演变几乎没有影响,而溶质膨胀系数对枝晶尖端移动速度有显著影响。本文中采用的算法极大地加快计算效率,因此,大规模的数值模拟使难以直接通过同步辐射实验观察的Al-Si合金凝固组织演变过程的研究成为可能。     

Oscillatory growth of nonfaceted dendrite and faceted plate during unidirectional solidification

Nonfaceted dendrite and faceted plate in succinonitrile-0.7 wt.% salol and camphor-47.4 wt.% and −35 wt.% naphthalene mixtures were in situ observed during unidirectional solidification. Nonfaceted dendrite oscillates in the growth direction during unidirectional solidification, alternatively repeating fast and slow growth. The faceted phase, whose growth is operated by a two dimensional nucleation mode, also shows oscillation of growth velocity. The oscillation in the faceted phase is due to the intrinsic growth nature, while in the nonfaceted phase it is due to experimental artifacts, that is, thermal fluctuations in the cold and hot zones. The implications of the observed dendrite tip fluctuation in relation with the initiation of dendrite sidebranching have been discussed.     

Mechanism of competitive grain growth in directional solidification of a nickel-base superalloy

The structure evolution of bicrystal (BC) samples during directional solidification (DS) was explored in an attempt to understand the mechanism of competitive grain growth. It was found that in the case of diverging dendrites the favorably oriented grain overgrows the misaligned grain. However, in the case of converging dendrites the result differs from the prediction of the generally accepted model for competitive grain growth. First, the unfavorably oriented dendrites are able to overgrow the favorably oriented dendrites. Second, the misaligned grain overgrows the favorably oriented grain by blocking the dendrites of the favorably oriented grain at the grain boundary. Based on the experimental results, the process by which a favored 〈0 0 1〉 texture is developed during DS process of a nickel-base superalloy is illustrated.     

Lattice Boltzmann modeling of dendritic growth in a forced melt convection

A two-dimensional (2D) lattice Boltzmann-based model is developed to simulate solutal dendritic growth of binary alloys in the presence of forced flow. The model adopts the lattice Boltzmann method (LBM) that describes transport phenomena by the evolution of distribution functions of moving pseudoparticles to numerically solve fluid flow and solute transport governed by both convection and diffusion. Based on the LBM-calculated solutal field, the dynamics of dendritic growth is determined according to a previously proposed local solutal equilibrium approach. After detailed model analysis and validation, the model is applied to simulate single and equiaxed multidendritic growth of Al–Cu alloys with forced convection. The results demonstrate the quantitative, numerically stable and computationally efficient capabilities of the proposed model. It is found that the solute distribution and dendritic growth are strongly influenced by convection, producing asymmetrical dendrites that grow faster in the upstream direction, but mostly slower in the downstream direction.     

不同择优生长取向角枝晶生长的数值模拟

通过耦合溶质扩散方程,并考虑成分过冷和曲率过冷对界面平衡溶质成分的影响,建立改进的元胞自动机模型来模拟溶质扩散控制的立方晶系合金的枝晶生长过程。模型在计算固液界面生长速率时考虑立方晶系枝晶择优生长取向100的影响,同时采用斜中心差分格式对界面生长速率方程进行离散,从而能够模拟择优生长取向与坐标轴成不同夹角的枝晶生长形貌演变。为验证模型的可靠性,模拟NH4Cl-H2O系透明合金单个等轴枝晶以及不同择优生长取向角的多个等轴枝晶和柱状枝晶的形貌演化,模拟结果与实验结果吻合较好。     

Influence of a high magnetic field on columnar dendrite growth during directional solidification

The influence of a high magnetic field on the growth of MnBi, α-Al and Al₃Ni dendrites in directionally solidified Bi–Mn, Al–Cu and Al–Ni alloys have been investigated. Results indicate that the magnetic field changes the dendrite growth significantly. Indeed, the magnetic field aligns the primary dendrite arm and the effect is different for different dendrites. For the MnBi dendrite, an axial high magnetic field enhanced the growth of the primary dendrite arm along the solidification direction; however, for the α-Al and Al₃Ni dendrites, the magnetic field caused the primary dendrite arm to deviate from the solidification direction. At a lower growth speed, a high magnetic field is capable of causing the occurrence of the columnar-to-equiaxed transition (CET). Moreover, it has also been observed that a high magnetic field affects the growth of the high-order (i.e., secondary and tertiary) dendrite arms of the α-Al dendrite at a higher growth speed; as a consequence, the field enhances the branching of the dendrite and the formation of the (1 1 1)-twin planes. The above results may be attributed to the alignment of the primary dendrite arm under a high magnetic field and the effect of a high magnetic field on crystalline anisotropy during directional solidification.     

Multi-scale coupling simulation in directional solidification of superalloy based on cellular automaton-finite difference method

Casting microstructure evolution is difficult to describe quantitatively by only a separate simulation of dendrite scale or grain scale, and the numerical simulation of these two scales is difficult to render compatible. A three-dimensional cellular automaton model couplling both dendritic scale and grain scale is developed to simulate the microstructure evolution of the nickel-based single crystal superalloy DD406. Besides, a macro–mesoscopic/microscopic coupling solution algorithm is proposed to improve computational efficiency. The simulation results of dendrite growth and grain growth of the alloy are obtained and compared with the results given in previous reports. The results show that the primary dendritic arm spacing and secondary dendritic arm spacing of the dendritic growth are consistent with the theoretical and experimental results. The mesoscopic grain simulation can be used to obtain results similar to those of microscopic dendrites simulation. It is indicated that the developed model is feasible and effective.     

Progress on modeling and simulation of directional solidification of superalloy turbine blade casting

Directional solidified turbine blades of Ni-based superalloy are widely used as key parts of the gas turbine engines.The mechanical properties of the blade are greatly influenced by the final microstructure and the grain orientation determined directly by the grain selector geometry of the casting.In this paper,mathematical models were proposed for three dimensional simulation of the grain growth and microstructure evolution in directional solidification of turbine blade casting.Ray-tracing method was applied to calculate the temperature variation of the blade.Based on the thermo model of heat transfer,the competitive grain growth within the starter block and the spiral of the grain selector,the grain growth in the blade and the microstructure evolution were simulated via a modified Cellular Automaton method.Validation experiments were carried out,and the measured results were compared quantitatively with the predicted results.The simulated cooling curves and microstructures corresponded well with the experimental results.The proposed models could be used to predict the grain morphology and the competitive grain evolution during directional solidification.     

行波磁场对定向凝固Pb-Sn合金枝晶生长的影响

在1g的重力加速度条件下,研究熔体对流对向上生长的定向凝固Pb-33%Sn合金枝晶生长行为的影响。熔体对流由行波磁场进行调制。当行波磁场方向由向上转变为向下时,一次枝晶间距逐渐增大,一次枝晶间距的分布更加紧凑,且峰值趋于降低。分析表明：行波磁场对熔体对流的调制作用与改变重力加速度的效果类似,当抽拉速率为50μm/s,行波磁场强度为1mT时,在向上和向下的行波磁场作用下有效重力加速度分别为3.07g和0.22g。     

Carbide phases in a multicomponent superalloy Ni-Co-W-Cr-Ta-Re

Physicochemical phase analysis is used to investigate carbide phases in a high-temperature nickelbased alloy ZhS32 after the alloy has been subjected to various heat treatments and aging regimes within a temperature range of 850–1250°C. The MC, M₂₃C₆, and M₆C carbide phases have been identified.