•A combined DCA-FD model for predicting dendrite growth is developed.•Model validations are performed by in-situ observation using HT-CLSM and other experimental results.•Hundreds of dendrites distribution at a large scale and 3-D polycrystalline growth are successfully simulated.•The DS dendritic evolution behavior and detail morphologies are also simulated.Dendritic structures are the predominant microstructural constituents of nickel-based superalloys, an understanding of the dendrite growth is required in order to obtain the desirable microstructure and improve the performance of castings. For this reason, numerical simulation method and an in-situ observation technology by employing high temperature confocal laser scanning microscopy (HT-CLSM) were used to investigate dendrite growth during solidification process. A combined cellular automaton-finite difference (CA-FD) model allowing for the prediction of dendrite growth of binary alloys was developed. The algorithm of cells capture was modified, and a deterministic cellular automaton (DCA) model was proposed to describe neighborhood tracking. The dendrite and detail morphology, especially hundreds of dendrites distribution at a large scale and three-dimensional (3-D) polycrystalline growth, were successfully simulated based on this model. The dendritic morphologies of samples before and after HT-CLSM were both observed by optical microscope (OM) and scanning electron microscope (SEM). The experimental observations presented a reasonable agreement with the simulation results. It was also found that primary or secondary dendrite arm spacing, and segregation pattern were significantly influenced by dendrite growth. Furthermore, the directional solidification (DS) dendritic evolution behavior and detail morphology were also simulated based on the proposed model, and the simulation results also agree well with experimental results.

•A GPU computing method is developed for accelerating phase-field simulations.•The efficiency and accuracy of the GPU computing method have been tested.•Effects of temperature gradient on dendrite morphologies are investigated.•The poly-crystal competitive growth in directional solidification is investigated.The microstructure formation of a nickel-based superalloy during solidification in three dimensions was investigated using the phase-field method. To accelerate the large-scale phase-field simulation, a parallel computing approach was developed using the graphic processing unit (GPU), and the limitation of insufficient GPU memory was circumvented by employing an asynchronous concurrent algorithm. The performance of the GPU-based parallel computing method was tested and the results demonstrate that a maximum performance of 774.292 GFLOPS (giga floating-point operations per second) can be obtained using a single NVIDIA GTX1080 GPU. In simulations of isothermal solidification, the microstructure evolution of a single and multiple dendrites under different undercooling levels was shown in detail. During the solidification, the dendrite tip growth velocity and fraction solid were recorded and then analyzed. In simulations of directional solidification, the formation of primary dendrite arms under different temperature gradients was investigated, and the simulated microstructure was in good agreement with experimental observations. Additionally, the distribution of primary dendrite arm spacing was quantitatively analyzed by Voronoi tessellation. Finally, simulation of polycrystalline growth in directional solidification was conducted to study the dendrite competitive growth. The unusual overgrowth phenomenon was observed in the initial growth stage, while as the solidification process proceeded, the dendrites with small inclination angles were more likely to overgrow the dendrites with large inclination angles.Download high-res image (285KB)Download full-size image

Analysis of solidification conditions, compositions and heat treatment parameters and their mutual interaction on the microstructure evolution is of great importance for designing components with desired mechanical properties. The present paper aims at widening the knowledge on the correlation of solidification microstructure refining scale, Mg composition and heat treatment parameters with the mechanical properties in Al-7Si-Mg cast aluminum alloys. The results reveal that the advantage of fine solidification microstructure can be inherited after heat treatment, with the finer microstructure being characterized by higher tensile properties. Furthermore, with the solidification microstructure refining, the fracture mode transforms from quasi-cleavage to dimple and fracture path transforms from transgranular to intergranular. With the increase of Mg composition, both yield strength and ultimate tensile strength increase, while the elongation decreases. Higher artificial aging temperature can decrease the peak strength. Different solution treatment can produce the different tensile properties because of the different microstructures and composition. A yield strength model using an experiment-based term ∆σ0 to account the effect of solidification and solution treatment is proposed, and the relationship between yield strength and ultimate tensile strength is described using an empirical equation.

•Deformation temperature has a great influence on RX sensitivity.•Stacking faults can facilitate the RX nucleation.•Both RX nucleation rate and grain boundary motion rate are higher with higher plastic strains.•The γ′ phase retards the movement of RX grain boundaries.•Eutectics undergo RX when plastic deformation is high. Otherwise, they retard the RX grain boundary motion.Experimentation by TEM, EBSD and optical microscope is used to understand recrystallization in a Ni-based single crystal superalloy. Hot compression is employed at different temperatures to provide driving force for recrystallization. Recrystallization sensitivity for this investigated alloy is provided. The results indicate that deformation temperature, as well as annealing conditions, has a great influence on recrystallization behavior. Samples deformed around 980 °C have the highest propensity for recrystallization, and stacking faults can facilitate the recrystallization process by themal twinning nucleation. Microstructural observation shows that as-cast inhomogeneity plays a significant role in the microstructure evolution, especially below γ′ phase solvus. Recrystallization nucleates first and grow rapidly in the dendritic arms. In the interdendritic regions, thermal twinning play the dominant role, and small grains remain after recrystallization is completed. Grain coarsening is rather difficult owing to abundant twinning grain boundaries. The eutectics in the IDRs can undergo recrystallization by themselves in the case of high plastic strains, and impede the grain boundaries at low plastic strains.

Numerical heat-transfer and turbulent flow model for an industrial high-pressure gas quenching vacuum furnace was established to simulate the heating, holding and gas fan quenching of a low rhenium-bearing Ni-based single crystal turbine blade. The mesh of simplified furnace model was built using finite volume method and the boundary conditions were set up according to the practical process. Simulation results show that the turbine blade geometry and the mutual shielding among blades have significant influence on the uniformity of the temperature distribution. The temperature distribution at sharp corner, thin wall and corner part is higher than that at thick wall part of blade during heating, and the isotherms show a toroidal line to the center of thick wall. The temperature of sheltered units is lower than that of the remaining part of blade. When there is no shelteration among multiple blades, the temperature distribution for all blades is almost identical. The fluid velocity field, temperature field and cooling curves of the single and multiple turbine blades during gas fan quenching were also simulated. Modeling results indicate that the loading tray, free outlet and the location of turbine blades have important influences on the flow field. The high-speed gas flows out from the nozzle is divided by loading tray, and the free outlet enhanced the two vortex flow at the end of the furnace door. The closer the blade is to the exhaust outlet and the nozzle, the greater the flow velocity is and the more adequate the flow is. The blade geometry has an effect on the cooling for single blade and multiple blades during gas fan quenching, and the effects in double layers differs from that in single layer. For single blade, the cooing rate at thin-walled part is lower than that at thick-walled part, the cooling rate at sharp corner is greater than that at tenon and blade platform, and the temperature at regions close to the internal position is decreased more slowly than that close to the surface. For multiple blades in single layer, the temperature at sharp corner or thin wall in the blade that close to the nozzles is much lower, and the temperature distribution of blades is almost parallel. The cooling rate inside the air current channel is lower than that of at the position near blade platform and tenon, and the effect of blade location to the nozzles on the temperature field inside the blade is lower than that on the blade surface. For multiple blades in double layers, the flow velocity is low, and the flow is not uniform for blades in the second-layer due to the shielding of blades in the first-layer. the cooling rate of blades in the second-layer is lower than that in the first-layer. The cooling rate of blade close to the nozzles in the first-layer is the higher than that of blade away from the nozzles in the second-layer, and the temperature distribution on blades in the same layer is almost parallel. The cooling rate in thin wall position of blade away from the nozzles is larger than that in tenon of the blade closer to the nozzles in the same layer. The cooling rate for blades in the second- layer is much lower both in thin wall and tenon for blades away from the nozzles.

Due to the extensive application of Al-Si alloys in the automotive and aerospace industries as structural components, an understanding of their microstructural formation, such as dendrite and (Al+Si) eutectic, is of great importance to control the desirable microstructure, so as to modify the performance of castings. Since previous major themes of microstructural simulation are dendrite and regular eutectic growth, few efforts have been paid to simulate the irregular eutectic growth. Therefore, a multiphase cellular automaton (CA) model is developed and applied to simulate the time-dependent Al-Si irregular eutectic growth. Prior to model establishment, related experiments were carried out to investigate the influence of cooling rate and Sr modification on the growth of eutectic Si. This CA model incorporates several aspects, including growth algorithms and nucleation criterion, to achieve the competitive and cooperative growth mechanism for nonfaceted-faceted Al-Si irregular eutectic. The growth kinetics considers thermal undercooling, constitutional undercooling, and curvature undercooling, as well as the anisotropic characteristic of eutectic Si growth. The capturing rule takes into account the effects of modification on the silicon growth behaviors. The simulated results indicate that for unmodified alloy, the higher eutectic undercooling results in the higher eutectic growth velocity, and a more refined eutectic microstructure as well as narrower eutectic lamellar spacing. For modified alloy, the eutectic silicon tends to be obvious fibrous morphology and the morphology of eutectic Si is determined by both chemical modifier and cooling rate. The predicted microstructure of AI-7Si alloy under different solidification conditions shows that this proposed model can successfully reproduce both dendrite and eutectic microstructures.

A semi-quantitative, macroscopic, phenomenon-based, thermo-elastic–plastic model was developed to predict the final plastic strains of single crystal nickel-based superalloys by considering their orthotropic mechanical properties. Various cases were considered and simulated to investigate the basic factors that influence the final plasticity. Thermo-mechanical numerical analysis was conducted to predict the recrystallization sites of simplified cored rods, with the results in good agreement with the experimental results. These hollowed rods with thin walls showed an increased propensity for recrystallization. The geometric features, especially stress concentration sites, are more significant to the induced plasticity than the material's orientation or shell/core materials. This paper also attempts to provide useful suggestions, such as introducing filets, to avoid causing plastic strains during the casting process that induce recrystallization.

Hot compression tests on cylinders using nickel-based single crystal superalloy DD6 were conducted to introduce the stored energy for recrystallization. Annealing was carried out at different temperatures for different time to investigate the kinetics of recrystallization of DD6. The experimental results show that the recrystallization rate increases gradually with temperature. The stress, strain and stored energy distribution of single crystal superalloy were modeled based one macroscopic phenomenon-based elastic-plastic model, considering the orthotropic properties of SX superalloys. Recrystallization microstructure on the cross-section perpendicular to the cylinder axis was simulated using cellular automaton (CA) method. The model can predict experimental results.

Since most typical alloys in industrial applications are multicomponent with three or more components, and various CA models proposed in the past mainly focus on the binary alloys, a two-dimensional modified cellular automaton model allowing for the quantitatively predicting dendrite growth of multicomponent alloys in the low Péclet number regime is presented. The elimination of the mesh-induced anisotropy is achieved by adopting a modified virtual front tracking method. A new efficient method based on the lever rule is applied to calculate the solid fraction increment of the interfacial cells. The thermodynamic data such as liquidus temperature, the partition coefficients, and the slope of liquidus surface, needed for determining the dynamics of dendrite growth, are obtained by coupling with PanEngine. This model is applied to simulate the dendrite morphology and microsegregation of Al–Cu–Mg ternary alloy both for single and multi-dendrites growth. The simulated results demonstrate that the difference of the concentration distribution profiles ahead of the dendrite tip for each alloying element mainly results from the different partition coefficients and solute diffusion coefficients. Comparison with the prediction of analytical model is carried out and it reveals the correctness of the model. Consequently, the difference in interdendritic microsegregation behavior of different components is analyzed.

Directional solidified (DS) turbine blades are widely used in advanced gas turbine engine. The size and orientation of columnar grains have great influence on the high temperature property and performance of the turbine blade. Numerical simulation of the directional solidification process is an effective way to investigate the grain’s growth and morphology, and hence to optimize the process. In this paper, a mathematical model was presented to study the directional solidified microstructures at different withdrawal rates. Ray-tracing method was applied to calculate the temperature variation of the blade. By using a Modified Cellular Automation (MCA) method and a simple linear interpolation method, the mushy zone and the microstructure evolution were studied in detail. Experimental validations were carried out at different withdrawal rates. The calculated cooling curves and microstructure agreed well with those experimental. It is indicated that the withdrawal rate affects the temperature distribution and growth rate of the grain directly, which determines the final size and morphology of the columnar grain. A moderate withdrawal rate can lead to high quality DS turbine blades for industrial application.