Qingyan Xu

A Modified Cellular Automaton Method for the Modeling of the Dendritic Morphology of Binary Alloys

Abstract A cellular automaton (CA)-based model for the precise two-dimensional simulation of the dendritic morphology of cast aluminum alloys was developed. Compared with previous CA models, the new model considers the solidification process in more detail, solving the solute and heat conservation equations in the modeling domain, including calculation of the solid fraction, the tip velocity, and the solute diffusion process, all of which have significant influence on the dendrite evolution. The rotating grids technique was used in the simulation to avoid anisotropy introduced by the square grid. Dendritic grain profiles for different crystallographic orientations show the existence of a great number of regular and parallel secondary and tertiary arms. The simulation results for the secondary arm spacing and grain size were compared with experimental data and with results reported in the literature. A good agreement was found between the simulated results and the experimental data. It can be concluded that the model can be used to predict the dendritic microstructure of aluminum alloy in a quantitative manner.

Multiscale Modeling and Simulation of Directional Solidification Process of Turbine Blade Casting with MCA Method

Nickel-based superalloy turbine blade castings are widely used as a key part in aero engines. However, due to the complex manufacturing processes, the complicated internal structure, and the interaction between different parts of the turbine blade, casting defects, such as stray grains, often happen during the directional solidification of turbine blade castings, which causes low production yield and high production cost. To improve the quality of the directionally solidified turbine blade castings, modeling and simulation technique has been employed to study the microstructure evolution as well as to optimize the casting process. In this article, a modified cellular automaton (MCA) method was used to simulate the directional solidification of turbine blade casting. The MCA method was coupled with macro heat transfer and micro grain growth kinetics to simulate the microstructure evolution during the directional solidification. In addition, a ray tracing method was proposed to calculate the heat transfer, especially the heat radiation of multiple blade castings in a Bridgman furnace. A competitive mechanism was incorporated into the grain growth model to describe the grain selection behavior phenomena of multiple columnar grains in the grain selector. With the proposed models, the microstructure evolution and related defects could be simulated, while the processing parameters optimized and the blade casting quality guaranteed as well. Several experiments were carried out to validate the proposed models, and good agreement between the simulated and experimental results was achieved.

Numerical Simulation and Optimization of Directional Solidification Process of Single Crystal Superalloy Casting

The rapid development of numerical modeling techniques has led to more accurate results in modeling metal solidification processes. In this study, the cellular automaton-finite difference (CA-FD) method was used to simulate the directional solidification (DS) process of single crystal (SX) superalloy blade samples. Experiments were carried out to validate the simulation results. Meanwhile, an intelligent model based on fuzzy control theory was built to optimize the complicate DS process. Several key parameters, such as mushy zone width and temperature difference at the cast-mold interface, were recognized as the input variables. The input variables were functioned with the multivariable fuzzy rule to get the output adjustment of withdrawal rate (v) (a key technological parameter). The multivariable fuzzy rule was built, based on the structure feature of casting, such as the relationship between section area, and the delay time of the temperature change response by changing v, and the professional experience of the operator as well. Then, the fuzzy controlling model coupled with CA-FD method could be used to optimize v in real-time during the manufacturing process. The optimized process was proven to be more flexible and adaptive for a steady and stray-grain free DS process.

Numerical simulation of directional solidification of single crystal turbine blade casting

Abstract As the key parts of turbine engines, single crystal superalloy turbine blades directly determine the engines performance and service time. In this paper, a mathematical model based on the modified cellular automaton and finite difference method was developed for the three-dimensional simulation of solidification process of single crystal turbine blade castings. Using a ray tracing method, the complex heat radiation among the multiple blade castings and the furnace wall was considered in the model. The microstructure evolution was simulated with the modified cellular automaton method. A discrete layer by layer calculation method was proposed to couple the macro- and microsimulations. Simulation results show that with proper varying withdrawal rates, it is possible to increase the productivity and avoid the grain defects at the same time for single crystal blade castings. Experiments with constant and varying withdrawal rates were carried out to validate the proposed model.

Stochastic modeling of dendritic microstructure of aluminum alloy

Stochastic modeling was carried out for simulating the evolution of dendritic grains during the solidification process of aluminum alloy. The model includes time-dependent calculations for temperature distribution, solute redistribution in the liquid phases, curvature of the dendritic tip, and growth anisotropy. In the model, a shape function was proposed to represent the equiaxed dendritic shape and the growing grain. The nucleation process was calculated by continuous nucleation. However, the location and the crystallographic orientation are chosen randomly among all possible nucleation sites and the possible directions, respectively. A numerical algorithm based on the coordinate transformation approach was developed to explicitly track the sharp solid/liquid (S/L) interface. The microstructure simulation scheme was developed to model the grain formation. In order to verify the modeling results, sample castings were cast in sand and metal mold. Experimental and numerical results agreed well.

Numerical Simulation of Unidirectional Solidification Process of Turbine Blade Castings

A mathematical model for three-dimensional simulation of unidirectional solidification process and microstructure evolution of Ni-based superalloy investment castings was developed based on CA-FD method. The modified ray tracing method was used to solve the complicated heat radiation transfer among the multiple blades and outer space during withdrawal process. Various withdrawal rates were used. During one process high withdrawal rate was used first before the platform approached the baffle. Then the low withdrawal rate was used to reduce the temperature difference of the platform in horizontal section and avoid the defects formed in the corner of the platform. The experimental cooling curves of different positions in the blades and microstructure were compared with the simulation results. Both the results showed that the various withdrawal rates process was effective to reduce the temperature difference of the platform and avoid the formation of stray grains. This process could be helpful to increase the productivity.

Modeling of Unidirectional Growth in a Single Crystal Turbine Blade Casting

Single crystal superalloy turbine blade are widely used in aero-engineering. However, there are often grain defects occurring during the fabrication of blade by casting. It is important to study the formation of microstructure related defects in turbine blades. Single crystal blade sample castings of a nickel-base superalloy were produced at different withdrawal rates by the directional solidification process and investment casting. There was a difference between the microstructure morphology at the top part of the turbine blade sample castings and the one at the bottom. Higher withdrawal rates led to more differences in the microstructure and a higher probability of crystallographic defect formation such as high angle boundaries at locations with an abrupt change of the transversal section area. To further investigate the formation of grain defects, a numerical simulation technique was used to predict the crystallographic defects occurring during directional solidification. The simulation results agreed with the experimental ones.

Simulation and Experimental Studies on Grain Selection and Structure Design of the Spiral Selector for Casting Single Crystal Ni-Based Superalloy

Grain selection is an important process in single crystal turbine blades manufacturing. Selector structure is a control factor of grain selection, as well as directional solidification (DS). In this study, the grain selection and structure design of the spiral selector were investigated through experimentation and simulation. A heat transfer model and a 3D microstructure growth model were established based on the Cellular automaton-Finite difference (CA-FD) method for the grain selector. Consequently, the temperature field, the microstructure and the grain orientation distribution were simulated and further verified. The average error of the temperature result was less than 1.5%. The grain selection mechanisms were further analyzed and validated through simulations. The structural design specifications of the selector were suggested based on the two grain selection effects. The structural parameters of the spiral selector, namely, the spiral tunnel diameter (dw), the spiral pitch (hb) and the spiral diameter (hs), were studied and the design criteria of these parameters were proposed. The experimental and simulation results demonstrated that the improved selector could accurately and efficiently produce a single crystal structure.

Microstructure Simulation of Magnesium Alloy

A cellular automaton (CA)-based model for two-dimensional simulation of the dendritic morphology of magnesium alloys was developed. The model considers solving the solute and heat conservation equations in the modeling domain, including calculation of the solid fraction, the tip velocity, and the solute diffusion process, all of which have significant influence on the dendrite evolution. The microstructure of a step-shape die cast part of AZ91D magnesium alloys was investigated utilizing SEM-EBSD analysis. The microstructure simulation results were compared with the experimental results and they were in good agreement on grain size.

Dendrite growth modelling of cast magnesium alloy

Abstract Cast magnesium alloy are commonly used in 3C electronic and auto industry. Therefore, microstructure simulation of Mg alloy during solidification process not only has important academic values, but also has strong background in industrial application. Based on the crystallographic feature of magnesium alloy with hexagonal close packed structure, two-dimensional growth model of dendrite was established, which employed dendrite shape functions to describe the growing contours of dendrite arms and considered the kinetics of dendrite growth and the coarsening of the secondary dendrite arms. Then a new stochastic simulation method named virtual growth centre calculation model was proposed. Finally, a step shaped sample casting of magnesium alloy was cast to validate the proposed models.