1. Introduction
Aluminum alloys have become crucial materials in various industries, especially in automotive and aerospace, due to their low density and high specific strength. Low pressure die casting (LPDC) is a widely used method for manufacturing aluminum alloy components as it offers several advantages such as smooth filling, the ability to form complex thin-walled castings, high productivity, and good quality control. In recent decades, numerical simulation techniques have been increasingly applied to the LPDC process to optimize the process, reduce defects, and predict the mechanical properties of the castings. This article aims to provide a comprehensive review of the numerical simulation of the LPDC process of aluminum alloys, covering the development of simulation techniques, macro and micro simulations, and future directions.
1.1 Significance of Aluminum Alloys in Automotive Industry
According to the energy-saving and new energy vehicle technology roadmap released by the Society of Automotive Engineers in 2020, the development of automotive materials focuses on improving the application system of high-strength steel in the short term, forming a lightweight alloy application system in the medium term, and achieving a multi-material hybrid application system in the long term. Aluminum alloys, with their excellent properties such as high specific strength and thermal conductivity, are key materials in the automotive and aerospace fields. The lightweight advantage of aluminum makes it have a broad demand space in the automotive material field, and the amount of aluminum used in a single vehicle has great growth potential.
1.2 Advantages of Low Pressure Die Casting
LPDC is an anti-gravity casting method that applies a certain pressure on the liquid alloy surface in a holding furnace or crucible to make the liquid metal fill the mold cavity from bottom to top along a riser tube and solidify under a certain pressure. It has many advantages, including high productivity, smooth filling under pressure, controllable filling speed, high dimensional accuracy, the ability to form complex structural castings, less prone to oxidation inclusions, and dense microstructure. These advantages make it widely used in the production of automotive components such as wheels and engine cylinder heads.
1.3 Role of Numerical Simulation in LPDC
Numerical simulation plays a crucial role in understanding and optimizing the LPDC process. By establishing physical-mathematical models and using computer simulation techniques, it is possible to predict the formation of casting defects, optimize the casting process, and improve the quality of castings. It can also help in understanding the evolution of the microstructure and predicting the mechanical properties of the castings, which is essential for ensuring the performance of the final products.
2. Development of Numerical Simulation Techniques for LPDC of Aluminum Alloys
The development of numerical simulation techniques for LPDC of aluminum alloys has evolved over the years, with significant progress in both macro and micro simulations.
2.1 Early Developments
The numerical simulation of the LPDC process began in the 1980s. Early research focused on developing algorithms for calculating the flow field, such as the MAC algorithm, SMAC algorithm, and Finite Volume method. These algorithms laid the foundation for subsequent simulations.
2.2 Commercial Software and Their Applications
In recent years, a series of commercial software for casting numerical simulation has been developed, such as MAGMASOFT, ProCAST, Flow 3D, and AnyCasting. These software can simulate the filling, heat conduction, solidification process, and stress field of casting. They have been widely used in the actual production of casting enterprises, helping to reduce costs and shorten the R & D cycle. In China, some universities and research institutions have also developed their own casting numerical simulation software, such as FT-Star developed by Tsinghua University, Huazhu CAE developed by Huazhong University of Science and Technology, and CASTsoft developed by North China Institute of Technology.
3. Macro Numerical Simulations
Macro numerical simulations mainly focus on the filling process and the solidification process of LPDC.
3.1 Filling Process Simulation
3.1.1 Governing Equations
The simulation of the filling process mainly solves the continuity equation, momentum conservation equation, and energy conservation equation of the aluminum alloy liquid flow and tracks the free surface of the liquid aluminum alloy fluid. The mass conservation and momentum conservation are generally solved using the continuity equation and Navier – Stokes equation, and the energy conservation is solved using the heat conduction differential equation.
| Equation | Description |
|---|---|
| Continuity equation | (in three dimensions) |
| Navier – Stokes equation | |
| Heat conduction differential equation |
3.1.2 Common Algorithms
There are several common algorithms for filling process simulation. The SIMPLE algorithm proposed by SuhasV. Patankar and the SOLA – VOF algorithm proposed by the US LOS Alamos laboratory are widely used. These algorithms have been applied in many research and practical applications to simulate the filling process of LPDC.
| Algorithm | Features |
|---|---|
| SIMPLE algorithm | Solves the pressure – velocity coupling problem effectively |
| SOLA – VOF algorithm | Can handle complex free surface problems |
3.2 Solidification Process Simulation
3.2.1 Heat Transfer Equation
The solidification process of LPDC is a complex physical and chemical process involving heat transfer, solute transfer, momentum transfer, and phase change. The heat exchange during the solidification process is simulated using the heat transfer equation.
3.2.2 Latent Heat Treatment Methods
Common latent heat treatment methods include the equivalent specific heat method, temperature recovery method, and enthalpy method. These methods are used to deal with the release of latent heat during the solidification process.
| Method | Principle |
|---|---|
| Equivalent specific heat method | Treats the latent heat as an equivalent specific heat |
| Temperature recovery method | Accounts for the temperature change due to latent heat release |
| Enthalpy method | Considers the total enthalpy change during the solidification process |
4. Micro Numerical Simulations
Micro numerical simulations focus on the evolution of the microstructure of aluminum alloys during LPDC, including the growth of primary phases and eutectic phases.
4.1 Primary Phase Dendrite Growth Simulation
4.1.1 Modeling Approaches
The two main methods for simulating the growth of primary phase dendrites are the Cellular Automaton (CA) method and the Phase Field (PF) method. The CA method is based on physical principles and growth kinetics theory and is widely used due to its advantages such as considering the influence of temperature and flow fields, achieving macro – micro coupling, and having high computational efficiency. The PF method is based on the Ginzburg – Landau theory and has certain limitations in terms of computational efficiency.
| Method | Basis | Advantages | Disadvantages |
|---|---|---|---|
| CA method | Physical principles and growth kinetics theory | Considers temperature and flow fields, macro – micro coupling, high computational efficiency | Grid size limitations |
| PF method | Ginzburg – Landau theory | Comprehensive consideration of thermodynamic factors | High computational cost |
4.1.2 Nucleation Models
In the aluminum alloy solidification process, the nucleation mode of dendrites is usually heterogeneous nucleation. There are two main nucleation models: the instantaneous nucleation model and the continuous nucleation model. The continuous nucleation model based on the Gaussian distribution is often used in the LPDC process of aluminum alloys.
| Model | Assumption | Applicability |
|---|---|---|
| Instantaneous nucleation model | All nucleation occurs instantaneously at the nucleation temperature | Single heterogeneous nucleation with the same size |
| Continuous nucleation model | The number of nucleations depends on the undercooling degree | Aluminum alloy LPDC process |
4.11 Growth Simulation Using CA Method
The CA method discretizes the solidification process in time and space. By dividing the calculation domain into small CA cells and considering the state values and variables of each cell, the growth of dendrites can be simulated. The evolution of the microstructure, such as the refinement of grains and the secondary dendrite arm spacing, can be obtained.
| Variable | Description |
|---|---|
| State values (CA cells) | Liquid, solid, interface |
| Variables (CA cells) | Temperature, concentration, solid fraction, growth orientation |
4.2 Eutectic Phase Growth Simulation
4.2.1 Eutectic Structures and Growth Mechanisms
In the aluminum – silicon alloy system, the α(Al)+β(Si) eutectic is a typical non – regular eutectic structure. The eutectic growth process involves the competition and cooperation of the two phases in the liquid phase. The growth of the eutectic phases is mainly affected by solute diffusion and interface tension.
| Eutectic structure | Characteristics | Growth factors |
|---|---|---|
| α(Al)+β(Si) eutectic | Non – regular eutectic | Solute diffusion, interface tension |
4.2.2 Simulation Studies
Researchers have used various methods to study the eutectic growth process. CA models have been widely used to simulate the eutectic growth of aluminum – silicon alloys, considering factors such as nucleation, orientation, and solute redistribution.
| Study | Method | Focus |
|---|---|---|
| Shi et al. | CA models (2D and 3D) | CBr4 – C2Cl6 transparent alloy eutectic growth, influence of pulling speed on eutectic spacing |
| Zhu et al. | CA model and experiment | Cooperation and competition growth mechanism of eutectic phases, influence of diffusion and growth speed on regular eutectic evolution |
5. Mechanical Property Prediction Simulation
The mechanical properties of aluminum alloy castings are affected by the casting process and heat treatment process. Numerical simulation is used to predict these properties.
5.1 Cast State Mechanical Property Prediction
In the prediction of the cast state mechanical properties of aluminum alloys, the secondary dendrite arm spacing (SDAS) is often used to establish relevant calculation models.
| Model | Basis |
|---|---|
| SDAS – based model | Relationship between SDAS and mechanical properties |
5.2 Heat – Treated Mechanical Property Prediction
For the prediction of the mechanical properties after heat treatment, many researchers have constructed prediction models for the mechanical properties after heat treatment. These models consider factors such as precipitate nucleation, growth, and coarsening.
| Model | Focus |
|---|---|
| Kinetic model + yield strength model (Esmaeili et al.) | Al – Mg – Si – Cu alloy artificial aging precipitation hardening behavior |
| Precipitate nucleation, growth, coarsening coupled model (Liu et al.) | Alloy yield strength and precipitate size, volume fraction relationship |
6. Challenges and Future Directions
Although significant progress has been made in the numerical simulation of the LPDC process of aluminum alloys, there are still some challenges and areas for future development.
6.1 Challenges
6.1.1 Accuracy of Numerical Simulation
The accuracy of numerical simulation needs to be improved. There may be errors in the simulation results due to simplifications in the models and inaccuracies in the input parameters.
6.1.2 Computational Efficiency
The computational efficiency of numerical simulation is relatively low, especially for large – scale and complex simulations. This limits the application of numerical simulation in some cases.
6.1.2 Depth of Multi – Scale Coupling
In the existing multi – scale numerical simulations, the coupling between macro and micro simulations is often weak or not fully realized. This affects the consistency and accuracy of the simulation results.
6.2 Future Directions
6.2.1 Deepening the Application of ICME
Future research should further develop the application of Integrated Computational Materials Engineering (ICME) in LPDC, deeply couple macro and micro simulations, and realize the information transfer between macro and micro to build a full – process simulation system of the LPDC process. This will improve the consistency and accuracy of the simulation results.
6.2.2 Accelerating Numerical Simulation with High – Performance Computing
With the support of high – performance computing and parallel computing technologies, the numerical simulation speed of LPDC should be accelerated, the simulation calculation domain should be expanded, and rapid multi – scale simulations of large and complex thin – walled LPDC castings should be realized.
6.2.3 Combining Big Data and Machine Learning
To design new casting processes for LPDC castings with target mechanical properties, big data and machine learning methods should be combined with numerical simulation techniques. By mining laws from large – scale simulation data, the relationship between composition – process – organization – performance should be established, and the corresponding process for target performance castings should be obtained quickly to accelerate the development of the LPDC process.
7. Conclusion
Numerical simulation techniques have made significant contributions to the understanding and optimization of the LPDC process of aluminum alloys. Through macro and micro simulations, it is possible to predict the formation of casting defects, understand the evolution of the microstructure, and predict the mechanical properties of the castings. However, there are still challenges in terms of accuracy, computational efficiency, and multi – scale coupling. Future research should focus on addressing these challenges and further developing the numerical simulation techniques to improve the quality and performance of aluminum alloy castings produced by LPDC.