Pressure casting is the process of filling liquid or semi liquid metal into a mold cavity at a high speed under high pressure, causing it to solidify and form under pressure. Magnesium alloys have excellent die-casting performance, and magnesium alloy products made by die-casting often have high dimensional accuracy. However, due to the rapid filling and solidification of molten metal under high speed and pressure during the die-casting process, defects such as shrinkage, porosity, and porosity are inevitably generated inside the casting, resulting in low mechanical properties and inability to meet the requirements of high stress. Therefore, in the product design stage, using numerical simulation to predict casting defects has practical significance in improving product quality and reducing resource waste.
In the past 30 years, with the rapid development of computers, numerical simulation has been increasingly valued by people. MONAGHAN J J made the first attempt to use SPH to solve free surface flow problems. Researchers applied the Smoothed Particle Hydrodynamics (SPH) method to simulate die-casting of complex thin-walled parts, demonstrating that the SPH method can better capture the flow state of molten metal under high-speed motion during the die-casting filling process. In response to the problem of shrinkage and porosity in the solidification process of guide vane castings, numerical simulation analysis of the temperature field during the solidification process of guide vane castings was carried out using MAGMA software. The locations where shrinkage and porosity defects are prone to occur were predicted. By establishing the temperature field required for sequential solidification, a reasonable casting process was obtained. A SPH method prediction model was established to address the issue of shrinkage defects during casting solidification. The particles that meet the conditions for forming shrinkage were converted into virtual particles, and the virtual particle model no longer participated in heat transfer calculations. A SPH method shrinkage defect model was established and the calculated results were compared with experiments. A cold insulation defect prediction model was established based on the SPH method, and numerical simulation calculations were carried out, which were compared with experimental results. A new FDM/FEM model was established to simulate the temperature field during the solidification process of squeeze casting, and the FDM/FEM model was validated using squeeze casting experiments. The numerical simulation results were consistent with the experimental results. The extrusion casting process of a gearbox was simulated using finite element software, and the shrinkage and porosity defects were predicted to determine the process parameters with the lowest shrinkage rate. However, there are few reports on the application of SPH method for predicting shrinkage defects.
This study will conduct numerical simulation calculations on the AM60B magnesium alloy bracket produced by a certain factory, and use a coupling method of smooth particle hydrodynamics (SPH) and finite element method (FEM) to predict the shrinkage defects of the bracket. Due to the characteristics of easy model establishment and programming, good adaptability, and ease of handling complex geometric shapes in numerical simulations, the SPH method is adopted to simulate the flow field, temperature field, and solidification field of the die-casting process. The Niyama criterion is added to the SPH program to predict the shrinkage porosity of castings after solidification, and the prediction results are compared and verified with ProCAST software to prove the accuracy of predicting shrinkage porosity results under the SPH method. The FEM method is commonly used for stress-strain analysis in pressure casting processes, with high calculation accuracy and fast speed. Therefore, the FEM method is adopted to calculate the stress field of castings and provide a basis for predicting the occurrence of shrinkage and porosity, aiming to provide reference for the production of related parts.
The bracket casting belongs to a moderately complex structural component, mainly used for support and connection. Its three-dimensional solid model and basic pouring system are shown in Figure 1. The contour dimensions of the casting are 108 mm × 206 mm × 586 mm, and the material is AM60B magnesium alloy, with its composition shown in Table 1. The casting material is H13 steel, with its composition shown in Table 2. The thermal properties parameters of castings and molds are shown in Table 3.
The total number of particles in the SPH program for castings and molds is 2161788, including 2000916 boundary virtual particles and 160872 solid metal particles. To improve computational efficiency, in the FEM program, the total number of grid divisions is 410834 and the number of nodes is 426904. In ProCAST software, the mold grid size is 10 mm with 581212 grids, and the casting grid size is 2 mm with 188192 grids.
The process parameters for the bracket are set using the process parameters provided by a certain factory, as shown in Table 4. For the setting of interface heat transfer conditions, since both the casting and the mold are made of metal materials and have a consistent interface, the heat transfer coefficient is selected as 2000 W/(m2 · K); For the part of the mold in direct contact with air, the heat transfer coefficient is 41.86 W/(m2 · K). Set the gravity acceleration to 9.8 m/s2, the gravity direction to the negative z-axis direction, and the punch injection direction to the positive x-axis direction.
Simulate the pressure casting filling process of support parts using SPH method. The punch in the pressure chamber moves along the positive x-axis direction to fill the mold cavity with molten metal in the runner. The time required for the completion of casting filling is 0.0307 seconds. Figure 2 shows the filling state of the support at different time points during the filling process. The left side of the figure shows the SPH simulation results, and the right side shows the ProCAST software simulation results. It can be seen that the simulation results of SPH filling process are basically consistent with those of ProCAST simulation. Therefore, by comparing the simulation results of the SPH filling process with those of ProCAST, it was found that the simulation results of the flow field and temperature field during the SPH filling process were basically consistent with them, indicating that the SPH method can simulate the flow state of liquid metal in the mold cavity very well.
Shrinkage is the formation of small and dispersed pores in the final solidification zone of a casting without the replenishment of molten metal, and the dispersed area of shrinkage is larger than that of shrinkage pores, often existing inside the casting. Figure 3 shows the simulation results of the ZY and XY sections of the bracket using the SPH program. In order to display the real particles with shrinkage more clearly in the SPH program, a judgment statement was added to the program. That is, when the Niyama criterion value of the real particles is ≥ 0.5 ℃ 0.5 ∙ s0.5/mm, the criterion value is uniformly set to 0.5 ℃ 0.5 ∙ s0.5/mm. Figure 4 shows the ZY profile along the centerline of the simulation calculation results using ProCAST software. Comparing Figure 3 and Figure 4, it can be seen that the predicted occurrence of shrinkage porosity in key positions is almost identical, both occurring in the thicker center of the bracket and some edges adjacent to thinner molds. This shows the accuracy of SPH combined with Niyama criterion in predicting shrinkage porosity results.
In order to achieve the coupling of the filling process model established by the SPH method and the solidification process model established by the FEM method, a region search method was adopted, which takes the FEM node as the center, constructs a spherical space with the finite element element mesh length as the radius, and searches for SPH particles in the spherical space. Then, by weighting the distance coefficient between SPH particles and FEM nodes, the initial temperature information of the finite element nodes is obtained, and the temperature field results are transmitted from SPH particles to FEM mesh, ensuring the integrity and accuracy of data transmission. Finally, the finite element method is used to simulate the stress field variation process during pressure casting solidification. Figure 5 shows the temperature field results corresponding to the completion of the filling process based on the SPH method and the initial temperature field results of the solidification process simulation based on the FEM method. It can be seen that the use of region search method can effectively transfer the temperature field results of SPH filling simulation to the initial temperature field of FEM solidification process, and the results also indicate that the temperature load transfer basically meets the calculation requirements.
Figure 6 shows the ZY and XY cross-sectional views of the stress field simulated by the FEM program for the support. By comparing the circles in Figure 6 with Figure 3, it can be seen that the stress at the location where the bracket undergoes shrinkage is relatively small. This is because under pressure casting, the metal liquid fills the mold quickly, the holding time is short, and the casting does not solidify sufficiently under the action of force. The solidification shrinkage in a certain part of the casting will cause the metal liquid in the uncured part to flow towards this part for supplementary shrinkage. If the resistance encountered during the supplementary shrinkage process is quite large, that is, the process pressure loss is considerable, and the supplementary shrinkage channel is not smooth enough, and the pressure applied to the metal liquid is not enough to withstand this pressure loss and flow to the part that needs to be supplemented, then the solidified part cannot be supplemented, ultimately resulting in shrinkage defects.
main conclusion
(1) The SPH-FEM coupling method is applied to simulate the pressure casting process of support parts. The SPH method is used to simulate the filling process and temperature field, and the FEM method is combined to calculate the stress field during the solidification process. Due to the solidification of the bracket under the action of force, it will affect the temperature of the bracket. Therefore, it provides support for the subsequent SPH calculation of the temperature field during the solidification process, in order to more accurately predict shrinkage defects. And compared with ProCAST software, it shows that the SPH-FEM coupled method program calculates accurately and runs reliably.
(2) The Niyama criterion was added to the SPH program for predicting stent shrinkage defects, and compared and analyzed with the simulation results of ProCAST software. The simulation results showed that the two were basically consistent. At the same time, by combining the self-developed FEM program for stress field calculation during the solidification process, it was found that the shrinkage and looseness of the support were distributed in the thicker central part and some edges near the thinner mold. Perhaps due to the relatively low stress in these areas, the resistance during the process of replenishing the molten metal is high and cannot be fully replenished.
[Article source]
Volume 45, Issue 4, 2025: "Prediction of Shrinkage Defects in Pressure Casting Based on SPH-FEM Coupling Method"
Wang Tiancheng 1 Ge Taotao 1 Jia Jinbo 1 Niu Xiaofeng 1 Hou Hua 2, 3 Zhao Yuhong 2
