Starting at the beginning of the 1980s, the research and development activities around the topic of casting process simulation increased substantially in multiple locations. In addition to the activities at the Technical University of Den- mark around Hansen (Fig. 3), work groups were established world-wide, including J. T. Berry and R. D. Pelke in the United States, E. Niyama in Japan, W. Kurz in Luasanne, F. Durand in Grenoble and most notably, Prof. P.R. Sahm in Aachen at the Foundry Institute (Fig. 4). Important mile- stones were the introduction of the term, “criteria function” by Hansen and Berry (1980), the introduction of a criteria function to depict centerline porosities by Niyama (1982), as well as the proposal of a criteria function to detect hot tears in steel castings by E. Flender and P.N. Hansen (1984). By the end of the 1980s, the first solutions to simulate the mold filling were provided.
In the 1990s, development activities focused on the simula- tion of stresses and distortions in castings (Hattel and Han- sen, 1990), as well as the first steps were taken to predict microstructures and mechanical properties by I. Svensson and M. Wessèn in Sweden.
The Methods
Numerical simulation is the process of solving a physical model through mathema tical (differential) equations and the display of the calculated domain (the casting and the mold) through discrete single elements. In order to calculate the differential equations, several methods were developed (FEM, FDM, FVM, BM, MM, etc.), which will not be dis- cussed in detail here.
In 1924, E. Schmidt developed a graphical method to solve 1-D heat conduction problems. In 1949 and 1959, important contributions regarding the analytical solution of heat transfer problems were provided by L.R. Ingersol, O.J. Zo bel and A.C. Ingersoll, as well as by H.S. Carslaw and J.C. Jaeger. The finite element method (FEM) was developed in 1945, to solve special load calculations. In 1956, the first structural simulations were conducted on airplane wings at Bo eing. In 1967, the reference book, “The Finite Element Method”, was published by O.C. Zienkiewicz. Hansen performed 2-D- and 3-D solidifica- tion calculations for the first time in 1975 utilizing the finite volume method (FVM).
Each method has specific benefits and drawbacks and can yield good qualitative results depending on its area of ap- plication. The finite element methods have their roots in load simulations. The finite difference and finite volume methods come from the fluid flow simulation and show benefits in the description of heat and material transport phenomena.
The method to be selected has to be seen as independent from the subdivision of the calculation domain (i.e. the
International Journal of Metalcasting/Spring 10
The first steps of describing the process in virtual terms were taken by focusing on heat transfer calculations and focused on the solidification process. As a result, the entire field of casting process simulation is often called solidi- fication simulation. However, the whole process is called “casting” - not “solidification”. The mold filling is an inte- gral part of the process and therefore must be considered. This is not only important for the gating layout but for the detection of filling related defects as well. Indeed, the in- homogeneous temperature distribution in the melt caused by the filling process has in many cases an impact on the solidification process (Fig. 5).
Even today, the dynamics of the mold filling process are of- ten underestimated by practitioners. Key words like “quiet filling” and “laminar flow” are frequently used, but from a physical point of view, all filling processes from sand cast- ings to high pressure die castings are highly turbulent. This fact is based on the rheological properties of metal melts. The energy that is created by the flowing melt is so high that it cannot be eliminated through foundry technological efforts. Therefore, strong turbulences and eddy currents are found inside the melt even when the melt surface appears to be ris- ing quietly (Fig. 6). Many casting defects result from these under-surface movements, as well as reactions between melt and mold material. These defects include mold defects, air entrapments, oxidation defects, slag entrainments or metal- lurgical challenges.
The fundamentals of the flow simulation provide quantitative information of velocities, pressures and temperatures. These are the tools the casting expert uses to develop robust gating systems. The question of pressurized or non-pressurized gat- ing systems can be answered quantitatively. Critical velocities
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casting and the mold). FEM, as well as Finite Difference Method (FDM) or FVM can all utilize both unstructu red (tetrahedrons, pentahedrons or hexahedrons) and struc- tured meshes (regular he xahedrons). As with the meth- ods, all meshes have specific benefits and drawbacks. For example, while linear tetrahedrons experience numerical problems, they approximate the geometry very accurately. Hexahedrons, however, have superior calculation quality, but the transition between the casting and the mold has to be fitted using specific algorithms. Therefore mixed ap- proaches, depending on application and physics, are cur- rently used (i.e. tetrahedrons with additional gap nodes or regular hexahedrons with boundary adjustments).
Eventually the choice of which numerical method and mesh is used is driven by finding the best compromise be- tween the quality (accuracy) of the calculation, optional automatic enmeshment and calculation time. There is no ideal route, for simulation: there is only the best adjusted solution to the specific requirements of the casting pro- cess and the foundry.
The Basis of Simulation—Filling and Solidification
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