Micro-Macro Coupling in Casting Simulations

"Casting processes involve phenomena that occur on widely disparate length-scales. Simulation of macroscopic effects, such as heat transfer and convection, are generally addressed by solving the appropriate equations in discretized form on a finite-element mesh. Microscopic phenomena are described by micromodels that may be empirical or analytical in form. Coupling of phenomena in these two regimes is a critical issue in predicting microstructure and defect formation resulting from macroscopic process conditions. A formalism has been developed for expressing micromodels in a consistent manner using stereological parameters to quantify the geometric characteristics of the developing microstructure. This approach provides a robust and physically consistent method for coupling local micromodels with the macroscopic fields. The macroscopic state variables at each node serve as global constraints on the micromodels that are applied to a local unit volume. An outline of an equiaxed solidification model based on this approach is presented, along with preliminary simulation results. Coupling of convection and enthalpy effects between the micro and macro regimes is also discussed. IntroductionThe primary goal of casting simulations is to improve the reliability of cast parts while minimizing cost and development time. Effective simulations can speed up the mold design process and reduce the likelihood of defective parts by refining a particular casting process on a computer, reducing the dependence on cost- and time-intensive prototype castings. The challenge in developing effective simulations stems from the need to address physical processes that occur over a wide range of length-scales, from microscopic (atomic) and mesoscopic (microstructural) scales to macroscopic distances comparable to the size of the casting itself. Overviews of the various thermophysical phenomena and computational factors that are important in solidification modeling are provided in the literature by Rappaz [1] and Tseng et al. [2].Macroscopically, the solidification process is largely governed by the rate of heat flow from the alloy through the mold wall. Another important effect that occurs on the scale of the casting size is convective flow of the melt, which is driven by density-variations in the melt. Macroscopic calculations employ finite-element or finite-difference methods to solve the sets of equations that govern these effects, and the spatial resolution is determined by the grid spacings used for the calculations. Typical spatial resolutions are on the order of 10-2 to 10-3"" meters. This represents a compromise between the resolution required to simulate the continuum transport processes accurately, and the computational time required to model the entire solidification and cooling process."