Modeling of the Solidification Process—Historical Survey

Abstract

The modeling of solidification processes is a broad field covering many different types of activities. On one level, technical aspects of casting processes are investigated by computer simulations. The modeling is then a tool for the designer and the calculations may even be integrated with a CAD/CAM system. A more fundamental level may consider how the microstructure develops during solidification and how it can be controlled. This article gives a brief historical survey of the modeling of solidification processes.A well-known rule of thumb, often given in textbooks, states that the solidification time for a simple casting is proportional to its squared volume-to-area ratio. This rule is named after Chovrinov, who verified it experimentally in 1940. The mathematical treatment of solidification, however, has a much older tradition started more than 100 year s earlier in 1831 when Lamé and Clapeyron analyzed the growth of a solid crust generated by cooling a liquid. Their analysis showed that the thickness of the solid is proportional to the square root of time, which is also the essence of Chovrinov's rule. Their basic idea was that the solidification rate was controlled by the removal of latent heat. That idea may seem quite obvious to us, but a necessary pre-equisite for it is the concept of heat as quantifiable and transportable. Actually, Fourier had made his mathematical analysis of heat propagation only 20 years earlier and had won the prize of the French Academy of Sciences in 1811 for his contribution.