# The Solidification Modulus Explained

by Rene Romeike

Designing a feeding system using physical solidification simulation can be very time-consuming. On the other hand, every foundryman is familiar with the use of what is known as the solidification modulus. But what exactly does it stand for and how does it work?

The solidification modulus is an important parameter for the design of feeding systems. Its significance has been recognized in the worldwide foundry industry for decades. Expressed in geometric terms, it is quite simply the ratio of the casting volume to the cooling-effective portion of its surface.

However, this representation is only useful when considering bodies that are sufficiently easy to calculate, such as a pyramid, a cuboid or a cylinder. Typical castings must therefore first be broken down into simpler partial volumes in order to analyze the modulus. Figure 2 - Decomposition of a casting model into simpler bodies that allow geometric calculation of the solidification modulus.

But the solidification modulus is not just a geometric property. As early as 1940, the Czech foundry engineer Nicolas Chvorinov established a direct connection to the solidification time. He proposed that the solidification time is proportional to the square of the modulus with a process-dependent factor called "mold constant". Figure 3 - Chvorinov's original publication, which first established the modulus as a means of assessing solidification time.

This relationship allows the definition of a point-local modulus value and at the same time provides a method for its numerical computation. In contrast to the geometric approach, the local solidification time is now calculated by means of a physical simulation and the modulus is thereby inferred. Figure 4 - Comparison of the geometric modulus and the thermal modulus for the same part.

To avoid isolated solidifying areas, the local solidification time must increase continuously from each end zone to its feeder. A positive gradient in the solidification time implies a positive temperature gradient along the feeding path, thus enabling safe liquid and mass feeding. Due to the proportionality described by Chvorinov's rule, this effect of directed solidification can already be observed in the modulus field. The benefit of this analysis is that the gating and feeding system can now be designed accurately on the basis of the calculated values. Subsequent optimization is no longer necessary.