How much can grain refining reduce the solidification-cracking susceptibility?

Grain refining can reduce effectively the susceptibility of alloys to cracking during solidification in welding, casting and additive manufacturing. The present study showed that the relationship between temperature T and the fraction of solid f_S of an alloy during solidification (which can be calculated easily from the alloy composition using commercial thermodynamic software and databases) can be used to estimate how the extent of grain refining affects the cracking susceptibility. It was shown that, when grain refining decreases the grain diameter by a factor of n, the ratio of the surface area to the volume of grains increases by a factor of n to allow more coalescence between grains to resist solidification cracking. For columnar grains, the grain diameter is proportional to (f_S)^1/2, and the cracking susceptibility index |dT/d(f_S)^1/2| decreases to (1/n) |dT/d(f_S)^1/2|. For equiaxed grains, the grain diameter is proportional to (f_S)^1/3, and the index |dT/d(f_S)^1/3| decreases to (1/n) |dT/d(f_S)^1/3|. The curve of T vs. (f_S)^1/2 or T vs. (f_S)^1/3 was calculated, and the maximum steepness |dT/d(f_S)^1/2| or |dT/d(f_S)^1/3| up to f_S = 0.98 was used as the index. Good agreement between the index and cracking-susceptibility tests in welding and casting was shown.