An Axisymmetric Analytical Model for Cracking During Solidification and Its Comparison with the RDG Model

An analytical model was developed to calculate the susceptibility of an alloy to cracking during solidification. Instead of treating the mushy zone as a porous medium like in the prominent analytical model developed by RDG, the present model considered the shape of columnar dendrites in the mushy zone. The columnar dendrites were assumed to be axisymmetric, and the shape of their outer contours was calculated based on the curve of T vs (f_S)^1/2 of the alloy, where T is temperature and f_S the solid fraction. The columnar dendrites were assumed to grow at the steady state in their axial direction, and the liquid between the dendrites was assumed to flow annularly in the opposite direction to compensate for solidification shrinkage and transverse tension. The model, checked by CFD modeling, was compared with both the RDG model and the simple index |dT/d(f_S)^1/2| for the susceptibility to cracking during solidification.