The prominent RDG model proposed by

The prominent RDG model proposed by Rappaz, Drezet and Gremaud [11] considers both uniaxial tensile deformation and shrinkage feeding. Unlike empirical formulas, the model has a physically sound basis. Columnar dendritic grains growing in one direction were considered, with tensile deformation acting normal to the growth direction and liquid feeding opposite to the growth direction. The differential control volume for mass balance analysis consisted of both dendrite arms and the liquid between them. A steady-state differential mass-balance equation involving both phases was applied, following the two-phase approach of Wang et al. [12]. The equation was integrated over the mushy zone to determine the velocity distribution of the liquid in the mushy zone. The velocity was then related to Darcy’s law and further integrated across the mushy zone. A void was assumed to form and give rise to a crack when the liquid pressure in the mushy zone fell below a certain cavitation pressure pc. The maximum deformation rate e_p;max sustainable by the mushy zone before a hot tear nucleates at the root of the dendrites was determined by the following equation: