A granular model of solidification as applied to hot tearing

Hot cracking is a spontaneous failure of an alloy during solidification. It is a severe problem for casting industry as it reduces the productivity of cast houses and limits the range of alloys compositions that can be industrially produced. Hot tears occurs at the end of solidification, when solid grains are separated by thin liquid films. At this stage of solidification, fluid flow between the grains is difficult and the solid network is not continuous enough to transmit stresses. The material is extremely brittle. Moreover, the deformation induced by the thermal shrinkage of the material tends to localize in hot spots, i.e., in zones which solidify at last. These zones become in tension and the concomitant effect of the tensile stress with the intrinsic brittleness of the material result in a hot crack. Even though the general mechanisms of hot tearing are understood, the importance of each physical parameter remains ill defined. The present work is mainly focused on the derivation of a granular model of mushy zone (the zone where solid and liquid coexist) for aluminium alloys, i.e., a model which explicitly considers the behaviour of each grain while being sufficiently simple to allow the computation of large mushy zones. First, a solidification model based on the Voronoi diagram of a random set of nuclei is derived. This model computes the solidification in each polyhedron considering back-diffusion and coalescence. Second, a pressure drop calculation is performed in the network of connected liquid channels assuming the centre of solid grains to be fixed. This model considers a Poiseuille flow in each channel, Kirchhoff's conservation of flow at nodal points and flow Losses compensating solidification (KPL model). Finally, the displacement of the solid grain centres is considered and the mechanical behaviour of the mushy zone is computed assuming perfectly rigid solid grains. This model shows the progressive formation of grain clusters and the localization of fluid flow at high solid fraction. Therefore, it allows to define transitions in the behaviour of the mushy zone. These transitions are essential for hot cracking models, but should be introduced as parameters in continuum approaches. Finally, the mechanical model shows a strong localization of deformation in liquid channels normal to the stress direction. Such channels create ideal sites for the nucleation and the propagation of hot cracks.