Development of Stress in a Dendritic Network Due to Shrinkage Induced Flow

"A mathematical model that calculates the stress development in a coherent and stationary dendritic network due to interdendritic flow is proposed. The fluid flow is assumed to be related to the solidification shrinkage, and under the assumption of no porosity formation and unidirectional solidification, the shrinkage-induced flow within the mushy zone is calculated analytically. The interdendritic melt flow exerts a force on the solid network and an analytical expression for the stress build-up in the network is developed. Parameter studies illustrating the influence of cooling conditions, mushy zone length, dendrite coherency, fraction solid, volume fraction of eutectic, and solidification shrinkage upon the stress development within the solid network are presented. Comparing the magnitude of the calculated stresses to measurements of the strength in equiaxed mushy zones shows that it is possible for the stresses to exceed the strength, thereby resulting in reorientation or collapse of the dendritic network.IntroductionInterdendritic fluid flow is at present regarded as a very important mechanism for feeding of shrinkage during solidification of metal alloys. Solidification of many alloys is often characterised by heterogeneous nucleation of the primary phase on substrates in the melt with subsequent evolution of equiaxed dendrites. These equiaxed dendrites can initially grow freely, but impinge on each other and form a continuous dendritic network, ie. dendrite coherency, quite early in the solidification process. Measurements of the dendrite coherency point have shown that the dendritic network is established at solid fractions ranging between 0.1 and 0.5, and most often around about 0.2 [l]. Depending on the alloy composition this means that as much as 70 to 80% of the volumetric shrinkage has to be compensated by flow of liquid through the interdendritic network. Interdendritic flow occurs with a much larger resistance compared to free flow of the liquid and flow of a liquid with dispersed crystals. The pressure drop associated with the interdendritic flow increases rapidly with decreasing fraction ofliquid."