Modeling the Fluid-Flow-Induced Stress and Collapse in a Dendritic Network

An analytical approach to the stress development in the coherent dendritic network during solidification is proposed. Under the assumption that stresses are developed in the network as a result of the friction resisting shrinkage-induced interdendritic fluid flow, the model predicts the stresses in the solid. The calculations reflect the expected effects of postponed dendrite coherency, slower solidification conditions, and variations of eutectic volume fraction and shrinkage. Comparing the calculated stresses to the measured shear strength of 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.