A mesoscale granular model for the mechanical behavior of alloys during solidification
We present a two-dimensional granular model for the mechanical behavior of an ensemble of globular grains, during solidification. The grain structure is produced by a Voronoi tessellation based on an array of predefined nuclei. We consider the fluid flow caused by grain movement and solidification shrinkage in the network of channels that is formed by the faces of the grains in the tessellation. We develop the governing equations for the flow rate and pressure drop across each channel when the grains are allowed to move, and we then assemble the equations into a global expression that conserves mass and force in the system. We show that the formulation is consistent with dissipative formulations of non-equilibrium thermodynamics. Several example problems are presented to illustrate the effect of tensile strains and the availability of liquid to feed the deforming microstructure. For solid fractions below gs=0.97, we find that the fluid is able to feed the deformation at low strain, even if external feeding is not permitted. For solid fractions above gs=0.97, clusters of grains with "dry" boundaries form, and fluid flow becomes highly localized.