A granular model of equiaxed mushy zones: Formation of a coherent solid and localization of feeding

Abstract

The gradual transformation of a mushy zone during alloy solidification, from a continuous liquid film network to a fully coherent solid, has been simulated using a granular model. Based on a Voronoi tessellation of a random set of nucleation centers, solidification within each polyhedron is computed considering back-diffusion and coalescence. In the network of connected liquid films, a pressure drop calculation is performed assuming a Poiseuille flow in each channel, Kirchhoff's conservation of flow at nodal points and flow Losses compensating solidification shrinkage (KPL model). In addition to intergranular liquid pressure maps, the model shows the progressive formation of grains clusters, the localisation of the flow at very high solid fraction, and thus natural transitions of the mushy zone.

Measurement of Mechanical Coherency Temperature and Solid Volume Fraction in Al-Zn Alloys Using In Situ X-ray Diffraction During Casting

“…With the in situ XRD measurements, the lattice parameter is expected to exhibit such a behavior as long as individual grains or grain clusters grow without transmitting any macroscopic tensile strains. [26,27] At mechanical coherency, solid bridges are well established between grains and grain clusters and macroscopic strains and stresses start to develop possibly leading to the formation of micropores and hot tears, as reported in Figure 3.…”

Simulation of Semi-Solid Material Mechanical Behavior Using a Combined Discrete/Finite Element Method

“…As in the previous 2D solidification model, [15][16][17][18] the master diffusion equation controlling the evolution of the solid-liquid interface in a tetrahedron can be derived from a solute balance integrated over the solid and liquid phases. This equation is given as follows [31] :…”

“…These pyramids are divided further into tetrahedral elements to model solidification by subdividing each Voronoi facet into triangles (Figure 1(d)). As in the previous model designed for 2D geometries, [15][16][17][18] the solute exchange between [31] tetrahedral pyramids is neglected to reduce the microsegregation model to a 1D problem in spherical coordinates. Complete, or infinite, diffusion is assumed in the liquid, with some back-diffusion assumed in the solid.…”

“…Generation of this geometry requires a methodology for simulating the solidification of numerous grains. Previous work by the authors [15][16][17][18][19]33] has resulted in the development of a 3D granular solidification model known as GMS-3D, [31] which is able to generate the required solid-liquid two-phase geometry at a fixed g s . In this model, the grain structure is derived from a Voronoi tessellation of random nucleation centers.…”

“…[15] The model is therefore ideally suited for granular simulations linking the behavior of a microscopic model to macroscopic properties of the material. Verne`de et al [17,18] have used this 2D granular approach to simulate the fluid flow caused by grain movement and solidification shrinkage in an Al-Cu alloy. Phillion et al, [19,20] using a similar approach based on 2D granular geometry, predicted the mechanical behavior of an equiaxed granular semisolid Al-Mg alloy.…”