A model has been developed which simulates inverse segregation and microporosity formation in directionally solidified alloys. Based upon a finite difference scheme, the model takes into account volume changes associated with density variations during solidification. The continuity equations for the mass, the solute, and the energy together with the Darcy equation describing the flow in the mushy zone are solved in a mixed Lagrangian-Eulerian representation. All nodal points within the liquid phase move with the fluid velocity, whereas nodes are fixed in space as soon as they are reached by dendrite tips. When the dendrite tips arrive at the end of the ingot, the remaining inter-dendritic liquid partially compensates for the solidification shrinkage occurring deeper within the volume. Since the size of the ingot remains fixed from that point on (absence of a purely liquid region), air (macroporosity) is introduced at the mesh points to satisfy the mass balance, starting from the top of the mushy zone. The formation of microporosity is also accounted for in the model through a calculation of local hydrogen segregation. Using this model, it is shown that inverse segregation decreases with increasing hydrogen content (or volume fraction of microporosity). The results of the simulation are compared with experimental results obtained on an Al-Cu alloy solidified under well-controlled directional conditions.
展开▼
