Grain refinement induced by electromagnetic stirring: A dendrite fragmentation criterion

Abstract

The influence of electromagnetic stirring (EMS) on grain refinement has been studied for two copper-base alloys (Cu-1 wt pct Ni-1 wt pct Pb-0.2 wt pct P and Cu-4 wt pct Zn-4 wt pct Sn-4 wt pct Pb) solidified in a Bridgman furnace. Metallographic inspection of the specimens, temperature measurements during solidification, and numerical simulations performed with CALCOSOFT revealed that the efficiency of EMS is strongly dependent upon the penetration of the liquid in the mushy zone and therefore upon the position of the convection vortices with respect to the liquidus front. In particular, the low-concentration alloy could be grain refined only at high power and when the coil was moved close to the liquidus front. These results were analyzed on the basis of a dendrite fragmentation criterion similar to Flemings’ criterion for local remelting of the mushy zone. Considering that the component of the fluid flow velocity along the thermal gradient, $u_{l,G} = \frac{{u_e \cdot \nabla T}}{{\left\| {\nabla T} \right\|}}$, must be larger than the casting speed, V _c , dendrite fragmentation occurs if

$$C_R \approx \frac{1}{{V_c }}\frac{K}{{g_l \cdot \mu }}\frac{{B_0^2 }}{{\mu _0 d_{ind} }} > 1$$

at some depth within the mushy zone where dendrite arms are sufficiently developed, typically 8 λ ₂, where λ ₂ is the final secondary dendrite arm spacing, K is the permeability of the mushy zone, g _l is the volume fraction of liquid, μ is the dynamic viscosity, B ₀ is the magnetic field, μ ₀ is the permeability of vacuum, and d _ind is the distance between the inductor and the liquidus front.