Bridging Capillary-Driven Fragmentation and Grain Transport with Mixed Columnar-Equiaxed Solidification

Abstract

In this study, a first attempt is made to bridge capillary-driven fragmentation and grain transport using a mixed columnar-equiaxed solidification model. Grain transport is an intrinsic feature of the employed solidification model which has been extensively investigated over the years. Regarding the capillary-driven fragmentation event, a new correlation between the number of fragments and interfacial area density of the columnar structure was recently established by Cool and Voorhees (2017) based on experimental research under isothermal conditions. Here, we propose to modify Cool and Voorhees’ equation to extend its range of applicability to the solidification-dominant stage without destroying the agreement with the reported measurements in the coarsening-dominant stage. With this improvement in the mixed columnar-equiaxed solidification model, capillary effects can be isolated from the motion of the phases during fragmentation events, which facilitates understanding of the results. Under pure diffusive solidification conditions (no flow or crystal sedimentation), the simulation results were validated against phase-field simulations. In more realistic scenarios where liquid flow and fragment sedimentation are both considered, the simulations indicate very reasonable results for the detection of columnar-to-equiaxed transition, which suggests that the newly proposed model can be an important tool for industrial casting applications. Moreover, flow direction and intensity were shown to affect the potential for local fragmentation. Graphic Abstract

Modeling Dendrite Coarsening and Remelting during Directional Solidification of Al-06wt.%Cu Alloy

“…In contrast, for K = 1 × 10 −23 µm 3 s −1 , r = 0.3 and n = 0.83, Equation (11) (dashed black line) exhibits a better fit to Equation (10) when the time exceeds the critical time t* in all the analyzed cases, indicating improved accuracy during the final stage of coarsening. Indeed, H. Neumann-Heyme et al [14] reported that r = 0.4 was used for the simulations and r = 0.25 for the experiments. The coarsening exponent (n) and fitting parameter (r) differed significantly in the case with an initial arm radius of r = 7 µm, compared to other cases.…”

“…Ref. [14] reports a large uncertainty in the exponent (r) due to limited measurement ranges and focuses solely on solid fractions under 0.4. This suggests that (r) is mainly influenced by dendrite growth rather than coarsening.…”

“…C M.G. Rodrigues et al [14] simulated Bridging capillary-driven fragmentation and grain transport using a mixed columnar-equiaxed solidification model. However, the implementation of the interfacial area density was validated against the phase-field simulations of Neumann-Heyme et al [15].…”

Numerical study on the formation of spurious grains and freckles during the directional solidification of superalloys

“…The production rate of fragments via the capillary-driven mechanism ( capillary frag N ) was calculated based on equation (2) [15,16], in which a is an alloy-dependent constant, and SV is the interfacial area density. A general expression for SV was shown in equation (3) [17], which accounted for the effects of dendrite growth, coarsening, and interface coalescence.…”

“…The initial size of the formed fragments ( 0 e,frag 4) [18]. Since a spherical morphology was assumed for the equiaxed grains, the corresponding mass transfer rate ( capillary frag M ) from the columnar to the equiaxed due to the capillary-driven fragmentation can be calculated by equation ( 5) [16]. (2)…”