A Two-Dimensional Phase-Field Investigation on Unidirectionally Solidified Tip-Splitting Microstructures

Abstract

The onset of morphological instabilities along a solidifying interface has a tendency to influence the microstructural characteristics of cast alloys. In the present study, the initiation as well as the mechanism of microstructural pattern formation is investigated by a quantitative phase-field approach. For energetically isotropic interfaces, we show that the presence of grain boundary grooves promotes the initiation of morphological instabilities, and with progressive solidification, they subsequently amplify into tip-splitting microstructures. We also demonstrate that the grain boundary groove shape influences the amplification of the ridge-shaped instability near the pit region. The structural transition of tip splitting to dendritic microstructures is showcased through the effect of interfacial anisotropy. In addition, the prediction of the tip-splitting position is discussed through an analytical criterion, wherein the sign of the surface Laplacian of interfacial curvature dictates the formation of crest and trough positions in a tip-splitting pattern. In complete agreement with the sharp-interface theory, our phase-field simulations validate the analytically obtained tip-splitting position and suggest that the two tips evolve symmetrically on either side of the hindered concave region. Furthermore, the role of lattice anisotropy on the tip-splitting phenomenon is also discussed in detail.

Numerical Simulation of Solidification Processes

“…Three of the papers were focused on phase-field modeling of dendritic microstructure evolution and presented studies on permeability measurements of 3D microstructures generated by phase-field simulation of the solidification of an Al-Si alloy during chill casting [3]; a phase-field study on the interaction between grains during columnar-toequiaxed transition in laser welding [4]; and a two-dimensional phase-field investigation of unidirectionally solidified tip-splitting microstructures [5].…”