PurposeIn this work, with a goal to ultimately forward the advancement of additive manufacturing research, the author applies the Wheeler-Boettinger-McFadden model through a progressive series of increasingly complex solidification problems illustrating the evolution of both dendritic as well as columnar growth morphologies. For purposes of convenience, the author assumes idyllic solutions (i.e. the excess energies associated with mixing solid and liquid phases can be neglected).Design/methodology/approachIn this work, the author applied the phase-field model through a progressive series of increasingly complex solidification problems, illustrating the evolution of both dendritic as well as columnar growth morphologies. Beginning with a non-isothermal treatment of pure Ni, the author further examined the isothermal and directional solidification of Cu–Ni binary alloys.Findings(1) Consistent with previous simulation results, solidification simulations from each of the three cases revealed the presence of parabolic, dendrite tips evolving along directions of maximum interface energy. (2) For pure Ni simulations, changes in the anisotropy and noise magnitudes resulted in an increase of secondary dendritic branches and changes in the direction of propagation. The overall shape of the primary structure tended also to elongate with increased anisotropy. (3) For simulations of isothermal solidification of Ni–Cu binary alloys, the development of primary and secondary dendrite arm formation followed similar patterns associated with a pure substance. Calculations of dendrite tip velocity tended to increase monotonically with increasing anisotropy in accordance with previous research. (4) Simulations of directional solidification of Ni–Cu binary alloys with a linear temperature profile demonstrated the presence of cellular dendrites with relatively weak side-branching. The occurrence of solute trapping was also apparent between the primary dendrite columns. Dendrite tip velocities increased with increasing cooling rate.Originality/valueThis research, particularly the section devoted to directional solidification of binary alloys, describes a novel numerical framework and platform for the parametric analysis of various microstructural related quantities, including the effects due to changes in temperature gradient and cooling rate. Both the evolution of the phase and concentration are resolved.
Interfacial instabilities in directional solidification of dilute binary alloys: The Kuramoto-Sivashinsky equation
