Constrained crystal growth during solidification of particles and splats in uniform droplet sprays

Uniform Droplet Spraying of Magnesium Alloys: Modeling of Apollonian Fractal Structures on Micrograph Sections

“…V/v = 1 2 πAB. The solidified 3D structure of these materials consists of densely packed dendrite crystals intertwined with globular grains in a hybrid fractal topology.…”

“…The boundary conditions, including convection in a cooling fluid, radiation to ambient space, and conduction to a solid substrate, are also assumed to be known. If quasi-stationary solidification prevails inside the material, with an insignificant internal melt flow field and convective transport to the solid phase, the heat transfer is dominated by Laplace linear conduction [1,4]:…”

“…For example, level-set methods [24] have been implemented to determine the coupled thermo-fluid fields in UDS droplets impinging and solidifying on a flat cooling substrate. For such simple UDS droplet conditions and for real-time computational efficiency, semi-analytical techniques have also been successfully employed [1], based on the linear time-varying superposition of Green's functions. Similarly, in the deposition of UDS droplets over a translating flat substrate into a bead deposit of the semi-elliptical cross section, the temperature field was determined semi-analytically by the superposition of traveling Green's (or Rosenthal) functions G [4]:…”

“…A variety of advanced manufacturing processes have been developed based on the concept of rapid solidification processing (RSP), where the fast liquid-to-solid phase transformation (melt quenching) is utilized for the fabrication of parts with a unique microstructure and properties, as compared to the counterparts fabricated by conventional casting methods. Particularly, RSP-based metal additive manufacturing (AM) techniques, such as uniform droplet spraying (UDS) [1][2][3][4], laser powder bed fusion [5][6][7], and direct energy deposition [8][9][10], have attracted significant attention in recent years due to their exceptional design flexibility and rapid prototyping capability. The microstructure and properties of AM-fabricated metallic parts are closely connected to the equilibrium thermodynamics of solidification and/or non-equilibrium kinetics in RSP [11,12].…”

“…However, such growth is topologically confined by the expansion of adjacent grains, yielding densely packed domain morphologies. A framework for such constrained grain growth has recently been developed, with the eventual confined grain size connected with differential attributes of the dynamic temperature field during RSP [1,4]. Thus, arm fragmentation and nucleation-initiated constrained growth complements Brownian networks of branching dendrites with Apollonian packs of globular grains in a space-filing, hybrid fractal material structure [20,21].…”