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

A variety of advanced manufacturing processes have been developed based on the concept of rapid solidification processing (RSP), such as uniform droplet spraying (UDS) for the additive manufacturing of metals and alloys. This article introduces a morphological simulation of fractal dendric structures deposited by UDS of magnesium (Mg) alloys on two-dimensional (2D) planar sections. The fractal structure evolution is modeled as Apollonian packs of generalized ellipsoidal domains growing out of nuclei and dendrite arm fragments. The model employs descriptions of the dynamic thermal field based on superposed Green’s/Rosenthal functions with source images for initial/boundary effects, along with alloy phase diagrams and the classical solidification theory for nucleation and fragmentation rates. The initiation of grains is followed by their free and constrained growth by adjacent domains, represented via potential fields of level-set methods, for the effective mapping of the solidified topology and its metrics (grain size and fractal dimension of densely packed domains). The model is validated by comparing modeling results against micrographs of three UDS-deposited Mg–Zn–Y alloys. The further evolution of this real-time computational model and its application as a process observer for feedback control in 3D printing, as well as for off-line material design and optimization, is discussed.