Theoretical Study of Alpha Case Formation during Titanium Casting

Scale analyses indicate that three distinct contaminant mass-transfer processes, occurring on distinct time scales, underlie formation of the alpha case on small titanium castings. High rates of mold-to-liquid metal mass transfer occur during an extremely short induction period, the length of which is determined by the time required for heterogeneously nucleated solidification fronts to cover mold surface asperities. Following the induction period, but prior to complete cast solidification, mold contaminants diffuse through a rapidly growing solidification layer, where the solid-phase mass-diffusion boundary layer grows at a rate approximately an order of magnitude slower than the solidification front. Finally, following complete solidification and until the part is removed from the mold, contaminant mass transfer continues via solid diffusion. Based on the scale analyses, an analytical model that incorporates an empirical relation between titanium solid phase oxygen concentration and titanium microhardness is developed and compared against representative experimental near-surface microhardness measurements.