A new mathematical model for investigating solidification, solute transportation, and TiN precipitation in a micro-alloy steel containing Ti

In order to investigate the segregation process and clarify its effect on the formation of TiN during the solidification of a micro-alloy steel containing titanium (Ti), a new mathematical model concerning solute transportation, solidification, as well as TiN precipitation was successfully established and verified. The transportation of solute elements was described using the Brody-Fleming microsegregation model, while the thermodynamic principles governing the precipitation of TiN were derived within the framework of the model. Additionally, the model accounts for variations in the diffusion coefficient due to phase transition and the influence of non-equilibrium solidification on solute distribution. High-temperature tests were conducted to validate the mathematical model. Results show that during solidification, due to selective crystallization, there is positive segregation of Ti and N in the solidifying front. What’s more, due to the high cooling rate near the surface of this steel, negative segregation is easier to be formed in the surface area. The highest concentration of TiN precipitation is found in the 1/4 width of this steel. High-temperature experiment shows that when the solidifying front reaches the 1/4 width of the specimen, the concentration product of Ti and N elements biased at the solidifying front reaches the thermodynamic conditions of TiN precipitation, and exists a higher concentration of TiN distributed in this region. To address this phenomenon, a comparative analysis of the effects of cooling rate and initial solute element content on TiN precipitation behavior was conducted. An increase in the surface cooling rate accelerates the progression of the solidification front and diminishes solute segregation near the front, thereby reducing TiN precipitation. However, with the increase of the initial solute element content, the concentration product of Ti and N elements rises, then the content of TiN precipitation increases. The results of this model provide important insight into the micro segregation and TiN precipitation mechanism of the micro-alloy steels bearing titanium.