Thermodynamic Calculation of Grain Boundary Composition in Ferritic Steels and Its Application for Controlling the Hall–Petch Coefficient

The Hall–Petch coefficient, which is the slope of the Hall–Petch relationship, was investigated as a means of increasing the yield strength of ferritic steels through highly efficient grain refinement strengthening. Because the Hall–Petch coefficient increases with the grain boundary segregation of solute elements such as carbon, the equilibrium grain boundary segregation behavior was theoretically calculated using the Hillert–Ohtani model, and the para-equilibrium grain boundary segregation, in which only carbon undergoes equilibrium segregation without diffusion of substitutional solute elements, was also discussed. The calculated results were correlated with the experimentally obtained Hall–Petch coefficients. To control the grain boundary segregation behavior, the solubility of carbon in ferrite was changed by altering the solution-treatment temperature, and the co-segregation of carbon steel with the addition of a third element, Mn or Si, was investigated in this study. As a result, good correspondence between the theoretically calculated values of grain boundary segregation and the experimental values of the Hall–Petch coefficient was confirmed for Fe–C and Fe–Mn–C alloys.