An analytical model of grain growth considering the conjoint effects of precipitate pinning and solute drag in steel

An analytical model is developed to explain the kinetics of grain growth in steel that takes into account all feasible prime phenomena; namely, surface energy reduction, precipitate pinning effect and solute drag effect. The shapes of matrix grains and the precipitates are assumed to be tetrakeidecahedron and spherical, respectively. A single solute and a single type of precipitate are further assumed to be responsible for the solute drag and the precipitate pinning, respectively. An explanation of drag energy is provided in terms of Gibbs free energy change for solute segregation that eventually merges to the well-known Langmuir-McLean relationship. The developed model is validated in view of the existing database in available literature. A new methodology of grain growth analysis is accordingly proposed on the basis of the conceptualised 'effective migration coefficient' of the system.