A new model of microsegregation for macrosegregation computation in multicomponent steels. Part I: theoretical formulation and algorithm

The goal of this paper is to present a new microsegregation model for multicomponent steels designed to be coupled with a macrosegregation code, which takes into account the thermodynamic equilibriums between phases and the peritectic transformation. Among the great diversity of microsegregation models available in literature, very few can fulfil all these requirements. If it is the case, some simplifying assumptions must be adopted to increase the time efficiency of the microsegregation model but this often results in the restriction of its validity. In the model presented in this paper, a numerical approach is used to solve the diffusion equation in each phase, which implies the definition of a microsegregation mesh, whose number of nodes must be limited to have realistic calculation time by the resulting micro–macro code. To keep the number of nodes low and ensure mass conservation during calculation, an original algorithm is presented in this paper to ensure the stability of the solution, which is not a trivial problem because of the sharp solute gradients at the δ / γ interface during the peritectic transformation.