Evaluation of Concentration Dependent Diffusivities of Manganese in the Diffusion Joint Fe/FeMn-Steel by Means of Mathematical-Analytical Methods

摘要

When developing new types of materials with special properties for the automotive industry, steels with high content of manganese (up to 25 wt.% Mn) were studied. These steels embody increased failure resistance, high level of deformation hardening, plastic response and high value of energy absorption in crash situations [1,2]. The aim of our work was to study an interaction of a FeMn alloy with pure iron from the view of diffusion processes. For that purpose, diffusion joints Fe/FeMn-steel were created and long-term heated at the temperatures of 800, 900 and 1050°C. Dependences of diffusivities of Mn on its concentration were calculated from concentration profiles of manganese after diffusion heating applying three analytical methods. In the first method, constant values of diffusivities D_i, i= 1,2 for both Fe and steel were taken into account. In the second case a modified Matano-Boltzmann method utilizing polynomials was applied, which simplifies solution in numerous cases. The third method performs the solution of the non-linear equation of diffusion on the assumption of a linear dependence of diffusivity on concentration applying a procedure based on perturbation calculus. The results of the solution will be graphically documented in details together with the description of experiments.