A numerical study on solid phase transformation of a plain C-Mn steel

Abstract

Study on solid phase transformation using a computational method includes numerical and mathematical modelling, has incited a lot of interest among the researchers across the globe due to its diverse and emerging applications in engineering. In addition, the advancement of materials in the recent decades has flourished, especially in case of steel due to its superior properties over the other materials and wide applications in every sector of the engineering. Such properties of the steel depend on the transformed phases during its cooling. In this context, there are several research works cited in the literature on solid transformation of phases mostly involve experimental investigations. In practice, a real time prediction of such transformation is necessary in order to control the properties of the steel, which is difficult in experimentation. Moreover, experimentation is very expensive in nature. This work, therefore, includes a numerical study on solid phase transformation of a plain C-Mn steel. It involves mathematical modelling of heat transfer, and subsequent development of a numerical code in the FORTRAN platform. The numerical code is developed based on the finite volume method (FVM) considering the Crank-Nicolson scheme for discretizing the governing equations. The subsequent solution of the finally obtained discretized simultaneous equations is performed on the basis of TDMA algorithm. Suitable boundary conditions are then considered in the present work to represent the cooling behaviour of the steel, phase transformation phenomena and evolution of the fraction of phases depending on the heating condition, holding time, and cooling condition of the material. In the model, the phase transformation is considered using the Avrami equation, which allows to calculate the fraction of transformation. Along with the transformed fraction, this work is also predicted the transformation time of each phase during cooling. The developed code is then validated with a previously cited literature. With a good agreement, this code is extended to predict the evolution of the phases during cooling of the plain C-Mn steel. Since cooling rate is a major process parameter to control the transformation of the phases, a parametric study is also included under different cooling rates.