Numerical simulation for material processing by using the phase-field method and the homogenization method

The phase-field simulation and the multi-scale analysis are coupled in this paper to develop the material design simulator for carbon steel. With many empirical studies for carbon steels using SEM or TEM, it is well known fact that the macroscopic mechanical properties of the steels are strongly affected by the geometrical features of their microscopic structures. And the thermal treatments are also known to change the micro structures. We employ the phase-field method to simulate the change caused by the thermal treatments and the multi-scale analysis based on the mathematical homogenization method to clarify the effects of it for macroscopic mechanical properties. Connecting by the concept of the digital image engineering, the whole simulations of the carbon steel are achieved, the SEM or TEM observation of micro structures, the simulation of thermal treatment, and evaluation of mechanical properties.