Development of hybrid model for modeling of diffusion phase transformation
Authors: Łach Łukasz , Svyetlichnyy Dmytro 
Published: March 2020

Purpose
Some functional properties of engineering materials, i.e. physical, mechanical and thermal ones, depend directly on the microstructure, which is a result of processes occurring in the material during the forming and thermomechanical processing. The proper microstructure can be obtained in many cases by the phase transformation. This phenomenon is one of the most important processes during hot forming and heat treatment. The purpose of this paper is to develop a new comprehensive hybrid model for modeling diffusion phase transformations. A problem has been divided into several tasks and is carried out on several stages. The purpose of this stage is a development of the structure of a hybrid model, development of an algorithm used in the diffusion module and one-dimensional heat flow and diffusion modeling. Generally, the processes of phase transformations are studied well enough but there are not many tools for their complex simulations. The problems of phase transformation simulation are related to the proper consideration of diffusion, movement of phase boundaries and kinetics of transformation. The proposed new model at the final stage of development will take into account the varying grain growth rate, different shape of growing grains and will allow for proper modeling of heat flow and carbon diffusion during the transformation in many processes, where heating, annealing and cooling can be considered (e.g. homogenizing and normalizing).

Design/methodology/approach
One of the most suitable methods for modeling of microstructure evolution during the phase transformation is cellular automata (CA), while lattice Boltzmann method (LBM) suits for modeling of diffusion and heat flow. Then, the proposed new hybrid model is based on CA and LBM methods and uses high performing parallel computations.

Findings
The first simulation results obtained for one-dimensional modeling confirm the correctness of interaction between LBM and CA in common numerical solution and the possibility of using these methods for modeling of phase transformations. The advantages of the LBM method can be used for the simulation of heat flow and diffusion during the transformation taking into account the results obtained from the simulations. LBM creates completely new possibilities for modeling of phase transformations in combination with CA.

Practical implications
The studies are focused on diffusion phase transformations in solid state in condition of low cooling rate (e.g. transformation of austenite into ferrite and pearlite) and during the heating and annealing (e.g. transformation of the ferrite-pearlite structure into austenite, the alignment of carbon concentration in austenite and growth of austenite grains) in carbon steels within a wide range of carbon content. The paper presents the comprehensive modeling system, which can operate with the technological processes with phase transformation during heating, annealing or cooling.

Originality/value
A brief review of the modeling of phase transformations and a description of the structure of a new CA and LBM hybrid model and its modules are presented in the paper. In the first stage of model implementation, the one-dimensional LBM model of diffusion and heat flow was developed. The examples of simulation results for several variants of modeling with different boundary conditions are shown.