Internal Variable and Cellular Automata-Finite Element Models of Heat Treatment
Heat treatment is one of the most important process es in advanced steel products manufacturing. While production processes are still being optimised, numerical modelling of heat treatment is very useful. Finite Elements Method (FEM) is widely used in these cases, due to its proved potential fo r modelling of continuous, macroscopic phenomena. However, its capability to simulate microscale and noncontinuous processes is very limited. Introducing e mpirical model of phase changes into FEM, usually based on Internal Variable Method (IVM) is useful when the information about volume fraction of the phases in the domain a nd stresses due to phase change satisfies the requirements. Notwithstanding, it is difficult to obtain information in-depth about microstructure during heat treatment, because it requires more sophisticated description of phase change process. Those problems can be resolved with multiscale modelling. One of the current approaches in this fi eld employs FEM for computing of temperature, stress and strain fields, while non-co ntinuous, microscale model is based on Cellular Automata (CA) method [1]. Recently, several CA models concerning phase transformation have been proposed, e.g. [2]. In th is paper Cellular Automata ‐ Finite Elements (CAFE) is applied for modelling of both macroscopic and microscopic influence of heat treatment. It also takes into acc ount a stochastic character of processes, which is hard to obtain in typical FEM or IVM solut ion. The advantage of CAFE model ensues from direct representation of microstructure. Although the current microstructural CA model is two-dimensional, it reproduces topological and morphological relations between components of microstructure. The state of CA cells is updated synchronically in cons ecutive time steps. Every cell includes state vector representing fractions of all phases. Thermodynamics of phase transition is a base for a rule-based knowledge rep resentation in the CA model. However, the nondeterministic definition of neighbo urhood and probabilistic energy
A three-dimensional frontal cellular automaton model for simulation of microstructure evolution—initial microstructure module
This paper presents a three-dimensional frontal cellular automaton (FCA)-based model for modelling of microstructure evolution during technological processes. It is a hierarchical system. The first level is the FCAs, the second level contains modules of microstructural phenomena and the third level is presented by the models of technological processes. The module of the initial microstructure (IM) is one of the components of the second level. The IM allows one to obtain a digital material representation of given parameters, which can be used by other modules for further simulation. The parameters that must be assured by the IM module are the following: shape of the grains and distributions of the grain size, crystallographic orientation and boundary disorientation angles. To obtain the required parameters, the FCAs are first used as a tool for the creation of the basic microstructure characterized by the shape of the grains. The grain size distribution is obtained by the method, which changes nucleation and grain growth conditions. After the creation of the microstructure, crystallographic parameters are established. Distribution of the crystallographic orientation and boundary disorientation angles can be obtained independently or as associated parameters. Some examples of microstructures obtained by the IM module are presented in this paper.
Cellular automaton model to simulate nucleation and growth of ferrite grains for low-carbon steels
A two-dimensional cellular automaton model was developed for the simulation of nucleation and growth of ferrite grains at various cooling rates in low-carbon steels. The model calculates the diffusion of the solute and temperature fields in an explicit finite method and incorporates local temperature and concentration changes into a nucleation or growth function, which is utilized by the automaton in a probabilistic fashion. The modeling provides an efficient way to understand how those physical processes dynamically progress and affect nucleation and growth of ferrite grains.