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
Reorganization of cellular space during the modeling of the microstructure evolution by frontal cellular automata
Abstract The prediction of the microstructure evolution is one of the most significant problems in materials science. The objective of this paper is development of principles of the cellular space reorganization and their implementation into the three-dimensional frontal cellular automata (FCA) for modeling of the microstructure evolution during the multi-stage deformation. Motivation for the reorganization and principles governing this process are presented in the paper. The FCA cells do not keep the form of undistorted cubes during the simulation, but they get deformed. That leads to the necessity of space reorganization. Different conditions on the boundaries of the cellular space are taken into consideration as they are closely connected with the developed algorithms of the reorganization. These two variants of the reorganization are described in detail. The first one can be used when cellular space can be reduced; and the second one, when the reduction of modeled volume is not acceptable. A short description of frontal cellular automata is presented in this paper. The model consists of two parts: deformation and microstructure evolution. The independence of the grain growing from the shape and the sizes of the cell is ensured by so-called “virtual front tracking” algorithm. The microstructural part of the model simulates two phenomena: nucleation and growth of new grains. In this paper only static recrystallization is considered. When the recrystallization is simulated, the nucleation and the grain boundary migration depend on the deformation parameters such as: temperature, strain, strain rate, dislocation density and crystallographic orientation. This phenomenon, along with the deformation, can be modeled over a wide range of multi-stage deformation processes. The process of flat rolling is chosen as the simplest example. The data needed for the FCA simulation is received from the simple numerical calculations. The results of the simulation of the microstructure evolution obtained during the last five passes of the flat rolling are also presented in the paper.
Changes in Quartz During Heating and the Possible Effects on Si Production
In Si and FeSi production, the main Si source is SiO2, in the form of quartz. Reactions with SiO2 generate SiO gas that further reacts with SiC to Si. During heating, quartz will transform to other SiO2 modifications with cristobalite as the stable high-temperature phase. Transformation to cristobalite is a slow process. Its rate has been investigated for several industrial quartz sources and has been shown to vary considerably among the different quartz types. Other differences in behavior during heating between these quartz sources, such as softening temperature and volume expansion, have also been studied. The quartz-cristobalite ratio will affect the rate of reactions involving SiO2. The industrial consequences and other implications of the observed difference between quartz types are discussed. Initial studies of industrial quartz were published by Ringdalen et al. In the current work, a new experimental method has been developed, and an investigation of several new quartz sources has confirmed the earlier observed large variation between different sources. The repeatability of the data has been studied and the effect of gas atmosphere investigated. The results from the earlier work are included as a basis for the discussion.