scholarly journals Modeling of Microstructure Evolution during Deformation Processes by Cellular Automata—Boundary Conditions and Space Reorganization Aspects

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1377
Author(s):  
Łukasz Łach
Keyword(s):  
Cellular Automata ◽  
Boundary Conditions ◽  
Microstructure Evolution ◽  
Decision Rules ◽  
Plastic Working ◽  
Shape Rolling ◽  
Representative Volume ◽  
Deformation Processes ◽  
Numerical Tools ◽  
Selection Of

Cellular automata (CA) are efficient and effective numerical tools for modeling various phenomena and processes, e.g., microstructure evolution in plastic working processes. In many cases, the analysis of phenomena can be carried out only in a limited space and on representative volume. This limitation determines the geometry of CA space hence boundary conditions are very important issues in modeling. The paper discusses different boundary conditions that can be applied to modeling. Taking into account the transformation of the modeling space, the model should allow the selection of boundary conditions. The modeling of certain phenomena and processes is directly related to changes in the geometry of a representative volume and therefore may require changes or reorganization of the modeled CA space. Four reorganization options are presented: halving, cutting and bonding, doubling, and straightening. A choice of boundary conditions may depend on particular space reorganization as used for the modeling of microstructure evolution. A set of decision rules for selecting space reorganization options taking into account the changes of CA shape and sizes is also presented. The modeling of flat and shape rolling processes utilizing some of the described techniques is shown.

Multiscale Model of Shape Rolling Taking into Account the Microstructure Evolution - Schedule Design by Finite Element Method

2013 ◽  
Vol 871 ◽  
pp. 263-268 ◽  
Author(s):  
Łukasz Łach ◽  
Dmytro Svyetlichnyy
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Cellular Automata ◽  
Microstructure Evolution ◽  
Fem Simulation ◽  
Multiscale Model ◽  
Fem Modeling ◽  
Shape Rolling ◽  
Strain And Strain Rate ◽  
Element Method

The material properties are strongly depended on the microstructure. Recently, for modeling and prediction of microstructure evolution during the forming processes a cellular automata method is used. Combination of several methods in multiscale model allows to extend the possibilities of each method and obtain more reliable results, which are close to the real conditions. The objective of this study is development of multiscale model of microstructure evolution during the shape rolling process and use it for simulation of rolling of 5 mm round bars. Model uses for calculations the finite element (FEM) and cellular automata (CA) methods. Modeling consists of three stages: design of the shape rolling schedule with the definition of shape and sizes of grooves (FEM simulation of each pass, starting from the last pass), FEM modeling of shape rolling in the proper sequence of the passes, modeling of microstructure evolution by frontal cellular automata (FCA). Stages (especially the last two) can be repeated several times to optimize the technology in view of final microstructure. The paper presents the first stage of modeling, which includes design and selection of grooves scheme with used the finite element method. The last six passes were modeled. The rolling scheme obtained from the modeling in the next stage is simulated by FEM to obtain thermomechanical parameters of the process. Then, temperature, strain and strain rate distributions in bar cross-sections, rolling time and inter-pass time will be used as input data for modeling by FCA.

Multiscale Model of Shape Rolling Taking into Account the Microstructure Evolution – Frontal Cellular Automata

2014 ◽  
Vol 998-999 ◽  
pp. 545-548 ◽  
Author(s):  
Łukasz Łach ◽  
Dmytro Svyetlichnyy
Keyword(s):  
Grain Size ◽  
Cellular Automata ◽  
Microstructure Evolution ◽  
Multiscale Model ◽  
Rolling Process ◽  
Shape Rolling ◽  
Technological Processes ◽  
Average Grain Size ◽  
Macro Scale ◽  
Time Changes

Properties of traditional materials including steels can be improved by using the prediction and control of microstructure evolution in technological processes. Models of microstructure evolution, which take into account the technological conditions, allow to optimize the process in view of final product properties. A multiscale model of microstructure evolution have been developed and adopted for simulation of the shape rolling process. The model contains module based on finite element method (FEM) for simulation of technological processes and cellular automata (CA) module for simulation of microstructure evolution. Design and selection of grooves and simulations of rolling process in macro scale are realized by FEM. The modeling results obtained by FEM are transferred to CA and used as input data. The results of simulations of microstructure evolution can be presented as snapshots of microstructure at arbitrary time, changes of average grain size, a grain size distribution, recrystallization fraction and flow stress during the process. The results of microstructure evolution obtained by FCA for 5mm round bars rolled in diamond and oval grooves are presented in the paper.

Evolution of Microstructure during the Shape Rolling Modeled by Cellular Automata

2012 ◽  
Vol 504-506 ◽  
pp. 187-192 ◽  
Author(s):  
Łukasz Łach ◽  
Dmytro S. Svyetlichnyy
Keyword(s):  
Finite Element Method ◽  
Numerical Modeling ◽  
Cellular Automata ◽  
Microstructure Evolution ◽  
Input Data ◽  
Rolling Process ◽  
Computational Effort ◽  
Shape Rolling ◽  
Microstructure Modeling ◽  
Evolution Of Microstructure

The numerical modeling of microstructure evolution in the forming processes is used different schemes and different tools. One of the methods is cellular automata (CA), and recently an interest in cellular automata for modeling of forming processes is increased constantly. Cellular automata are considered as one of the most optimal tool for microstructure modeling because of the computational effort and the obtained results. The paper presents the use of frontal cellular automata (FCA) for modeling microstructure evolution during the rolling process. The use of frontal cellular automata in combination with other methods is related to the possibility of obtaining more accurate and reliable results and has undeniable advantages. Results of the modeling of the process by finite element method (FEM) are input data for further simulation by FCA. Some examples of microstructure as results of FCA simulation are presented in the paper.

Multiscale Model of Shape Rolling Taking into Account the Microstructure Evolution – Finite Element Modeling

2014 ◽  
Vol 1025-1026 ◽  
pp. 379-384 ◽  
Author(s):  
Łukasz Łach ◽  
Dmytro Svyetlichnyy
Keyword(s):  
Finite Element ◽  
Cellular Automata ◽  
Finite Element Modeling ◽  
Strain Rate ◽  
Microstructure Evolution ◽  
Multiscale Model ◽  
Rolling Process ◽  
Shape Rolling ◽  
Element Modeling ◽  
Simulation Results

The use of appropriate forming processes allows to obtain materials of required quality, which are fulfill different technological criteria. The basic type of properties, which are fundamental for material use in specific operating conditions, are mechanical ones. They directly depend on the microstructure. Model of microstructure evolution allows for multi-criteria optimization of technological processes in view of final product properties, taking into account technological conditions. The objective of this study is development a multiscale model of microstructure evolution during the shape rolling process and presentation the finite element modeling results for 5 mm round bars rolled in diamond, oval and round grooves. The model allows to obtain parameters of technological process (by means of finite element model - FEM) and microstructural parameters (with use cellular automata - CA). FEM is used for design and selection of the grooves on the first stage [1] and for the simulations of shape rolling process in macro scale on the second stage. The next stage includes the use of FEM modeling results for simulation of microstructure evolution by cellular automata. The article presents the simulation results of shape rolling (5 mm round bars in diamond - oval scheme) with used the finite element method. This stage is the second one in the calculation sequence of the developed multiscale model. The basic process parameters such as temperature, components of strain and strain rate tensors and strain rate intensity at arbitrary points of deformed material are the modeling results. Selected FEM simulation results are presented in the article.

scholarly journals An Application Of The Theory Of Scale Of Banach Spaces

2015 ◽  
Vol 29 (1) ◽  
pp. 51-59
Author(s):  
Łukasz Dawidowski
Keyword(s):  
Banach Space ◽  
Cauchy Problem ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Banach Spaces ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Scale Of Banach Spaces ◽  
The Cauchy Problem ◽  
Selection Of

AbstractThe abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity of the solutions.

Simulation of microstructure evolution during recrystallization using a high resolution three dimensional cellular automaton

2004 ◽  
Vol 120 ◽  
pp. 225-230
Author(s):  
P. Mukhopadhyay ◽  
M. Loeck ◽  
G. Gottstein
Keyword(s):  
High Resolution ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Microstructure Evolution ◽  
Static Recrystallization ◽  
Three Dimensional ◽  
Computation Time ◽  
Recrystallization Process ◽  
Recovery Condition ◽  
Physically Based

A more refined 3D cellular Automata (CA) algorithm has been developed which has increased the resolution of the space and reduced the computation time and can take care of the complexity of recrystallization process through physically based solutions. This model includes recovery, condition for nucleation and orientation dependent variable nuclei growth as a process of primary static recrystallization. Incorporation of microchemistry effects makes this model suitable for simulating recrystallization behaviour in terms of texture, kinetics and microstructure of different alloys. The model is flexible to couple up with other simulation programs on a common database.

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