A Combined Method to Model Dynamic Recrystallization Based on Cellular Automaton and a Phenomenological (CAP) Approach
Abstract
:1. Introduction
2. Continuous Dynamic Recrystallization (CDRX)
3. The CA Model Concept
3.1. Evolution of Dislocation Density
3.2. Generation of Initial Microstructure
3.3. Modeling of CDRX
3.4. The Module of Geometry Changes
4. Simulation Stages
5. Simulation Results and Discussion
6. Conclusions
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- The recrystallization was considered as a one-step reaction without any large-scale growth, which is the characteristic of the CDRX phenomenon.
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- The size of CDRX grains was determined by using the subgrains’ size, which was formulated based on the phenomenological approach.
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- Volume fractions of the recrystallized area were well estimated by utilizing the proposed model.
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- Flow stress curves of the TiNiFe alloy were accurately forecasted by the presented CA model.
Author Contributions
Acknowledgments
Conflicts of Interest
Data Availability
Nomenclature
Area of one cell | T | Temperature | |
B | Burger’s vector | Tm | Melting point |
C | A constant | Ix, Iy | Nominal deformation at two principal directions |
Dsub | Subgrain size | The vector in the deformed position | |
D | Average size of DRX grains | The vector in the undeformed position | |
dε | Strain increment | Deformation matrix | |
fDRX | DRX fraction | Dislocation interaction term | |
K1 | A constant showing the effect of work hardening | 0 | Work hardening rate |
K2 | A constant showing the effect of softening | Shear modulus | |
Nucleation rate | Shear modulus at room temperature | ||
Number of cells belonging to the given grain | Poisson’s ratio | ||
NDRX | Total number of recrystallized cells | Dislocation density | |
Ntotal | Total number of cells | Flow stress | |
Q | Nucleation activation energy | Z | Zener–Hollomon parameter |
R | Gas constant |
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Azarbarmas, M.; Mirjavadi, S.S.; Ghasemi, A.; Hamouda, A.M. A Combined Method to Model Dynamic Recrystallization Based on Cellular Automaton and a Phenomenological (CAP) Approach. Metals 2018, 8, 923. https://doi.org/10.3390/met8110923
Azarbarmas M, Mirjavadi SS, Ghasemi A, Hamouda AM. A Combined Method to Model Dynamic Recrystallization Based on Cellular Automaton and a Phenomenological (CAP) Approach. Metals. 2018; 8(11):923. https://doi.org/10.3390/met8110923
Chicago/Turabian StyleAzarbarmas, Morteza, Seyed Sajad Mirjavadi, Ali Ghasemi, and Abdel Magid Hamouda. 2018. "A Combined Method to Model Dynamic Recrystallization Based on Cellular Automaton and a Phenomenological (CAP) Approach" Metals 8, no. 11: 923. https://doi.org/10.3390/met8110923