A REVIEW OF NUMERICAL MODELING METHODS FOR THE EVOLUTION OF THE METAL GRAIN STRUCTURE DURING MELTING AND CRYSTALLIZATION FOR ADDITIVE TECHNOLOGIES
Authors:
1.
KNITU-KAI im. A. N. Tupoleva
(Kafedra Lazernyh i additivnyh tehnologiy, Assistent)
graduate student from 01.01.2023 until now
graduate student from 01.01.2023 until now
2.
Kazan National Research Technical University named after A.N. Tupolev
Type:
Article
Pages:
from 141
to 150
Status:
Published
Received:
23.12.2025
Accepted:
23.12.2025
Published:
23.12.2025
Language:
Russian
Keywords:
MATHEMATICAL MODELING, CRYSTALLIZATION, ADDITIVE TECHNOLOGIES, PHASE FIELD METHOD, CELLULAR AUTOMATA METHOD, MONTE CARLO METHOD
Abstract (English):
This paper presents a comparative review of modeling methods for the evolution of microstructure during melting and crystallization under the influence of a laser source. The physical foundations of the melting and crystallization processes, as well as the main approaches to their modeling, are considered. The principles of models development based on phase field, cellular automata and Monte Carlo methods are discussed in detail. From a physical point of view, the most accurate method of modeling microstructural changes is the phase field method, which allows taking into account the phenomena of segregation, dendrite growth, and the influence of the shape of the melt pool on the direction and shape of grain growth. However, the phase field method has a disadvantage in the form of the complexity of its software implementation and high computational costs. The cellular automata method is simpler and more efficient in terms of implementation, but, like the Monte Carlo method, it is random stochastic in nature and inferior in accuracy. The results of recent studies related to the modeling of microstructure changes during direct metal deposition and selective laser melting by various methods are presented. Trends towards the creation of new calculation optimization algorithms used to create crystallization models, such as the use of adaptive mesh and a modified firefly algorithm, have been identified. The need to calculate the dynamics of the temperature field resulting from laser exposure to the material served as a prerequisite for the creation of related multiphysical models combining methods for modeling the evolution of microstructure and dynamics of temperature effects (finite element method, smoothed particle hydrodynamics and volume of fluid method).
This paper presents a comparative review of modeling methods for the evolution of microstructure during melting and crystallization under the influence of a laser source. The physical foundations of the melting and crystallization processes, as well as the main approaches to their modeling, are considered. The principles of models development based on phase field, cellular automata and Monte Carlo methods are discussed in detail. From a physical point of view, the most accurate method of modeling microstructural changes is the phase field method, which allows taking into account the phenomena of segregation, dendrite growth, and the influence of the shape of the melt pool on the direction and shape of grain growth. However, the phase field method has a disadvantage in the form of the complexity of its software implementation and high computational costs. The cellular automata method is simpler and more efficient in terms of implementation, but, like the Monte Carlo method, it is random stochastic in nature and inferior in accuracy. The results of recent studies related to the modeling of microstructure changes during direct metal deposition and selective laser melting by various methods are presented. Trends towards the creation of new calculation optimization algorithms used to create crystallization models, such as the use of adaptive mesh and a modified firefly algorithm, have been identified. The need to calculate the dynamics of the temperature field resulting from laser exposure to the material served as a prerequisite for the creation of related multiphysical models combining methods for modeling the evolution of microstructure and dynamics of temperature effects (finite element method, smoothed particle hydrodynamics and volume of fluid method).
Keywords:
MATHEMATICAL MODELING, CRYSTALLIZATION, ADDITIVE TECHNOLOGIES, PHASE FIELD METHOD, CELLULAR AUTOMATA METHOD, MONTE CARLO METHOD
MATHEMATICAL MODELING, CRYSTALLIZATION, ADDITIVE TECHNOLOGIES, PHASE FIELD METHOD, CELLULAR AUTOMATA METHOD, MONTE CARLO METHOD
