CN112053747B - Double-scale cellular automata model - Google Patents
Double-scale cellular automata model Download PDFInfo
- Publication number
- CN112053747B CN112053747B CN201911222700.4A CN201911222700A CN112053747B CN 112053747 B CN112053747 B CN 112053747B CN 201911222700 A CN201911222700 A CN 201911222700A CN 112053747 B CN112053747 B CN 112053747B
- Authority
- CN
- China
- Prior art keywords
- ferrite
- austenite
- model
- cementite
- carbon
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
- G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
- G16C60/00—Computational materials science, i.e. ICT specially adapted for investigating the physical or chemical properties of materials or phenomena associated with their design, synthesis, processing, characterisation or utilisation
Landscapes
- Engineering & Computer Science (AREA)
- Computing Systems (AREA)
- Theoretical Computer Science (AREA)
- Life Sciences & Earth Sciences (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Bioinformatics & Computational Biology (AREA)
- Heat Treatment Of Steel (AREA)
Abstract
The invention provides a double-scale cellular automaton model which is used for quantitatively describing the microstructure evolution generated in the material in the low-carbon steel annealing process. The model of the invention mainly comprises an initial tissue geometric model with discrete space, an austenite nucleation and growth model, an interface migration model of ferrite and cementite dissolution and a carbon diffusion model. In the process of constructing the model, firstly, carrying out space dispersion on an initial microstructure of low-carbon steel through equivalent cells containing double-scale subcells to establish an initial microstructure geometric model; then, the microstructure evolution of the austenitizing transformation process is described by a nucleation model, an interface migration model, and a carbon diffusion model. Compared with the traditional single-scale cellular automaton model, the model disclosed by the invention can more accurately reflect the microstructure evolution characteristics of the low-carbon steel annealing process, and realize quantitative prediction on the microstructure morphology evolution and transformation dynamics of the low-carbon steel annealing process.
Description
Technical Field
The invention relates to the field of integrated computing material engineering, in particular to a double-scale cellular automaton model applied to microstructure evolution behavior simulation in the low-carbon steel annealing treatment process.
Background
Integrated Computing Materials Engineering (ICME) links complex material metallurgical processes with material chemical compositions and processing techniques, and provides reliable auxiliary information for material design and processing technique formulation and optimization through virtual experiments. In the preparation and modification processes of the steel material, solid phase transition is one of important phenomena, the microstructure evolution generated in the heat treatment process has a decisive effect on the final mechanical property of the material, and the accurate microstructure evolution morphology characteristics and dynamics prediction in the heat treatment process have important significance on the performance regulation and control of the steel material.
In order to adjust the structure and properties of the material, the steel material is usually heated to an austenite phase region or a two-phase region during heat treatment to completely or partially austenitize the structure, and the austenitizing process mainly involves ferrite and cementite structure dissolution and the generation of a new austenite structure. The structural state of the austenitizing process, such as the distribution of alloying elements and the microstructure morphology, is closely related to the texture morphology, grain size and mechanical properties of the material obtained after cooling.
Computer simulations, which typically study the evolution behavior of microstructures during continuous annealing of ferrous materials, include macroscopic mathematical models and mesoscale models. With the development of numerical analysis methods, currently, some mainstream commercial finite element software, such as msc.marc, simulfact, form, and sysfly, are integrated with corresponding macroscopic tissue transformation models, and have been applied to industrial production to a certain extent. However, most of the macroscopic mathematical models belong to empirical or semi-empirical models, deep research on the microscopic mechanism of the transformation process is lacked, the accuracy of the prediction result usually depends on a large amount of experimental data for checking, and the model parameters have certain dependence on material components and processing technology, so that the universality of the model is poor.
The macroscopic mathematical model can only predict the comprehensive statistical information of the material structure evolution, such as grain size distribution, transformation dynamics and the like, and cannot describe the microstructure information in the structure evolution process, such as microstructure morphology characteristics, texture, alloy element concentration distribution and the like. The evolution process of the microstructures determines the final structure and the performance of the material, so that the prediction and the control of the microstructure evolution in the material processing process through a numerical simulation technology have important significance. With the continuous improvement of computer performance and the development of numerical calculation methods, dynamic and quantitative simulation of the microstructure evolution in the material production and processing process at mesoscopic and even microscopic scales has become possible. The mesoscale simulation method is based on the microscopic physical mechanism of material tissue transformation, quantitatively describes the evolution of the microstructure structure variable through a corresponding physical model, and solves the actual problem through the dispersion of space and time, thereby realizing the dynamic simulation of the material microstructure evolution in the transformation process. Currently, mesoscale simulation has been widely applied in various fields of metal material processing, including casting, welding, plastic forming, and heat treatment. The mesoscale simulation method comprises a volume unit representing method, a Monte Carlo method, a phase field method, a cellular automaton method and the like.
Cellular Automaton (CA) was first proposed by ullam and Von Neumann in the 40's of the 19 th century for the establishment of theoretical models of self-replication of living systems for the study of the evolution of living systems and the self-replication behavior of organisms. The cellular automata method can be used for describing the dynamic evolution law of a complex system in discrete space and time. With the development of the last twenty-three years, the cellular automata method gradually becomes one of the important methods for simulating the evolution of the microstructure of the material.
In the last 90 s, foreign scholars used the cellular automata method for the first time for the simulation of the recrystallization process and successfully predicted the morphological characteristics and transformation kinetics of the microstructure in the recrystallization process. In 1998, Kumar et al firstly applied the cellular automata method to the research of the structural evolution simulation of the austenite-ferrite transformation process, and they simulated the competition behavior between ferrite nucleation and early growth in the austenite decomposition process under continuous cooling conditions by using the established cellular automata model, and simulated the transformation starting temperature and ferrite grain size at different cooling speeds. Zheng et al established a recrystallization and phase-change coupled cellular automata model, focused on the microstructure evolution behavior under the interaction of ferrite recrystallization and austenitizing transformation in the annealing process of the critical zone of cold-rolled dual-phase steel, and discussed the influence of the heating process on the rotational transformation mechanics and the structure morphology, but when processing the austenitizing transformation of the pearlite structure, the pearlite structure is assumed to be a single phase with fixed carbon content, and the ferrite and cementite structures in the pearlite cluster are dissolved simultaneously when the austenitizing transformation, which is different from the reality, and also influences the final transformation kinetics and the accuracy of the microstructure morphology prediction result. Meanwhile, patent 201610184252.3 proposes a novel neighbor trapping method based on cellular automata, which can finally obtain and derive the grain morphology, solute fraction, temperature distribution and dendritic crystal tip growth speed.
The traditional cellular automata model can only model the tissue transformation in a single scale, and cannot consider the multi-scale characteristics of the initial tissue, such as the size difference of ferrite sheets and cementite sheets in pearlite, and the influence on the microstructure evolution. The size of the cementite lamellae within the pearlite cluster is typically 10-8m is of the order of magnitude, and the pearlite clusters and ferrite grain sizes are 10-5～10-4m magnitude, difference between the twoIs huge. The conventional cellular automata model generally assumes a uniform single phase of ferrite and cementite mixed structure within a pearlite body when simulating the austenitizing process of the pearlite structure. During austenitization, ferrite and cementite lamellae in the pearlite dissolve simultaneously, and the carbon content of the newly generated austenite is assumed to be the same as that of the original pearlite structure. However, in real cases, ferrite and cementite dissolution in pearlite do not proceed simultaneously due to the difference in dissolution rate. In the austenitizing process of the pearlite structure, cementite dissolution has great influence on the austenitizing transformation kinetics and the structure morphology. Therefore, the traditional cellular automata model cannot accurately reflect the structure transformation of the annealing process of the critical area of the cold-rolled dual-phase steel.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a novel double-scale cellular automaton model in order to consider the influence of the structural characteristics of ferrite lamella and cementite lamella in the actual pearlite structure on the evolution of the microstructure in the austenitizing process. According to the model, quantitative description of the geometric structures of ferrite and cementite in a pearlite cluster is realized by embedding two subcells with different sizes in the traditional single-scale cells, and reliable simulation and prediction of microstructure evolution morphology characteristics and transformation dynamics generated in the annealing process of low-carbon steel containing pearlite structures are realized on the basis of a traditional structure evolution physical model.
The invention is realized by the following technical scheme:
a dual-scale cellular automaton model is characterized in that the chemical components of low-carbon steel selected by the model are expressed as Fe-0.2C (wt.%), after the low-carbon steel is subjected to normalizing treatment, the initial structure comprises a ferrite structure with the volume fraction of about 85% and a pearlite structure with the volume fraction of 15%, for the pearlite structure, ferrite and cementite sub-cells are respectively arranged in a single cellular unit of the cellular automaton model, an equivalent cellular unit is formed, and the unit sizes of the ferrite and the cementite sub-cells in the equivalent cellular unit are given by the following formula:
in the formula, LiUnit size representing ferrite or cementite subunit cell, fiRepresents the volume fraction of ferrite or cementite, LCFor equivalent cellular unit size, when annealing low carbon steel, the microstructure interface evolution corresponding to austenite nucleation and growth and ferrite and cementite dissolution processes can be simulated by the evolution of state variables of equivalent cells including ferrite and cementite subcells.
When the low-carbon steel annealing process generates austenitizing transformation, the nucleation rate of austenite is given by a classical nucleation theory model:
in the formula, K1Is a constant related to the density of nucleation sites, K2K is the boltzmann constant, a constant related to the energy of all potential nucleation interfaces,
is the diffusion coefficient of carbon atoms in austenite, T is the annealing temperature, Δ GNDriving force for austenite nuclei, Δ GNDepending on the heating temperature and the local carbon concentration, the nucleation driving force Δ G of austenite is generated when austenite is nucleated in the pearlite clusterNCan be expressed as:
in the formula (I), the compound is shown in the specification,
as a temperature-dependent scaling factor, CPAnd CγThe average carbon concentration of pearlite and the equilibrium carbon concentration of austenite relative to ferrite at the current temperature, respectively.
When the low-carbon steel annealing process generates austenitizing transformation, the austenite growth and the interface migration behavior generated when ferrite and cementite are dissolved are described by adopting a mixed control model, and the migration rates of different phase interfaces can be uniformly expressed as:
vij＝MijΔGij
wherein v isijAs interface migration rate, MijFor interfacial mobility, Δ GijFor the chemical driving force of interfacial migration, i and j represent the different constituent phases on both sides of the interface, respectively.
Further, the interfacial mobility is exponential with temperature and can be expressed as:
in the formula (I), the compound is shown in the specification,
is the coefficient of interface mobility, QijFor interfacial diffusion activation energy, R and T are the universal gas constant and absolute temperature, respectively.
For the interface migration model, where the chemical driving force for interface migration can be approximated as a linear function of the difference between the carbon concentration at the interface and the equilibrium carbon concentration, the chemical driving force for interface migration can be expressed for the austenite-cementite and ferrite-cementite interfaces as:
in the formula (I), the compound is shown in the specification,
is a temperature-dependent scaling factor,
is the equilibrium carbon concentration of austenite or ferrite relative to cementite, ci/θIs austenite/cementite or ferrite/cementiteThe carbon concentration at the interface, i represents austenite or ferrite, and θ represents cementite;
for an austenite-ferrite interface, the chemical driving force for the interface migration can be expressed as:
in the formula (I), the compound is shown in the specification,
is a proportionality coefficient, cγ/αAnd
the carbon concentration at the austenite/ferrite interface and the equilibrium carbon concentration of austenite relative to ferrite, respectively;
further, the chemical driving force of austenite nucleation and interface migration is closely related to the carbon concentration distribution inside the structure, and during the annealing process, the carbon element generated by the cementite dissolution process will diffuse to the interface front through austenite and ferrite, thereby providing the carbon element needed for austenite growth, and the diffusion of the carbon element can be expressed by Fick's second law:
wherein φ represents a structural mark, which represents a ferrite or austenite phase, CφIs the concentration of carbon in the phase phi,
for the diffusion coefficient of carbon atoms in phase φ, the carbon diffusion coefficient versus temperature can be expressed as:
in the formula (I), the compound is shown in the specification,
is a constant number of times, and is,
activating energy for carbon diffusion.
Advantageous effects
The microstructure evolution of the low-carbon steel annealing process can be effectively simulated through the double-scale cellular automaton model, and the microstructure evolution morphology characteristics and transformation dynamics under the combined action of austenite generation and ferrite dissolution and cementite dissolution during austenitizing transformation can be accurately reflected, which cannot be realized by the traditional single-scale cellular automaton model.
Drawings
FIG. 1(a) is a metallographic image of an initial structure of a low carbon steel according to the present invention; (b) the cellular automaton initial organization model is established.
Fig. 2 is a schematic diagram of a dual-scale cellular automaton model.
Fig. 3 is an example of simulation results of a two-scale cellular automaton model of austenite nucleation growth in a ferrite/pearlite structure: (a) the microstructure morphology, (b) the volume fraction distribution of cementite, and (c) the carbon concentration distribution in austenite.
Detailed Description
The invention is described in detail below with reference to the drawings and examples of the specification:
the chemical components of the low-carbon steel selected by the model are expressed as Fe-0.2C (wt.%), after the low-carbon steel is subjected to normalizing treatment, the initial structure of the low-carbon steel comprises ferrite with the volume fraction of about 85% and pearlite with the volume fraction of 15% according to metallographic determination, as shown in figure 1(a), and an initial structure geometric model is directly established after being processed by a metallographic picture, as shown in figure 1 (b).
For the pearlite structure, the cellular automata model is provided with a ferrite and a cementite sub-cellular respectively in a single cellular unit thereof on the basis of the initial structure geometric model, thereby constituting an equivalent cellular unit, and as shown in fig. 2, the unit sizes of the ferrite and the cementite sub-cellular in the equivalent cellular unit are given by the following formula:
in the formula, LiUnit size representing ferrite or cementite subcells, fiRepresents the volume fraction of ferrite or cementite, LCFor equivalent cellular unit size, austenite nucleation and growth, and microstructure interface migration corresponding to ferrite and cementite dissolution processes can be simulated by the evolution of state variables of equivalent cells including ferrite and cementite subcells when annealing low carbon steel.
When the low-carbon steel annealing process generates austenitizing transformation, the nucleation rate of austenite is given by a classical nucleation theory model:
in the formula, K1Is a constant related to the density of nucleation sites, K2K is the boltzmann constant, a constant related to the energy of all potential nucleation interfaces,
is the diffusion coefficient of carbon atoms in austenite, T is the annealing temperature, Δ GNDriving force for austenite nuclei, Δ GNDepending on the heating temperature and the local carbon concentration, the nucleation driving force Δ G of austenite is generated when austenite is nucleated in the pearlite clusterNCan be expressed as:
in the formula (I), the compound is shown in the specification,
as a temperature-dependent scaling factor, CPAnd CγAverage carbon concentration of pearlite and current temperature, respectivelyThe equilibrium carbon concentration of the austenite relative to the ferrite.
When the low-carbon steel annealing process generates austenitizing transformation, the austenite growth and the interface migration behavior generated when ferrite and cementite are dissolved are described by adopting a mixed control model, and the migration rates of different phase interfaces can be uniformly expressed as:
vij＝MijΔGij
wherein v isijAs the rate of interfacial migration, MijFor interfacial mobility, Δ GijFor the chemical driving force of interfacial migration, i and j represent the different constituent phases on both sides of the interface, respectively.
Further, the interfacial mobility is exponential with temperature and can be expressed as:
in the formula (I), the compound is shown in the specification,
is the coefficient of interface mobility, QijFor interfacial diffusion activation energy, R and T are the universal gas constant and absolute temperature, respectively.
For the interface migration model, where the chemical driving force for interface migration can be approximated as a linear function of the difference between the carbon concentration at the interface and the equilibrium carbon concentration, the chemical driving force for interface migration can be expressed for the austenite-cementite and ferrite-cementite interfaces as:
in the formula (I), the compound is shown in the specification,
the scaling factor, which is temperature dependent, can be calculated by thermodynamic software, such as Thermal-Calc,
is the equilibrium carbon concentration of austenite or ferrite relative to cementite, ci/θIs the carbon concentration at the austenite/cementite or ferrite/cementite interface, i represents austenite or ferrite, θ represents cementite;
for an austenite-ferrite interface, the chemical driving force for the interface migration can be expressed as:
in the formula (I), the compound is shown in the specification,
is a proportionality coefficient, cγ/αAnd
the carbon concentration at the austenite/ferrite interface and the equilibrium carbon concentration of austenite relative to ferrite, respectively;
further, the chemical driving force of austenite nucleation and interface migration is closely related to the carbon concentration distribution inside the structure, and during the annealing process, the carbon element generated by the cementite dissolution process will diffuse to the interface front through austenite and ferrite, thereby providing the carbon element needed for austenite growth, and the diffusion of the carbon element can be expressed by Fick's second law:
wherein φ represents a structural mark, which represents a ferrite or austenite phase, CφIs the concentration of carbon in the phase phi,
for the diffusion coefficient of carbon atoms in phase φ, the relationship of carbon diffusion coefficient to temperature can be expressed as:
in the formula (I), the compound is shown in the specification,
is a constant number of times, and is,
activating energy for carbon diffusion.
FIG. 3 is the result of the evolution of the austenitized structure simulated by the dual-scale cellular automaton model shown in FIG. 2 under the annealing condition of isothermal 0.5s at 800 ℃. As can be seen from fig. 3(a), austenite rapidly grows into pearlite after nucleation at the pearlite-ferrite interface. The austenite transformation is accompanied by the dissolution of ferrite and cementite, and at the annealing temperature of 800 ℃, the ferrite-austenite transformation requires less carbon elements, and after the ferrite is rapidly dissolved, some undissolved cementite still exists in the newly generated austenite, as shown in fig. 3 (b). These undissolved cementite will continue to dissolve as the austenite grows and transfer the carbon released by the dissolution into the austenite, thereby providing the necessary carbon for the austenite to grow into the surrounding ferrite. Under the action of cementite dissolution and carbon diffusion, a non-uniformly distributed carbon concentration field is formed in austenite, and the carbon concentration around the austenite-pearlite interface and the austenite containing undissolved cementite is high, as shown in fig. 3 (c). Under the influence of carbon content, a pearlite lamellar structure and a heat treatment process, the phenomenon that ferrite and cementite are asynchronously dissolved in the austenitizing process of a pearlite structure is common in experiments. The process can be effectively simulated through the double-scale cellular automaton model, which cannot be realized by the traditional single-scale cellular automaton model.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.
Claims (6)
1. A dual-scale cellular automaton model is characterized in that the chemical composition of low-carbon steel selected by the model is expressed as Fe-0.2C (wt.%), after the low-carbon steel is subjected to normalizing treatment, the initial structure comprises a ferrite structure with the volume fraction of about 85% and a pearlite structure with the volume fraction of 15%, and for the pearlite structure, ferrite and cementite sub-cells are respectively arranged in a single cellular unit of the cellular automaton model, so that an equivalent cellular unit is formed, and the unit size of the ferrite and the cementite sub-cells in the equivalent cellular unit is given by the following formula:
in the formula, LiUnit size representing ferrite or cementite subunit cell, fiRepresents the volume fraction of ferrite or cementite, LCFor equivalent cellular unit size, when the low carbon steel is annealed, the microstructure interface evolution corresponding to austenite nucleation and growth and ferrite and cementite dissolution processes can be simulated by the evolution of state variables of equivalent cells including ferrite and cementite subcells.
2. The dual-scale cellular automaton model of claim 1, wherein the nucleation rate of austenite during the mild steel annealing process is given by a nucleation theory model:
in the formula, K1Is a constant related to the density of nucleation sites, K2K is the boltzmann constant, a constant related to the energy of all potential nucleation interfaces,
is the diffusion coefficient of carbon atoms in austenite, T is the annealing temperature, Δ GNDriving force for austenite nuclei, Δ GNDepending on the heating temperature and the local carbon concentration, the driving force Δ G for austenite nucleation is determined when austenite nucleates in the pearlite clusterNCan be expressed as:
in the formula (I), the compound is shown in the specification,
as a temperature-dependent scaling factor, CPAnd CγThe average carbon concentration of pearlite and the equilibrium carbon concentration of austenite relative to ferrite at the current temperature, respectively.
3. The dual-scale cellular automata model of claim 2, wherein when austenitizing transformation occurs during annealing of the low-carbon steel, the migration behaviors of the austenite and the ferrite and the cementite corresponding to the dissolution of the ferrite are described by using a hybrid control model, and the migration rates of different phase interfaces can be uniformly expressed as:
vij＝MijΔGij
wherein v isijAs the rate of interfacial migration, MijFor interfacial mobility, Δ GijFor the chemical driving force of interfacial migration, i and j represent the different constituent phases on both sides of the interface, respectively.
4. The dual-scale cellular automaton model of claim 3, the interfacial mobility M beingijIs exponential to temperature and can be expressed as:
in the formula (I), the compound is shown in the specification,
is a boundaryCoefficient of surface mobility, QijFor interfacial diffusion activation energy, R and T are the universal gas constant and absolute temperature, respectively.
5. The dual-scale cellular automaton model of claim 3, the interfacial migration chemical driving force Δ GijWhich can be approximated as a linear function of the difference between the carbon concentration at the interface and the equilibrium carbon concentration, the chemical driving force for interface migration can be expressed for the austenite-cementite and ferrite-cementite interfaces as:
in the formula (I), the compound is shown in the specification,
is a temperature-dependent scaling factor,
is the equilibrium carbon concentration of austenite or ferrite relative to cementite, ci/θIs the carbon concentration at the austenite/cementite or ferrite/cementite interface, i represents austenite or ferrite, θ represents cementite;
for an austenite-ferrite interface, the chemical driving force for the interface migration can be expressed as:
in the formula (I), the compound is shown in the specification,
is a proportionality coefficient, cγ/αAnd
the carbon concentration at the austenite/ferrite interface and the equilibrium carbon concentration of austenite relative to ferrite, respectively.
6. The dual-scale cellular automaton model of claim 3, the driving force Δ G for austenite nucleationNAnd chemical driving force Δ G for interfacial migrationijIn close relation to the carbon concentration distribution inside the structure, during the annealing process, the carbon element generated by the cementite dissolution process will diffuse to the interface front through austenite and ferrite, thereby providing the carbon element needed for austenite growth, and the diffusion of the carbon element can be expressed by Fick's second law:
wherein φ represents a structural mark, which represents a ferrite or austenite phase, CφIs the concentration of carbon in the phase phi,
is the diffusion coefficient of carbon atoms in phase phi;
the carbon diffusion coefficient versus temperature can be expressed as:
in the formula (I), the compound is shown in the specification,
is a constant number of times, and is,
activating energy for carbon diffusion.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911222700.4A CN112053747B (en) | 2019-12-03 | 2019-12-03 | Double-scale cellular automata model |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201911222700.4A CN112053747B (en) | 2019-12-03 | 2019-12-03 | Double-scale cellular automata model |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112053747A CN112053747A (en) | 2020-12-08 |
| CN112053747B true CN112053747B (en) | 2022-05-27 |
Family
ID=73609660
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201911222700.4A Active CN112053747B (en) | 2019-12-03 | 2019-12-03 | Double-scale cellular automata model |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112053747B (en) |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104603785A (en) * | 2012-08-31 | 2015-05-06 | 株式会社东芝 | Method and system for predicting material structure |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2013185019A1 (en) * | 2012-06-07 | 2013-12-12 | The Regents Of The University Of California | Predicting the influence of mineral additions on reaction and property development in cementitious mixtures |
-
2019
- 2019-12-03 CN CN201911222700.4A patent/CN112053747B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104603785A (en) * | 2012-08-31 | 2015-05-06 | 株式会社东芝 | Method and system for predicting material structure |
Non-Patent Citations (2)
| Title |
|---|
| Cellular automaton model to simulate nucleation and growth;L.Zhang 等;《CAMBRIDGE JOURNALS》;20020930;2251-2259 * |
| Micro-scale Cellular Automaton Modeling of Interface Evolution;Gang Shen, Cheng-Wu Zheng, Jian-Feng Gu, Dian-Zhong Li;《Acta Metallurgica Sinica》;20180206;713-722 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112053747A (en) | 2020-12-08 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Chen et al. | Modeling the dynamic recrystallization in austenitic stainless steel using cellular automaton method | |
| Liu et al. | Study of dynamic recrystallization in a Ni-based superalloy by experiments and cellular automaton model | |
| Rudnizki et al. | Phase-field modeling of austenite formation from a ferrite plus pearlite microstructure during annealing of cold-rolled dual-phase steel | |
| Madej et al. | Multi scale cellular automata and finite element based model for cold deformation and annealing of a ferritic–pearlitic microstructure | |
| Chen et al. | Mesoscale modeling and simulation of microstructure evolution during dynamic recrystallization of a Ni-based superalloy | |
| Pietrzyk et al. | Modelling phase transformations in steel | |
| Huyan et al. | Simulation of the growth of austenite from as-quenched martensite in medium Mn steels | |
| Derazkola et al. | Review on modeling and simulation of dynamic recrystallization of martensitic stainless steels during bulk hot deformation | |
| Lin et al. | Study of microstructural evolution during static recrystallization in a low alloy steel | |
| Zhu et al. | Modeling of the austenitization of ultra-high strength steel with cellular automation method | |
| Huo et al. | Microstructure evolution and unified constitutive equations for the elevated temperature deformation of SAE 52100 bearing steel | |
| Kundu et al. | Prediction of phase transformation and microstructure in steel using cellular automaton technique | |
| Wrożyna et al. | Experimental and numerical simulations of phase transformations occurring during continuous annealing of DP steel strips | |
| Sitko et al. | Time and length scale issues in numerical modelling of dynamic recrystallization based on the multi space cellular automata method | |
| Chen et al. | Genetic optimized Al–Mg alloy constitutive modeling and activation energy analysis | |
| Feng et al. | Mechanical properties and deformation behaviour of TWIP steel at different strain rates | |
| Chen et al. | Dissolution of β particles in an Al Mg Si alloy during DSC runs | |
| CN112053747B (en) | Double-scale cellular automata model | |
| Duan et al. | Cellular automata coupled finite element simulation for dynamic recrystallization of extruded AZ80A magnesium alloy | |
| CN112053748B (en) | Double-scale cellular automaton model simulation method for austenitizing tissue evolution | |
| Xu et al. | A 3D cellular automaton with inhomogeneous nucleation for simulating dynamic recrystallization of low-alloy steel with mixed-grain microstructure | |
| Liu et al. | Formation mechanism of lamellar alpha in titanium through accurate simulation | |
| Yang et al. | Study of static recrystallization behavior of a nitrogen-alloyed ultralow carbon austenitic stainless steel by experiment and simulation | |
| Han et al. | Microstructural evolution of Fe–32% Ni alloy during large strain multi-axial forging | |
| Wu et al. | Simulating the Effect of Temperature Gradient on Grain Growth of 6061-T6 Aluminum Alloy via Monte Carlo Potts Algorithm. |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |