WO2014034964A2

WO2014034964A2 - Method and system for predicting material structure

Info

Publication number: WO2014034964A2
Application number: PCT/JP2013/074166
Authority: WO
Inventors: Yasutaka Nishida; Fumihiko Aiga
Original assignee: Kabushiki Kaisha Toshiba
Priority date: 2012-08-31
Filing date: 2013-09-02
Publication date: 2014-03-06
Also published as: CN104603785A; CN104603785B; JP5749233B2; IN2015DN01798A; WO2014034964A3; JP2014048208A; EP2891092A2

Abstract

According to one embodiment, a material structure prediction method of predicting a material structure which causes phase transformation from a parent phase to a new phase by nucleation resulting from a temperature change of a material is disclosed. The method can prearrange nucleation candidate nuclei in the material. The method can determine whether the nucleation has occurred in each of the prearranged nucleation candidate nuclei. In addition, the method can calculate time evolution of a structure of the new phase by regarding, as the new phase, the nucleation candidate nucleus for which it is determined that the nucleation has occurred.

Description

D E S C R I P T I O N

METHOD AND SYSTEM FOR PREDICTING MATERIAL STRUCTURE

Cross-Reference to Related Applications This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2012-192525, filed August 31, 2012, the entire contents of which are incorporated herein by reference.

Field

Embodiments described herein relate generally to a prediction method and prediction system for predicting a material structure.

Background

Generally, iron and steel materials (steel

materials) are used in various applications, e.g., transporting machines such as vehicles and ships, and architectural structures such as buildings and bridges. Demands have arisen for further improving the material quality characteristic such as the strength,

formability, or weldability of the steel material.

This applies not only to the steel material but also to all materials. It is also known that the material quality characteristics of a material have a close relationship with the microscopic material structure. For example, the relationship between the grain size and stress characteristic of a metallographic structure such as steel is known as the Hall-Petch rule. The strength of a steel material increases as the

metallographic structure becomes finer. The

microstructure of a steel material is determined by a crystal structure change from a solid phase to a solid phase (i.e., phase transformation in a solid phase) in a heat treatment (e.g., cooling, heating, or an isothermal process) during the manufacturing process. Accordingly, the material quality characteristics of a steel material can be improved by structure control by a heat treatment.

A typical steel manufacturing process is hot rolling. In hot rolling, a heated steel material is deformed by rolls and processed into a sheet material or the like. In the manufacturing process, it is possible to variously change the metallographic structure of a steel material by controlling the generation of phase transformation and the grain growth of a crystal after that by manipulating the processing and temperature conditions. It is thus possible to separately manufacture steel materials having material quality characteristics matching applications. To set appropriate hot-rolling conditions for a desired steel material, therefore, it is important to grasp the relationship between the process conditions of, e.g., cooling or rolling and the material structure.

These relationships between the manufacturing processes and material structures are accumulated as semi-empirical data. To search for proper process conditions, optimum conditions are determined by narrowing down by repeating trial rolling (experimental rolling) . Unfortunately, this method of repeating trial manufacture requires a high cost and much labor, and hence is inefficient from the viewpoint of product development. Recently, therefore, a material structure prediction technique using computer simulation is regarded as important in order to increase the process efficiency and reduce the cost of product development.

Generally, the spatial scale of the metallographic structure of a steel material, the internal

microstructures of a magnetic material and dielectric material, and the phase separation of a polymer is about a few μπι to a few ten ,μιη. This scale is

sufficiently larger than micro sizes of atoms, but sufficiently smaller than visible macro sizes. A scale like this which is neither micro nor macro is often called a meso (intermediate) scale. Accordingly, a mesoscale prediction technique is presumably effective in predicting the behaviors of the metallographic structures of these materials.

In the meso scale, however, no firmly effective technique is known. This background has the following reason. Since the number of atoms in the meso scale is much larger than that in the micro scale, an approach using the first principle calculation or the like is difficult from the viewpoint of the calculation cost. On the other hand, a macroscale approach is basically inapplicable to various phenomena in the meso scale that is a more micro scale.

Recently, therefore, approaches to the material structure prediction technique by various methods such as the Monte Carlo method and cellular automaton are being made. One of these approaches is the.

multi-phase-field (MPF) method.

The MPF method is a method by which an order parameter characterizing the state of a phase is introduced to each phase, and the time evolution of a structure when phase transformation occurs is simulated by a numerical calculation based on a thermodynamic function. The MPF method can kinetically predict a structure formation process based on the minimization of the total free energy. The MPF method is applied to various fields. Examples are solidification, spinodal decomposition, austenite/ferrite transformation, and martensite transformation.

The advantage of the MPF method is the ability to directly use the Gibbs free energy conforming to a phase diagram by cooperating with the calculation method of the CALPHAD (CALculation of PHAse Diagram) method. Accordingly, the MPF method can simulate a structure.. formation -process conforming to a phase diagram. Also, real-time step implication is difficult in the Monte Carlo method and cellular automaton. By contrast, the time step of simulation in the MPF method corresponds to the real time itself. Furthermore, the MPF method is an excellent method because it is capable of calculations including the influence of curvature (i.e., the Gibbs-Thomson effect) in interface growth.

As described above, the MPF method is a very versatile material structure prediction technique. The MPF method is also phenomenology including parameters that are determined by experiments. Accordingly, the MPF method can perform kinetically energetically quantitative simulation by appropriately using the physical property values of existing substances. As a practical example, the MPF method is extremely powerful when predicting the microstructure of phase separation of an alloy in conformity with a phase diagram.

Brief Description of the Drawings

FIG. 1 is a flowchart showing the procedure of a steel material prediction method performed by a

material structure prediction apparatus according to an embodiment ;

FIG. 2 is an equilibrium state diagram of a low-carbon portion of steel;

FIG. 3 is a simplified view showing grains in a parent phase as a target material of the material structure prediction apparatus according to the embodiment ;

FIG. 4 is a graph showing a method of allocating order parameters to the grains in the parent phase as a target material of the material structure prediction apparatus according to the embodiment;

FIG. 5 is a simplified view showing a parent phase to be simulated by the material structure prediction apparatus according to the embodiment;

FIG. 6 is a simplified view showing a method of setting the arrangement of nucleation candidate sites performed by the material structure prediction

apparatus according to the embodiment;

FIG. 7 is a graph showing a linearization state drawing method for low-carbon steel in the material structure prediction apparatus according to the

embodiment;

FIG. 8 is a flowchart showing the arithmetic procedure of a numerical solution using the MPF method in the material structure prediction apparatus

according to the embodiment;

FIG. 9 is a view showing various parameters used in calculations by the material structure prediction apparatus according to the embodiment;

FIG. 10 is a graph showing the ferrite deposition rates of calculation results obtained by the material structure prediction apparatus according to the

embodiment; FIG. 11 is a transition diagram showing the time evolution of a material structure of calculation results obtained by the material structure prediction apparatus according to the embodiment;

FIG. 12.is a graph showing the changes in ferrite deposition rate when parameters contained in a

nucleation ratio equation are changed by the material structure prediction apparatus according to the

embodiment ;

FIG. 13 is a graph showing the changes in

nucleation ratio when the parameters contained in the nucleation ratio equation are changed by the material structure prediction apparatus according to the

embodiment ;

FIG. 14 is a view showing calculation conditions used in calculations performed by the material

structure prediction apparatus according to the

embodiment; and

FIG. 15 is a graph showing the ferrite deposition rates of prediction results obtained by the material structure prediction apparatus according to the

embodiment and an experimental result.

Detailed Description

Embodiments will be explained below with reference to the accompanying drawings.

Results obtained by the MPF method may be

qualitative. It means that the MPF method, which is phenomenology, can predict a tendency of experimental results, but it may be difficult to find a quantitative agreement between a simulation result and an

experimental result by the MPF method.

For example, if the MPF method is applied to γ/ -phase transformation of steel in a continuous cooling process at a given cooling rate, a result of predicting temperature dependence of a ferrite

deposition rate will qualitatively agree with

experimental results. However, the results thus predicted may not quantitatively agree with a behavior at a high temperature portion or an experimental result in a low temperature portion.

This problem is not limited to the MPF method. A method for quantitatively predicting a material

structure which causes phase transformation due to a temperature change has not been known.

Therefore, a problem to be solved by the

embodiment is to provide a material structure

prediction method and prediction system, which can quantitatively predict a material structure that causes phase transformation due to a temperature change.

In general, according to one embodiment, a

material structure prediction method of predicting a material structure which causes phase transformation from a parent phase to a new phase by nucleation resulting from a temperature change of a material is disclosed. The method can prearrange^' nucleation candidate nuclei in the material. The method can determine whether the nucleation has occurred in each of the prearranged nucleation candidate nuclei. In addition, the method can calculate time evolution of a structure of the new phase by regarding, as the new phase, the nucleation candidate nucleus for which it is determined that the nucleation has occurred.

(Embodiment )

First, phenomena of a material as a prediction target will be explained by mainly taking a steel material as an example. Note that the material is not limited to a steel material and may also be a magnetic material (an alloy or oxide made of, e.g., copper, iron, platinum, palladium, cobalt, chromium, nickel, neodymium, barium, bismuth, or samarium) , a dielectric material, or a functional material represented by a polymer organic material like a block copolymer such as polystyrene-methyl polymethacrylate .

FIG. 2 is an equilibrium state diagram for a low-carbon portion of steel. Carbon steel generally called a steel material practically has a carbon content of up to about 6.67% as mass% (wt%) . A

material having a carbon concentration higher than that is rarely used. Therefore, the behavior in a narrow low-carbon region is important in a phase diagram of steel. In this low-carbon region alone, only two or three characteristic phases appear. For the sake of simplicity, a case in which a solute mainly contains only carbon will be explained below.

Features found in the steel phase diagram will be described below. Pure iron containing no solute

(carbon) has a magnetic transformation point at 768°C. Pure iron is a ferromagnetic material at a temperature equal to or lower than the magnetic transformation point, and a paramagnetic material at a temperature higher than that. This temperature is called an A2 transformation point. When the temperature is raised from 910°C (1,183K), pure iron changes from a iron having a body-centered cubic structure to γ iron having a face-centered cubic structure. This temperature is called an A3 transformation point. When the

temperature is further raised to 1,390°C (1,663K), pure iron transforms from γ iron having a face-centered cubic structure back to a structure having a

body-centered cubic structure again (δ iron) . This temperature is called an A4 transformation point. When the temperature is further raised to 1,534°C (1,807K), δ iron melts into a liquid.

Low-carbon steel containing a very small amount of carbon will be explained below. In this steel, carbon dissolves in each of a iron, γ iron, and δ iron

described above and forms a solid solution. a iron dissolves by about 0.02 massl at 723°C (996K). This a iron is called a ferrite phase. γ iron that forms a solid solution with carbon over a broad range in a region where the temperature is equal to or higher than the A3 transformation point is called an austenite phase. When the temperature is equal to or lower than the Al point, a structure called a pearlite phase is formed. This pearlite phase has a lamellar structure formed by eutectoid of ferrite and a cementite phase that dissolves high-concentration carbon. Generally, phase transformation dominant in a continuous cooling process in a steel material hot-rolling step is

solid-phase transformation from γ iron that is stable in the region where the temperature is equal to or higher than the A3 transformation point, to a iron that is stable at low temperatures (or to martensite formed by diffusionless transformation when quenching is performed) , and hence is called γ/ -phase

transformation (or martensite transformation when quenching is performed) .

The γ/α-phase transformation of a steel material is the grain growth of the a-iron phase in which the diffusions of solutes competitively occur due the difference between the phase stabilities of the crystal phases of γ iron and a iron, and the difference between the solute dissolution concentrations of these crystal phases. Accordingly, the γ/α-phase transformation is called diffusion phase transformation because solute diffusion occurs. The γ/ -phase transformation forms various microstructures because the grain growth of the a-iron phase is influenced by, e.g., the solute

concentrations or cooling conditions. On the other hand, the martensite transformation is diffusionless phase transformation in which the orientation (variant) of the crystal changes. In this phase transformation phenomenon, it is possible, by the MPF method, to simultaneously handle the diffusion of atoms and the interface movement of grains caused by the phase transformation driving force resulting from the

thermodynamic phase stability.

Next, a material structure prediction method according to this embodiment will be explained. This prediction method is mainly operated by a computer.

The explanation will be made by using a material structure prediction apparatus configured such that a computer executes the material structure prediction method in accordance with a program.

FIG. 1 is a flowchart showing the procedure of a method of predicting the time evolution of the

structure of a new phase, which is performed by the material structure prediction apparatus according to the embodiment .

An operator inputs various parameters to the material structure prediction apparatus (step S101) .

The input parameters are the start time of the transformation of a new phase (a deposited phase, e.g., a ferrite phase) , the end temperature of the

transformation, the number of initially deposited new nuclei (ferrite nuclei), the designation of a

prediction target region (two-dimensional or

three-dimensional) , the spatial step of the prediction target region, the step width of the time evolution, the number of parent phases (e.g., austenite phases), the carbon concentration, the cooling rate, the

temperature history pattern, the phase transformation entropy difference between the new phase and parent phase, and the interface energy, interface width, and interface mobility as the necessary initial conditions of the MPF method. A thermodynamic quantity required for the operation when the parameters are input is calculated by using the CALPHAD method.

Then, the operator sets and designates an

input/output file to the material structure prediction apparatus (step S102). Consequently, the material structure prediction apparatus performs an operation of reading the coordinates of a parent phase. The parent phase is loaded as data from a Voronoi diagram, a grain growth calculation by cellular automaton, a grain growth calculation by the MPF method, a calculation by the Monte Carlo method, or a structure photograph taken by a scanning electron microscope (SEM) or the like.

Subsequently, the material structure prediction apparatus performs an initial parameter condition setting process as will be explained below (step S103) .

The data of the parent phase is expressed by using, e.g., an order parameter as a coordinate

function. The order parameter is calculated based on a phase-interface dynamics equation.

A method of allocating an order parameter <j> to each grain of the parent phase will be explained in detail below with reference to FIGS. 3 and 4. Assume that a polycrystal has two phases, i . e . , an a-phase and β-phase, and contains grains belonging to these phases. Referring to FIG. 3, al to a6 indicate grains belonging to the a-phase, and βΐ and β2 indicate grains belonging to the β-phase. The boundaries between these grains are grain boundaries.

The order parameter φ is allocated to each grain in a calculation region. As shown in FIG. 4, an order parameter is prepared for each grain. For example, 1 is allocated to order parameter φ_α3 of grain a3 in a region where grain a3 exists, and 0 is allocated to φ_α3 in a region where the grain does not exist. This process is performed for each grain. In the interface (grain boundary) between grains, the order parameters φ are smoothly connected by a sine function. Also, a condition is set such that the sum of grains of the order parameters φ is 1 at an arbitrary coordinate position of a calculation region. This expresses position information of each phase (e.g., the grain boundary of the parent phase) . For example, in the boundary (grain boundary) between two different grains, the order parameter <j> at the coordinate position of the boundary is 0.5. In a triple-j unction (three-point intersection) region, the order parameter φ is about 0.33.

Based on the input or set information, the

material structure prediction apparatus performs initialization for predicting the material structure. For example, the material structure prediction

apparatus sets the arrangement of candidate coordinates of initially deposited new nuclei as the

initialization. The setting of the arrangement of the candidate coordinates of the initially deposited new nuclei will be described below with reference to

FIG. 5. FIG. 5 is a simplified view showing the parent phase to be simulated by the material structure

prediction apparatus.

The material structure prediction apparatus arranges nucleation candidate sites (to be also

referred to as dummy sites, nucleation candidate nuclei, or ferrite candidate nuclei hereinafter) DS . As time t changes from 0 to time tl, the material structure prediction apparatus stochastically changes the nucleation candidate sites DS into nucleation sites NS in accordance with the nucleation ratio. Each nucleation candidate site changes into a phase

transformation nucleus based on the classical

nucleation theory. This change from the nucleation candidate sites DS to the nucleation sites NS means that the nuclei of a new phase are formed from the nucleation candidate sites DS .

The material structure prediction apparatus calculates the coordinates of nuclei formable in a calculation region, thereby determining the number of nuclei of the nucleation candidate sites DS . Whether nuclei are formed from the nucleation candidate sites DS depends on the nucleation ratio set for each

nucleation candidate site. The nucleation ratio represents the probability at which nuclei are formed per unit time. If all the nucleation ratios are high, therefore, nuclei may be formed from all the nucleation candidate sites DS as the time elapses. On the other hand, if the nucleation ratio is low, the nucleation candidate site DS from which no nucleus is formed even when the time elapses may remain. Accordingly, the simulation of nucleation behaves in accordance with the nucleation ratio.

To perform simulation to generate nuclei together with the nucleation ratio in order to calculate the interface growth of the ferrite phase after nucleation by the MPF method, the number of order parameters of the new phase must be varied with the elapse of time. The nucleation candidate sites DS can be set in arbitrary positions of the parent phase, but it is also possible to preferentially arrangement triple junctions or grain boundaries. The coordinates of grain

boundaries or triple junctions can be detected by referring to the order parameters of the parent phase. For example, it is possible to determine that a

coordinate point at which the order parameter φ is 0.5 is a parent phase grain boundary position.

A method of setting the arrangement of the

nucleation candidate sites DS will be explained with reference to FIG. 6.

The operator designates (inputs) a number N of nucleation candidate sites DS to be generated in a calculation target region for predicting a material structure, and a minimum distance Rmin between adjacent nuclei .

The material structure prediction apparatus performs arithmetic processing for arranging the coordinates of the N nucleation candidate sites DS .

The coordinates of the nucleation candidate sites DS are determined based on the order parameters φ of the parent phase. In this method, the nucleation candidate sites DS are arranged before the coordinates of the grain boundaries and triple junctions.

The material structure prediction apparatus arranges the nucleation candidate sites DS based on the minimum distance Rmin between adjacent nuclei

designated by the operator. Assuming that the distance between the Ith and (I + l)th nucleation candidate nuclei (ferrite candidate nuclei) is R(I, I + 1), this R(I, I + 1) must satisfy R(I, I + 1) > Rmin (I = 1, 2,..., N - 1), as shown in FIG. 6. The minimum

distance Rmin between adjacent nuclei corresponds to the average adjacent distance between nuclei. By appropriately setting the number N of nucleation candidate nuclei and the minimum distance Rmin between adjacent nuclei in the calculation target region, the deviation and dispersion of the arrangement of the nucleation candidate nuclei are reflected on the calculation target region.

After the arrangement of the nucleation candidate sites is determined, the initial condition of

nucleation is set (step S104). More specifically, the material structure prediction apparatus designates a nucleation ratio that gives the probability at which the nucleation candidate sites change into nuclei of the new phase. As the nucleation ratio, the following equation used as a standard for steel materials is used. Note that for a magnetic material, dielectric material, or polymer material, it is also possible to use a nucleation ratio modeled in accordance with a phenomenon of the material:

... (1) where AG_V is the Gibbs free energy difference between the parent phase and new phase, R is a gas constant, T is the temperature, N is the number of nucleation candidate sites DS, S is the area of the prediction target region, Dy is the diffusion coefficient of a constituent element of the parent phase, [K^-^/m^] is a constant depending on the interface energy or dislocation density, and k2 [J^/mol^] is a constant depending on the activation energy.

After setting the initial parameter condition and initial nucleation condition, the material structure prediction apparatus starts simulation of the steel material (time t = 0) (step S105) . After starting the simulation of the steel material, the material

structure prediction apparatus executes a series of procedures LP2 for generating a new phase in accordance with a preset timing at which nucleation occurs (step S106) . When the new phase is generated, the material structure prediction apparatus calculates the time evolution of the structure of the nuclear new phase by the MPF method (step S107) . The material structure prediction apparatus calculates a diffusion equation based on the calculation result obtained by the MPF method (step S108). The material structure prediction apparatus repeats the arithmetic processing from step S106 to step S108 until a termination condition is met (step S109) . If the termination condition is met, the material structure prediction apparatus outputs information of the predicted material structure as the arithmetic processing result (step S110).

The series of procedures LP2 for simulating nucleation will be explained below.

The material structure prediction apparatus calculates nucleation ratios Is of all of the N

nucleation candidate sites DS (step S201) . The

material structure prediction apparatus compares the nucleation ratio Is of each nucleation candidate site with a random number within the range of 0 (inclusive) to 1 (inclusive) (step S203) . If the nucleation ratio Is is equal to or smaller than the random number, the material structure prediction apparatus determines that no nucleation has occurred in the nucleation candidate site (No in step S203) . If the nucleation ratio Is is larger than the random number, the material structure prediction apparatus determines that nucleation has occurred in the nucleation candidate site (Yes in step S203) . The nucleation candidate site for which

nucleation has occurred is a nucleation site. This nucleation site is saved in a memory (step S204). The material structure prediction apparatus repeats the above-described procedures until comparison for all of the N nucleation candidate sites is complete (step

5205) , thereby simulating nucleation (steps S202 to

5206) .

Next, a series of procedures for calculating the time evolution of the structure of the new phase in which nucleation has started will be explained.

In the case of the γ/α-phase transformation of a steel material, the growth of a new phase after nucleation is diffusion type phase transformation in which the diffusion of a solute accompanies the interface movement. Therefore, it is necessary to simultaneously handle the interface growth of the new phase (a ferrite phase in the case of the γ/α-phase transformation of a steel material), and atomic diffusion that occurs due to the solute dissolution concentration difference between the new phase and the parent phase (an austenite phase in the case of the γ/ -phase deformation of a steel material).

The MPF method is effective for analysis like this. In the MPF method, a phase φϊ (i is a suffix representing 1st to Nth crystal grains) and a carbon concentration c are introduced as order parameters describing the system. The phase φί indicates the a-phase or γ-phase. The phase φί and carbon

concentration c are represented as follows:

Phase φ^, ί), Carbon concentration c(,i) ... (2)

An MPF equation of a non-conservative field is used for the time evolution of a phase, an MPF equation of a conservative field (diffusion equation) is used for the change in concentration with time, and they are expressed in the form of simultaneous equations.

Consequently, equations (3), (4), and (5) below

describe the γ/α-phase transformation. These equations correspond to a system including N (i = 1, 2, 3,..., N) phases. The N crystal grains have the a-phase or γ-phase:

(3) where t is time, AGj _j_ is the Gibbs free energy

difference between the parent phase and new phase, η is the phase interface width, μ is the interface mobility, σ is the interface energy, n is the number of phases having correlation with a given phase, and φ is an order parameter:

N

n =∑S_j ... (4) where Sj = 1 when 0<^.( ,t)^-l is met, and Sj = 0 in other cases.

where Dy is the diffusion coefficient of carbon in the austenite phase, and D_a is the diffusion coefficient of carbon in the ferrite phase.

The most important point of the MPF method is to describe the free energy of a system necessary and sufficient to describe a system of interest (in this case, low-carbon steel), as accurately as possible by using order parameters. This can be achieved by using the CALPHAD method. On the other hand, it is

inefficient to load calculation data of the CALPHAD method and perform calculations each time, from the viewpoint of the calculation cost. When processing not a transformation phenomenon such as massive

transformation but a deposition phenomenon, not all calculation data of the CALPHAD method is necessary, and an equilibrium composition at each temperature need only be known. When handling a phase diagram in this case, approximation can be performed to some extent. An example of the approximation is a linearization state drawing method.

The linearization state drawing method is a method of approximating a region of interest in a phase diagram by a straight line.

FIG. 7 is a graph showing the linearization state drawing method for low-carbon steel. In an actual phase diagram, a curve is drawn for the change in carbon concentration as indicated by a graph Lr (the broken line) . On the other hand, the linearization state drawing method approximates the curve of the graph Lr by a straight line as indicated by a graph La (the solid line) . Assuming that these functions of straight line approximation are represented by F(c) (T = F(c)) and G(c) (T = G(c)) as functions of the temperature by using the approximation by the linearization state drawing method, a proportionality constant k of the equilibrium carbon concentration of the ferrite phase and austenite phase at a temperature T is represented by :

In the linearization state diagram, k(T) can be obtained for each temperature from equation (6) when the functions F(c) and G(c) can be determined once. It is also possible to conversely determine the

temperature from the concentrations of the -phase and γ-phase. Accordingly, the diffusion equation

represented by equation (5) can be deformed as follows by using the linearization state drawing method. The carbon concentration of each phase is represented by equation (7) below by using the order parameters of the a-phase and γ-phase:

... (7)

In this case, the following equation holds: • .. (8)

Furthermore, equation (7) can be rewritten as equations (9) and (10) :

(9)

... (10)

By substituting the carbon concentrations of the phases represented by equations (9) and (10) into equation (5), a carbon diffusion equation to which the linearization state drawing method is applied is obtained as indicated by the following equation:

(ID

FIG. 8 is a flowchart showing the arithmetic procedure of a numerical solution using the MPF method according to this embodiment.

The arithmetic procedure of the numerical solution using the MPF method will be explained below. In this embodiment, an arithmetic procedure for N = 2 will be explained for the sake of simplicity. However, the same procedure can be used even when N is another general value.

Assume that the system is at a given temperature T at given time t_a. Assume also that at this time, MPF functions φ and φγ of the phases can be calculated from MPF equation (3) (step S301) . The carbon concentration at time t_a is calculated from the MPF functions φα and φγ (step S302). Based on the calculated carbon

concentration, a diffusion equation at time t_a is calculated (step S303). Consequently, the carbon concentrations of the a-phase and γ-phase at the temperature T at time t_a are obtained from equations (9) and (10) (step S304) .

At the carbon concentrations obtained from

equations (9) and (10), if the temperatures of the a-phase and γ-phase in the equilibrium state satisfy a local equilibrium state, the local temperatures of these phases can be obtained from the functions F(c) and G(c) indicated by equations (6) and (7). The local temperatures of the a-phase and γ-phase are represented as follows:

Local temperature of a - phase : T°^q

•-. (12)

Local temperature of / - phase : T^*q

For example, the linearized functions F(c) and G(c) are represented as follows:

.F(C) = -10350.0 - c + 891.5 ... (13)

G(c) = -186.2 c + 851.8 ... (14)

The thermodynamic phase transformation driving force at a temperature near the equilibrium temperature is proportional to a supercooling degree ΔΤ

representing a deviation of the system temperature from the equilibrium temperature. This is represented by:

Αϋ,,^ΑΗ,,-ΤΑΞ,,

The supercooling degree ΔΤ at time t_a can be calculated by equations (16), (17), and (18) below (step S305) :

AT ={l_e -τ)=^ΑΤ_α+ΑΤ_γ) ... (18)

Thermodynamic driving force ΔΘγα = Sy (Te - T) at given time t_a is obtained by equation (15) to (18). Syoc is the phase transformation entropy difference between the parent phase (equivalent to the austenite phase in the case of the γ/α-phase transform of a steel material) , and the new phase (equivalent to the ferrite phase in the case of the γ/α-phase transformation of a steel material) . The MPF equation is solved again by substituting the newly obtained thermodynamic driving Δΰγα into equation (3) (step S306) .

Based on the calculation result of the MPF

equation, an MPF function φ_α at time t_a + At in the next time step is obtained (steps S307 and S301) . The above-described procedure is repeated by substituting the new MPF function φ_α into equations (9) and (10) (steps S301 to S307) . By repeating these procedures, the time evolution of the MPF function φ_α is

successively obtained. The MPF function φ_α under the initial condition (transformation start time) is determined by the spatial distribution of the initially set nucleation candidate sites. As the carbon

concentration c, the value of the equilibrium carbon concentration at the initially set temperature is input from the equilibrium state diagram of the calculation.

By repeating the above-described arithmetic routine until a desired time step, the time evolution of the order parameters and the time revolution of the carbon concentrations representing the phases (the ferrite phase and austenite phase in the case of γ/α-phase transformation of a steel material) are obtained. Since the structural shape of the phase can be displayed by the order parameter, the change in material structure can be checked by the time evolution of the order parameter. It is also possible to check the change in structural shape with time from the change in carbon concentration distribution with time.

Next, a method of determining whether nucleation has been started for the nucleation candidate

coordinates will be explained.

The time evolution of the structure of the new phase for which nucleation has been started is

calculated for only new-phase grains having caused nucleation with parent-phase grains. In the material structure prediction apparatus, nucleation candidate sites are introduced and the order parameters of nucleation candidate nuclei are defined in advance during the initialization of the material structure prediction method.

While calculating the time evolution of the structure of the new phase for which nucleation has been started in time step At, the material structure prediction apparatus determines, for each time step Atnuc, whether nucleation has been started for all nucleation candidate sites of the new phase with respect to the nucleation candidate coordinates.

Whether nucleation has been started for the nucleation candidate site of the new phase is

determined by comparing the nucleation ratio with a random number within the range of 0 (inclusive) to 1 (inclusive) . The nucleation candidate site as a determination target is selected at random by a random number. It is also possible to preferentially select . nucleation candidate site at a specific nucleation coordinate point by a method other than a random number. For example, the priority of nucleation of each nucleation candidate site can be set by

determining the start of nucleation by weighting the nucleation ratio of the nucleation candidate site.

For a new-phase nucleus for which nucleation has occurred in accordance with the nucleation ratio as the time evolution advances, nuclear growth is caused by the time evolution by calculating the time evolution of the structure of the new phase. On the other hand, for a new-phase nucleus for which no nucleation has not occurred, the time evolution of the structure of the new phase is not calculated by regarding that the nucleus is still a nucleation candidate site, thereby causing no nuclear growth.

The nucleation determination step Atnuc of

determining whether nucleation has been started is properly adjusted with respect to the time step At of calculating the time evolution of the structure of the new phase. For example, if the nucleation

determination step Atnuc is excessively larger than At, the change in nucleation becomes coarse with respect to the change in time evolution of the structure.

Consequently, it becomes impossible to simulate

accurate structure formation reflecting the nucleation ratio.

Quantitative γ/ -phase transformation can be predicted by the material structure prediction method performed by the material structure prediction

apparatus. This will be explained below by taking a steel material as an example. FIGS. 10 and 11 illustrate examples of the

calculation results obtained by the material structure prediction apparatus according to this embodiment.

FIG. 10 is a graph showing the ferrite deposition rates obtained by the calculation results. FIG. 11 is a transition diagram showing the transition of the material structure obtained by the calculation results . Also, FIG. 9 shows various parameters used in the calculations shown in FIGS. 10 and 11. Note that the interface mobility is defined as follows:

Referring to FIG. 11, filled portions indicate the new phase (ferrite phase), and unfilled portions indicate the parent phase (austenite phase) . Also, lines indicate the grain boundaries.

As shown in FIGS. 10 and 11, the ferrite

transformation rate changes with the nucleation ratio. In addition, simulation in which the carbon

concentration in the γ/α interface increases with the growth of the ferrite phase is expressed.

FIGS. 12 and 13 illustrate the calculation results obtained by the material structure prediction apparatus when the parameters contained in equation (1) of the nucleation ratio are changed. FIG. 12 shows the change in ferrite deposition rate (transformation rate) .

FIG. 13 shows the change in nucleation ratio. In FIGS. 12 and 13, the ferrite deposition rate changes in accordance with the change in nucleation ratio, as in the FIGS. 10 and 11.

This demonstrates that the material structure prediction apparatus can calculate a material structure by taking the nucleation ratio into account. The material structure prediction apparatus can also simulate the statuses of various kinds of nucleation by adjusting the parameters contained in equation (1) of the nucleation ratio. For example, it is possible to set a high nucleation ratio at the calculation start temperature. This allows the material structure prediction apparatus to simulate a conventionally performed assumption (so-called site saturation) by which nucleation during phase transformation is caused at once at the start of the phase transformation, as a condition for using the MPF method.

The result of comparison of the prediction result obtained by the material structure prediction apparatus according to this embodiment with the actual

experimental result will be explained with reference to FIGS. 14 and 15.

First, the initial conditions will be explained. The calculation region of a metal material was a two-dimensional region of 60 [μπι] x 60

. The number of nucleation candidates was 29. The initial carbon concentration was set at 0.1 [mass%] in order to match that of the experimental conditions. The cooling rate was 10 [K/s] . Other calculation conditions and analytical conditions are as shown in FIG. 14. Note that the definition of the interface mobility is as indicated by equation (19) .

FIG. 15 shows the result of comparison of the calculation result obtained by the material structure prediction apparatus with the experimental result. A solid line CR1 indicates the calculation result

obtained by the material structure prediction

apparatus. Square symbols indicate experimental data described in "Militzer, M., et al . "Three-dimensional phase field modelling of the austenite-to-ferrite transformation." Acta materialia 54.15 (2006): 3961- 3972". A dotted line CR2 indicates the calculation result obtained by the conventional method under the same conditions.

This comparison result shown in FIG. 15 reveals that the calculation result obtained by the

conventional method does not quantitatively agree with the experimental data. Also, disagreement on the high-temperature side is caused by site-saturation approximation of the conventional method.

On the other hand, the calculation result obtained by the present embodiment quantitatively rather agrees with the experimental data over the entire temperature region. Since the material structure prediction apparatus introduces the nucleation ratio to the calculations, the apparatus has improved the

quantitative disagreement on the high-temperature side found in the conventional method.

From the foregoing, quantitative prediction can be obtained from the calculation result obtained by the material structure prediction apparatus.

This embodiment can achieve the following effects.

In the prediction method performed by the material structure prediction apparatus, the structure of a material that causes phase transformation due to a temperature change can quantitatively be predicted by incorporating nucleation based on the classical

nucleation theory into the MPF method.

In the prediction method performed by the material structure prediction apparatus, the MPF method that is originally a method of describing a phase

transformation phenomenon of a secondary phase

transition is applied to a nucleation type primary phase transformation. That is, the material structure prediction apparatus can simulate structure formation by the MPF method directly taking account of the fluctuation in nucleation with time, without using the initial nucleation site-saturation assumption used in the conventional MPF method. More specifically, the material structure prediction apparatus arranges nucleation candidate sites, and stochastically changes, with the elapse of time, the nucleation candidate sites into nucleation sites in accordance with the nucleation ratio. This makes it possible to increase the accuracy of prediction of the temporal transformation end temperature and material structure.

In the prediction method performed by the material structure prediction apparatus, nucleation candidate sites are predetermined. The method of predetermining nucleation candidate sites is equivalent to predefining the order parameters of ferrite candidate nuclei.

Therefore, the number of new phases varies only within the range of the defined number of order parameters . This obviates the need for any complicated programming in order to shift nucleation simulation to new-phase ( ferrite-phase) interface growth simulation by the MPF method. Also, numerical instability of the solution of a differential equation hardly occurs when the local carbon concentration abruptly changes due to sudden addition of an order parameter.

The prediction method performed by the material structure prediction apparatus can predict a material quality characteristic to be obtained in a given processing step. This prediction result can be used to examine an optimum condition for obtaining a desired material quality characteristic. This can reduce the enormous cost and labor consumed by, e.g., a method of repeating trial rolling. The prediction result can also be used in guideline search for a heat treatment (e.g., cooling, heating, or an isothermal process) for giving a material quality characteristic matching the requirement of a steel material user.

Accordingly, the material structure prediction apparatus can reduce the development cost in the manufacturing process, and can also be used as a development assisting tool in the development of a desired product. For example, the material structure prediction apparatus can be used in the site of a steel material manufacturing process.

Furthermore, the material structure prediction apparatus can similarly be used for inorganic materials such as a magnetic material and dielectric material, and organic materials such as a polymer material represented by a block copolymer, as well as steel materials. For example, the magnetic characteristic of a composite magnetic material (typical examples are permalloy, cobalt, and particularly, iron-platinum) having a nanoscale microstructure regarded as effective for a high-density magnetic device, or the magnetic characteristic of a polycrystalline permanent magnetic material represented by a neodymium compound or

samarium compound has a close relationship with the structure. Also, the material structure prediction technique is important for a dielectric material (e.g., a thin film) whose dielectric characteristic depends on the micro-structure, and a polymer material such as a block copolymer exhibiting nanoscale-order micro phase separation, when searching for a guideline of the manufacturing process. Therefore, the material structure prediction apparatus is usable in these fields .

The conventional MPF method poses the problem of quantitative characteristics because the method is based on the phenomenology of secondary phase

transition. Therefore, when applying the MPF method to nucleation type primary phase transition such as that of a steel material, nucleation during phase

transformation is performed by site saturation. The MPF method has no quantitative characteristics perhaps because of this assumption.

This is so because in γ/ -phase transformation of steel during a continuous cooling process performed at a given cooling rate, the nucleation ratio presumably changes as the time elapses (or as the temperature decreases) , so nucleation probably continuously occurs even during the continuous cooling process.

Accordingly, the nucleation assumption at the start of transformation obtained by site saturation is sometimes inappropriate. As a consequence, the deposition rate of a new phase does not quantitatively agree with the experimental result. This lack of the quantitative characteristics is crucial when predicting a continuous cooling transformation diagram (CCT curve) of a steel material by using the conventional MPF method. To sublimate this technique to a practical material prediction technique, a calculation method that

introduces the nucleation ratio or the like to the MPF method is probably necessary. This problem similarly arises in a system in which the physical properties are largely influenced by the material structure of, e.g., an inorganic material such as a magnetic material or dielectric material, or an organic material such as a polymer material represented by a block copolymer, as well as a steel material. This problem is important because the problem of the nucleation assumption of the simulation result obtained by the conventional MPF method is sometimes pertinent to process prediction. "Process prediction" herein mentioned is, e.g., the aging time of a magnet material, the annealing time of a polymer, or different behaviors of structure

formation resulting from nucleation upon

crystallization in solidification or the like.

The result of the conventional MPF method lacking the quantitative characteristics can qualitatively predict the experimental result because the description of the MPF method is kinetically appropriate.

From the viewpoints of these features, the

material structure prediction method performed by the material structure prediction apparatus makes it possible to practically use the prediction results by improving the handling of nucleation in the initial stages of phase transformation.

Note that steel has mainly be explained as a material that causes nucleation type phase

transformation in the embodiment, but the embodiments are not limited to the above-described material. For example, as the material that causes nucleation type phase transformation, it is also possible to use a metal material, a steel material (containing carbon, manganese, silicon, niobium, nickel, aluminum, or nitrogen as a solute) , a magnetic material (an alloy or oxide made of, e.g., copper, iron, platinum, palladium, cobalt, chromium, nickel, neodymium, barium, bismuth, or samarium) , a dielectric material, or a functional material such as a polymeric organic material, e.g., a block copolymer such as polystyrene-methyl

polymethacrylate, as a material structure prediction target. For example, a magnetic material causes nucleation or phase separation due to a heat treatment (including an isothermal process, annealing, and aging) such as heating or cooling, and consequently forms various microstructures . A dielectric material and polymer material also realize various structural forms by annealing such as heating or annealing.

Accordingly, the same arrangement as that of the embodiment can be used to quantitatively predict a material structure formed by phase transformation or phase separation during annealing of these materials. For example, the prediction method performed by the material structure prediction apparatus is applicable to an organic material crystallization process.

Carbon has mainly been explained as a solute in the embodiment, but the solute is not limited to this. The solute may also contain manganese, silicon, niobium, nickel, aluminum, or nitrogen, instead of carbon. In this case, a multicomponent-system

equilibrium state diagram slightly different from the equilibrium state diagram shown in FIG. 2 is obtained. By taking this into consideration, therefore, the same effects as those of the embodiment can be obtained by using the same arrangement as that of the embodiment even when a solute other than carbon is contained.

Although phase transformation from the austenite phase to the ferrite phase of a steel material has mainly been explained in the embodiment, the

embodiments are not limited to this. It is possible to select an arbitrary combination of the parent phase and new phase. For example, it is possible to predict a material structure by phase transformation of an arbitrary combination of the ferrite phase, austenite phase, perlite phase, martensite phase, bainite phase, and cementite phase of a steel material. It is also possible to predict a material structure by phase transformation of an arbitrary combination of phases of any material other than a steel material.

In the embodiment, a material structure is predicted by calculating the time evolution of the structure of a new phase. However, it is also possible to calculate the time evolution of the structure of a parent phase in the same manner as that for a new phase .

Processing of a given part of the arithmetic processing performed by the material structure

prediction apparatus (computer) in the embodiment may also be performed by a human. The principle and theory based on the material structure prediction method according to the embodiment use the law of nature.

Therefore, even when a human performs processing of a part of the material structure prediction method, the material structure prediction method according to the embodiment uses the law of nature as a whole.

A computer constructing the material structure prediction apparatus can have any configuration. For example, the computer includes an arithmetic unit such as a processor of any kind, and a storage unit such as a memory or hard disk. In addition, the computer can include an input/output unit and display unit.

Furthermore, the computer can be any kind of a computer such as a microcomputer or personal computer.

The material structure prediction method according to this embodiment can be incorporated into any system (including an apparatus). For example, the material structure prediction method can be incorporated as a part of a manufacturing process into a product

manufacturing system. A system into which the material structure prediction method is thus incorporated can manufacture a product having a desired material

quality .

While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms;

furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their

equivalents are intended to cover such forms or

modifications as would fall within the scope and spirit of the inventions.

Claims

C L A I M S

1. A material structure prediction method of predicting a material structure which causes phase transformation from a parent phase to a new phase by nucleation resulting from a temperature change of a material, comprising:

prearranging nucleation candidate nuclei in the material ;

determining whether the nucleation has occurred in each of the prearranged nucleation candidate nuclei; and

calculating time evolution of a structure of the new phase by regarding, as the new phase, the

nucleation candidate nucleus for which it is determined that the nucleation has occurred.

2. The method according to claim 1, wherein the calculating the time evolution of the structure of the new phase comprises calculating diffusion of a

constituent element of the new phase by an equation based on phase interface dynamics.

3. The method according to claim 2, wherein the equation based on phase interface dynamics uses a Gibbs. free energy difference between the parent phase and the new phase, a phase interface width, an interface

mobility, and an interface energy.

4. The method according to claim 1, wherein the nucleation candidate nuclei are arranged based on the number of nucleation candidate nuclei to be generated in a calculation region of the material, and an

adjacent-nuclei distance as a distance between the nucleation candidate nuclei.

5. The method according to claim 1, further comprising calculating time evolution of a structure of the parent phase.

6. The method according to claim 1, wherein the determining whether the nucleation has occurred in each of the prearranged nucleation candidate nuclei is performed by comparing a nucleation ratio determined for each nucleation candidate nucleus with a random number .

7. The method according to claim 1, wherein the determining whether the nucleation has occurred in each of the prearranged nucleation candidate nuclei is performed based on a nucleation ratio determined for each nucleation candidate nucleus based on priority of start of the nucleation.

8. A material structure prediction system for predicting a material structure which causes phase transformation from a parent phase to a new phase by nucleation resulting from a temperature change of a material, comprising:

an arranging unit configured to prearrange

nucleation candidate nuclei in the material;

a determining unit configured to determine whether the nucleation has occurred in each of the nucleation candidate nuclei prearranged by the arranging unit; and a calculating unit configured to calculate time evolution of a structure of the new phase by regarding, as the new phase, the nucleation candidate nucleus for which it is determined by the determining unit that the nucleation has occurred.

9. The system according to claim 8, wherein the calculating unit calculates diffusion of a constituent element of the new phase by an equation based on phase interface dynamics.

10. The system according to claim 9, wherein the equation based on phase interface dynamics uses a Gibbs free energy difference between the parent phase and the new phase, a phase interface width, an interface, mobility, and an interface energy.

11. The system according to claim 8, wherein the arranging unit arranges the nucleation candidate nuclei based on the number of nucleation candidate nuclei to be generated in a calculation region of the material, and an ad acent-nuclei distance as a distance between the nucleation candidate nuclei.

12. The system according to claim 8, further comprising a time evolution calculating unit configured to calculate time evolution of a structure of the parent phase.

13. The system according to claim 8, wherein the determining unit performs determination by comparing a nucleation ratio determined for each of the prearranged nucleation candidate nucleus with a random number.

14. The system according to claim 8, wherein the determining unit performs determination based on a nucleation ratio determined for each of the prearranged nucleation candidate nucleus based on priority of start of the nucleation.