JPH10267917A - Prediction method of precipitates in steel - Google Patents

Abstract

(57) [Problem] To provide a method for accurately and easily predicting a precipitation phenomenon in a structure transformed from γ. (I) A method for predicting a precipitation phenomenon in a structure transformed from austenite (γ), wherein a solid solution concentration of an alloy element in γ is determined, and a region to be predicted is divided into minute regions. The following (1), (2), and (3) are calculated for each minute region, and when the total deposition rate does not exceed a certain value and does not reach the cooling end temperature, the time at which the time interval is added is calculated. And (3) performing (1), (2), and (3), and calculating the precipitates in the steel material when the total precipitation rate exceeds a certain value or when the cooling end temperature is reached.
(1) Determine the temperature at that time. (2) Determine the type of phase to be transformed from γ, and calculate the transformation rate. (3) The structure is changed to a transformation phase in accordance with the transformation rate, and the density of precipitate nuclei in the transformation phase and the growth of the precipitate are calculated. (II) The method for predicting precipitates according to (I), wherein the dislocation density ρ, the diffusion constant D, or both of them are increased or decreased according to the transformation phase from γ in the calculation of the precipitation nucleus density.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

TECHNICAL FIELD The present invention relates to quality control of steel products,
The present invention relates to a method for predicting precipitates in a steel material, which is useful for improvement of a manufacturing method and the like, and which predicts the state of precipitates in a steel material manufactured through a phase transformation with high accuracy and simply by calculation.

[0002]

2. Description of the Related Art If the structure and mechanical properties of a steel material can be quantitatively predicted from the chemical composition and the manufacturing conditions of the steel material, it is not necessary to take a test piece and actually perform a test, thereby improving the yield. It is useful not only directly but also for improving the manufacturing method. For this reason, the development of a method for predicting the quality of steel has been energetically performed.

[0003] In these material prediction methods, a method is employed in which a calculation model is created for each metallurgical phenomenon during the manufacture of a steel material, and the whole is integrated to calculate the structure and mechanical properties of the steel material. Is common. Prediction of precipitates also plays an important role in this. In the prediction of the precipitates, particles that precipitate during and after transformation from austenite (hereinafter referred to as “γ”) to ferrite, for example, the average diameter of precipitates such as Nb, Ti, and V carbides, A rate or the like is calculated.

In general, particles precipitated in γ at a high temperature have too large a particle diameter of the precipitate, so that it is not possible to greatly strengthen the steel after transformation. However, the particles that precipitate during and after the transformation from γ are very fine and strengthen the steel, resulting in effects such as changing the toughness. For this reason, emphasis is placed on methods of predicting precipitation phenomena that occur during and after transformation. Structures that transform from γ depending on the cooling rate and the like include ferrite, pearlite, bainite, martensite, and the like, and these are collectively referred to as “transformed phase”.

[0005] As a method of predicting the precipitates in these steel materials, for example, Japanese Patent Application Laid-Open No. 5-72200 discloses a general method of predicting the quality of steel sheets manufactured by normalizing. . However, in this disclosure, the specific structure of each model is not clear, and it is unknown to those skilled in the art how to calculate. In other known documents, there is no specific example of a model for accurately calculating a precipitation phenomenon during and after transformation from γ.

[0006]

An object of the present invention is to specifically and simply calculate the precipitation phenomena during and after transformation from γ, that is, the average precipitated particle density, the average precipitated particle diameter, the amount of precipitates, and the like. To provide a simple method.

[0007]

Means for Solving the Problems The present inventors incorporate the following items into a model for predicting precipitation phenomena during and after transformation from γ so that the prediction of precipitates becomes highly accurate and simple. Could be confirmed.

(A) The nucleation site of the precipitate is limited to the dislocation in the transformation phase transformed from γ. (B) The matrix is divided into minute regions, and the diffusion of alloy elements constituting the precipitate is limited to the minute regions.

(C) The diffusion rate of the alloy element is changed depending on the dislocation density of the transformed phase. That is, the diffusion rate in bainite having a higher dislocation density than the diffusion rate in ferrite is increased.

FIG. 1 is a diagram illustrating an outline of a method for predicting a precipitation phenomenon in the method of the present invention incorporating the above items. In the method illustrated in the figure, the transformation rate of the transformation phase over time is calculated by the Johnson-Mehl-Avrami equation described later, and the density of the precipitate nuclei and the precipitates grown from the precipitate nuclei are transformed for each transformed microregion. This is a method in which the material diameter and the like are calculated, and the entire precipitation rate is obtained.

The present invention incorporates the above items (a), (b) and (c) and has been completed through a number of verifications. The gist of the present invention lies in the following method for predicting precipitates (see FIG. 1). .

(I) A method for predicting a precipitation phenomenon in a structure transformed from austenite, comprising determining a solid solution concentration of an alloy element in austenite, dividing a region to be predicted in steel into minute regions, The following calculations (1), (2), and (3) are performed for each minute region, and the total deposition rate is calculated from the amount of precipitation in each minute region. When the end temperature has not been reached, the time obtained by adding a time step to that time is further described in (1) below.
(2) and (3) are performed, and when the total precipitation rate exceeds a certain value, or when the cooling end temperature is reached, the calculation is terminated. Do).

(1) The temperature at that time is determined.

(2) Determine the type of phase that transforms from austenite and calculate the transformation rate.

(3) The structure is changed to a transformation phase corresponding to the transformation rate, and the density of precipitate nuclei in the transformation phase and the growth of the precipitate are calculated.

(II) In the calculation of the precipitation nucleus density, the method for predicting precipitates in steel material according to [Invention 1] is to increase or decrease the dislocation density ρ and / or the diffusion constant D according to the transformation phase from austenite. Invention 2)).

Here, the precipitation phenomena targeted by [Invention 1] and [Invention 2] cover the stage from the generation of the precipitation nuclei to the early stage of growth, and the precipitates thereafter become coarse and coarse. This does not include the stage where so-called Ostwald ripening occurs. The “transformation phase” is not limited to a single structure in each prediction, and may be, for example, a mixed structure of ferrite and bainite. The target “steel material” corresponds to a thick steel plate, a hot-rolled steel plate, a bar steel, a steel bar, a seamless steel pipe, and the like.

Next, the above (a), (b) and (c), which are the basic items of the present invention, will be described in detail.

(A) Nucleation site of precipitates The nucleation sites of precipitates are limited to dislocations in the transformation phase transformed from γ. The reason is that in the γ temperature range, the temperature at which the precipitation rate is greatest is at a temperature higher than the Ar ₃ point, and in the temperature range where transformation occurs, the precipitation rate is very slow, so there is no need to consider nucleation in γ. It is. Also,
The nucleation sites on and near the interface between γ and the transformation phase are the most prominent nucleation sites. it was decided to include in the constant a ₁ included in the formula for calculating the.

(B) Matrix division In this model, it is assumed that nuclei of precipitates are formed after transformation. For example, even in one ferrite grain, the nucleation time varies depending on each part. The distance that the alloy element can move is smaller than the ferrite grain size, and the model easily reflects that the nucleus of the precipitate formed quickly has a limit in obtaining the alloy element from the part without the nucleus and continuing to grow. Need to be done. Therefore, one of the most important ideas in the present invention has been devised. In other words, the distance over which the alloy element can move is smaller than the ferrite grain size, and it is simple to say that there is a limit to the nuclei of the precipitates generated earlier that can be obtained by collecting the alloy element from a portion without nuclei and continuing to grow. In order to incorporate it into the calculation, we decided to divide the matrix into small regions for calculation.

An appropriate number of divisions can be estimated as follows. For example, the order of the grain size of the transformation phase, ie, ferrite, at 700 ° C. is 10 μm, while the order of one-hour travel distance of the alloying element is 0.1 μm, which is one hundredth of the ferrite grain size. At 600 ° C., both the ferrite grain size and the moving distance of the alloy element are reduced by one order of magnitude. Therefore, the matrix is divided into 100.

It should be noted that the following is added while adding a bit
Clarify that the matrix partitioning in the present invention is based on a new technical idea. That is, the above-mentioned Japanese Patent Application Laid-Open No. 5-72200 describes that mesh division is performed. However, this mesh division is intended to investigate variations in mechanical properties in each part of a steel sheet. Is qualitatively different. Accordingly, the size of the m point referred to in the publication is a size (10 mm × 10 mm × 100 mm) from which a tensile test specimen or a Charpy impact test specimen can be cut out.
mm), and the order of division is different from the division of a minute region of 10 μm or less performed by the method of the present invention.

(C) Setting diffusion constants and the like in accordance with the type of transformation phase (in the case of [Invention 2]) The present inventor has found that when bainite is formed, compared to ferrite which is assumed to be formed at the same temperature, We have experimentally found that the speed is fast. The reason for this is that the dislocation density is higher in bainite than in ferrite, and the higher dislocation density leads to an increase in nucleation density and an increase in the diffusion rate of each element, thereby promoting precipitation. Therefore, in order to accurately predict the precipitation phenomenon, it is necessary to create a model in consideration of one or both of the increase in the dislocation density and the increase in the diffusion rate.

[0024]

DETAILED DESCRIPTION OF THE INVENTION Next, limited items of the method of the present invention will be described with reference to FIG.

1. Time and temperature The temperature is determined in advance for each time by the cooling curve. The start of the time may be arbitrarily determined, but the time at which no transformation has occurred from γ is defined as the start of the time. The cooling curves include isothermal holding, continuous cooling, forced cooling after rolling, slow cooling after rolling, and regulated cooling after rolling. However, a cooling curve such as furnace cooling, in which the coagulation and coarsening of precipitates cannot be ignored, is not an object of the present invention because the heating time in the temperature range of 600 ° C. or more is long. In the present invention, the precipitation rate of precipitates that greatly affect the strength toughness is zero.
% To a constant value, for example, about 95%, or to the cooling end temperature.

2. Calculation of Transformation Rate of Transformed Phase In the present invention, information is required on how the transformation rate of a phase transformed from γ changes over time. To calculate the transformation rate, the following equation (Johnson-Mehl
-Avrami formula) can be used.

F (t) = 1-exp (−k · t ⁿ ) Where, t: time (s) k, n: constant In the above formula, k and n are constants, and the facts of experiments can be easily reflected through k and n to accurately predict the transformation rate. Specific numerical values of n and k will be described in Examples described later.

3. Precipitation nucleus density There are roughly two methods for calculating the precipitation nucleus density. One is to give a finite nucleation rate, in which case the number of nuclei continues to increase until the end of the precipitation. Another method is to make the density of the nucleus constant regardless of time (zero nuc
leation rate). In the case of this precipitation calculation, the latter was judged to be more desirable. The reason is that a) the nucleation site is a previously limited place such as on the dislocation or on the interface between γ and the transformation phase. In, the time variation of the dislocation density, which is a promising nucleation site, is small, and c) the calculation with the nucleus density constant is better in the experimental results. An equation is used to calculate the density of precipitation nuclei in the transformation phase, I (/ m ³ ).

I = A ₁ · ρ · D · C · σ ^0.5 · V · (kT) ^−0.5 · a ⁻⁴ · exp (−ΔG ^* / kT) where A ₁ is a constant and ρ is the dislocation density (1 / m ² ), D and C are the diffusion constant (m ² / s) and the solid solution concentration (mol fraction) of the alloy element of interest, respectively, and σ is the interface energy (J / m ^2), molar volume (m ³ of V are precipitates), k is Boltzmann's constant ^{(1.38 × 10 -23 J / K} ), T is the absolute temperature (K), a lattice constant of the matrix (m) . ΔG ^* is the activation energy (J) for the formation of precipitation nuclei.

In the formula, the dislocation density in the phase where precipitation occurs,
Interfacial energy, diffusion constant, etc. are taken into account, and depending on the type of phase transformed from γ, dislocation density or diffusion constant or product of dislocation density and diffusion constant can be changed to approximate the actual phenomenon ([Invention 2]).

Note that ΔG ^* in the above equation is a free energy change ΔG (r) due to precipitation nucleation represented by the following equation.
Is the maximum value of.

ΔG (r) = (4/3) · π · r ³ · ΔG _v + ΔE _d (r) + 4π · r ² · σ where r is the radius of the precipitate (m), ΔG _v is the driving force for precipitation per unit volume (J / m ³ ), and ΔE _d (r) is the elastic energy of dislocations changed by the formation of precipitation nuclei, and is expressed by the following equation.

ΔE _d (r) = (G · b ² · r / 2π) · ln (2r / r ₀ ) + G · b ² · r / 5... Where G is the rigidity (N / m ² ), b is the Burgers vector of the dislocation
(m) and r ₀ represent the radius (m) of the dislocation core.

4. Growth Rate of Precipitate In the present invention, since the coarsening of the precipitate is treated in the initial stage of precipitation where negligible, all the precipitate nuclei are assumed to grow as precipitates without disappearing. In the calculation of the growth rate of the precipitates, it is assumed that the diffusion of the alloy element controls the growth, and the equation of growth of the spherical particles is used. The radius (m) of the nucleus generated at a certain time u (s) at a time t (s) can be obtained by an equation and an equation.

R (t) = β · (tu) ^1/2・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ β = (2 (C ₀ -C _r ) / (C _p -C _r ) · D} ^1/2 where C _p and C _r are each at the interface The concentration (mol fraction) of the alloy element in the precipitate and the matrix in equilibrium, and C ₀ is the initial solid solution concentration (mol fraction) of the alloy element. Ti is 0.0
When the solid solution is 5 wt%, the molar fraction is 5.8 × 10 ^−4.
Is approximated.

The use of the equation and the equation allows simple approximation by making the shape of the precipitate spherical.
In addition, sufficient accuracy for deriving the average diameter and the like of the precipitates is provided.

5. Volume Ratio of Precipitate Using the concept of expanded volume, the ratio X _S (t) of the amount of precipitation that has progressed with respect to the amount of precipitation in an equilibrium state can be determined by the following equation. As shown in FIG. 1, when the X _S exceeds a certain value, or ends the calculation when reaching the cooling end temperature. The constant value of this X _S, for example preferably set to 95% or the like.

X _S (t) = 1−exp (−X _E (t) / X _F ) where X _E ( t) (m ³ ) is the total volume (expanded volume) of the precipitate when the individual precipitate grows in isolation, and is calculated by the following equation.

[0039]

(Equation 1)

Further, X _F is the equilibrium precipitation rate (volume fraction), determined by the following equation.

[0041] _{X F = (C 0 -C r} ) / (C p -C r) · V p / V m ····················· V p , V _m are the molar volumes of the precipitate and ferrite (m
³ ).

The ratio X _K of the precipitation amount to the initial solid solution amount of each alloy element is determined by X _K = X _S · (C ₀ -C _r ) / C ₀ .

X _S (t)> (constant value) is a condition for the completion of precipitation,
Therefore, the calculation of the growth of the precipitated particles is stopped.

[0044]

EXAMPLES Next, the effects of the present invention will be described with reference to examples.

Table 1 shows the chemical compositions of the test steels used in the examples.

[0046]

[Table 1]

After heating these steels to 1200 ° C. to make them gamma, prediction of carbide precipitation while maintaining the temperature isothermally at 550 to 800 ° C. was carried out by the method of the present invention. The actual measurement of the precipitate was performed using a steel test piece (diameter 10 mm, length 50
mm), the same heat treatment was performed, and then electrolysis was performed under the conditions commonly used for this type of steel, and the extraction residue was analyzed.

Table 2 shows the measured values of the parameter k of the transformation rate of bainite transformed from γ.

[0049]

[Table 2]

The parameter n other than k in the above equation
Was almost 1. The progress of transformation from γ was performed by an equation using these parameters. In the transformation from γ, no alloying element was distributed, and the concentration of the alloying element was the same in the γ-transformed phase, while the carbon atoms were distributed between the γ-transformed phase. That is, the concentration of solute carbon in ferrite was determined assuming that para equilibrium was established.

Table 3 shows the concentration of dissolved carbon in ferrite in the Fe-1.5% Mn system.

[0052]

[Table 3]

Table 4 shows the solubility product constants A and B used in the calculation of the concentration of solid solution carbon in the ferrite.

[0054]

[Table 4]

Next, the diffusion constant of the alloy element in the ferrite is affected by the fact that the ferrite becomes a ferromagnetic material at a temperature lower than the Curie temperature. The lattice diffusion constant of Ti and V in ferrite must take into account the effect that the self-diffusion constant of iron decreases due to the effect of ferromagnetism.

Table 5 shows the lattice diffusion constants of Ti and V in ferrite in consideration of the effect of ferromagnetism.

[0057]

[Table 5]

Although there is no diffusion constant of Nb in ferrite,
It was inferred from the fact that the values of the diffusion constants of Nb and V in γ were close to each other, and the value of the diffusion constant of V in ferrite was used instead.

FIG. 2 shows the prediction results using the method of the present invention in the case of Ti steel. At a temperature of 750 ° C. to 650 ° C., ferrite is generated for each steel type in Table 1. In this prediction, A ₁ and wherein in the formula, and σ in the formula, was fitting parameters to match the prediction result to the experimental results. In FIG. 2, the value of σ is set to 0.8 J / m ² , and the value of A ₁ is set to 5 × so that the experimental result of precipitation matches the calculated value.
I chose ^10-3 . Later, the value of the A ₁ is a constant for all steels were only the value of σ is changed by steel grades. As can be seen by comparing the experimental value indicated by the black circle in the figure with the calculated value indicated by the solid line, the precipitation phenomenon of TiC was able to be accurately reproduced.

FIG. 3 shows, as a comparative example, the prediction results for Ti steel when the matrix was not divided into minute regions. Since the diffusion range of Ti was not limited, the curve showing the change in the amount of precipitation did not match the experimental data.

FIG. 4 shows the prediction results for the Nb steel. Using the value of σ = 0.50 J / m ² , the experimental result could be well reproduced.

FIG. 5 shows a prediction result in the case of V steel. σ
It was found that the experimental result could be reproduced well using the value of 0.48 J / m ² .

FIG. 6 (a) shows bainite formation 60
4 shows the results of the prediction at 0 ° C. according to the method of the invention. The apparent diffusion rate of Ti in bainite is 5.
The calculation was performed assuming that the number was four times ([Invention 2]). As a result, the deposition rate was in good agreement with the experimental value.

FIG. 6B shows, as a comparative example, the precipitation rate calculated assuming that the diffusion rate in bainite is the same as that in ferrite. The predicted value in this comparative example was almost zero, even though the deposition rate of the experimental value exceeded 0.3, and no agreement was observed with the experimental value.

[0065]

According to the method of the present invention, the state of the precipitates in the steel material can be accurately and simply predicted, which contributes to the improvement of the technology for predicting the quality of the steel sheet, the quality control in the production of the steel material, and the improvement of the production method. It is expected.

[Brief description of the drawings]

FIG. 1 is a diagram schematically showing the method of the present invention.

FIG. 2 is a diagram showing a prediction result of a precipitation rate of TiC precipitated in ferrite of Ti steel using the method of the present invention.

FIG. 3 is a diagram showing a prediction result of a precipitation rate of TiC precipitated in ferrite of Ti steel when a matrix is not divided into minute regions.

FIG. 4 is a view showing a prediction result of a precipitation rate of NbC precipitated in ferrite of Nb steel using the method of the present invention.

FIG. 5 is a diagram showing a prediction result of a precipitation rate of VC precipitated in ferrite of V steel using the method of the present invention.

FIG. 6 (a) is a diagram showing a prediction result of a precipitation rate of TiC precipitated in bainite in a Ti steel using the method of the present invention. (B) It is a figure which shows the precipitation rate of TiC which predicted the diffusion rate of Ti in bainite in Ti steel as the same as that in ferrite.

Claims (2)

[Claims] 1. A method for predicting a precipitation phenomenon in a structure transformed from austenite, comprising determining a solid solution concentration of an alloy element in austenite, dividing a prediction target region in steel into minute regions, and The calculations of (1), (2), and (3) are performed for each minute region, and the total deposition rate is calculated from the amount of precipitation in each minute region.
When the temperature does not reach the cooling end temperature, the following (1), (2) and (3) are further calculated for the time obtained by adding the time interval to the time, and when the total deposition rate exceeds a certain value. Or a method for predicting a precipitate in a steel material, wherein the calculation is terminated when the cooling end temperature is reached. (1) Determine the temperature at that time. (2) Determine the type of phase that transforms from austenite and calculate the transformation rate. (3) The structure is changed to a transformation phase in accordance with the transformation rate, and the density of precipitate nuclei in the transformation phase and the growth of the precipitate are calculated. 2. The prediction of precipitates in steel according to claim 1, wherein in the calculation of the precipitation nucleus density, the dislocation density ρ and / or the diffusion constant D are increased or decreased according to the transformation phase from austenite. Method.