JP2597986B2 - Manufacturing method of hot rolled steel - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for adjusting a steel material when a steel material such as a thick plate and a hot strip is manufactured by hot rolling.

(Conventional technology and its problems) The material of steel can be generally expressed as the sum of the term determined by the microstructure, the term determined by the grain size, and the term of other strengthening mechanisms. For example, for the tensile strength (TS), It can be displayed as shown in equation 30).

TS = f (σ _f , σ _P , σ _b , σ _m , V _f , V _P , V _b , V _m , d _f , β) (30) where σ is a parameter representing the strength of each tissue, and V Is a parameter representing the volume fraction of each tissue, and d represents the particle size. The subscripts f, p, b, and m indicate ferrite, pearlite, bainite, and martensite, respectively. Here, β is a parameter representing another strengthening mechanism (for example, precipitation strengthening, processing strengthening, etc.).

Conventionally, as a strength estimation model, there is only a simple multiple regression model in which components, hot rolling end temperature, winding or cooling stop temperature are variables, and the influence of microstructure, ferrite grain size and the like are included in these models. Is not taken into account. The reason why such an inexact multiple regression model withstands the use is that the model only applies to products in one rolling mill, and the manufacturing conditions are such that rolling starts under constant heating conditions, The rolling conditions, including the rolling end temperature, determine the grain size, from the product thickness and composition, and (dominate the transformation behavior).
This is because the cooling temperature range and the cooling rate are also used under strong restraint conditions such that they are automatically determined from the rolling end temperature and the winding temperature. Therefore, the conventional model can be applied only under the specific conditions as described above, and it is necessary to expand the range of rolled material by applying it to other lines and changing rolling conditions and subsequent cooling conditions extensively. Cannot meet the demands of the new era.

Attempts to adjust the material using a model in which the material of the steel material is described in correspondence with the microstructure have been made, for example, in Japanese Patent Publication No. 58-2246 and Japanese Patent Application Laid-Open No. Sho 59-67324. Japanese Patent Publication No. 58-2246 describes a method of calculating the volume ratio of the transformed structure from the cooling curve and predicting the material of the steel material from the volume ratio of the transformed structure. Is not done at all. In JP-A-59-67324, the ultimate austenite grain size and residual strain are calculated from the rolling load of the actual rolling mill, and the ferrite grain size is calculated in the subsequent cooling process. Describes the method of estimating the strengthening, but the hardness and volume fraction of the microstructure cannot be predicted. JP-A-59-67324 states that the austenite grain size, which has a large effect on the final material, can be predicted from the actual rolling load, but Senuma et al.
According to the 101st Symposium on Plastic Working “Constitutive Equations and Numerical Analysis of High-Temperature Deformation Behavior of Metals” (P21-P32), the effect of initial grain size on hot deformation resistance is considered to be small as shown in Fig. 11. Looking at the experimental results, it is questionable whether the method of JP-A-59-67324 can accurately predict the austenite grain size.

(Means for Solving the Problems) Based on the above findings, the present invention solves all of the above-mentioned disadvantages of the prior art, and controls hot rolling to control essential factors governing the quality of hot rolled steel. The purpose of the present invention is to provide a production method by adjusting the quality of steel materials. For this purpose, the austenite grain size and residual strain immediately before cooling are calculated from rolling conditions, which are not performed in the prior art, and each microstructure (ferrite) is calculated from subsequent cooling conditions. , Pearlite, bainite, martensite), the volume ratio, hardness, and ferrite grain size are calculated with high accuracy, and the steel material is calculated from these micro factors. to production conditions between rolled steel sheet, so as to obtain the material of the steel after between target and the heat-rolled, intended to broadly adjust the manufacturing conditions of the steel, Ar ₃ transformation 1. ordinary carbon steel In order to determine the manufacturing conditions when rolling and then cooling to obtain a product, the average austenite grain immediately before the start of cooling is first determined from the components, slab heating conditions, and rolling conditions based on a relational expression predetermined by experiments. The diameter d _γ and the residual strain Δε are calculated, and then each structure (ferrite, pearlite, bainite, martensite) after the completion of cooling from the subsequent cooling conditions and d _γ , Δε
The volume ratio, hardness, and grain size of the steel are calculated based on a relational equation determined in advance by experiments, and the material of the final hot-rolled steel material is determined in advance by experiments from these microstructures (volume ratio, hardness, and grain size of the structure). By calculating based on the determined relational expression, adjusting the production conditions (components, slab heating conditions, rolling conditions, cooling conditions) so that the material becomes the target material, and rolling and cooling by the conditions. A method for producing a hot-rolled steel material, wherein a target material is obtained.

2. The method according to claim 1, wherein when the normal carbon steel is rolled at the Ar ₃ transformation point or higher and then cooled to obtain a product, the material of the final hot-rolled steel material is calculated according to the following.

Heating conditions (heating rate α (° C / s), heating temperature T ₀ (° C),
From the isothermal holding time t _O (s), the average γ particle size on the exit side of the heating furnace is calculated using the equation (1).

From the processing conditions (processing temperature T _i , additional strain ε _i , strain rate _i ) in each pass of the hot rolling a predetermined number of times, the critical strain of dynamic recrystallization in which the additional strain ε is given by equation (2) ε _c
Dynamic recrystallization at the time of greater than static recrystallization, divided into three groups of non-recrystallization, static recrystallization upon application strain epsilon is less than epsilon _c, as divided into 2 groups of non-recrystallized,
Dynamic recrystallization, static recrystallization, unrecrystallized space factor f _D , f _S ,
f _N and particle diameters d _D , d _S , and d _N are (3), (4),
The calculation is performed using the equations (5), (6), (7), and (8).

Equation (9) for the dynamic recrystallization of grain growth between passes
The static recrystallization is calculated by equation (10), and the average austenite grain size _γi immediately before the next pass is calculated by equation (11).

The residual distortion Δε _i immediately before the next pass is calculated using (12) in consideration of the recovery of distortion between passes, and in the next pass, the residual distortion Δε _i of the previous pass is added to the additional strain ε _{i + 1.} Is the effective distortion.

The same recrystallization behavior as described above is calculated from the effective strain and _γi , and the recrystallization behavior is repeated a predetermined number of times to obtain the average austenite grain size _γ and the residual strain Δε before the start of cooling.
Is calculated.

Using these _γ and Δε as initial conditions, equations (13), (1) for estimating the isothermal transformation rate of ferrite, pearlite, and bainite
Apply the transformation rate addition rule for any cooling curve using Equations 4) and (15) to obtain the final ferrite, pearlite,
The volume fraction of bainite is calculated, and the volume fraction of martensite is calculated by subtracting the sum of the volume fractions of ferrite, pearlite, and bainite from 1. However consumption rate of latency for transformation and starting from the equilibrium transformation temperature Ae _3, Ae ₃ are determined by (16).

Temperature calculated by equation (17) in the above transformation rate calculation
For ferrite that appears above TPE, use equation (18)
For ferrites that appear below and above 723K, (1
Calculate the hardness according to the cooling curve using equation (9), then (20)
Calculate the final ferrite hardness using the formula, pearlite,
For bainite, the final hardness is calculated using equations (21) and (22).

Then a final ferrite volume fraction X _f and latency tau ₁ is completely consumed, transformation using the temperature Ar ₃ to start (23) and d _fo calculated from the equation using a cooling stop temperature CT (24) The final ferrite grain size d _f is calculated from the equation.

The ferrite particle size (d _f ), ferrite volume fraction and hardness (X _f , H _f ), pearlite volume fraction and hardness (X _p , H _p ), bainite volume fraction and hardness ( X _b ,
H _b ), using the martensite volume fraction (X _m )
According to equation (29), tensile strength TS, yield strength YS, total elongation T
El, uniform elongation U · El, and local elongation L · El are calculated.

d _γo ² = (K ₁ · α ^-a ) ² + A ₁ · exp [-A ₂ / T ₀ ] · T ₀ ^b
(1) a is an index indicating the effect of the heating rate on the average particle size of the heating furnace b. b is an index indicating the effect of the heating temperature on the average particle size of the heating furnace A ₁ is the heating temperature on the average particle size of the heating furnace factor a ₂ representing the effect furnace coefficient average output energy represents the effect of heating temperature on side diameter B represents the effect of heating temperature on average output side diameter heating furnace C is heated furnaces average output side grain Statistical correction constant of diameter ε _c = A ₃ · d _o ^c · exp (A ₄ / RT _i ) (2) T _i is the rolling temperature, R is the gas constant A ₃ is the statistical correction of the crystal limit strain during dynamic The coefficient A ₄ is the energy representing the effect of temperature on the critical strain during dynamic c is the index representing the effect of the initial grain size on the critical strain during dynamic ε _s = A ₅ ｛1−exp (−d _o / K ₂ )｝ K ₂ = A ₆ · ^−d · exp (−A ₇ / T _i ) m = A ₈ · exp (A ₉ / T _i ) d and strain rate statistical correction factor a ₆ crystalline termination strain epsilon _s index a ₅ are dynamic in representing the influence of strain rate on dynamic time crystallization ended strain epsilon _s is on the dynamic when the crystal ends strain epsilon _s exponential statistical correction factor a ₇ of K ₂ representing the influence of temperature energy a ₈ representing the effect of temperature on the dynamic when the crystal ends strain epsilon _s is representative of the influence of the additional strain on the dynamic when the crystal space factor The statistical correction coefficient A ₉ of m is an index f representing the effect of additional strain on the crystal space factor in dynamic energy f _S = (1-f _D ) · (1-exp ｛− (T / τ _S ) ^c ｝)
(4) τ _S = A ₁₀ · ε ^−f .exp (A ₁₁ / RT _i ) where t is the time between passes e is an index representing the effect of time on the static recrystallization space factor f is the static recrystallization space statistical correction factor a ₁₁ of tau _S index a ₁₀ representing the influence of the distortion on the factor is representative of the effect of strain and temperature on the static recrystallization space factor of temperature on the static recrystallization space factor energy _{f N = 1-f D -f} S (5) d D = K 3 · Z -g (6) K 3 = a 12 · Q 0 -A 13 Q 0 = a 14 -A 15 · C representing the influence _{eq C eq = [% C]} + [% Mn] / 6 Z = · exp (Q 0 / RT) g is Zener's-Hollomon Paramete on dynamic recrystallization grain size
Index represents the effect of r A ₁₂ is dynamically recrystallized grains of dynamic recrystallization on the coefficient K ₃ in the radial coefficient A ₁₃ representing the influence of the activation energy Q ₀ is dynamically recrystallized grain size of the coefficient K ₃ of The statistical correction constant A ₁₄ is a statistical correction constant of the activation energy Q ₀ of dynamic recrystallization A ₁₅ is a coefficient d _S = A representing the effect of the carbon equivalent C _eq on the activation energy Q ₀ of dynamic recrystallization ₁₆ · d ₀ ^h · ε ^-i (7) h is an index representing the effect of the initial particle size on the static recrystallized grain size i is an index representing the effect of the strain on the static recrystallized grain size A ₁₆ is the static specific statistical correction factor recrystallized grain size _{d N = d 0 · exp (} -ε / 4) (8) d DG 2 = d D 2 + a 17 · C eq -j · exp (-A 18 / T) · t ^k (9) d _SG ² = d _S ² + A ₁₉ · C _eq ^−l · exp (−A ₂₀ / T) · t ^m (10) j represents the effect of carbon equivalent on dynamic recrystallized grain growth. The index k indicates the effect of time on dynamic recrystallized grain growth. M is an index indicating the effect of time on static recrystallized grain growth A ₁₇ is a statistical correction factor for dynamic recrystallized grain growth A ₁₈ is an index on dynamic recrystallized grain growth Energy ₁₉ representing the effect of temperature is a statistical correction factor for the growth of static recrystallized grains A ₂₀ is energy _γ = [f _D / d _DG ² + f _S / d representing the effect of temperature on the growth of static recrystallized grains _SG ² + f _N / d _N ² ] ^−1/2 (11) Δε = (f _D · ε _c + f _N · ε) · exp (−t / τ _k ) ⁿ (1
2) τ _k = A ₂₁ · exp (A ₂₂ / RT _i ) where n is an index representing the effect of time on residual strain A ₂₁ is a statistical correction factor for residual strain A ₂₂ is the effect of temperature on residual strain energy q = 1/2 ｛γ ² −β · γ ² · (α ² −γ ² ) ⁻¹ / ² · K ₅ + β · (α ² −γ ² ) ^1/2 · K ₆ α = e ^Δε , β = 1, γ = e ^Δε K ₇ = {α ² · (β ² -γ ² ) / β ² · (α ² -γ ² )}
^1/2 μ = arc cos (γ / α) _{K 4 = exp [B 3 +} B 4 · [% C] + B 5 · [% Mn] + B 6 · (T-273) + B 7 (T-273) 2] τ 1 = exp [B 8 · ln K '4 _{+ B 9 · ln T + B} 10 / T + B 11] X f max = 1 - [% C] / {B '11 + B 12 (T-273) + B 13 (T-273) 2} (T ≧ 993K) = 1- [ % C] / {B ′ ₁₁ + B ₁₂ · 993 + B ₁₃ · 993 ² ｝ (T ≧ 993 K) n ₁ is an index representing the effect of time on the ferrite volume fraction B ₁ represents the effect of residual strain on the ferrite volume fraction The coefficient B ₂ is a coefficient representing the effect of residual strain on the volume fraction of ferrite B ₃ is a statistical correction constant of the progress rate of ferrite transformation B ₄ is a coefficient representing the effect of C on the progress rate of ferrite transformation B ₅ is a ferrite transformation the effect coefficient B ₆ which represents the effect of Mn on the rate of progression of factor B ₇ which represents the effect of temperature on the rate of progression of ferrite transformation temperature on the rate of progression of ferrite transformation Factor B ₈ are coefficients B ₁₁ of the effect of temperature coefficient B ₁₀ Effect of temperature on the latency ferrite transformation coefficients B ₉ Effect of transformation progression rate on latency ferrite transformation on the latency ferrite transformation representing the ferrite statistical modified constant B _'11 is a coefficient indicating the statistical modified constant B ₁₂ the effect of temperature on the transformation capable ferrite transformation ratio X _{f max} the maximum transformation possible ferrite transformation ratio X _{f max} the maximum transformation latency coefficient B ₁₃ is showing the effect of temperature on the transformation capable ferrite transformation ratio X _{f max} the maximum _{K 8 = (1-X f} ) 2/3, X f: ferrite volume ratio _{K 9 = (1-X f} ) K 10 = exp [B 16 + B 17 · [% C] + B 18 · [% Mn] + B ₁₉ · (T−273) + B ₂₀ (T−273) ² ] τ ₂ = exp [B ₂₁ · lnK ′ ₁₀ + B ₂₂ · lnT + B ₂₃ / T + B ₂₄ ] X _{p max} = 1−X _{f max} (T = 993) n ₂ is an index representing the effect of time on the pearlite volume fraction B ₁₄ is a coefficient representing the effect of residual strain on the pearlite volume fraction B ₁₅ is a coefficient representing the effect of the residual strain on the pearlite volume fraction B ₁₆ is the pearlite transformation temperature statistical modified constant B ₁₇ of the traveling speed coefficient B ₁₉ coefficients B ₁₈ representing the effect of C on the rate of progression of pearlite transformation is representative of the effects of Mn on the rate of progression of pearlite transformation on the rate of progression of pearlite transformation coefficients representing the effects B ₂₀ are coefficients B ₂₁ indicating the effect of temperature on the rate of progression of pearlite transformation is variable on the latency pearlite transformation Coefficient B ₂₂ is latency statistical modified constant coefficients B ₂₃ Effect of temperature on the latency pearlite transformation coefficients B ₂₄ Effect of temperature on the latency pearlite transformation pearlite transformation effect in the rate of progress _{K 11 = (1-X f} -X p) 2/3 K 12 = (1-X f -X p) K 13 = exp [B 27 + B 28 · [% C] + B 29 · [% Mn] + B 30 · (T-273) + B 31 (T-273) 2] τ 3 = exp [B 32 · lnK '13 + B 33 · lnT + B 34 / T + B 35] X b max = 1-X f -X p n 3 is bainite index B ₂₅ representing the effect of time on the volume fraction coefficient B ₂₇ coefficients B ₂₆ representing the influence of the residual strain on bainite volume fraction representing the influence of the residual strain on bainite volume fraction statistical rate of advancement of bainite transformation Modification constant B ₂₈ is a coefficient representing the effect of C on the progress rate of bainite transformation B ₂₉ is a coefficient representing the effect of Mn on the progress rate of bainite transformation B ₃₀ is the effect of temperature on the progress rate of bainite transformation factor B ₃₁ are coefficients B ₃₂ indicating the effect of temperature on the rate of progression of bainite transformation of the effects of transformation progression rate on latency bainite transformation The number B ₃₃ is the coefficient of the effects of the temperature coefficient B ₃₄ Effect of temperature on the latency bainite transformation on the latency bainite transformation B ₃₅ is bainite transformation latency statistical modified constant _{Ae 3 = B 36 + B 37} · [% C] + B ₃₈ · (B ₃₉ − [% C]) ⁿ⁴
(16) n ₄ the exponent B ₃₆ is austenite and statistical modified constant B ₃₇ of the equilibrium temperature Ae ₃ of ferrite equilibrium temperature Ae ₃ of austenite and ferrite that represents the effect of carbon content on the equilibrium temperature Ae ₃ of austenite and ferrite coefficients represents the effect of carbon content on the B ₃₈ is constant TPE coefficient B ₃₉ representing the effect of carbon content on the equilibrium temperature Ae ₃ of austenite and ferrite that represents the effect of carbon content on the equilibrium temperature Ae ₃ of austenite and ferrite _{= B 40 + B 41 · [} % C] + B 42 · [% Mn] (17) B 40 is statistically corrected constant B ₄₁ temperature TPE no longer generated perlite of carbon content on the temperature TPE no longer generated pearlite factor B ₄₂ are coefficients _{H f o = C 1 · [} % C] + C 2 · [% Mn] + C 3 · [% Si] + C 4 representing the effect of Mn content on the temperature TPE no longer generated pearlite representation of the effects・ Ln t (18) (T ≧ TPE) t = ( Ar ₃ -T) / CR CR: cooling rate _{H f o = C 5 + C} 6 · [SC (T)] + C 7 · (T-723) n5 · ln
_{t SC (T) = C 8} · exp (C '8 / T) (19) H f = H f o + C 9 · SC (T) (20) H p = Σ [ΔX p · H (T)] / ΣΔX _p (21) H (T) = C ₁₀ · (Ae ₁ −T) ^-1 Ae ₁ = C ₁₁ + C ₁₂ · [% Mn] ΔX _p : Perlite amount appearing at each temperature H _b = C ₁₃ + C ₁₄ ^{· [% C] n6 + C} 15 · [% Mn] + C 16 · [% Si] + C 17 · (T-723) n7 · ln t (22) n 5 is the temperature on the ferrite hardness at TPE below 723K or higher the effect of the index n ₆ representing the influence index C ₁ exponent n ₇ is representative of the effect of temperature on the bainitic hardness representing the influence of carbon on the bainite hardness carbon content on the ferrite hardness at least TPE Coefficient C ₂ represents the effect of the amount of Mn on the ferrite hardness above TPE C ₃ represents the effect of the amount of Si on the ferrite hardness above TPE C ₄ represents the ferrite hardness above TPE coefficient representing the time of effect on C ₅ is TPE below 723K Factor C ₇ statistical correction coefficient C ₆ ferrite hardness at above representation of the effects of the equilibrium dissolved carbon amount on the ferrite hardness at TPE below 723K or higher temperature on the ferrite hardness at TPE below 723K or higher When the coefficient C ₈ representing the effect of time solid equilibrium on the final Fillite hardness in the energy C ₉ is 723K statistical correction coefficient C _'8 equilibrium dissolved carbon amount representing the effect of temperature on the equilibrium solid solution carbon content factor C ₁₃ coefficients C ₁₁ statistically modify constants C ₁₂ of Ae ₁ coefficients C ₁₀ representing the effect of溶炭elementary charges representing the effect of temperature on the bainite hardness representing the effect of Mn content on the Ae ₁ is bainite statistical modification stiffness constants C ₁₄ is the effect of the coefficient C ₁₅ is the coefficient C ₁₆ representing the effect of Mn content on the bainite hardness Si content on bainitic hardness representing the effect of carbon content on the bainite hardness temperature and time coefficient C ₁₇ representing the on bainite hardness Coefficient representing the effect n ₈ is an index representing the effect of the initial grain size on ferrite grain growth after cooling is stopped.f ₁ is a coefficient representing the effect of austenite grain size on ferrite grain size.f ₂ is the effect of residual strain on ferrite grain size. factor f ₆ is ferrite coefficient f ₃ coefficients f ₄ representing the effect of the Ar ₃ on ferrite grain size coefficient f ₅ indicating the effect of residual strain on the ferrite grain size that represents the effect of the residual strain on ferrite grain size factor f ₇ representing the effect of the ferrite volume fraction on particle size statistically modified constant f ₈ of the ferrite grain size statistically modified constant f ₉ of the ferrite grain growth after cooling stop on the ferrite grain growth after the cooling stop statistical modified constant effect of CT energy f ₁₀ representing the effect of temperature on the ferrite grain growth after the cooling stop h: coefficient g ₃ representing the effect of the bainite volume fraction and hardness coefficient g ₂ representing the effect of the ferrite volume fraction and hardness on the tensile strength final thickness g ₁ is on the tensile strength in the tensile strength coefficient g ₆ pulls strong representation of the effects of the ferrite grain size coefficient g ₄ is on the coefficient g ₅ tensile strength which represents the effect of the volume fraction of martensite on the tensile strength which represents the effect of pearlite volume fraction and hardness on pearlite volume coefficient g ₈ representing the effect of the hardness of each phase on the coefficient g ₉ is yield strength which represents the effect of the bainite volume fraction on yield strength on the statistical modified constant g ₇ is yield strength coefficient g ₁₀ statistical modified constant coefficients g ₁₂ is yield strength coefficient g ₁₁ representing the effect of the martensite volume fraction on yield strength which represents the effect of the ferrite grain size on the yield strength which represents the effect of the rate g ₁₃ is of ferrite volume fraction and hardness on the total elongation Martensite volume coefficient g ₁₄ representing the effect coefficient g ₁₅ representing the effect of the bainite volume fraction and hardness on the total elongation on the total elongation coefficient g ₁₆ representing the effect of pearlite volume fraction and hardness on total elongation coefficient g ₁₇ coefficients representing the effects of the ferrite grain size on the total elongation g ₁₈ coefficients g ₁₉ representing the effect of the volume fraction of ferrite and bainite on the total elongation of the plate thickness on the total elongation effect representing the effect of the rate G ₂₀ is a statistical correction constant for total elongation g ₂₁ is a coefficient representing the effect of ferrite volume fraction and hardness on uniform elongation g ₂₂ is a coefficient g representing the effect of bainite volume fraction and hardness on uniform elongation ₂₃ is a coefficient representing the effect of the pearlite volume fraction and hardness on uniform elongation g ₂₄ is a coefficient representing the effect of martensite volume fraction on uniform elongation g ₂₅ is a coefficient g ₂₆ representing the effect of ferrite grain size on uniform elongation Is uniform elongation The effect of pearlite volume fraction coefficient g ₂₉ coefficients g ₂₇ representing the effect of the thickness uniform elongation statistical modified constant g ₂₈ is representative of the effect of the ferrite volume fraction and hardness on local elongation on the on the local elongation to coefficient g ₃₀ representing the coefficients g ₃₁ representing the effect of the volume fraction of martensite on the local elongation coefficient g ₃₂ representing the effect of the ferrite grain size on the local elongation represents the effect of the volume fraction of ferrite and bainite on the local elongation coefficient g ₃₃ coefficients g ₃₄ representing the effect of thickness on the local elongation is a means a statistical correction factor local elongation.

For example, the equation (25) is used for the tensile strength TS. (2
5) constant for g ₁ to g ₆ of formula is determined in advance from the data of hardness and space factor, etc. beforehand tissue with minimal squares method. When the value of the constant is determined after the, H _f, H _p hardness of prediction and X _f and X _p prediction of the space factor and d _f of if possible prediction of particle size TS predictions such as Is also possible at the same time.

The prediction of the hardness of such H _f and H _p (18) using (22) from the equation. For estimating the space factor such as X _f and X _p,
Use the formula. The predicted particle size of d _f, from (3) (12)
Equations (23) and (24) are used.

The correspondence between the predicted value and the measured value as a result is shown in FIGS. That is, the particle size of d _f
Figure, Figure 3 for X _f, Figure 4 for the X _p, Figure 5 for X _b, Figure 6 for H _f, for H _p 7
FIG. 8 shows _Hb .

Then, by substituting the predicted values of the hardness, the space factor, and the particle size into the equation (25), the TS can be predicted. FIG. 1 shows the correspondence of the measured values in that case.

As described above, a model for predicting the TS of the actual rolled material was completed.This model was created, and the components, hot rolling conditions, etc. were changed, simulations were performed in various cases, and the target
Production conditions for obtaining TS can be determined. In this case, the final manufacturing condition is determined by selecting the condition with the lowest manufacturing cost from the manufacturing conditions presented by the simulation. As described above, the optimum manufacturing conditions for obtaining the target material can be determined.

(Operation) The description of the model in the present invention and the operation thereof will be described below.

The material of the hot-rolled steel material varies depending on not only components but also manufacturing conditions such as rolling conditions and cooling conditions. The present inventors have paid attention to the fact that the material of a steel material is associated with the microstructure of the steel material, and have constructed a model for predicting the material from manufacturing conditions through the microstructure. The model consists of two models, one for predicting the microstructure and the other for predicting the material from the microstructure. The model for predicting the microstructure further includes an austenite grain size model for calculating the austenite grain size before cooling and the residual strain, and these models. Is a transformation model for calculating the microstructure such as the volume fraction, the hardness, and the ferrite grain size of the transformed structure after completion of the cooling from the cooling condition with the initial conditions. The entire calculation flow is shown in FIG. 12, and refer to FIG. 12 in the following description.
The following describes each model.

Average austenite grain size after rolling and just before cooling
_γ and residual strain Δε have a large effect on the transformed microstructure fraction, hardness, and grain size generated by subsequent cooling, and influence the final steel material. These _γ and Δε are determined from the processing conditions (processing temperature T _i , additional strain ε _i , strain rate _i ) in the austenite region and the initial grain size d _γo . d _o is an austenite grain size of the rolling mill inlet of the first stage, in the case of reheating material heating temperature T _o, the heating rate alpha, is expressed using it depends isothermal holding time t _o (1) formula In the case of normal heating conditions, the influence of the heating temperature is the largest, and the finer the particles, the lower the temperature. Processing the austenite initial diameter d _o (working temperature T _i,
When the applied strain ε _i and the strain rate _i ), recrystallization is unlikely when the strain ε _i is small (or when the temperature T _i is low), but when ε _i is large (or high T _i ). In (2), static recrystallization occurs after processing, and the grains are refined. Recrystallization during processing (dynamic recrystallization) when a larger strain is applied
Occurs and the grains are further refined. The change in particle size at this time can be considered in two regions with the critical strain ε _C of dynamic recrystallization given by equation (2) as a boundary. In the region of ε _i ≧ ε _C , dynamic recrystallization is considered. , static recrystallization, divided into three groups of non-recrystallized, the ε _{i <ε C} static recrystallization, the non-recrystallized 2
At this time, ε _c becomes smaller as the temperature becomes higher and the initial grains become smaller.

Although space factor f _D of the dynamic recrystallization is epsilon _{i <the} epsilon _C zero, increases with epsilon _i is increased, epsilon _i is the temperature, the initial particle size, it exceeds the strain epsilon _S determined by the strain rate Becomes 1 and (3)
It can be expressed by an expression. epsilon _S is higher temperatures, as low strain rate, becomes a smaller value as the initial austenite grain diameter is small, indicating that the fast progress of dynamic recrystallization. The dynamic recrystallized grain size d _D obtained at this time does not depend on the added strain and the initial grain size at all.
Zener-Hollomo determined by temperature and strain rate as in equation (6)
It has the characteristic of being expressed by the m-factor Z, and becomes finer at lower temperatures and higher strain rates (higher Z). When dynamic recrystallization does not occur, static recrystallization occurs after processing for the entire region, and when dynamic recrystallization occurs, the remaining portion is subjected to processing. This static recrystallization space factor f _S of the time increased with time, the rate as additional distortion is large, fast that elevated temperatures, (4)
It is shown in the form of an expression. Also, the static recrystallized grain size d _S obtained at this time does not depend on the temperature and the strain rate as shown in the equation (7) symmetrically with the dynamic recrystallized grain size, but the initial grain size d _O , additional strain It has the characteristic of being determined by ε _i , and the finer the grain, the smaller the d _O and the larger the ε _i .

The dynamic and static recrystallized grains generated by one processing are
The grains are coarsened by grain growth until the start of the next processing or cooling. At this time, the dynamic recrystallized grains are a kind of processing and structure having a large amount of dislocations in the grains, and the dislocation density differs for each grain. Very fast grain growth is achieved by driving force. On the other hand, since the dislocation density in the grains of the grains that have undergone static recrystallization is extremely low, the driving force for the grain growth is almost only interface energy, and the grains grow relatively slowly.
Expressions (9) and (10) express these. dynamic,
Portion not the static recrystallization as non-recrystallized portion, the space factor f _N is expressed by equation (5), the particle diameter d _N can be expressed as takes in (8) the effect of flattening. By using the above equation, the average austenite grain size _γ after one machining and after the elapse of time t (immediately before the next machining or immediately before the start of cooling) is determined by the space factor occupied by grains belonging to each recrystallization form and Two-dimensional averaging is performed using the particle size of each grain grown during the time t, and is calculated in the form of equation (11). Regarding the release of the strain during the time t, ε _C is averaged in the dynamically recrystallized grains, zero is statically recrystallized grains, and additional strain remains in the non-recrystallized grains. As static recovery between (1
2) The residual strain Δε can be calculated by the equation (2).
By repeating the above process for the actual number of machining,
It is possible to obtain the average γ particle size _γ immediately before the start of cooling and the residual strain Δε. Next, for the cooling process, the isothermal transformation curve (TT
Based on the T curve), calculation is performed by the following method.

When the temperature of the steel material processed in the austenite region is equal to or lower than the equilibrium transformation temperature Ae _{3 represented} by the equation (16), the steel material is ready for transformation. At this time, when maintained at an isothermal temperature (Ae ₃ temperature or less), the transformation starts after consuming the incubation period τ determined by the components and the temperature, and thereafter, the transformation amount increases with time. The kinetics of the transformation progress at this time is Jo as shown in equation (a).
It can be expressed by the expression of hnson-Mehl type.

X (t) = 1−exp ｛−k · (t−τ) ⁿ ｝ (a) (where t ≧ τ) where τ is a latent period, and k and n are constants to be determined from experiments or theory. , X (t) are transformation amounts at time t during the isothermal transformation. n and k are important factors that can express the kinetics of transformation, the effects of processing, etc., and must be determined for each structure (ferrite, pearlite, bainite, etc.) that appears due to transformation. . γ
The effect of the residual strain Δε due to the processing in the region is as follows by Umemoto et al. (Iron and Steel vol. 70 (1984) No. 6). It is necessary to incorporate the three effects of increasing the number of new transformation nucleation sites such as deformation bands generated in the grains and increasing the nucleation rate confidence. According to the method of Umemoto et al., Can be expressed using the grain boundary area increase index q of γ grains elongated by rolling, can be expressed by a square of strain, and can be expressed by a first-order term of strain. Taking these effects into account and expressing equation (a), ferrite, pearlite, and bainite can be expressed as equations (13), (14), and (15), respectively. (13), (14), (15) K in the expression _{'4, K' 10, K} '13
Coefficients K ₄ , K ₁₀ , K excluding the effects of particle size d _γ and residual strain Δε
₁₃ is determined by the isothermal transformation temperature T and the components ([C%], [Mn%]), and the coefficient differs depending on each structure (ferrite, pearlite, bainite). By the time each tissue starts the isothermal transformation at the temperature T, the incubation period represented by τ ₁ , τ ₂ , τ ₃ must be consumed, and these are the isothermal transformation temperature T and K ′ which also incorporates the effect of processing. ₄ , K ′ ₁₀ , K ′ ₁₃ The maximum transformation rate of each structure can be predicted from the equilibrium diagram. For ferrite, X _{f max} can be described in terms of carbon content and transformation temperature, and the rest are _{XP max} and X _{b max} . When there is such an isothermal transformation curve (TTT curve), the transformation progress can be calculated using the addition rule in a normal cooling process. That is, the temperature change is divided into minute temperatures ΔT along the cooling curve, and the progress of the isothermal transformation at each temperature is added. The consumption of ferrite in the incubation period starts at Ae ₃ or less, and the consumption W is expressed by the formula (b). When W exceeds 1, the ferrite transformation starts.

W = ΣW _i (b) where W _i is a latent period consumed in one step from T to T−ΔT, and is expressed by equation (c). Here, CR is the average cooling rate during ΔT.

W _i = ΔT / CR / τ (T) (c) When the ferrite transformation is completed, the pearlite transformation is not completed, and the ferrite transformation is not completed up to the pearlite transformation end temperature TPE shown in equation (17). In such a case, the amount of transformation is calculated on the assumption that the bainite transformation will continue.

Each structure transformed during cooling softens during cooling after transformation and determines the final hardness of the structure. For ferrite that appears at or above the pearlite transformation end temperature TPE expressed by equation (17), the time from the hardness determined by the components ([C%], [Mn%], [Si%]) to TPE is (18) Softens according to the formula. Below TPE, it softens according to equation (19), which depends on temperature and time. At this time, the amount of solute carbon SC equilibrated at each temperature
(T) was taken into account. (19) After calculating to 450 ° C. by formula, and the final ferrite hardness H _f subtracted strengthening by solid-solution carbon content in equilibrium at 450 ° C.. For pearlite, pearlite hardness H determined by formation temperature
(T) is multiplied by the amount of generation ΔX _P and averaged over the total. At this time, the hardness of the pearlite formed at each temperature is considered to be determined by the lamella spacing of the pearlite, and this spacing is described by the degree of subcooling from the Ae ₁ transformation temperature determined by [Mn%]. It is expressed by equation (21). The hardness of the bainite can be calculated for the entire temperature range in which the bainite is formed, by using an equation taking into account the softening shown in the equation (22). Next, the ferrite grain size that appeared during this cooling is determined by the ferrite transformation start temperature Ar ₃ and the ferrite volume fraction, which are determined by the cooling rate and composition, initial γ grain size, and residual strain.
It can be calculated by equation (23) using X _f , the increase in nucleation sites due to processing, the increase in nucleation rate, and the initial γ grain size. Further, in the slow cooling after the cooling is stopped (or after the winding), the grain growth is caused by the coalescence of the ferrite grains. At this time, because of the slow cooling, the finally grown grain size is uniquely determined by the cooling stop temperature (or winding temperature) CT and the initial ferrite grain size _dfo , and can be expressed by equation (24).

It is thought that a mixing rule as established by Tomoda et al. (Iron and steel vol 61 (1975) No. 1) is established between the microstructure obtained in this way and the material of the final hot-rolled steel material. The relationship between the material and microstructure of steel containing various ratios of ferrite, pearlite, bainite, and martensite is decomposed into a part that deforms with constant strain and a part that deforms with constant stress. , Yield stress YS, Total elongation T ・ El, Uniform elongation U ・ El, Local elongation L ・ El
Equations (25) to (29) are obtained, and the material of the final hot-rolled steel material can be calculated by substituting each microstructure factor.

In this way, the microstructure is predicted from each factor in the manufacturing process,
By taking the method of determining the material of the steel from its microstructure, the material of the hot-rolled steel can be estimated regardless of the characteristics of each production line or changes in the production method, etc. By setting the rolling conditions and cooling conditions so as to match the material, it is possible to efficiently produce the required steel material with a good yield.

(Example) FIGS. 1 to 10 show the microstructure factors estimated when the method of the present invention is carried out in the hot rolling step and set as target values, that is, the structure fraction of ferrite, pearlite, and bainite, hardness, and the like. And ferrite grain size, and the final hot-rolled steel sheet material: tensile strength, total elongation, uniform elongation,
The correspondence between the local elongation and each actually measured value obtained in the process of manufacturing a hot-rolled steel material by this is shown. The components of the test steel used at this time are as shown in Table 1, and each coefficient used in the calculation is as shown below. As can be seen from FIGS. 1 to 10, according to the method of the present invention, the microstructure and material of each steel material can be estimated with high accuracy, and according to the relational expressions and coefficients provided by the present invention, the accuracy of obtaining the target material can be improved. High manufacturing conditions can be set.

Table 2 shows an example in which manufacturing conditions are set for a target material and a steel sheet is actually manufactured in detail. The coefficients used for the calculation are as shown below. In the first embodiment, in the setting 1, the TS is lower than the target. In the setting 2 in which the water cooling time was lengthened and the winding temperature was lowered as compared to the setting 1, the calculation result was that the target material was achieved. So, actually set 2
When the steel sheet was manufactured according to the manufacturing conditions described above, the material achieved the target. Similarly, in Example 2, since T.El was lower than the target in the setting 1 in the setting 1, the calculation result was that the target material was achieved by resetting the setting 2 in which the finish rolling temperature was increased. Therefore, when a steel sheet was actually manufactured in accordance with the manufacturing conditions of setting 2, the material achieved the target. As described above, according to the present invention, it is possible to set manufacturing conditions for obtaining a steel sheet of a target material.

a = 0.115 A ₁₂ = 0.1204 b = 0.24 A ₁₃ = 5254 A ₁ = 1.42 × 10 ⁹ A ₁₄ = 72600 A ₂ = 20000 A ₁₅ = 52200 B = 11.4 h = 0.25 C = 34 i = 0.5 C = 0.22 A ₁₆ = 9.71 A ₃ = 1.43 × 10 ^-5 j = 1.43 A ₄ = 18800 k = 0.3 d = 0.0723 l = 1.43 A ₅ = 2.25 m = 0.24 A ₆ = 472 A ₁₇ = 3900 A ₇ = 2960 A ₁₈ = 5380 A ₈ = 0.026 A ₁₉ = 3.68 x 10 ⁸ A ₉ = 4600 A ₂₀ = 20000 e = 1/3 n = 2/3 f = 2.36 A ₂₁ = 8.46 x 10 ^-9 A ₁₀ = 9.11 x 10 ^-15 A ₂₂ = _{43800 A 11 = 67670 g = 0.155} n 1 = 1 B 14 = 0.114 B 32 = -0.684 B 15 = 100 B 33 = 20 B 16 = 10.164 B 34 = 1.649 × 10 4 B 17 = -16.002 B 35 = 155.30 B ₁₈ = -0.980 B ₁₉ = 0.00791 n ₄ = 4.26 B ₂₀ = 2.313 x 10 ^-5 B ₃₆ = 1115 B ₂₁ = -0.917 B ₃₇ = 150.3 B ₂₂ = 20 B ₃₈ = 216 B ₂₃ = 1.956 x 10 ⁴ B ₃₉ = 0.765 B ₂₄ = -157.45 B ₄₀ = 951.30 n ₃ = 1.4 B ₄₁ = 156.07 B ₂₅ = 0.114 B ₄₂ = 26.809 B ₂₆ = 4 B ₂₇ = -28.784 n ₅ = 0.8 B ₂₈ = -11.484 n ₆ = -2 B ₂₉ = -1.112 n ₇ = 2 B ₃₀ = 0.131 C ₁ = 23584.7 B ₃₁ = -1.208 × 10 ^-4 C ₂ = 28.8 C ₃ = 47.6 f ₃ = 5.724 × 10 ^-3 C ₄ = −6.39 f ₄ = −0.533 C ₅ = 126.8 f ₅ = 4.0 C ₆ = 0.555 f _{6 = 0.131 C 7 = -0.0995 f} 7 = -3.107 C 8 = 96500 f 8 = 24.81 C '8 = 6100 f 9 = 151.56 C 9 = 0.555 C 10 = 46726.5 g 1 = 0.157 C 11 = 996 g 2 = 0.222 C ₁₂ = 13.9 g ₃ = 0.246 C ₁₃ = 130.9 g ₄ = 44.3 C ₁₄ = 1260.0 g ₅ = 1.60 C ₁₅ = 23.2 g ₆ = 4.65 C ₁₆ = 49.5 g ₇ = 0.104 C ₁₇ = -3.08 x 10 ^-4 g _{8 = 8.45 g 9 = 11.9 n} 8 = -0.589 g 10 = 2.60 f 1 = -0.469 g 11 = 1/99 f 2 = 0.114 g 12 = -7.96 g 13 = 0.112 g 33 = 0.998 g 14 = -0.072 g ₃₄ = 32.8 g ₁₅ = -0.212 g ₁₆ = -28.08 g ₁₇ = -1.13 g ₁₈ = -28.9 g ₁₉ = 0.449 g ₂₀ = 68.4 g ₂₁ = -0.057 g ₂₂ = -0.115 g ₂₃ = -0.105 g ₂₄ =- 0.005 g ₂₅ = -0.351 g ₂₆ = -0.57 g ₂₇ = 35.6 g ₂₈ = -0.066 g ₂₉ = -9.75 g ₃₀ = -15.7 g ₃₁ = -0.617 g ₃₂ = -19.7 (Effects of the Invention) Invention is considered in the past It is possible to accurately estimate a wide range of materials by combining with high-precision particle size prediction and tissue volume fraction prediction, including prediction of hardness of each microstructure that has not been performed. By selecting a high temperature, it is possible to manufacture a hot-rolled steel material of a material controlled with high precision, so that significant effects such as efficiency in hot rolling, improvement in yield, and reduction in cost can be obtained.

[Brief description of the drawings]

1, 9, and 10 show the mechanical properties (tensile strength TS, yield stress YS, total elongation T) actually obtained by the tensile test.
* El, uniform elongation L * El, local elongation L * El) and the value calculated by the method of the present invention. FIGS. 2 to 8 show the relationship between the calculated value and the actually measured value of the microscopic observation result (ferrite grain size, each tissue volume ratio, each tissue hardness) of the cut surface at the position where the tensile test is performed, by the method of the present invention. It is a thing. FIG. 11 is a stress-strain curve obtained by a hot rolling test by Senuma et al., And shows that the effect of the initial γ grain size is not large enough to be recognized. FIG. 12 shows an overall calculation flow chart of the present invention.

 ──────────────────────────────────────────────────の Continuing on the front page (72) Inventor Junichi Wakita 1 Nishinosu, Oita-shi, Nippon Steel Corporation Inside Oita Works, Ltd. (72) Inventor Kazuaki Esaka 1 Nishi-nosu, Oita-shi Oita Works

Claims (2)

(57) [Claims] When a normal carbon steel is rolled at an Ar ₃ transformation point or higher and then cooled to obtain a product, the production conditions are determined based on a relational expression determined in advance by an experiment. The average austenite grain size d _γ immediately before the start of cooling and the residual strain Δε are calculated from the heating conditions and rolling conditions, and then the respective structures (ferrite, pearlite, bainite, bainite) after the completion of cooling are calculated from the subsequent cooling conditions and d _γ , Δε. , Martensite), the volume ratio, hardness and grain size of the final hot-rolled steel are calculated from the microstructures (volume ratio, hardness and grain size of the structure) by experiments. Is calculated based on a relational expression determined in advance by experiments,
The production conditions (components, slab heating conditions, rolling conditions, cooling conditions) are adjusted so that the material becomes the target material, and the target material is obtained by rolling and cooling under the conditions. Production method of hot rolled steel. 2. The method according to claim 1, wherein when the normal carbon steel is rolled at the Ar ₃ transformation point or higher and then cooled to obtain a product, the material of the final hot-rolled steel material is calculated from the following. . Heating conditions (heating rate α (° C / s), heating temperature T ₀ (° C),
From the isothermal holding time t _O (s), the average γ particle size on the exit side of the heating furnace is calculated using the equation (1). From the processing conditions (processing temperature T _i , additional strain ε _i , strain rate _i ) in each pass of the hot rolling a predetermined number of times, the critical strain of dynamic recrystallization in which the additional strain ε is given by equation (2) ε _c
Dynamic recrystallization at the time of greater than static recrystallization, divided into three groups of non-recrystallization, static recrystallization upon application strain epsilon is less than epsilon _c, as divided into 2 groups of non-recrystallized,
Dynamic recrystallization, static recrystallization, unrecrystallized space factor f _D , f _S ,
f _N and particle diameters d _D , d _S , and d _N are (3), (4),
The calculation is performed using the equations (5), (6), (7), and (8). Equation (9) for the dynamic recrystallization of grain growth between passes
The static recrystallization is calculated by equation (10), and the average austenite grain size _γi immediately before the next pass is calculated by equation (11). The residual distortion Δε _i immediately before the next pass is calculated using (12) in consideration of the recovery of distortion between passes, and in the next pass, the residual distortion Δε _i of the previous pass is added to the additional strain ε _{i + 1.} Is the effective distortion. The same recrystallization behavior as described above is calculated from the effective strain and _γi , and the recrystallization behavior is repeated a predetermined number of times to obtain the average austenite grain size _γ and the residual strain Δε before the start of cooling.
Is calculated. Using these _γ and Δε as initial conditions, equations (13), (1) for estimating the isothermal transformation rate of ferrite, pearlite, and bainite
Apply the transformation rate addition rule for any cooling curve using Equations 4) and (15) to obtain the final ferrite, pearlite,
The volume fraction of bainite is calculated, and the volume fraction of martensite is calculated by subtracting the sum of the volume fractions of ferrite, pearlite, and bainite from 1. However consumption rate of latency for transformation and starting from the equilibrium transformation temperature Ae _3, Ae ₃ are determined by (16). Temperature calculated by equation (17) in the above transformation rate calculation
For ferrite that appears above TPE, use equation (18)
For ferrites that appear below and above 723K, (1
Calculate the hardness according to the cooling curve using equation (9), then (20)
Calculate the final ferrite hardness using the formula, pearlite,
For bainite, the final hardness is calculated using equations (21) and (22). Then a final ferrite volume fraction X _f and latency tau ₁ is completely consumed, transformation using the temperature Ar ₃ to start (23) and d _fo calculated from the equation using a cooling stop temperature CT (24) The final ferrite grain size d _f is calculated from the equation. The ferrite particle size (d _f ), ferrite volume fraction and hardness (X _f , H _f ), pearlite volume fraction and hardness (X _p , H _p ), bainite volume fraction and hardness ( X _b ,
H _b ), using the martensite volume fraction (X _m )
According to equation (29), tensile strength TS, yield strength YS, total elongation T
El, uniform elongation U · El, and local elongation L · El are calculated. a is an index indicating the effect of the heating rate on the average particle size of the heating furnace b. b is an index indicating the effect of the heating temperature on the average particle size of the heating furnace A ₁ is the heating temperature on the average particle size of the heating furnace factor a ₂ representing the effect furnace coefficient average output energy represents the effect of heating temperature on side diameter B represents the effect of heating temperature on average output side diameter heating furnace C is heated furnaces average output side grain Statistical correction constant of diameter ε _c = A ₃ · d _o ^c · exp (A ₄ / RT _i ) (2) T _i is the rolling temperature, R is the gas constant A ₃ is the statistical correction of the crystal limit strain during dynamic The coefficient A ₄ is the energy representing the effect of temperature on the critical strain during dynamic c is the index representing the effect of the initial grain size on the critical strain during dynamic ε _s = A ₅ ｛1−exp (−d _o / K ₂ )｝ K ₂ = A ₆ · ^−d · exp (−A ₇ / T _i ) m = A ₈ · exp (A ₉ / T _i ) d and strain rate statistical correction factor a ₆ crystalline termination strain epsilon _s index a ₅ are dynamic in representing the influence of strain rate on dynamic time crystallization ended strain epsilon _s is on the dynamic when the crystal ends strain epsilon _s exponential statistical correction factor a ₇ of K ₂ representing the influence of temperature energy a ₈ representing the effect of temperature on the dynamic when the crystal ends strain epsilon _s is representative of the influence of the additional strain on the dynamic when the crystal space factor The statistical correction coefficient A ₉ of m is an index f representing the effect of additional strain on the crystal space factor in dynamic energy f _S = (1-f _D ) · (1-exp ｛− (T / τ _S ) ^c ｝)
(4) τ _S = A ₁₀ · ε ^−f .exp (A ₁₁ / RT _i ) where t is the time between passes e is an index representing the effect of time on the static recrystallization space factor f is the static recrystallization space statistical correction factor a ₁₁ of tau _S index a ₁₀ representing the influence of the distortion on the factor is representative of the effect of strain and temperature on the static recrystallization space factor of temperature on the static recrystallization space factor energy _{f N = 1-f D -f} S (5) d D = K 3 · Z -g (6) K 3 = a 12 · Q 0 -A 13 Q 0 = a 14 -A 15 · C representing the influence _{eq C eq = [% C]} + [% Mn] / 6 Z = · exp (Q 0 / RT) g is Zener's-Hollomon Paramete on dynamic recrystallization grain size
Index represents the effect of r A ₁₂ is dynamically recrystallized grains of dynamic recrystallization on the coefficient K ₃ in the radial coefficient A ₁₃ representing the influence of the activation energy Q ₀ is dynamically recrystallized grain size of the coefficient K ₃ of The statistical correction constant A ₁₄ is a statistical correction constant of the activation energy Q ₀ of dynamic recrystallization A ₁₅ is a coefficient d _S = A representing the effect of the carbon equivalent C _eq on the activation energy Q ₀ of dynamic recrystallization ₁₆ · d ₀ ^h · ε ^-i (7) h is an index representing the effect of the initial particle size on the static recrystallized grain size i is an index representing the effect of the strain on the static recrystallized grain size A ₁₆ is the static specific statistical correction factor recrystallized grain size _{d N = d 0 · exp (} -ε / 4) (8) d DG 2 = d D 2 + a 17 · C eq -j · exp (-A 18 / T) · t ^k (9) d _SG ² = d _S ² + A ₁₉ · C _eq ^−l · exp (−A ₂₀ / T) · t ^m (10) j represents the effect of carbon equivalent on dynamic recrystallized grain growth. The index k indicates the effect of time on dynamic recrystallized grain growth. M is an index indicating the effect of time on static recrystallized grain growth A ₁₇ is a statistical correction factor for dynamic recrystallized grain growth A ₁₈ is an index on dynamic recrystallized grain growth Energy ₁₉ representing the effect of temperature is a statistical correction factor for the growth of static recrystallized grains A ₂₀ is energy _γ = [f _D / d _DG ² + f _S / d representing the effect of temperature on the growth of static recrystallized grains _SG ² + f _N / d _N ² ] ^−1/2 (11) Δε = (f _D · ε _c + f _N · ε) · exp (−t / τ _k ) ⁿ (1
2) τ _k = A ₂₁ · exp (A ₂₂ / RT _i ) where n is an index representing the effect of time on residual strain A ₂₁ is a statistical correction factor for residual strain A ₂₂ is the effect of temperature on residual strain energy q = 1/2 ｛γ ² −β · γ ² · (α ² −γ ² ) ⁻¹ / ² · K ₅ + β · (α ² −γ ² ) ^1/2 · K ₆ α = e ^Δε , β = 1, γ = e ^Δε K ₇ = {α ² · (β ² -γ ² ) / β ² · (α ² -γ ² )}
^1/2 μ = arc cos (γ / α) _{K 4 = exp [B 3 +} B 4 · [% C] + B 5 · [% Mn] + B 6 · (T-273) + B 7 (T-273) 2] τ 1 = exp [B 8 · ln K '4 _{+ B 9 · ln T + B} 10 / T + B 11] X f max = 1 - [% C] / {B '11 + B 12 (T-273) + B 13 (T-273) 2} (T ≧ 993K) = 1- [ % C] / {B ′ ₁₁ + B ₁₂ · 993 + B ₁₃ · 993 ² ｝ (T ≧ 993 K) n ₁ is an index representing the effect of time on the ferrite volume fraction B ₁ represents the effect of residual strain on the ferrite volume fraction The coefficient B ₂ is a coefficient representing the effect of residual strain on the volume fraction of ferrite B ₃ is a statistical correction constant of the progress rate of ferrite transformation B ₄ is a coefficient representing the effect of C on the progress rate of ferrite transformation B ₅ is a ferrite transformation the effect coefficient B ₆ which represents the effect of Mn on the rate of progression of factor B ₇ which represents the effect of temperature on the rate of progression of ferrite transformation temperature on the rate of progression of ferrite transformation Factor B ₈ are coefficients B ₁₁ of the effect of temperature coefficient B ₁₀ Effect of temperature on the latency ferrite transformation coefficients B ₉ Effect of transformation progression rate on latency ferrite transformation on the latency ferrite transformation representing the ferrite statistical modified constant B _'11 is a coefficient indicating the statistical modified constant B ₁₂ the effect of temperature on the transformation capable ferrite transformation ratio X _{f max} the maximum transformation possible ferrite transformation ratio X _{f max} the maximum transformation latency coefficient B ₁₃ is showing the effect of temperature on the transformation capable ferrite transformation ratio X _{f max} the maximum _{K 8 = (1-X f} ) 2/3, X f: ferrite volume ratio _{K 9 = (1-X f} ) K 10 = exp [B 16 + B 17 · [% C] + B 18 · [% Mn] + B ₁₉ · (T−273) + B ₂₀ (T−273) ² ] τ ₂ = exp [B ₂₁ · lnK ′ ₁₀ + B ₂₂ · lnT + B ₂₃ / T + B ₂₄ ] X _{p max} = 1−X _{f max} (T = 993) n ₂ is an index representing the effect of time on the pearlite volume fraction B ₁₄ is a coefficient representing the effect of residual strain on the pearlite volume fraction B ₁₅ is a coefficient representing the effect of the residual strain on the pearlite volume fraction B ₁₆ is the pearlite transformation temperature statistical modified constant B ₁₇ of the traveling speed coefficient B ₁₉ coefficients B ₁₈ representing the effect of C on the rate of progression of pearlite transformation is representative of the effects of Mn on the rate of progression of pearlite transformation on the rate of progression of pearlite transformation coefficients representing the effects B ₂₀ are coefficients B ₂₁ indicating the effect of temperature on the rate of progression of pearlite transformation is variable on the latency pearlite transformation Coefficient B ₂₂ is latency statistical modified constant coefficients B ₂₃ Effect of temperature on the latency pearlite transformation coefficients B ₂₄ Effect of temperature on the latency pearlite transformation pearlite transformation effect in the rate of progress _{K 11 = (1-X f} -X p) 2/3 K 12 = (1-X f -X p) K 13 = exp [B 27 + B 28 · [% C] + B 29 · [% Mn] + B 30 · (T-273) + B 31 (T-273) 2] τ 3 = exp [B 32 · lnK '13 + B 33 · lnT + B 34 / T + B 35] X b max = 1-X f -X p n 3 is bainite index B ₂₅ representing the effect of time on the volume fraction coefficient B ₂₇ coefficients B ₂₆ representing the influence of the residual strain on bainite volume fraction representing the influence of the residual strain on bainite volume fraction statistical rate of advancement of bainite transformation Modification constant B ₂₈ is a coefficient representing the effect of C on the progress rate of bainite transformation B ₂₉ is a coefficient representing the effect of Mn on the progress rate of bainite transformation B ₃₀ is the effect of temperature on the progress rate of bainite transformation factor B ₃₁ are coefficients B ₃₂ indicating the effect of temperature on the rate of progression of bainite transformation of the effects of transformation progression rate on latency bainite transformation The number B ₃₃ is the coefficient of the effects of the temperature coefficient B ₃₄ Effect of temperature on the latency bainite transformation on the latency bainite transformation B ₃₅ is bainite transformation latency statistical modified constant _{Ae 3 = B 36 + B 37} · [% C] + B ₃₈ · (B ₃₉ − [% C]) ⁿ⁴
(16) n ₄ the exponent B ₃₆ is austenite and statistical modified constant B ₃₇ of the equilibrium temperature Ae ₃ of ferrite equilibrium temperature Ae ₃ of austenite and ferrite that represents the effect of carbon content on the equilibrium temperature Ae ₃ of austenite and ferrite coefficients represents the effect of carbon content on the B ₃₈ is constant TPE coefficient B ₃₉ representing the effect of carbon content on the equilibrium temperature Ae ₃ of austenite and ferrite that represents the effect of carbon content on the equilibrium temperature Ae ₃ of austenite and ferrite _{= B 40 + B 41 · [} % C] + B 42 · [% Mn] (17) B 40 is statistically corrected constant B ₄₁ temperature TPE no longer generated perlite of carbon content on the temperature TPE no longer generated pearlite factor B ₄₂ are coefficients _{H f o = C 1 · [} % C] + C 2 · [% Mn] + C 3 · [% Si] + C 4 representing the effect of Mn content on the temperature TPE no longer generated pearlite representation of the effects・ Ln t (18) (T ≧ TPE) t = ( Ar ₃ -T) / CR CR: cooling rate _{H f o = C 5 + C} 6 · [SC (T)] + C 7 · (T-723) n5 · ln
_{t SC (T) = C 8} · exp (C '8 / T) (19) H f = H f o + C 9 · SC (T) (20) H p = Σ [ΔX p · H (T)] / ΣΔX _p (21) H (T) = C ₁₀ · (Ae ₁ −T) ^-1 Ae ₁ = C ₁₁ + C ₁₂ · [% Mn] ΔX _p : Perlite amount appearing at each temperature H _b = C ₁₃ + C ₁₄ ^{· [% C] n6 + C} 15 · [% Mn] + C 16 · [% Si] + C 17 · (T-723) n7 · ln t (22) n 5 is the temperature on the ferrite hardness at TPE below 723K or higher the effect of the index n ₆ representing the influence index C ₁ exponent n ₇ is representative of the effect of temperature on the bainitic hardness representing the influence of carbon on the bainite hardness carbon content on the ferrite hardness at least TPE Coefficient C ₂ represents the effect of the amount of Mn on the ferrite hardness above TPE C ₃ represents the effect of the amount of Si on the ferrite hardness above TPE C ₄ represents the ferrite hardness above TPE coefficient representing the time of effect on C ₅ is TPE below 723K Factor C ₇ statistical correction coefficient C ₆ ferrite hardness at above representation of the effects of the equilibrium dissolved carbon amount on the ferrite hardness at TPE below 723K or higher temperature on the ferrite hardness at TPE below 723K or higher When the coefficient C ₈ representing the effect of time solid equilibrium on the final Fillite hardness in the energy C ₉ is 723K statistical correction coefficient C _'8 equilibrium dissolved carbon amount representing the effect of temperature on the equilibrium solid solution carbon content factor C ₁₃ coefficients C ₁₁ statistically modify constants C ₁₂ of Ae ₁ coefficients C ₁₀ representing the effect of溶炭elementary charges representing the effect of temperature on the bainite hardness representing the effect of Mn content on the Ae ₁ is bainite statistical modification stiffness constants C ₁₄ is the effect of the coefficient C ₁₅ is the coefficient C ₁₆ representing the effect of Mn content on the bainite hardness Si content on bainitic hardness representing the effect of carbon content on the bainite hardness temperature and time coefficient C ₁₇ representing the on bainite hardness Coefficient representing the effect n ₈ is an index representing the effect of the initial grain size on ferrite grain growth after cooling is stopped.f ₁ is a coefficient representing the effect of austenite grain size on ferrite grain size.f ₂ is the effect of residual strain on ferrite grain size. factor f ₆ is ferrite coefficient f ₃ coefficients f ₄ representing the effect of the Ar ₃ on ferrite grain size coefficient f ₅ indicating the effect of residual strain on the ferrite grain size that represents the effect of the residual strain on ferrite grain size factor f ₇ representing the effect of the ferrite volume fraction on particle size statistically modified constant f ₈ of the ferrite grain size statistically modified constant f ₉ of the ferrite grain growth after cooling stop on the ferrite grain growth after the cooling stop statistical modified constant effect of CT energy f ₁₀ representing the effect of temperature on the ferrite grain growth after the cooling stop h: coefficient g ₃ representing the effect of the bainite volume fraction and hardness coefficient g ₂ representing the effect of the ferrite volume fraction and hardness on the tensile strength final thickness g ₁ is on the tensile strength in the tensile strength coefficient g ₆ pulls strong representation of the effects of the ferrite grain size coefficient g ₄ is on the coefficient g ₅ tensile strength which represents the effect of the volume fraction of martensite on the tensile strength which represents the effect of pearlite volume fraction and hardness on pearlite volume coefficient g ₈ representing the effect of the hardness of each phase on the coefficient g ₉ is yield strength which represents the effect of the bainite volume fraction on yield strength on the statistical modified constant g ₇ is yield strength coefficient g ₁₀ statistical modified constant coefficients g ₁₂ is yield strength coefficient g ₁₁ representing the effect of the martensite volume fraction on yield strength which represents the effect of the ferrite grain size on the yield strength which represents the effect of the rate g ₁₃ is of ferrite volume fraction and hardness on the total elongation Martensite volume coefficient g ₁₄ representing the effect coefficient g ₁₅ representing the effect of the bainite volume fraction and hardness on the total elongation on the total elongation coefficient g ₁₆ representing the effect of pearlite volume fraction and hardness on total elongation coefficient g ₁₇ coefficients representing the effects of the ferrite grain size on the total elongation g ₁₈ coefficients g ₁₉ representing the effect of the volume fraction of ferrite and bainite on the total elongation of the plate thickness on the total elongation effect representing the effect of the rate G ₂₀ is a statistical correction constant for total elongation g ₂₁ is a coefficient representing the effect of ferrite volume fraction and hardness on uniform elongation g ₂₂ is a coefficient g representing the effect of bainite volume fraction and hardness on uniform elongation ₂₃ is a coefficient representing the effect of the pearlite volume fraction and hardness on uniform elongation g ₂₄ is a coefficient representing the effect of martensite volume fraction on uniform elongation g ₂₅ is a coefficient g ₂₆ representing the effect of ferrite grain size on uniform elongation Is uniform elongation The effect of pearlite volume fraction coefficient g ₂₉ coefficients g ₂₇ representing the effect of the thickness uniform elongation statistical modified constant g ₂₈ is representative of the effect of the ferrite volume fraction and hardness on local elongation on the on the local elongation to coefficient g ₃₀ representing the coefficients g ₃₁ representing the effect of the volume fraction of martensite on the local elongation coefficient g ₃₂ representing the effect of the ferrite grain size on the local elongation represents the effect of the volume fraction of ferrite and bainite on the local elongation The coefficient g ₃₃ is a coefficient expressing the effect of the thickness on the local elongation g ₃₄ is a statistical correction coefficient of the local elongation