JPH08246045A - Method for measuring ferritic nucleation velocity and rate of growth - Google Patents

Abstract

PURPOSE: To easily and precisely obtain nucleation velocity and parabolic growth rate constant by computing under specific conditions by using respective measured values of ferritic volume fraction and grain size at the time of ferritic transformation from austenitic single phase region. CONSTITUTION: Ferritic transformation is performed by means of isothermal holding at a temp. not higher than the Ae3 point from austenitic single phase region. Ferritic volume fraction Xf and grain size Df are measured, and nucleation velocity Is and parabolic growth rate constant α are determined from equations 1, 2, 3. In these equations, S is the interfacial area of austenite per unit volume before the initiation of ferritic transformation, Cg is the carbon concentration of the austenite in the interface, Ca is the carbon concentration of the ferrite in the interface, C0 is the carbon concentration before the initiation of transformation of austenite, (t) is isothermal transformation holding time, ns is the number of ferritic nuclei per austenitic unit interfacial area forming in the isothermal transformation holding time (t), and πis the ratio of the circumference of a circle to its diameter. By controlling the ferritic structure, control of material and improvement of yield are enabled.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for measuring the nucleation rate and growth rate of ferrite when a ferrite transformation is performed from an austenite single phase state, and particularly contributes to improving the prediction accuracy of the ferrite structure.

Therefore, the present invention particularly contributes to the control of the ferrite structure when controlling the materials such as the yield stress and the toughness value which are greatly influenced by the ferrite structure, or to the improvement of the accuracy of the technique for predicting those materials. .

[0003]

2. Description of the Related Art The ferrite structure of steel is an important factor affecting yield stress and toughness. The ferrite transformation from the austenite single phase is a phenomenon in which ferrite nuclei are generated at a certain generation rate in the austenite single phase, and the individual nuclei thus generated grow with time. Therefore, in order to control the ferrite structure or predict the transformation rate and grain size of the ferrite structure, it is first necessary to accurately measure the nucleation rate and growth rate of ferrite.

By the way, it is difficult to measure the nucleation rate and the growth rate in ferrite transformation of practical steel,
There are often problems with accuracy. For example, "Zeightschr
"Iftfur Metallkunde" 77 (1986) p36 shows an experimental example in which a constant temperature transformation experiment is performed to actually measure the nucleation rate and the growth rate. This method is water cooling from a certain isothermal holding temperature, counting the number of ferrite grains on the old austenite grain boundaries for each test piece, and nucleating from the amount of increase by the isothermal holding time of the ferrite grains per old austenite grain boundary area. Based on the measurement of the speed and the measurement of the thickness of the ferrite that grows in the direction perpendicular to the austenite grain boundaries, the growth rate of the ferrite is calculated from the amount of increase in the thickness of the ferrite due to the constant temperature holding time. Due to the nature of this method, water cooling from the constant temperature holding temperature is required at intervals of several seconds (average of about 5 seconds or less), so a large number of samples are required and it is necessary to enumerate ferrite grains, which is extremely complicated.

Further, "Transformation Behavior of Steel" (1989) p.
1, "Iron and Steel" 8 (1987) p1026, the time derivative of ferrite transformation progress (ferrite transformation rate) is derived by constant-velocity cooling experiment, and the calculated ferrite volume ratio becomes an approximate value. A method of determining the nucleation rate and growth rate by trial and error is introduced, but since the measured transformation rate is indirectly determined so as to match the calculated value,
The measurement method is simple, but the transformation rate can be predicted with the determined nucleation rate and growth rate, but the grain size cannot be predicted, so it is difficult to obtain accurate nucleation rate and growth rate.

In addition, "Materials and Processes" 6 (199
3) For p682 and p760, by changing the isothermal holding time, the ferrite thickness was measured in the direction perpendicular to the old austenite grain boundaries of the water-cooled sample during the isothermal transformation, and the largest ferrite among them was measured immediately after the isothermal holding was started. It is considered that nucleation occurred, and the parabolic rate constant of ferrite was determined from the change over time.After that, a method for obtaining the nucleation rate of ferrite from the transformation rate equation from the measured average particle size of the isothermally transformed material is shown. ing. In this method, of the thickness of the ferrite measured perpendicularly from the former austenite grain boundaries, the maximum is considered to have nucleated immediately after the start of the isothermal holding, but from the viewpoint of quantitative morphology, it seems to be the maximum. Ferrite is also likely to be a small ferrite depending on the cross section of the cut, and even if the true maximum ferrite is measured, it is possible to measure the maximum ferrite larger depending on the cut surface for the same reason. Therefore, the parabolic velocity constant is always overestimated due to its large property. Since the nucleation rate is calculated using this excessively evaluated parabolic rate constant and the same equation (3) as in the method of the present invention, the nucleation rate in equation (3) is always evaluated higher than the actual value. Will be.

[0007] In these conventional methods, it is necessary to carefully measure by a very complicated method for obtaining the nucleation rate and the growth rate or the parabolic growth rate constant, or is it simple but there is a limit to the measurement accuracy? Had to make either choice.

[0008]

As described above, according to the conventional method, either simple measurement is not accurate, or accurate measurement is very complicated and time-consuming. In order to construct a predictive model of ferrite structure with high accuracy, it was necessary to measure and confirm the nucleation rate and growth rate of ferrite transformation under many conditions. Therefore, it is considered essential to develop a method that can measure the nucleation rate and the growth rate easily and with high accuracy.

The object of the present invention is to accurately and simply measure the nucleation rate of ferrite, which is indispensable for establishing a highly accurate prediction method that is the basis of ferrite structure control, and the growth rate represented by a parabolic growth rate constant. Is to provide a method that can be done.

[0010]

Means for Solving the Problems The inventors of the present invention have conducted a study on the progress of ferrite transformation by an isothermal transformation experiment using an experimental apparatus capable of simulating the hot working and the subsequent cooling process. From the above, using the measured values of the volume fraction X _f of ferrite and the grain size D _f when the ferrite transformation is performed while keeping the temperature constant at Ae ₃ point or less, the following (1), (2) and (3) ), The method of the present invention has been found in which the nucleation rate I _S and the parabolic growth rate constant α are determined.

[0011]

[Equation 2]

X _f : volume fraction of ferrite transformation S: grain boundary area of austenite per unit volume before initiation of ferrite transformation C _g : interface between ferrite and austenite carbon concentration on austenite side C _a : interface between ferrite and austenite ferrite side of the carbon concentration C _o: carbon concentration before the start transformation austenite alpha: parabolic growth rate constant t: isothermal transformation retention time [pi: pi I _s: per grain boundary area austenite units ferrite nucleation rate D _f: Average ferrite grain size n _S : Number of ferrite nuclei per austenite unit grain boundary area generated during isothermal transformation holding time t

[0013]

[Function] For measuring the nucleation rate and growth rate of ferrite
The method of the present invention and the operation thereof will be described in detail. Well
First, the formula used here will be described. Formula (1)
Is a known equation that describes the progress of the ferrite isothermal transformation,
For example, "ISIJ.int."32(1992) 261
Is shown in. C in equation (1) _g And C_a Is strange
Of ferrite / austenite interface at normal temperature
At each equilibrium carbon concentration on the side of stenite and the side of ferrite
C_o Is the initial carbon concentration of austenite. this
When C_g And C_a "Materials and processes"Three(199
0), thermodynamic calculation program disclosed in p871
Can be found using. Also, commercially available thermodynamic calculations
It can be calculated similarly using software. Also,
S is the austenite per unit volume before the start of ferrite transformation
It is the grain boundary area of the austenite and there is no residual strain in austenite.
Squid or very small (remain as a rough guide
(When the strain is 0.01 or less), the austenite grain size is
It can be obtained by measuring. When residual strain becomes large
But, I disclosed it in "Iron and Steel" 70 (1984) p557.
It can be calculated in a certain way.

I _s is the nucleation rate per unit grain boundary area of austenite. α is the parabolic growth rate constant,
It can be converted into the growth rate (v) by the following formula. v = (1/2) αt ^1/2 (4) Therefore, measuring the parabolic growth rate constant α is nothing but measuring the growth rate. Here, t is the holding time after the isothermal transformation.

X is an integral variable standardized by the size of the maximum ferrite and can be obtained by the following equation (5). x = α (t-τ) ^1/2 / αt ^1/2 (5) [where (t-τ) is the elapsed time since the nucleus of interest is generated]

[0016] (2) the average ferrite grain diameter D _f, the number n _S of ferrite grains per unit grain boundary area of the O-stay night to generate the isothermal transformation holding time t, the transformation rate X _f and particle per unit volume It is a relational expression of the boundary area S, and
nst. Metals. 19 (1918), p145
Is shown in.

The equation (3) is an equation representing the number of ferrite grains n _S per unit grain boundary area of austenite generated during the isothermal transformation holding time t, π is the circular constant, and other symbols are as described above. Have the same meaning.

This equation (3) is applicable only when the transformation proceeds while repeating nucleation and growth, the nucleation is very fast, and the austenite grain boundaries are filled in a short time (generally less than 1 second). The case is inappropriately applied.

If the transformation rate X _{f of} ferrite and the average grain size D _f can be measured, other variables except the nucleation rate I _s and the parabolic growth rate constant α can either be measured or calculated. .

Next, an experiment necessary for measuring the nucleation rate I _s and the parabolic growth rate constant α will be described. First,
A steel of known composition is heated to a temperature of Ae ₃ or higher to completely transform it into an austenite single phase. In order to see the effect of the residual strain after heating, it is necessary to add strain to the test piece using a hot working device such as a rolling mill or a forging machine and / or a device that can simulate them. Next, 30 ° C /
It is cooled to a temperature at which ferrite transformation takes place at a cooling rate of s or more, held for a certain period of time to perform isothermal transformation, and then rapidly cooled. If ferrite nuclei are generated in this first cooling process, it will hinder accurate measurement thereafter. Therefore, it is necessary to cool at a cooling rate as high as possible, preferably 30 ° C./s or more. In the next isothermal holding, the isothermal holding must be interrupted before the austenite grain boundaries are completely covered with ferrite, and rapid cooling must be carried out to maintain this state. This holding time cannot be unconditionally specified because it changes depending on the composition of the steel, the austenite grain size, and the residual strain, but 0.1 wt% C-0.25 wt% Si-1.
In the case of 5 wt% Mn, when there is no residual strain and the isothermal transformation is performed at 700 ° C., it takes about 1000 seconds or less for coarse grains having an austenite grain size of about 300 μm or more, and this time decreases as the austenite grain size decreases to about 50 μm. It will be as short as 300 seconds. When the residual strain becomes large, this time shifts to the short time side, and when the isothermal transformation temperature becomes low, the time shifts to the short time side. Conversely, when the isothermal transformation temperature rises, this time shifts to the long time side. Regarding the steel composition, when the alloying element amount of C or Mn is decreased, it shifts to the short side, and when it is increased, it shifts to the long side.

Next, the material rapidly cooled from the isothermal transformation holding temperature is polished and etched according to the usual metallographic observation method to obtain the transformation rate X _f and average grain size D _f of ferrite. In the examples, the ferrite transformation rate X _f was obtained by the point calculation method and the average ferrite grain size D _f was obtained by the quadrature method, but it can also be obtained by using an image analyzer or the like.

At this stage, (1), (2) and (3)
The only unknowns in the equation were I _s and α. on the other hand,
Since equation (3) n _S can be transformed from equation (2) into n _S = 2X _f / (3SD _f ³ ) (6), the left side n _{S of} equation (3) will also be obtained, and other variables Since the values are also fixed, all the values in the equation (1) can be obtained by actual measurement or calculation.

However, even if there are two unknowns and two equations, a solution does not always exist, and even if there is a solution, the equation cannot be solved unless the solution method is known. However, the present inventor will explain that there is a solution as follows and that the solution of the equation can be found by the method described below.

For example, 0.1 wt% C-0.25 wt
% Si-1.5 wt% Mn steel, austenite grain size is 51 μm, isothermal transformation temperature 700 ° C., transformation time 50
The relation between the nucleation rate I _s and the parabolic growth rate constant α satisfying the formula (1) and the I _s satisfying the formula (3) in the case of the experiment in seconds.
The relationship between and is plotted in FIG. The former curve is a monotonically decreasing function and the latter curve is a monotonically increasing function, and the two intersect at only one point. Therefore, this solution turns out to be the only solution. In this way, we could confirm that there is a unique solution for I _s and α.

Next, a numerical calculation algorithm for obtaining a solution will be described with reference to the schematic diagram of FIG. First, by substituting an appropriate initial value α (0) for α in equation (3), I _s satisfying equation (3)
Calculate (0). Next, I _s (0) is substituted into the equation (1),
Α (1) that satisfies the expression (1) is obtained. Furthermore, this α
Substituting (1) into equation (3), I _s satisfying equation (3)
Find (1). By repeating this,
α (n) and I _s (n) for the nth time are 5 to 5 regardless of the initial values.
Iterative calculation about 20 times converges to an almost constant value. At this time, the integral was obtained by numerical calculation, and I _s was obtained by the pinching and shooting method. The pinching method can be replaced with the steepest method, the Newton method, or the like.

With respect to the nucleation rate and growth rate of ferrite in the method of the present invention, the experiment has been very complicated but accurate measurement has been conventionally made, or a method that can be easily conducted but has a large error has been selected. and only measures the holding temperature and the holding time t of the isothermal transformation to measure the ferrite transformation ratio X _f of the quenched materials average ferrite grain diameter D _f from the holding temperature, nucleation rate I _s and the parabolic growth rate constant That is, this is an epoch-making method in which the growth rate α can be accurately determined. INDUSTRIAL APPLICABILITY The method of the present invention is applicable to both hot-rolled steel products such as hot-rolled steel plates and thick steel plates, or continuously annealed steel products such as cold-rolled steel plates having a composite structure.

[0027]

Example Four types of steel shown in Table 1 were melted.

[0028]

[Table 1]

Table 2 shows the conditions under which the nucleation rate and the parabolic growth rate constant were actually measured by the method of the present invention, and the results thereof.

[0030]

[Table 2]

The experiment was carried out by using an apparatus for simulating hot rolling [Thermec Master Z manufactured by Fuji Denwa Koki Co., Ltd.]. Actually, the nucleation rate I measured by the method of the present invention
FIG. 3 shows the prediction accuracy when _s and the parabolic growth rate constant α are substituted into (1) to (3). As shown in FIG. 3, it is possible to faithfully reproduce the progress of transformation and the change in grain size due to the constant temperature. This is because the method of the present invention can accurately measure the nucleation rate and the parabolic growth rate constant.

FIG. 4 shows the calculation accuracy of the transformation rate that can be reproduced by the nucleation rate and the parabolic rate constant obtained by the method of the present invention, and FIG. 5 shows the calculation accuracy of the particle size. The conventional method referred to here is the method shown in “Materials and Processes” 6 (1993) p682 and 760. in this way,
As already mentioned, since the nucleation rate and the parabolic growth rate constant are always overestimated, both the transformation rate and the grain size become larger than the actual values. On the other hand, since the method of the present invention can accurately measure the nucleation rate and the parabolic growth rate constant, the transformation rate and the grain size can be calculated accurately.

[0033]

As is apparent from the above description, the nucleation rate of ferrite is forced to make a choice between the conventional method which is complicated but accurate measurement and the method which is inferior in accuracy but can be easily measured. Regarding the method of measuring the growth rate, that is, the parabolic growth rate constant, the method of the present invention can measure the nucleation rate and the parabolic growth rate constant simply and accurately.

As a result, the ferrite structure can be accurately predicted, and the material control and the yield improvement can be achieved by controlling the ferrite structure of the steel material manufactured by the hot rolling process and / or the steel material manufactured by the continuous annealing process. It is possible and the economic effect is very large.

[Brief description of drawings]

FIG. 1 is a diagram showing that there are solutions that satisfy (1) and (3) in the method of the present invention.

FIG. 2 schematically shows a solution method for easily reaching a solution.

FIG. 3 is a diagram showing that the progress of transformation and changes in grain size are faithfully reproduced by the nucleation rate and the parabolic growth rate constant measured by the method of the present invention.

FIG. 4 is a diagram comparing the calculation accuracy of the transformation rate and the grain size reproduced by the nucleation rate and the parabolic growth rate constant measured by the method of the present invention with those by the conventional method.

FIG. 5 is a diagram comparing the calculation accuracy of the transformation rate and the grain size reproduced by the nucleation rate and the parabolic growth rate constant measured by the method of the present invention with those by the conventional method.

Claims (1)

[Claims] 1. Using the measured values of the volume fraction X _f of ferrite and the grain size D _f when the ferrite transformation is carried out from the austenite single-phase region at a temperature of Ae ₃ point or less by constant temperature, the following ( 1), (2) and (3) from the equation, the nucleation rate and method of measuring the growth rate of the ferrite and obtains the nucleation rate I _s and the parabolic growth rate constant alpha. [Equation 1] X _f : Volume fraction of ferrite transformation S: Grain boundary area of austenite per unit volume before initiation of ferrite transformation C _g : Carbon concentration on austenite side of interface between ferrite and austenite C _a : On ferrite side of interface between ferrite and austenite Carbon concentration C _o : Carbon concentration before initiation of austenite transformation α: Parabolic growth rate constant t: Constant temperature transformation retention time π: Circular ratio I _S : Ferrite nucleation rate per unit grain boundary area of austenite D _f : Average ferrite grain Diameter n _S : Number of ferrite nuclei per unit grain boundary area of austenite generated during isothermal transformation holding time t