KR102226653B1 - Isothermal Transformation Diagram Adjustment Method of Metal - Google Patents

Abstract

The present invention relates to a method for adjusting an isothermal transformation diagram of a metallic material.
The present invention is a first step of executing the Jomini test; A second step of determining a sample point; A third step of measuring the phase fraction; A fourth step of using the initial IT diagram; A fifth step of performing finite element analysis; A sixth step of predicting the phase fraction; A seventh step of calculating and calculating an objective function; And an eighth step of determining whether the error, which is the value calculated in the seventh step, is minimized, and ending if the error is the minimum value.

Description

Isothermal Transformation Diagram Adjustment Method of Metal}

The present invention relates to a method for adjusting an isothermal transformation diagram of a metallic material.

Efforts to reduce vehicle weight are steadily driven by engineers and researchers to improve the strength of parts and extend their lifespan.

In addition, simulation techniques have been developed that can handle fully combined mechanical and metallurgical problems. However, since the metallurgical properties of the material are still not sufficiently considered, it can lead to substantial errors and inaccurate metallurgical predictions for metal formation and heat treatment processes.

The present invention is intended to improve substantial errors and inaccurate metallurgical predictions for metal forming and heat treatment processes.

The solution means of the present invention comprises: a first step of executing a Jomini test; A second step of determining a sample point; A third step of measuring the phase fraction; A fourth step of using the initial IT diagram; A fifth step of performing finite element analysis; A sixth step of predicting the phase fraction; A seventh step of calculating and calculating an objective function; A method of adjusting an isothermal transformation diagram of a metal material including an eighth step of determining whether an error, which is a value calculated in the seventh step, is minimized, and ending if it is the minimum value may be provided.

The present invention can adjust and optimize the IT diagram of metallic materials using the Jomini test.

The present invention is based on a finite element optimization process, and an error (difference) between a target phase fraction and a corresponding finite element solution at a sample point can be repeatedly minimized using an optimization tool.

For example, a standard jomini test of AISI 52100 bearing steel can be used to confirm the feasibility and reliability of the adjustment method of the present invention.

The three optimization parameters for each IT diagram curve can be mathematically applied to the modified Kiridaldi model.

This optimization parameter is an optimization design variable, and the curve obtained from the modified Kiridaldi model can be used as an initial guess in the optimization process, and the error can be minimized to approximate the experimental IT diagram.

Good agreement can be found between the optimized diagram and the experimental diagram reported in the literature.

By comparing the predicted phase fraction using the experimental IT diagram, the IT diagram obtained from the modified Kiridaldi model, and the IT diagram obtained from the optimized model, the adjustment or optimization procedure can greatly improve the accuracy of the predicted phase fraction of the model.

1 is a conceptual flow diagram of a proposed method for coordinating an IT diagram according to the present invention.
2 is a diagram of an AISI 52100 lecture experiment IT diagram and a modified Kiridaldi model.
3 is a diagram illustrating a transformation from a Tt system to a T'-t' system.
4 is a diagram showing a sample point for measuring the temperature of a specimen.
5 is a diagram showing measured and predicted cooling curves at sample points.
6 is a diagram showing a finite element model and sample points.
7 is a diagram showing the change of the objective function as a function of the number of repetitions.
8 is a diagram of an optimized Kiridaldi model using an experimental IT diagram and a modified Kiridaldi model.
9A to 9D are comparison diagrams of phase fractions predicted by the three models.
10A to 10D are phase fraction diagrams predicted using the modified Kiridaldi model.
11 is a diagram of a phase fraction predicted using an experimental and adjusted Kiridaldi model.

Isothermal Transformation (hereinafter abbreviated as'IT') and Continuous Cooling Transformation (CCT) diagrams are important for heat treatment processing of metal materials. A lot of experimental work was done to determine this diagram.

The IT diagram is a curve representing the transformation of subcooled austenite caused by rapid cooling in terms of time and temperature. After dropping to a certain temperature, the phase change is confirmed while taking a long time.

In addition, in the IT diagram, the transformation start and end times of a metal material, for example, steel are obtained at a constant temperature below the A1 transformation point, and the transformation start and end lines at each temperature are shown on a log scale.

In the case of the equilibrium phase, a phase is formed after a certain period of time after the temperature drops, so the actual phase that can appear at that temperature is one of the measures that can be used to determine how much of the phase changes with time. One is the IT diagram.

This IT diagram can be referred to as a Time Temperature transformation diagram in another expression.

Conversely, the CCT diagram determines the cooling rate (Temperature/sec), and you can see what phases are formed when the temperature drops at that cooling rate. That is, the CCT diagram can confirm the non-equilibrium phase according to the cooling rate.

However, the wide range of alloy specifications or combinations, combined with the sensitivity of compositional change and dependence on grain size, makes it impossible to create sufficient diagrams for general use.

To overcome this problem, a lot of research has been conducted to develop a model that can provide IT diagrams for various steels with various chemical components.

The Jominy end quench test is one of the most reliable methods used to measure the hardenability of steel.

Such a rough end quenching test involves heating a cylindrical steel specimen to an austenitizing temperature and then quenching one end to form a variety of microstructures consisting of various phases including martensite, bainite, ferrite, perlite and austenite. Can be made of.

The Jomini test is well suited for developing IT or CCT curves using appropriate models.

In the present invention, by combining the finite element method and the optimization method using the standard jomini test, the error between the experimental jomini test result and the finite element prediction based on the model's IT diagram is minimized to improve the IT diagram of a metal material (especially steel). Is to optimize.

Hereinafter, specific details for carrying out the present invention will be described in detail with reference to the accompanying exemplary drawings.

[How to adjust IT diagram]

The present invention is a new method of adjusting the IT diagram of a steel material, and will be described with reference to FIGS. 1 to 11 as follows.

1 is a conceptual flow diagram of a proposed method for adjusting the IT diagram of the present invention.

Referring to FIG. 1, the method for adjusting an IT diagram of the present invention includes a first step (S1) of performing a jomini test of an object; A second step (S2) of determining a sample point of the object; A third step (S3) of measuring the phase fraction; A fourth step (S4) using the initial IT diagram; A fifth step (S5) of performing finite element analysis; A sixth step (S6) of predicting the phase fraction by finite element analysis; A seventh step (S7) of calculating and calculating an objective function; It may include an eighth step of determining whether the error, which is the value calculated in the seventh step, is minimized, and ending if it is the minimum value.

The object can be steel, and the minimization in step 8 is to minimize the error between the target phase fraction and the predicted phase fraction obtained using the experimental and calculated IT diagram.

If the error is not minimized in the eighth step, a finite element analysis is performed again to predict the phase fraction, and a ninth step (S9) of minimizing the error by calculating an objective function may be included.

In the process of moving from the eighth step (S8) to the ninth step (S9), a step of improving (changing) a parameter may be performed.

The finite element optimization method can minimize the error between the target phase fraction and the predicted phase fraction obtained by using the experimental and calculated IT diagrams, respectively.

The adjustment parameters applied to the model are the design variables to be determined.

As an object, for example, a jomini test of AISI 52100 steel can be used to confirm the feasibility and reliability of the adjustment method according to the present invention.

Information about the phase fraction at some sample points, called a target phase fraction, can be obtained from a plane cross section of the Jomini test sample.

The target points can be shared with control points for finite element prediction and IT diagram optimization. The j-th phase fraction measured at the i-th sample point may be applied _{as a related target value X j,tar(i) to be minimized in the objective function of Equation 1 below.}

Where X _j,pre(i) and W _j are the j-th phase fraction predicted by finite element analysis at the i-th sample point and the j-th phase fraction predicted by the weight factor of the j-th phase, respectively to be. n and m are the number of sample points and phases, respectively.

Therefore, the objective function Ψ ₀ can be defined as an error at the sample point. The target phase fraction can be determined in an experimental or theoretical way.

In order to verify the optimization procedure of the present invention shown in FIG. 1, as an embodiment, an optimized IT diagram of a modified Kiridaldy model of AISI 52100 steel can be obtained.

The target phase fraction in an embodiment can be obtained from finite element prediction using an experimental IT diagram. Modified Kyridaldi models and equations of IT diagrams for a given chemical composition and particle size can already be provided from the literature.

2 is a diagram for comparing the experimental IT diagram of the AISI 52100 steel and the theoretical IT diagram of the modified Kiridaldi model. Referring to FIG. 2, the experimental IT diagram and the theoretical IT diagram of the modified Kiridaldi model are compared, respectively. It can be used for target IT diagrams and initial IT diagrams.

In particular, there is a big difference between experimental and theoretical diagrams. In order to adjust the diagram of the IT diagram using some parameters that are optimally determined, two transformation equations can be defined as follows.

Here, T and t are the temperature and time in the untransformed system, and the parameters T'and t'are the temperature and time after transformation, respectively, and can be represented by the adjusted curve shown in FIG. 3.

The constants a, b and c are the adjustment parameters, i.e. the so-called design parameters of the optimization problem, and can be used to optimally adjust the theoretical IT diagram. Adjustment parameters can be obtained for each curve in the IT diagram.

For example, referring to FIG. 3, parameters of the pearlite initiation curve are a _Ps , b _Ps, and c _Ps . Thus, the total number of optimization design parameters for each phase is six, including the adjustment parameters of the initiation and termination curves.

Koisinen-Marburger's non-diffusion transformation model can be used to calculate the martensite and austenite phase fractions.

The martensite onset temperature (M _s ) obtained using JMatPro simulation software can agree well with the experimental values in the reference IT diagram.

Therefore, the optimization problem can be defined as follows.

The design parameters that minimize _{the objective function Ψ 0} can be determined according to some inequality or equivalent constraints.

To optimize the initial IT diagram (modified Kyridaldi model), the initial guesses of a, b and c can be assumed to be 1.0, 0.0 and 0.0, respectively.

During the optimization process, the key idea is to check each phase adjustment parameter, i.e., the design parameter, as an iterative method of predicting the phase fraction closest to the target phase fraction with the objective function described in Equation 1.

GRSM (Global Response Surface Model) can be used as an optimization technique.

[Acquisition of optimized thermal conditions]

The roughness end-quench test of AISI 52100 steel can be analyzed first according to standard ASTM A255 to optimally determine the thermal conditions that have a significant impact on the heat transfer analysis.

An axisymmetric finite element model with 2,000 quadrilateral finite elements based on thermoviscoplasticity can be used.

Table 1 shows the chemical composition ratio of steel materials. Referring to FIG. 4, in the Jomini test, the specimen may be heated to an austenitizing temperature of 850° C. and then cooled at one end by spraying water.

The density of the material was assumed to be constant at ^{7860 kg/m 3.} The heat capacity and thermal conductivity of the steel materials used in the present invention were obtained at different temperatures using JMatPro software, and are summarized in Table 2.

The cylindrical and upper surfaces of the specimen, i.e., the free surface, can be exposed to natural convection and radiation. Heat loss through these free surfaces can be analyzed taking into account convection and radiation.

Radiant heat transfer from this free surface can be calculated as an emissivity of 0.7 using the Stefan-Boltzmann law. Convective heat transfer at the surface can be explained by Newton's law of cooling

Where A, h, T _s and T _a are the surface area, convective heat transfer coefficient, surface temperature and ambient temperature, respectively. The free surface parameter h can be calculated using the formula for natural convection.

The convective heat transfer coefficient h _q of the quenched floor cannot be calculated simply. In particular, h _q has a decisive influence on all predictions related to temperature and can be highly dependent on the surface temperature.

Thus, the optimized convective heat transfer coefficient of the annealed bottom surface can be determined by minimizing the difference between the cooling curve obtained in the experiment and the prediction at a specific sample point, i.e. solving the optimization problem.

It can be assumed that h _{q is temperature dependent and interpolated linearly by a series of h q} values at the optimally determined sample temperature.

The objective function is shown in Equation 5 below.

Here, T _j,pre(i) and T _j,exp(i) are the predicted and experimental temperatures of the i-th sample point and the j-th sampling time during cooling, respectively.

The parameters n and m are the number of sample points (1-5 in Fig. 4) and the number of times sampled, respectively.

Referring to FIG. 5, _{the experimental temperature obtained using the optimized h q} value (Table 3) and the corresponding predicted value agree well. The maximum difference between the measured and predicted temperature is about 50°C at sample points 1 and 2. This error can be calculated at a temperature of less than 300°C at which the diffusion phase transformation ends.

Composition ratio of AISI 52100 steel (wt%) C Mn Si Ni Cr Mo 1.08 0.53 0.25 0.33 1.46 0.08 ASTM grain size: 7.0

Thermal properties of AISI 52100 steel T(℃) 900 700 500 300 100 Specific heat (J/gK) 0.60 0.93 0.68 0.56 0.47 Thermal conductivity
(W/mK) 27.6 31.4 35.1 37.4 35.2

Optimal convective membrane coefficient at the quenched end T(℃) 20 400 580 650 850 h _f (W/m ² K) 43.8 32.4 31.5 10.6 2.0

[IT diagram optimization]

The Jomini test is simulated using a reference IT diagram of steel, and a target phase fraction value for optimization of the adjustment parameters defined in Equations 2 and 3 is obtained using the optimized thermal condition. I can.

Table 4 lists the predicted phase fraction values calculated from 17 sample points on the flat cross section of the specimen shown in FIG. 6.

The coordinates of the sample point and the predicted phase fraction of the location
Sample point x(mm) y(mm) Austenite (%) Pearlite (%) Bainite
(%) Martensite (%) One
11.4
1.5
5.5
0.0
0.0
94.5 2
11.6
3.1
5.5
0.0
0.0
94.5 3
11.5
5.0
5.5
0.0
0.0
94.5 4
11.6
7.2
5.5
0.0
0.0
94.5 5
11.5
9.0
5.5
0.0
0.0
94.5 6
11.4
11.1
5.5
0.0
0.1
94.4 7
11.3
12.9
5.5
0.0
0.3
94.2 8
11.3
13.4
5.5
0.0
0.4
94.2 9
11.7
15.4
5.5
0.0
0.7
93.8 10
11.7
20.1
5.4
0.3
1.4
92.9 11
11.7
25.3
5.3
1.0
1.8
91.9 12
11.7
30.0
5.3
2.7
1.4
90.7 13
11.3
35.7
5.1
7.3
0.8
86.9 14
11.3
45.2
3.7
33.0
0.1
63.2 15
11.3
50.4
2.1
61.3
0.1
36.5 16
11.3
55.1
0.6
89.2
0.0
10.2 17
11.3
60.3
0.0
99.5
0.0
0.4
Average
-
-
4.5
17.3
0.41
77.7

The optimization of the IT curve, that is, the optimization calculation of the adjustment parameters defined in Equation 2 and Equation 3, is performed using the HyperSTUDY optimization tool to determine the difference between the experiment and the prediction at 17 sample points. It can be realized by repeatedly decreasing.

Referring to Fig. 2, for AISI 52100 steel, four curves in the IT diagram including pearlite and bainite initiation and termination should be optimally adjusted.

Therefore, optimization variables are a _Ps , b _Ps , c _{Ps for pearlite initiation, a Pf} , b _Pf , c _Pf for pearlite initiation, a _Bs , b _Bs , c _{Bs for bainite initiation and a Bf} , b for bainite termination _Bf and c _Bf .

The constraints of the adjustment parameters can be specified as follows.

Where a includes a _Ps ,a _Pf ,a _Bs and a _Bf , b includes b _Ps ,b _Pf ,b _Bs and b _Bf , and c _Ps , c _Pf , c _Bs and c _Bf do.

For the initial guess, a ₀ =1.0, b ₀ =0.0, c ₀ =0.0 can be used for all phases. This initial guess provides the same IT diagram with the modified Kiridaldi model, and the diagram approaches the experimental diagram through optimization, that is, minimization of the objective function defined in Equation 1.

Two cases of optimization with different weighting factors can be performed as given in Table 5.

In Case 1, the same weighting factor may be applied to all phases of Equation 1. In case 2, a weighting factor can be unevenly assigned for the average phase fraction given in Table 4 in order to give more importance to the phases with smaller fractions such as bainite and austenite.

In both cases (cases 1 and 2), optimization can be performed independently for both perlite and bainite.

In FIG. 7, the horizontal axis represents the number of repetitions and the vertical axis represents the objective function. As a result of repetition of about 350 times, the objective function values of Case 1 and Case 2 converge to 0.15 and 0.21, respectively.

Table 6 lists the tuning parameters optimized for both cases.

Fig. 7 shows that the reduction of the objective function value for the bainite curve in Case 1 is considerably smaller than that of perlite, so that the optimization cannot properly adjust the bainite curve.

Conversely, the objective function value can be reduced during the optimization of perlite and bainite in case 2 where a weighting factor is applied.

Weight fraction in the optimization case Optimization case W _austenite W _pearlite W _bainite W _martensite Case 1 1.0 1.0 1.0 1.0 Case 2 10.0 2.0 100.0 1.0

Optimization tuning parameters Optimal case Pearlite initiation
Perlite termination Bainite initiation Bainite finish a _Ps b _Ps c _Ps a _Pf b _Pf c _Pf a _Bs b _Bs c _Bs a _Bf b _Bf c _Bf Case 1
2.10
-2.84
3.1
2.58
-4.80
3.7
0.14
1.21
-5.1
0.81
0.48
-8.3 Case 2
2.08
-2.85
-1.3
2.58
-4.78
2.6
0.71
0.05
25.1
0.95
-0.17
-6.3

[Results and Review]

8 shows an IT diagram obtained using an experimental, modified Kiridaldi model and an optimization model (cases 1 and 2).

There are significant differences between the experimental IT diagram and the initial IT diagram from the Kiridaldi model.

By applying the optimal adjustment parameters obtained in the two optimized cases, the modified Kiridaldi model can be improved, and the difference between the experiment and the model can be significantly reduced.

The initiation and termination curves of the perlite phase transformation are in good agreement with the relevant curves in the experimental IT diagram when the optimized tuning parameters obtained in Cases 1 and 2 are applied.

In both cases (cases 1 and 2), the difference between the model and the experiment on the bainite curve also decreases.

However, there are still significant discrepancies between the bainite's experimental initiation and termination curves and those obtained in Case 1.

This discrepancy is due to the small fraction of bainite at the sample point compared to other phases, especially martensite. The average bainite fraction of the sample points is 0.41%, which is less than the average fraction of all other phases (see Table 4).

Therefore, the objective function during optimization is greatly influenced by the pearlite initiation and termination curves, so that the pearlite curve can be more efficiently optimized.

Referring to Fig. 8, the optimization model obtained in Case 2 provides an acceptable curve for bainite and pearlite transformations due to the weighting factor applied to the objective function.

9A to 9D show distributions of predicted austenite, pearlite, bainite and martensite fractions using an experimental IT diagram, a modified Kyridaldi model, and an IT diagram optimized using two optimization cases.

The same finite element model described above applies to all simulations, only the IT diagram used in the simulation is different.

Improving the prediction using the optimized adjustment parameters can be clearly indicated by the qualitative method of FIG. 9.

The distribution of the predicted phase fractions of all phases is similar to that predicted using the experimental IT diagram. However, referring to FIG. 9C, when the experimental IT diagram, optimization case 1 and case 2 are used, respectively, the maximum values of the predicted bainite fraction are 2.0%, 1.1%, and 1.8%, respectively.

The distribution of the bainite fraction in Case 1 exactly matches the experimental IT diagram. The prediction using the modified Kiridaldi model does not match the prediction using the experimental IT diagram at all.

10A to 10D are diagrams showing a quantitative comparison between a predicted phase fraction using an experimental IT diagram with a fraction of a modified and optimized Kiridaldi model.

The R squared values for austenite, pearlite and martensite predicted by Case 1 of the optimized Kyridaldi model were 0.93, 0.96 and 0.92, respectively, and the error between the experimental data and the optimized Kyridaldi model (case 1) was negligible. to be.

The R squared value for the bainite phase is 0.41, which is very far from 1.0. However, the data points for the bainite fraction predicted by case 1 are less scattered in Fig. 10c compared to the modified Kiridaldi model.

By applying the optimized Kyridaldi model obtained in case 2, the R squared values of austenite, perlite and martensite were improved to 0.93, 0.96, 0.96 and 0.92, respectively.

Referring to FIG. 11, in order to reliably evaluate the optimized model, the phase fraction is predicted at 40 sample points distributed on the flat cross section of the Jomini test piece.

These sample points are not the same as the sample points used in the optimization for training the model (Table 4). Therefore, this model can be used to evaluate the reliability of the model.

11 shows that the mean R squared values in Case 1 and Case 2 are 0.9982 and 0.9994, respectively.

Since both values are very close to 1.0, it shows that the optimized model can predict the phase fraction of all phases with great confidence. However, the IT diagram obtained in Case 2 is closer to the experimental IT diagram than in Case 1.

The optimized model of Case 2 indicates that all phase fractions can be correctly predicted even for phases with small fractions such as bainite.

If bainite, ie, an objective function balanced with a weighting factor, is used to optimize, it is possible to predict a reliable phase fraction not only in the Jomini test with small bainite and austenite fractions, but also in other heat treatment processes.

[conclusion]

The IT diagram adjustment method of the present invention uses a finite element solution, and can use actual experiments including phase fractions and optimization techniques measured at designated sample points.

The adjustment parameters defined in the modified Kiridaldi model are used as design variables in the optimization process, and this can minimize the objective error function between the target phase fraction and the predicted phase fraction at the sample points.

With the adjustment method of the present invention, it is possible to obtain three adjustment parameters for each curve in the IT diagram.

The adjustment method of the present invention is practical and feasible, since it is possible to adjust the modified Kiridaldi model for the general steel using the standard Jomini test.

As a result, it can be shown that the Kiridaldi model can reliably predict the phase fraction after applying the optimized adjustment parameters.

However, the IT diagram obtained from the modified Kiridaldi model provides an initial guess for optimization.

By optimizing the tuning parameters, you can bring your initial guesses closer to the experimental IT diagram.

According to the present invention, the error between the phase fraction predicted using the adjusted model IT diagram and the experimental IT diagram can be sufficiently small in actual use.

S1: first step S2: second step
S3: third step S4: fourth step
S5: fifth step S6: sixth step
S7: the seventh step S8: the eighth step
S9: the ninth step

Claims (4)

A first step of executing the Jomini test;
A second step of determining a sample point;
A third step of measuring the phase fraction;
A fourth step of using the initial IT diagram;
A fifth step of performing finite element analysis;
A sixth step of predicting the phase fraction;
A seventh step of calculating and calculating an objective function;
An eighth step of determining whether the error, which is the value calculated in the seventh step, is minimized, and ending if the error is the minimum value;
Including,
Minimization in the eighth step,
To minimize the error between the target phase fraction obtained by the experimental IT diagram and the predicted phase fraction obtained using the theoretical IT diagram, the error is a method of adjusting the isothermal transformation diagram of a metal material calculated by the objective function of the following equation (1).
[Equation 1]

Where, X _j,pre(i) and W _j are the j-th phase fraction and j-th phase weight factors predicted by finite element analysis at the i-th sample point, respectively, and n and m are each sample point It is the number of awards and awards.
The method of claim 1,
If the error is not minimized in the eighth step, the method of adjusting an isothermal transformation diagram of a metallic material comprising a ninth step of changing a parameter and performing a finite element analysis again.
delete The method of claim 1,
The fourth step of using the initial IT diagram,
A method of adjusting an isothermal transformation diagram of a metal material, which is a step of optimally adjusting the theoretical IT diagram by the following equations 2 and 3.
[Equation 2]

[Equation 3]

Where a, b, c are design parameters during optimization, T and t are temperature and time in an untransformed system, and parameters T'and t'are temperature and time after transformation, respectively.

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