Analysis method of carbon concentration distribution

Abstract

To enhance analysis accuracy of a carbon concentration distribution.SOLUTION: A distribution of a carbon concentration is analyzed based on a diffusion equation with a driving force of a carbon concentration gradient in a steel material. A carbide is formed in the steel material by carburization treatment. The diffusion equation is represented by an equation (I) and an equation (II) described in Claim 1, where D in the equation (I) is calculated from an equation (III) described in Claim 1 or an equation (IV) below. Furthermore, a parameter (in other words, a diffusion flow rate, a diffusion coefficient, a mobility included in the diffusion equation) used in a calculation of a diffusion coefficient in the steel material and a diffusion simulation is corrected with a correction coefficient.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for analyzing the carbon concentration distribution in carburized steel materials.

Background Art

[0002] In steel products (such as drive system products like gears), in order to ensure necessary properties such as wear resistance and fatigue strength on the product surface, carburizing treatment is performed on processed products machined into a desired shape. In recent years, in view of reducing environmental impact, vacuum carburizing treatment typified by vacuum carburizing treatment has been spreading.

[0003] In vacuum carburizing treatment, in a heating furnace, in an atmosphere where a carburizing gas containing carbon is injected in a state where the gas is exhausted and the pressure is reduced, after heating the processed product at a constant temperature and for a certain time, the processed product is immersed in a cooling medium such as oil for cooling. In this vacuum carburizing treatment, there are a carburizing period in which the injection of the carburizing gas continues and a diffusion period in which the injection of the carburizing gas is stopped.

[0004] In vacuum carburizing treatment, when excessive carbon penetrates into the surface layer of the product and carbon does not sufficiently diffuse into the interior compared to the surface layer, coarse carbides may be formed, and characteristics such as the fatigue strength of the product may deteriorate. In order to avoid such problems, the techniques described below are disclosed.

[0005] In Patent Document 1, a carburizing pattern is set, and using a diffusion equation, the carbon concentration of an arbitrary cell in the surface layer of the target part is obtained. Then, by comparing the obtained carbon concentration with the desired carbon concentration, the set carburizing conditions are evaluated to determine pass or fail.

[0006] Patent Document 2 describes a vacuum carburizing treatment method that can suppress carburization variations in carburized parts. The carburizing process has a pre-stage carburizing process from the start of the carburizing process to the intersection time te, and a post-stage carburizing process from the intersection time te to the carburizing time ta. In the pre-stage carburizing process, the actual carburizing gas flow rate is set to be equal to or higher than the theoretical carburizing gas flow rate at the reference time ta / 5 from the start of the carburizing process and equal to or lower than the theoretical carburizing gas flow rate at the 20-second time point from the start of the carburizing process. In the post-stage carburizing process, the actual carburizing gas flow rate is within the range of 1.00 to 1.20 times the theoretical carburizing gas flow rate.

Prior Art Documents

Patent Documents

[0007]

Patent Document 1

Patent Document 2

Non-Patent Documents

[0008]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0009] In Patent Document 1, the diffusion coefficient included in the diffusion equation is regarded as a constant, and the carbon concentration distribution is analyzed. However, strictly speaking, the diffusion coefficient is a value that changes depending on the carbon concentration in γ, so the analysis accuracy of the carbon concentration distribution is low. Patent Document 2 aims to suppress carburization variations in carburized parts by setting the conditions of the vacuum carburizing treatment, and does not analyze the carbon concentration distribution of the steel material subjected to the vacuum carburizing treatment. An object of the present invention is to improve the analysis accuracy of the carbon concentration distribution.

Means for Solving the Problems

[0010] In order to solve the above problems, a method for analyzing the carbon concentration distribution according to the present invention is a method for analyzing the carbon concentration distribution in a carburized steel material using a diffusion equation. Carbides are formed in the steel material by the carburizing treatment. The diffusion equation is represented by the following formula (I) and the following formula (II), and D in the following formula (I) is calculated from the following formula (III) or the following formula (IV). A method for analyzing the carbon concentration distribution, characterized in that.

Number

[0011] (2) In the configuration of (1) above, the following settings may be made. In the precipitation region of the carbide in the steel material formed by the carburizing treatment, at least one of the diffusion coefficient D in formula (I), the diffusion flux J in formula (II), the diffusion coefficient D in formula (III) γ , and the mobility m in formula (IV) γ is multiplied by a correction coefficient, and the correction coefficient is set so as to satisfy the condition that the error between the distribution of the carbon concentration analyzed from the diffusion equation and the previously measured distribution of the carbon concentration is equal to or less than a threshold value.

[0012] (3) In the configuration of (1) or (2) above, when calculating D in formula (I) from formula (III), the maze degree λ represented by the following formula (V) may be multiplied to the right side of any one of formula (I), formula (II), and formula (III). When calculating D in formula (I) from formula (IV), the maze degree λ represented by the following formula (V) may be multiplied to the right side of any one of formula (I), formula (II), and formula (IV). λ = V γ n ···(V) V γ is the volume fraction of austenite [-], and n is an integer. [Advantages of the Invention]

[0013] According to the present invention, even in a steel material containing a duplex region of austenite and carbide during carburizing (for example, vacuum carburizing treatment, high-concentration carburizing, etc.), based on the diffusion equation using the carbon concentration gradient in the steel material as a driving force, the distribution of the carbon concentration can be accurately analyzed. Furthermore, by correcting the parameters used in the calculation of the diffusion coefficient in the steel material and the diffusion simulation (in other words, the diffusion flow rate, diffusion coefficient, and mobility included in the diffusion equation) with a correction coefficient, it becomes easier to ensure the accuracy when analyzing the carbon concentration in the carburized steel material. [Brief Description of the Drawings]

[0014]

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Embodiments for Carrying Out the Invention

[0015] (First Embodiment) The distribution of the carbon concentration inside the steel material when carburizing treatment is performed can be analyzed based on the diffusion simulation (diffusion equation based on the carbon concentration gradient in the steel material) and the calculation of the diffusion coefficient described later. (Diffusion Simulation Based on the Diffusion Equation) In carburizing treatment, carbon diffuses in the steel material and Fick's law holds. In this case, the diffusion flux J of carbon is represented by the diffusion equation of the following formula (1), and the amount of change in carbon concentration over time (∂C / ∂t) is represented by the diffusion equation of the following formula (2).

Number

[0016] (Diffusion simulation when carbides are formed) In high-concentration carburizing that controls the carbon potential in the atmosphere gas to a high level to form carbides and the above-described vacuum carburizing, carbides are formed during carburizing. In this case, in order to calculate the diffusion flux of carbon based on Equation (1), the diffusion coefficient of carbon corresponding to the austenite and carbide multi-phase region is required, and this diffusion coefficient varies greatly depending on the carbon concentration that changes with the carburizing state and the solid solution C concentration in austenite and the carbide formation amount that differ depending on the steel material components excluding carbon. In this case, in order to improve the analysis accuracy, it is necessary to derive the diffusion coefficients at different carbon concentrations and temperatures for each steel type and set them in the simulation. For example, a method of deriving the diffusion coefficient only through experiments like the decarburization method is not practical because the number of experiments increases excessively. Therefore, as will be described later, the present inventor has found a method of calculating the diffusion coefficient in a steel material including a duplex region by using the diffusion coefficient and mobility of carbon in austenite, and calculating the diffusion flux of carbon based on Equation (1).

[0017] (Calculation of Diffusion Coefficient in Duplex Region Using Diffusion Coefficient in Austenite) Even in a steel material containing a duplex region including austenite and carbide, the diffusion flux of carbon can be calculated based on Equation (1) by calculating the diffusion coefficient D in the steel material according to Equation (3). [Number] The definitions of the parameters included in Equation (3) are as follows. D: Diffusion coefficient of carbon in the steel material [m 2 / s].[ Dγ: Diffusion coefficient of carbon in austenite [m 2 / s].[ C: Carbon concentration in the steel material. Cγ: Carbon concentration in austenite. ∂: Partial differential symbol. Note that the carbon concentration may be in molar concentration [mol%] (or [-]) or in mass concentration [mass%] (or [-]).

[0018] (Calculation of Diffusion Coefficient in Duplex Region Using Mobility in Austenite) Even for a target including a duplex region including austenite and carbide, the diffusion flux of carbon can be calculated based on Equation (1) by calculating the diffusion coefficient in the steel material according to Equation (4). [Number] The definitions of the parameters included in Equation (4) are as follows. D: Diffusion coefficient of carbon in the steel material [m 2 / s].[ m γ : Mobility of carbon in austenite [m 2 ·mol / J·s].[ R: The gas constant (8.314 [J / (K·mol)]). T: The temperature [K]. C: The carbon concentration in the steel material. Cγ: The carbon concentration in austenite. γ γ : The activity coefficient of carbon in austenite [-]. ∂ is the partial derivative symbol. Note that the carbon concentration may be in molar concentration [mol%] (or [-]), or in mass concentration [mass%] (or [-]). As described above, the diffusion coefficient D in Equation (1) can be obtained from Equation (3) or Equation (4).

[0019] (Diffusion simulation using thermodynamic calculations) Details will be described later, but the parameters included in Equations (3) and (4) can be obtained by the following method. The carbon concentration Cγ and the activity coefficient γ of carbon in austenite included in Equations (3) and (4) γ may be obtained by thermodynamic calculations. Also, the diffusion coefficient Dγ in Equation (3) may be obtained from a value determined in advance by experiment using the steel material to be carburized, or from data reported as experimental data. The mobility m of carbon in austenite included in Equation (4) γ may be obtained by thermodynamic calculations using a thermodynamic database and a diffusion database. The carbon concentration C included in Equations (3) and (4) is a value obtained over time by diffusion simulation.

[0020] (Setting of the degree of maze) In the calculation of the diffusion coefficient in steel by the above equations (3) and (4), since a state where austenite single phase is continuous is assumed, when targeting steel containing a multi-phase region including austenite and carbide, in order to make the analysis more rigorous, in the multi-phase region, the labyrinth factor λ (where λ ≠ 1) shown in the following equation (5) may be multiplied by the right side of equations (3) and (4) to calculate the diffusion coefficient D of carbon in the steel. Since "in order to make the analysis more rigorous (omitted) it may be calculated", it is not essential to multiply by the labyrinth factor λ. In the single-phase region, λ = 1. Although it is mathematically obvious, the labyrinth factor λ may be multiplied by the right side of equation (1) without multiplying the right side of equation (3) or equation (4) by the labyrinth factor λ. Also, the labyrinth factor λ may be multiplied by the right side of equation (2) without multiplying the right side of equation (3) or equation (4) by the labyrinth factor λ.

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[0021] (Calculation method in diffusion simulation) Create mesh data by dividing the surface layer of the steel material to be carburized into a plurality of cells. The size of each cell can be set as appropriate, for example, it can be 1 to 500 μm. Also, the size of the cells can be made uniform, or it can be gradually increased from the surface of the steel material toward the inside (in other words, gradually decreased from the inside of the steel material toward the surface). The type of mesh element is not particularly limited. For example, in two dimensions, there are triangles and quadrilaterals, and in three dimensions, there are tetrahedrons, hexahedrons, etc., and they can be appropriately selected. Also, either primary elements or secondary elements can be used.

[0022] When targeting the site and shape (e.g., flat part) where carbon diffuses in the one-dimensional direction during carburizing, it may be modeled one-dimensionally. When the shape of the steel material is a round bar or a cylinder, the mesh data can be treated as one-dimensional by using a cylindrical coordinate system. When targeting a steel material (e.g., a steel material having an edge shape part) where carbon diffuses in the two-dimensional or three-dimensional direction during carburizing, two-dimensional or three-dimensional modeling is required. When targeting an axisymmetric shape steel material such as a notched round bar test piece, the mesh data can be treated as two-dimensional by using a cylindrical coordinate system. The analysis time (step time) of the diffusion simulation is not particularly limited, but for example, it can be 0.001 to 1.0 seconds.

[0023] At the surface of the steel material during the carburizing period of vacuum carburizing, it is assumed to be in equilibrium with graphite. Therefore, based on the chemical composition of the steel material to be carburized excluding carbon, the equilibrium phase and equilibrium composition in equilibrium with graphite at the carburizing temperature are obtained by well-known thermodynamic calculations. Based on the equilibrium phase and equilibrium composition obtained by the thermodynamic calculations, the carbon concentration in the steel material, the solid-solution C concentration in austenite, the volume fraction of austenite, and the activity coefficient of carbon in austenite can be specified.

[0024] On the other hand, during periods such as the diffusion period of vacuum carburizing when carbon intrusion from the surface of the steel material does not occur, it is considered a closed system. In the case where cementite (θ) precipitates on the surface or inside of a steel material by carburizing treatment, carbon in the steel material is distributed between cementite and austenite. Therefore, the equilibrium phase and equilibrium composition in the steel material at that time and at that position in terms of chemical composition are obtained by the above-described thermodynamic calculation, and the solid-solution C concentration in austenite, the volume fraction of austenite, and the activity coefficient of carbon in austenite can be specified.

[0025] Diffusion coefficient D of carbon in austenite of steel material γ may use a numerical value obtained in advance by an experiment using the steel material to be subjected to carburizing treatment, or may use data reported as experimental data. Mobility m of carbon in austenite in the steel material γ can be obtained, for example, from a thermodynamic calculation using a thermodynamic database and a diffusion database. Note that the diffusion coefficient D in austenite γ is required when obtaining the diffusion coefficient D in the steel material from Equation (3). For example, as the diffusion coefficient D of carbon in austenite γ the following Equation (6) shown in Non-Patent Document 1 above may be used.

Equation

[0026] Numerical analysis methods for performing a simulation based on a diffusion equation include, but are not particularly limited to, a difference method, a finite element method, a finite volume method, and the like.

[0027] (Second Embodiment) In this embodiment, by correcting the formulas (1) to (4) described in the first embodiment and performing diffusion simulation, it becomes easier to ensure the accuracy when analyzing the carbon concentration in the steel material subjected to carburizing treatment. Hereinafter, a method for correcting the diffusion simulation will be described using the flowchart of FIG. 1.

[0028] In step S101, based on the diffusion simulation, the distribution of the carbon concentration inside the steel material when carburizing treatment (for example, vacuum carburizing treatment) is performed is analyzed. By applying the conditions (temperature and time) of the carburizing treatment to the diffusion simulation, the distribution of the carbon concentration can be analyzed.

[0029] In step S102, after performing carburizing treatment on the steel material, the distribution of the carbon concentration inside this steel material is measured. The steel material used in the process of step S102 is the same as the steel material used in the process of step S101, and the conditions of the carburizing treatment used in the process of step S102 are the same as the conditions of the carburizing treatment used in the process of step S101. As the carburizing gas used in the carburizing treatment, for example, acetylene can be used. As the method for measuring the carbon concentration, a known measurement method can be appropriately adopted. For example, the distribution of the carbon concentration in the steel material can be measured using an electron probe microanalyzer (EPMA).

[0030] Note that the order of performing the processes of step S101 and step S102 is not particularly limited.

[0031] In step S103, a correction coefficient k[-] for correcting the diffusion simulation used in the process of step S101 is determined so that the error Ec between the distribution of the carbon concentration analyzed in the process of step S101 and the distribution of the carbon concentration measured in the process of step S102 is equal to or less than the threshold value Eth.

[0032] As the error Ec, for example, the mean absolute error (MAE) or the mean squared error (MSE) can be used. The threshold value Eth can be appropriately set in consideration of the analysis accuracy of the carbon concentration when the correction coefficient k is not set. Here, the smaller the threshold value Eth, the more the analysis accuracy of the carbon concentration can be improved. For example, when analyzing a steel material with an edge shape, the analysis accuracy can be improved by setting the threshold value Eth to 18% or less. Also, the threshold value Eth is preferably 15% or less, and more preferably 13% or less.

[0033] As described above, in the diffusion equations used in the diffusion simulation (corresponding to Equations (1) and (2)) and the calculation formulas for the diffusion coefficient D in the steel material (corresponding to Equations (3) and (4)), there are the carbon diffusion flux J, the diffusion coefficients D, Dγ, and the mobility m γ Although they are included, the diffusion simulation can be corrected by multiplying at least one of these parameters by the correction coefficient k. The correction coefficient k is a value greater than 0 and less than 1. Needless to say, the above-described correction coefficient k is set in the precipitation region of the carbide in the steel material formed by the carburizing treatment.

[0034] After arbitrarily setting the correction coefficient k, the carbon concentration is analyzed based on the diffusion simulation, and the error Ec is obtained. If this error Ec is equal to or less than the threshold value Eth, the correction coefficient k at the time when this error Ec is obtained is determined as the correction coefficient k for correcting the diffusion simulation. On the other hand, if the error Ec is greater than the threshold value Eth, the carbon concentration is analyzed based on the diffusion simulation after resetting the correction coefficient k, and the error Ec is obtained. Then, the correction coefficient k is continuously searched until the error Ec becomes equal to or less than the threshold value Eth.

[0035] In step S104, the diffusion simulation is corrected using the correction coefficient k determined in the process of step S103. Specifically, the parameters incorporated in the diffusion simulation (diffusion flux J, diffusion coefficients D, D γ , mobility m γMultiply the determined correction coefficient k to correct the diffusion simulation, and use the corrected diffusion simulation to analyze the carbon concentration in the carburized steel material. Here, even when the carburizing conditions, the shape (part) of the steel material, and the steel type change, the diffusion simulation can be corrected using the aforementioned correction coefficient k obtained in advance. However, the analysis accuracy is improved by performing the processes of steps S101 to S103 for each of the carburizing conditions, the shape (part) of the steel material, and the steel type, and determining the corresponding correction coefficient k.

[0036] According to the present embodiment, by correcting the diffusion simulation, it becomes easier to ensure the accuracy when analyzing the carbon concentration in the steel material by carburizing treatment. In particular, as can be understood from the examples described later, not only in the single-phase region where carbides do not precipitate, but also in a multi-phase region containing, for example, austenite and carbides, the distribution of the carbon concentration can be analyzed accurately.

[0037] (Correction of Diffusion Simulation) When correcting the diffusion simulation as described above, multiply the correction coefficient k to at least one of the diffusion flux J, the diffusion coefficient D, Dγ, and the mobility m included in the above diffusion equation and the calculation formula of the diffusion coefficient in the steel material. The following formulas (1a), (2a), (3a), and (4a) are the formulas obtained by multiplying the correction coefficient k to the parameters (diffusion flux J, diffusion coefficient D, Dγ, and mobility m) of the above formulas (1), (2), (3), and (4), respectively. γ and the mobility m γ When analyzing the distribution of the carbon concentration using formulas (1), (2), and (3), multiply the correction coefficient k to at least one of the diffusion coefficients D, Dγ, and the diffusion flux J as shown in formulas (1a), (2a), and (3a). γ and the mobility m γ ) [Number]

[0038] When analyzing the distribution of the carbon concentration using formulas (1), (2), and (3), multiply the correction coefficient k to at least one of the diffusion coefficients D, Dγ, and the diffusion flux J as shown in formulas (1a), (2a), and (3a). Since it is "at least one", the carbon concentration distribution may be analyzed using formula (1a), formula (2) and formula (3), or using formula (1), formula (2a) and formula (3), or using formula (1), formula (2) and formula (3a), or using formula (1a), formula (2a) and formula (3), or using formula (1), formula (2a) and formula (3a), or using formula (1a), formula (2) and formula (3a), or using formula (1a), formula (2a) and formula (3a). Different values may be used for the correction coefficient k included in each formula.

[0039] When analyzing the carbon concentration distribution using formula (1), formula (2) and formula (4), the diffusion coefficient D, the mobility m γ and at least one of the diffusion fluxes J is multiplied by the correction coefficient k. Since it is "at least one", the carbon concentration distribution may be analyzed using formula (1a), formula (2) and formula (4), or using formula (1), formula (2a) and formula (4), or using formula (1), formula (2) and formula (4a), or using formula (1a), formula (2a) and formula (4), or using formula (1), formula (2a) and formula (4a), or using formula (1a), formula (2) and formula (4a), or using formula (1a), formula (2a) and formula (4a). Different values may be used for the correction coefficient k included in each formula. Needless to say, the description regarding the "degree of labyrinth" in the first embodiment can be applied to the second embodiment.

[0040] (First Example) The first example is an example corresponding to the first embodiment. (Steel sample and carburizing conditions) As the steel material to be subjected to the vacuum carburizing treatment, a steel material sample having the composition shown in the following table was prepared.

Table 1

[0041] Figure 2 is a perspective view of the steel sample. Referring to this figure, the steel sample was made into a prismatic shape (steel with an edge-shaped part) with a trapezoidal cross-section. The long side L, short side S, and height H of the trapezoidal cross-section were 16 [mm], 10 [mm], and 10 [mm], respectively. The prism length K was 50 [mm]. The trapezoidal cross-section had two 90° angles and one angle α (60°).

[0042] As the vacuum carburizing treatment, a heating process of heating the steel sample to the carburizing temperature in a vacuumed heating furnace, a soaking process of soaking the steel sample at the carburizing temperature, a carburizing process of introducing carburizing gas (acetylene gas) into the furnace and carburizing the steel sample at the carburizing temperature, a diffusion process of diffusing the infiltrated carbon into the steel sample, a cooling process of cooling the temperature of the steel sample to the holding temperature, and a holding process of holding the temperature of the steel sample at the holding temperature were carried out in this order. Note that no carburizing gas was introduced in the processes other than the carburizing process. As the conditions of the vacuum carburizing treatment, the vacuum carburizing treatment condition A shown in the following table was set.

Table 2

[0043] (Measurement of carbon concentration) The steel sample was subjected to vacuum carburizing treatment under the above-mentioned carburizing conditions, and the carbon concentration (measured value) was measured for each of the treated steel samples. Figure 3 is a cross-sectional view of the steel sample. Referring to this figure, taking the cross-section at the center in the prism length direction of the steel sample (that is, the center of the length K in Figure 2) as the inspection position, the carbon concentration was measured in the measurement direction MD indicated by the arrow. The measurement direction MD was in two directions. Specifically, the line bisecting the right-angled part of the cross-section (hereinafter also referred to as the "90° angle part") was taken as the measurement direction MD, and the line bisecting the angle α part of the cross-section (hereinafter also referred to as the "60° angle part") was taken as the measurement direction MD. Needless to say, all measurement directions MD pass through the edge vertices (the vertices of the trapezoidal cross-section).

[0044] (Diffusion simulation) Hereinafter, the modeling method in the diffusion simulation will be described. In this embodiment, known finite element method-based analysis software (commercial product) incorporating a program for calculating the carbon diffusion flux J using the diffusion equation of the above formula (1) (diffusion equation with the gradient of the carbon concentration in the steel material as the driving force) was used. (I) Mesh data For the 90° corners and 60° corners, a two-dimensional cross-section of the region within a radius of 6 [mm] from the edge vertices was modeled, and mesh data was created so that the mesh on the steel surface was the finest. Specifically, the mesh size was set within the range of 1 to 500 [μm]. The type of mesh was a quadrilateral mesh. (II) Boundary conditions During the carburizing period (carburizing process) of the vacuum carburizing treatment, the carbon concentration at equilibrium with graphite obtained by thermodynamic calculation was given at the position corresponding to the surface of the steel material. Also, after the diffusion period (diffusion process), it was assumed that there was no carbon infiltration from the surface of the steel material, and a closed system was set. (III) Set temperature As the temperature condition of the vacuum carburizing treatment, the temperature shown in the above vacuum carburizing conditions was set in the calculation model. However, for the sake of calculation simplicity, the temperature in the cooling process was fixed at 880 [°C] and set in the analysis model. (IV) Diffusion coefficient D in the steel material The diffusion coefficient D in the steel material was calculated based on formula (3) or formula (4) and used in the diffusion simulation. The carbon concentration C in austenite included in formulas (3) and (4) γ , the activity coefficient γ in austenite γ were values calculated by thermodynamic calculation from the components at each position in the steel material and the set temperature described in (III) above. The diffusion coefficient D in austenite γ was calculated based on formula (6) and used in the diffusion simulation. The mobility m of carbon in austenite γThe values calculated by thermodynamic calculations using a thermodynamic database and a diffusion database were used. (V) Labyrinth factor The labyrinth factor was calculated based on Equation (5) and used in the diffusion simulation. That is, the labyrinth factor calculated based on Equation (5) was multiplied by the right side of Equation (3) or Equation (4) to calculate the diffusion coefficient D in the steel material. The volume fraction V of austenite contained in Equation (5) γ The values calculated by thermodynamic calculations were used. n was set to 2. (VI) Thermodynamic calculations The thermodynamic calculations were performed using commercially available thermodynamic calculation software Thermo-Calc. Commercially available thermodynamic database TCFE10 and diffusion database MOBFE1 were used for the calculations. (VII) Correction factor k In this example, in order to correspond to the first embodiment, the analysis with the correction factor k multiplied was not performed.

[0045] The conditions of the examples and comparative examples are summarized in Table 3 below. In Comparative Examples 1 and 3, the diffusion coefficient D in the steel material was the value calculated by Equation (6) of the diffusion coefficient in austenite (that is, the diffusion coefficient D γ ), and the simulation was performed. In Comparative Examples 2 and 4, the diffusion coefficient D in the steel material was a constant (43 μm 2 / s), and the simulation was performed. This constant is based on the literature value. [Table 3] Figures 4 and 5 show the simulation results. The state of the surface layer under this carburizing condition is such that the coarse carbides precipitated in the carburizing process are dissolved in the diffusion process and no coarse carbides remain. As is clear from Examples 1 to 4, by calculating the diffusion coefficient in the steel material by Equation (3) or (4) and performing a diffusion simulation based on the diffusion equation with the carbon concentration gradient in the steel material as the driving force, it was found that the analysis accuracy of the carbon concentration distribution was improved.

[0046] (Second Example) The second embodiment is an embodiment corresponding to the first and second embodiments. (Steel sample and carburizing conditions) The steel material composition and sample shape subjected to the vacuum carburizing treatment were the same as those in the first embodiment. As the vacuum carburizing treatment, a heating step of heating the steel sample to the carburizing temperature in a vacuumed heating furnace, a soaking step of soaking the steel sample at the carburizing temperature, a carburizing step of introducing carburizing gas (acetylene gas) into the furnace and performing carburizing treatment on the steel sample at the carburizing temperature, a diffusion step of diffusing the infiltrated carbon into the steel sample, a cooling step of cooling the temperature of the steel sample to the holding temperature, and a holding step of holding the temperature of the steel sample at the holding temperature were carried out in this order. Note that no carburizing gas was introduced in the steps other than the carburizing step. As the conditions of the vacuum carburizing treatment, the vacuum carburizing treatment conditions B and C shown in the following table were set. [Table 4] [Table 5] (Measurement of carbon concentration) The steel sample was subjected to vacuum carburizing treatment under the above-mentioned carburizing conditions, and the carbon concentration (measured value) was measured for each of the steel samples after the vacuum carburizing treatment. The method for measuring the carbon concentration was the same as that in the first embodiment.

[0047] (Diffusion simulation) Hereinafter, the modeling method in the diffusion simulation will be described. In this embodiment, analysis software (commercially available) based on the known finite element method incorporating a program for calculating the diffusion flux of carbon using the diffusion equation of the above formula (1) (diffusion equation with the gradient of carbon concentration in the steel material as the driving force) was used. (I) Mesh data It was made the same as in the first embodiment. (II) Boundary conditions It was made the same as in the first embodiment. (III) Set temperature It was made the same as in the first embodiment. (IV) Diffusion Coefficient D in Steel Material The diffusion coefficient D in the steel material was calculated based on Equation (3) and used for diffusion simulation. The carbon concentration C in austenite included in Equation (3) γ was the value calculated by thermodynamic calculation using the components at each position in the steel material and the set temperature described in (III) above. The diffusion coefficient D in austenite γ was calculated based on Equation (6) and used for diffusion simulation (V) Labyrinth Factor The labyrinth factor was calculated based on Equation (5) and used for diffusion simulation. That is, the labyrinth factor calculated based on Equation (5) was multiplied by the right side of Equation (3). The volume fraction V of austenite included in Equation (5) γ used the value calculated by thermodynamic calculation. n was set to 2. (VI) Thermodynamic Calculation It was the same as that in the first embodiment (VII) Calculation of Error Along the measurement direction MD, the mean absolute error (MAE) between the analytical value and the measured value of the carbon concentration in the range from the edge vertex of the 60° corner or 90° corner to 0.25 [mm] was calculated (VIII) Setting of Correction Coefficient k In Example 5, the correction coefficient k was not set. That is, Example 5 corresponded to the first embodiment, and the distribution of carbon concentration was analyzed using Equation (1), Equation (2), and Equation (3). In Examples 6 to 8, the correction coefficient k was set in the region where carbides were precipitated during the carburizing period (carburizing process) at the time after the diffusion period (diffusion process) in which carbides were dissolved. The correction coefficient was determined so that the analysis accuracy was improved under the conditions shown in Example 6. Specifically, the correction coefficient (0.77) was determined so that the mean absolute error (MAE) was 17% or less Note that the correction coefficient k was only multiplied by the right side of Equation (3). That is, the distribution of carbon concentration was analyzed using Equation (1), Equation (2), and Equation (3a). [Table 6]

[0048] Figures 6 to 9 are simulation results. Note that in the case of the present carburizing conditions, although some of the coarse carbides precipitated in the carburizing process are dissolved after the diffusion process, they remain in a residual state. The range where the carbon concentration near the surface is extremely high corresponds to the range where the coarse carbides remain. As is clear from the analysis results of the carbon concentration distributions of Examples 5 to 8, it was found that the simulation of the present embodiment is excellent in the analysis accuracy of the carbon concentration distribution. Also, as can be seen from the analysis results of Example 5, even when the correction coefficient is not set, in the range where no coarse carbides remain (for example, in Example 5, the range inside the steel material from about 0.3 mm from the edge vertex), it was found that the carbon concentration distribution can be analyzed with high accuracy. Furthermore, it was found that the simulations of Examples 6 to 8 corrected by the correction coefficient k can also analyze the carbon concentration distribution with high accuracy even in the region where the carbon concentration near the surface corresponding to the range where the coarse carbides remain is high.

[0049] (Example 3) Example 3 is an example corresponding to the case where the setting of the maze degree λ in the first embodiment and the second embodiment is different from that in the first example and the second example. (Steel material sample · Carburizing conditions) The steel material composition and sample shape subjected to the vacuum carburizing treatment were made the same as those in the first example and the second example. The vacuum carburizing conditions were any one of the vacuum carburizing treatment conditions A, vacuum carburizing treatment conditions B, and vacuum carburizing treatment conditions C described in the first example and the second example. (Measurement of carbon concentration) The same as in the first example. (Diffusion simulation) Hereinafter, the modeling method in the diffusion simulation will be described. In this example, analysis software (commercially available) based on the known finite element method in which a program for calculating the diffusion flux of carbon using the diffusion equation of the above formula (1) (diffusion equation with the gradient of the carbon concentration in the steel material as the driving force) is incorporated was used. (I) Mesh data The same as in the first example. (II) Boundary conditions The same as in the first embodiment was adopted. (III) Set temperature The same as in the first embodiment was adopted. (IV) Diffusion coefficient D in the steel material The diffusion coefficient D in the steel material was calculated based on Equation (3) and used for diffusion simulation. The carbon concentration C in austenite included in Equation (3) γ was the value calculated by thermodynamic calculation from the components at each position in the steel material and the set temperature described in (III) above. The diffusion coefficient D in austenite γ was calculated based on Equation (6) and used for diffusion simulation (V) Labyrinth factor In Examples 9 to 12, the labyrinth factor λ was not set. In Examples 13 to 16, the labyrinth factor was calculated based on Equation (5) and used for diffusion simulation. That is, the labyrinth factor calculated based on Equation (5) was multiplied by the right side of Equation (3). For the volume fraction Vγ of austenite included in Equation (5), the value calculated by thermodynamic calculation was used. n was set to 1. In Examples 17 to 24, the labyrinth factor was calculated based on Equation (5) and used for diffusion simulation. That is, the labyrinth factor calculated based on Equation (5) was multiplied by the right side of Equation (3). For the volume fraction Vγ of austenite included in Equation (5), the value calculated by thermodynamic calculation was used. n was set to 5 or 8. (VI) Thermodynamic calculation The same as in the first embodiment was adopted. (VII) Calculation of error Calculation was performed under the same conditions as in the second embodiment only when coarse carbides remained near the vertices of the edge portions in Examples 10 to 12, Examples 14 to 16, Examples 18 to 20, and Examples 22 to 24. (VIII) Setting of correction coefficient k In Examples 9, 10, 13, 14, 17, 18, 21, and 22, the correction coefficient k was not set. That is, these examples correspond to the first embodiment, and the distribution of carbon concentration was analyzed using Equations (1), (2), and (3). In Examples 11, 12, 15, and 16, the correction coefficient k was set in the region where carbides precipitated during the carburizing period (carburizing process) at a time after the diffusion period (diffusion process) in which the carbides were dissolved. The correction coefficient was determined so that the analysis accuracy was improved under the conditions shown in Example 11 or Example 15. Specifically, in Example 11, the correction coefficient (0.83) was determined so that the mean absolute error (MAE) was 11% or less. In Example 15, the correction coefficient (0.83) was determined so that the mean absolute error (MAE) was 18% or less. In Examples 19, 20, 23, and 24, the correction coefficient k was set in the region where carbides precipitated during the carburizing period (carburizing process) at a time after the diffusion period (diffusion process) in which the carbides were dissolved. The correction coefficient was determined so that the analysis accuracy was improved under the conditions shown in Example 19 or Example 23. Specifically, in Example 19, the correction coefficient (0.50) was determined so that the mean absolute error (MAE) was 40% or less. In Example 23, the correction coefficient (0.37) was determined so that the mean absolute error (MAE) was 40% or less. Note that the correction coefficient k was multiplied only on the right side of Equation (3). That is, the carbon concentration distribution was analyzed using Equations (1), (2), and (3a).

Table 7

[0050] Figures 10 to 25 are simulation results. Note that in Examples 10 to 12, 14 to 16, 18 to 20, and 22 to 24, although the coarse carbides precipitated during the carburizing process were partially dissolved after the diffusion process near the corner vertices, they remained. In Examples 9, 13, 17, and 21, the coarse carbides precipitated during the carburizing process were dissolved during the diffusion process, and almost no coarse carbides remained. Therefore, the range where the carbon concentration is extremely high corresponds to the range where the coarse carbides remain. As is clear from the analysis results of the carbon concentration distributions of Examples 9 to 24, it was found that the simulation of this example is superior in the analysis accuracy of the carbon concentration distribution to the comparative example.

[0051] Also, as can be seen from the analysis results of Example 9, Example 10, Example 13, Example 14, Example 17, Example 18, Example 21, and Example 22, even when the correction coefficient is not set, within the range where no coarse carbides remain (for example, in Example 10, the range inside the steel material from about 0.3 mm from the edge vertex), it was found that the carbon concentration distribution can be analyzed with high accuracy. In addition, the simulations of Example 11, Example 12, Example 15, Example 16, Example 19, Example 20, Example 23, and Example 24 corrected by the correction coefficient k showed that in the region with a high carbon concentration near the surface corresponding to the remaining range of coarse carbides, the carbon concentration distribution can be analyzed with even higher accuracy compared to the case where the correction coefficient is not set.

[0052] As can be seen from the analysis results of the second embodiment and the third embodiment, regardless of the presence or absence of the maze degree setting and the value of the integer n in the maze degree, it was found that the analysis can be performed with higher accuracy than the comparative example. That is, the integer n in the maze degree is not limited to the general values of 1 or 2, and even larger integers can ensure the required analysis accuracy (that is, higher analysis accuracy than the comparative example). The upper limit of the integer n varies depending on the degree of carbide formation that changes with the steel type components, etc., and thus cannot be uniquely defined. The integer n may be appropriately set so as to obtain the required analysis accuracy.

Explanation of Reference Signs

[0053] L Long side S Short side H Height K Prism length

Claims

1. A method for analyzing carbon concentration distribution in a carburized steel material using a diffusion equation, comprising the steps of: Carbide is formed in the steel material by the carburizing treatment, The steel contains a multi-phase region including austenite and carbides, The diffusion equation is represented by the following formula (I) and the following formula (II): A method for analyzing a carbon concentration distribution, comprising calculating D in the following formula (I) from the following formula (III) or the following formula (IV): [0010] In the above formula (I), J is the diffusion flux of carbon, D is the diffusion coefficient of carbon in the steel material, C is the carbon concentration in the steel material, and grad is the position gradient. In the above formula (II), C is the carbon concentration in the steel, t is time, div is the diffusion, and J is the diffusion flux of carbon. In the above formula (III), D γ is the diffusion coefficient of carbon in austenite, C is the carbon concentration in the steel, and C γ is the carbon concentration in austenite. In the above formula (IV), m γ is the mobility of carbon in austenite, R is the gas constant, T is the temperature, C is the carbon concentration in the steel, and C γ is the carbon concentration in austenite, and γ γ is the activity coefficient of carbon in austenite [-].

2. In the carbide precipitation region in the steel material formed by the carburizing treatment, the diffusion coefficient D of formula (I), the diffusion flux J of formula (II), the diffusion coefficient D of formula (III) γ , the mobility m of formula (IV) γ multiplying at least one of the above by a correction coefficient; 2. The method for analyzing a carbon concentration distribution according to claim 1, wherein the correction coefficient is set so as to satisfy a condition that an error between the carbon concentration distribution analyzed from the diffusion equation and the carbon concentration distribution measured in advance is equal to or less than a threshold value.

3. When calculating D in formula (I) from formula (III), multiply the right side of any one of formulas (I), (II), and (III) by the labyrinth degree λ represented by the following formula (V): When calculating D in formula (I) from formula (IV), the right side of any one of formulas (I), (II), and (IV) is multiplied by the labyrinth degree λ represented by the following formula (V):

3. The method for analyzing carbon concentration distribution according to claim 1 or 2. [0025] V γ is the volume fraction of austenite [-], and n is an integer.

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