Method for characterizing three-dimensional average size of inclusions in steel based on two-dimensional data statistics

Abstract

The invention discloses a characterization method for the three-dimensional average size of inclusions in steel based on two-dimensional data statistics. The characterization method comprises the following steps: obtaining the size data of the inclusions of a steel sample on a two-dimensional detection plane; according to the inclusion size data, calculating to obtain a statistical mean value and a statistical variance of the inclusion size on the two-dimensional detection plane; and on the basis of the statistical mean value and the statistical variance, the average size of the inclusions in the steel in the three-dimensional space is calculated through a preset theoretical model for reflecting mathematical correlation between the two-dimensional section statistical magnitude and the three-dimensional space size. On the basis of conventional two-dimensional plane inclusion measurement, statistics of the size variance of the inclusion in the detection plane is added, accurate derivation from a two-dimensional measurement result to a three-dimensional real size is achieved in combination with a theoretical formula, and the real size condition of the inclusion in the steel can be represented more accurately.

Description

Technical Field

[0001] This invention belongs to the field of iron and steel smelting technology, and in particular relates to a method for characterizing the three-dimensional average size of inclusions in steel based on two-dimensional data statistics. Background Technology

[0002] Inclusions in steel are a significant factor affecting steel quality, with inclusion size directly influencing the steel's service performance and lifespan. In oxide metallurgy, small inclusions can pin grain boundaries and inhibit grain growth, thereby improving the properties of steel materials. However, for most steel grades, large inclusions disrupt the continuity of the steel matrix, becoming stress concentration sources. They not only easily induce internal cracks or surface defects during hot working processes such as rolling and forging, but also tend to become fracture initiation points under complex conditions such as low temperatures and impact loads, significantly reducing the tensile strength, toughness, and fatigue life of the steel, severely impacting its safety and durability. Therefore, accurately characterizing and effectively controlling the size of inclusions in steel is crucial.

[0003] Currently, methods for characterizing the size of inclusions in steel mainly fall into two categories: one involves extracting inclusions from the steel and then observing and statistically analyzing them, such as acid etching and small-sample electrolysis; the other is metallography, which involves preparing a smooth surface on the steel sample and then observing and statistically analyzing the inclusions on the surface. In recent years, with the widespread use of automated scanning electron microscopes, metallography has been widely adopted in inclusion size assessment due to its advantages of simple sample preparation and high efficiency in measurement and statistics. However, the average size of inclusions measured by existing metallographic methods only reflects their size on the detection plane and cannot accurately characterize the true average size of inclusions in three-dimensional space. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for characterizing the three-dimensional average size of inclusions in steel based on two-dimensional data statistics, comprising:

[0005] Obtain the inclusion size data of the steel sample on the two-dimensional detection plane;

[0006] Based on the inclusion size data, the statistical mean and statistical variance of the inclusion size on the two-dimensional detection plane are calculated;

[0007] Then, based on the statistical mean and the statistical variance, the average size of inclusions in steel in three-dimensional space is calculated using a preset theoretical model that reflects the mathematical relationship between two-dimensional cross-sectional statistics and three-dimensional spatial dimensions.

[0008] Optionally, the inclusion size data of the steel sample on the two-dimensional detection plane is obtained, and the specific process includes:

[0009] Cut and mount the steel sample to prepare a standard specimen;

[0010] The observation surfaces of the standard specimen are successively ground and polished to obtain the prepared steel sample;

[0011] The prepared steel sample was scanned using an automated scanning electron microscope to identify and measure the cross-sectional dimensions of each inclusion.

[0012] Optionally, the prepared steel sample is scanned using an automated scanning electron microscope to identify and measure the cross-sectional dimensions of each inclusion, specifically including:

[0013] The prepared steel sample was placed into the scanning electron microscope sample chamber and evacuated to a predetermined low pressure.

[0014] The electron microscope filament is energized and stabilized to the predetermined operating voltage, and the backscatter mode is selected for imaging adjustment;

[0015] Set a scanning area of ​​no less than the predetermined minimum area on the detection plane of the steel sample, start the scan and record information including the location and size of the inclusions;

[0016] After the scan is completed, the number of valid inclusions is counted;

[0017] If the number of effective inclusions does not reach the predetermined statistical threshold, the steel sample inspection surface is re-ground and polished, and supplementary scanning is performed in the same or different areas until the total number of effective inclusions exceeds the predetermined statistical threshold.

[0018] Optionally, the specific process of calculating the statistical mean and statistical variance of the inclusion size on the two-dimensional detection plane based on the inclusion size data includes:

[0019] The statistical mean is the arithmetic mean of the cross-sectional dimensions of all valid inclusions; the statistical variance is the arithmetic mean of the squares of the differences between each dimension and the arithmetic mean.

[0020] Optionally, the formula for the preset theoretical model reflecting the mathematical relationship between two-dimensional cross-sectional statistics and three-dimensional spatial dimensions is as follows:

[0021] ;

[0022] Where, d m To detect the statistical mean of the size of inclusions on a plane, d s To detect the statistical variance of inclusion size on a plane, d0 is the average size of the inclusion in three-dimensional space.

[0023] Optionally, each observed inclusion cross-sectional profile is equivalent to a circle, and the diameter of the equivalent circle is used as the cross-sectional size data.

[0024] Optionally, the process of constructing the preset theoretical model reflecting the mathematical relationship between two-dimensional cross-sectional statistics and three-dimensional spatial dimensions includes:

[0025] Based on the assumption that the inclusions are spherical and uniformly distributed in the steel, the conditional expectation and conditional variance of the two-dimensional diameter of an inclusion with a given three-dimensional diameter observed on a random detection plane are obtained.

[0026] Based on the assumption that the three-dimensional diameter of the inclusion follows a log-normal distribution, the mathematical relationship between the mean, variance and log-normal distribution parameters of the three-dimensional diameter is obtained.

[0027] Based on the uniform distribution assumption, conditional expectation, and conditional variance, the conditional probability distribution of the diameter of the inclusion actually intercepted by the detection plane, as well as its first and second moments, are obtained.

[0028] Based on the conditional expectation, conditional variance, first moment, and second moment, a conversion relationship between the arithmetic mean and variance of the two-dimensional observations and the average size of the three-dimensional space is established through full probability analysis.

[0029] The present invention also proposes a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0030] The present invention also proposes a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0031] The present invention also proposes a computer program product, including a computer program that, when executed by a processor, implements the steps of the method.

[0032] Compared with the prior art, the present invention has the following advantages and technical effects:

[0033] Traditional metallographic methods for detecting inclusion size typically only yield the average size of inclusions on the detection plane. This method has limitations because two-dimensional measurements cannot fully reflect the true size of inclusions in three-dimensional space. This invention, however, builds upon this by deriving the variance of inclusion size on the detection plane. Combining this variance with the mean and variance of inclusion size on the detection plane, a theoretical calculation formula is used to derive the true average size of inclusions in three-dimensional space. This process fully considers the size distribution characteristics and spatial distribution patterns of inclusions in three-dimensional space, effectively overcoming the limitations of traditional two-dimensional measurements and enabling the calculation results to more accurately represent the true size of inclusions. Attached Figure Description

[0034] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0035] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram illustrating the construction process of the calculation model for the average size of inclusions in three-dimensional space according to an embodiment of the present invention. Detailed Implementation

[0037] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0038] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0039] Example 1

[0040] like Figure 1 As shown, this embodiment provides a method for characterizing the three-dimensional average size of inclusions in steel based on two-dimensional data statistics, including:

[0041] Obtain the inclusion size data of the steel sample on the two-dimensional detection plane;

[0042] Based on the inclusion size data, the statistical mean and statistical variance of the inclusion size on the two-dimensional detection plane are calculated;

[0043] Then, based on the statistical mean and the statistical variance, the average size of inclusions in steel in three-dimensional space is calculated using a preset theoretical model that reflects the mathematical relationship between two-dimensional cross-sectional statistics and three-dimensional spatial dimensions.

[0044] As a feasible implementation method, the specific steps include:

[0045] S1): Prepare the steel sample to be characterized;

[0046] S2): Place the prepared steel sample into an automated scanning electron microscope for observation;

[0047] S3): Statistically measure the mean and variance of the size of inclusions on the detection plane;

[0048] S4): Calculate the average size of the inclusions in three-dimensional space.

[0049] Furthermore, the preparation of the steel sample to be characterized in step S1) includes the following steps:

[0050] S1.1) Cut the steel sample to be characterized into a cube of 15 mm;

[0051] S1.2) The cut cube is placed into a hot mounting machine to create a circular sample with a diameter of 30 mm and a height of 20 mm.

[0052] S1.3) The mounted sample was polished using an automatic polishing machine, using 60, 240, 400, 800 and 1200 grit sandpaper in sequence, with dripping water for cooling and lubrication during polishing;

[0053] S1.4) The ground sample was polished using an automatic polishing machine, and polished with 6μm and 0.5μm polishing liquids in sequence;

[0054] S1.5) After polishing the sample, quickly remove the sample, rinse it with clean water, wipe the surface with anhydrous ethanol to remove residual polishing liquid and impurities, and then dry it.

[0055] Furthermore, step S2), which involves placing the prepared steel sample into an automated scanning electron microscope for observation, includes the following steps:

[0056] S2.1) Place the prepared steel sample into the sample chamber of the automated scanning electron microscope, and then evacuate it to below 10°C. -5 pa;

[0057] S2.2) Power on the filament of the automatic scanning electron microscope to stabilize the voltage to 15kV;

[0058] S2.3) Use backscatter mode to adjust focus, brightness, and contrast until the field of view is clear;

[0059] S2.4) Set the scanning area; the scanning area should be no less than 20 mm². 2 ;

[0060] S2.5) Start scanning, record and save the scan data. The scan data should at least include information on the location and size of the inclusions.

[0061] S2.6) After the scan is completed, count the number of valid inclusions N;

[0062] S2.7) When N is greater than 1000, proceed to the next step; if N is less than 1000, repeat the grinding and polishing, as well as the operation of scanning inclusions with an automatic scanning electron microscope, i.e., the operation from S1.3) to S2.6), and supplement the previously scanned inclusion data with the re-scanned inclusion data until the number of inclusions N is greater than 1000.

[0063] Furthermore, the mean and variance of the size of inclusions on the statistical detection plane in step S3) includes the following steps:

[0064] S3.1) The mean size of inclusions on the detection plane is calculated using the following formula.

[0065] (1)

[0066] Where, d m To detect the average size of inclusions on a plane, d i To detect the size of the i-th inclusion, N is the number of valid inclusions detected.

[0067] S3.2) The variance of the size of inclusions on the detection plane is statistically calculated using the following formula;

[0068] (2)

[0069] Where, d s To detect the variance of the size of inclusions on a plane.

[0070] Furthermore, the average size of the inclusions in S4) in three-dimensional space is calculated by the following formula:

[0071] (3)

[0072] Where d0 is the average size of the inclusion in three-dimensional space.

[0073] The feasible, pre-defined process of constructing a theoretical model reflecting the mathematical relationship between two-dimensional cross-sectional statistics and three-dimensional spatial dimensions includes:

[0074] Based on the assumption that the inclusions are spherical and uniformly distributed in the steel, the conditional expectation and conditional variance of the two-dimensional diameter of an inclusion with a given three-dimensional diameter observed on a random detection plane are obtained.

[0075] Based on the assumption that the three-dimensional diameter of the inclusion follows a log-normal distribution, the mathematical relationship between the mean, variance and log-normal distribution parameters of the three-dimensional diameter is obtained.

[0076] Based on the uniform distribution assumption, conditional expectation, and conditional variance, the conditional probability distribution of the diameter of the inclusion actually intercepted by the detection plane, as well as its first and second moments, are obtained.

[0077] Based on the conditional expectation, conditional variance, first moment, and second moment, a conversion relationship between the arithmetic mean and variance of the two-dimensional observations and the average size of the three-dimensional space is established through full probability analysis.

[0078] Feasible, such as Figure 2As shown, the derivation process of formula (3) includes:

[0079] T1. In the steel sample being tested, the size of inclusions is very small relative to the test volume and can be ignored. It is assumed that the inclusions are spherical and uniformly distributed within the steel sample. For an inclusion with a constant diameter d in three-dimensional space, its diameter on the two-dimensional test surface is d0. 2D It can be calculated using the following formula:

[0080] (4)

[0081] Where l is the distance from the center of the inclusion to the detection surface. Since the inclusions are uniformly distributed, l is... The probability density function of a uniformly distributed surface (where inclusions can be detected) can be expressed as:

[0082] (5)

[0083] Therefore, the diameter d on the two-dimensional detection surface 2D The expectation is:

[0084] (6)

[0085] at the same time:

[0086] (7)

[0087] Diameter d on the two-dimensional detection surface 2D The variance is:

[0088] (8)

[0089] T2. In actual practice, the three-dimensional spatial diameter d of the inclusions in the steel sample 3D It is not a constant; it is generally considered to follow a log-normal distribution, and its probability density function (PDF) is:

[0090] (9)

[0091] Where: μ and σ 2 Let Lnd be the mean and variance. The expected value and variance of the log-normal distribution are:

[0092] (10)

[0093] (11)

[0094] Assuming the mean and variance of the three-dimensional diameter of the inclusions are d0 and d1, respectively, i.e., d0 = E[d] and d1 = Var[d], then we have:

[0095] (12)

[0096] (13)

[0097] The PDF of the condition for the diameter of the inclusion intercepted on the detected plane is denoted as... According to the conditional probability formula:

[0098] (14)

[0099] in: It is the probability that the inclusion with diameter d will be intercepted by the plane. It is the total probability that all inclusions are intercepted by the plane, i.e., the normalization coefficient.

[0100] Assuming the sample height is h, and the inclusions are uniformly distributed within the sample, the probability density function of the inclusion center along the height direction is expressed as:

[0101] (15)

[0102] Choose any plane z = h0 (h0 is a constant; since the inclusions are uniformly distributed, the value of h0 has no effect on the result). The necessary and sufficient condition for an inclusion to be intercepted is that the distance from the center of the inclusion to the plane is less than the radius of the inclusion, i.e.:

[0103] (16)

[0104] The probability of an inclusion of any fixed diameter d being intercepted is equivalent to the probability of the inclusion center being intercepted. The probability of.

[0105] therefore:

[0106] (17)

[0107] The total probability that all inclusions are intercepted by the plane:

[0108] (18)

[0109] Wherein: E[d] is as shown in equation (10).

[0110] Therefore, the PDF condition for determining the diameter of the inclusion on the detected plane is:

[0111] (19)

[0112] Furthermore, the first moment, second moment, and variance of the diameter of the inclusion intercepted by the detected plane can be obtained as follows:

[0113] (20)

[0114] (twenty one)

[0115] (twenty two)

[0116] T3. When the three-dimensional spatial diameter d of the inclusions in the steel sample 3D When the distribution follows a log-normal distribution, the given three-dimensional spatial diameter d needs to be obtained by combining the total expectation formula and the total variance formula with T1. 3D Two-dimensional detection surface inclusion diameter d 2D The expected value and variance of T2 are used to obtain the distribution characteristics of the inclusion diameter intercepted on the detected surface, and the final diameter d on the two-dimensional detection surface is derived. 2D The mean and variance of.

[0117] Diameter d of inclusions on the two-dimensional detection surface 2D The mean is calculated using the formula for the total expectation:

[0118] (twenty three)

[0119] That is, the diameter d of the inclusions on the two-dimensional detection surface 2D The mean is equal to the diameter d of the inclusions on the two-dimensional detection surface when the three-dimensional spatial diameter d is given. 2D The conditional mean of the inclusion diameter d intercepted on the surface being tested. cross The expectation.

[0120] Substitute into the conditional mean expression:

[0121] (twenty four)

[0122] Extract the constant and use the surface being inspected to obtain the inclusion diameter d. cross The first moment is used to obtain the diameter d of the inclusions on the two-dimensional detection surface. 2D Mean:

[0123] (25)

[0124] Diameter d of inclusions on the two-dimensional detection surface 2D The variance is calculated using the total variance formula:

[0125] (26)

[0126] That is, variance is decomposed into the sum of the "expectation of conditional variance" and the "variance of conditional mean".

[0127] Expected value of conditional variance:

[0128] (27)

[0129] Variance of conditional mean:

[0130] (28)

[0131] Diameter d of inclusions on the two-dimensional detection surface 2D The variance can be solved as:

[0132] (29)

[0133] T4. The diameter d of the inclusions on the two-dimensional detection surface 2D The mean and variance are used to inversely calculate the three-dimensional spatial diameter d of the inclusion. 3D The mean of the equations can be obtained by solving equations (25) and (29) simultaneously:

[0134] (30)

[0135] Diameter d of inclusions on the two-dimensional detection surface 2D The mean and variance can be obtained through automated scanning electron microscopy (SEM) analysis, i.e., E[d] 2D ]=d m Var[d 2D ]=d s Therefore, we can obtain:

[0136] (31)

[0137] The beneficial effects of this embodiment are as follows: Traditional metallographic methods for detecting inclusion size typically only obtain the average size of inclusions on the detection plane. This method has certain limitations because two-dimensional planar measurements cannot fully reflect the true situation of inclusions in three-dimensional space. This invention, based on the above, further derives the dimensional variance of inclusions on the detection plane. Then, combining the mean and variance of inclusion sizes on the detection plane, a theoretical calculation formula is used to derive the true average size of inclusions in three-dimensional space. This process fully considers the size distribution characteristics and spatial distribution patterns of inclusions in three-dimensional space, effectively overcoming the limitations of traditional two-dimensional measurements, and making the calculation results more accurately represent the true size of inclusions.

[0138] Example 2

[0139] This embodiment provides a method for characterizing the three-dimensional average size of inclusions in steel based on two-dimensional data statistics, specifically including the following steps:

[0140] S1): Prepare the steel sample to be characterized;

[0141] S2): Place the prepared steel sample into an automated scanning electron microscope for observation;

[0142] S3): Statistically measure the mean and variance of the size of inclusions on the detection plane;

[0143] S4): Calculate the average size of the inclusions in three-dimensional space.

[0144] Furthermore, the preparation of the steel sample to be characterized in step S1) includes the following steps:

[0145] S1.1) Cut the steel sample to be characterized into a cube of 15 mm;

[0146] S1.2) The cut cube is placed into a hot mounting machine to create a circular sample with a diameter of 30 mm and a height of 20 mm.

[0147] S1.3) The mounted sample was polished using an automatic polishing machine, using 60, 240, 400, 800 and 1200 grit sandpaper in sequence, with dripping water for cooling and lubrication during polishing;

[0148] S1.4) The ground sample was polished using an automatic polishing machine, and polished with 6μm and 0.5μm polishing liquids in sequence;

[0149] S1.5) After polishing the sample, quickly remove the sample, rinse it with clean water, wipe the surface with anhydrous ethanol to remove residual polishing liquid and impurities, and then dry it.

[0150] Furthermore, step S2), which involves placing the prepared steel sample into an automated scanning electron microscope for observation, includes the following steps:

[0151] S2.1) Place the prepared steel sample into the sample chamber of the automated scanning electron microscope, and then evacuate it to below 10°C. -5 pa;

[0152] S2.2) Power on the filament of the automatic scanning electron microscope to stabilize the voltage to 15kV;

[0153] S2.3) Use backscatter mode to adjust focus, brightness, and contrast until the field of view is clear;

[0154] S2.4) Set the scanning area to 39.2 mm². 2 ;

[0155] S2.5) Start scanning, record and save the scan data. The scan data should at least include information on the location and size of the inclusions.

[0156] S2.6) After the scan is completed, the number of valid inclusions N is counted as 1226.

[0157] Furthermore, the mean and variance of the size of inclusions on the statistical detection plane in step S3) includes the following steps:

[0158] S3.1) The mean size of inclusions on the detection plane is calculated using the following formula:

[0159] ;

[0160] Where, d m To detect the average size of inclusions on a plane, d i To determine the size of the i-th inclusion, N is the number of effective inclusions detected. After calculation, d... m =1.92μm.

[0161] S3.2) The variance of the size of inclusions on the detection plane is statistically calculated using the following formula;

[0162] ;

[0163] Where, d s To detect the variance of inclusion dimensions on a plane. After calculation, d... s =0.76μm 2 .

[0164] Furthermore, the average size of the inclusions in S4) in three-dimensional space is calculated by the following formula:

[0165] ;

[0166] Where, d 3D Let d be the average size of the inclusion in three-dimensional space. 3D =2.19μm.

[0167] Example 2

[0168] This embodiment provides a method for characterizing the three-dimensional average size of inclusions in steel based on two-dimensional data statistics, specifically including the following steps:

[0169] S1): Prepare the steel sample to be characterized;

[0170] S2): Place the prepared steel sample into an automated scanning electron microscope for observation;

[0171] S3): Statistically measure the mean and variance of the size of inclusions on the detection plane;

[0172] S4): Calculate the average size of the inclusions in three-dimensional space.

[0173] Furthermore, the preparation of the steel sample to be characterized in step S1) includes the following steps:

[0174] S1.1) Cut the steel sample to be characterized into a cube of 15 mm;

[0175] S1.2) The cut cube is placed into a hot mounting machine to create a circular sample with a diameter of 30 mm and a height of 20 mm.

[0176] S1.3) The mounted sample was polished using an automatic polishing machine, using 60, 240, 400, 800 and 1200 grit sandpaper in sequence, with dripping water for cooling and lubrication during polishing;

[0177] S1.4) The ground sample was polished using an automatic polishing machine, and polished with 6μm and 0.5μm polishing liquids in sequence;

[0178] S1.5) After polishing the sample, quickly remove the sample, rinse it with clean water, wipe the surface with anhydrous ethanol to remove residual polishing liquid and impurities, and then dry it.

[0179] Furthermore, step S2), which involves placing the prepared steel sample into an automated scanning electron microscope for observation, includes the following steps:

[0180] S2.1) Place the prepared steel sample into the sample chamber of the automated scanning electron microscope, and then evacuate it to below 10°C. -5 pa;

[0181] S2.2) Power on the filament of the automatic scanning electron microscope to stabilize the voltage to 15kV;

[0182] S2.3) Use backscatter mode to adjust focus, brightness, and contrast until the field of view is clear;

[0183] S2.4) Set the scanning area to 46.3 mm². 2 ;

[0184] S2.5) Start scanning, record and save the scan data. The scan data should at least include information on the location and size of the inclusions.

[0185] S2.6) After the scan is completed, the number of valid inclusions N is 1132.

[0186] Furthermore, the mean and variance of the size of inclusions on the statistical detection plane in step S3) includes the following steps:

[0187] S3.1) The mean size of inclusions on the detection plane is calculated using the following formula:

[0188] ;

[0189] Where, d m To detect the average size of inclusions on a plane, d i To determine the size of the i-th inclusion, N is the number of effective inclusions detected. After calculation, d... m=2.36μm.

[0190] S3.2) The variance of the size of inclusions on the detection plane is statistically calculated using the following formula;

[0191] ;

[0192] Where, d s To detect the variance of inclusion dimensions on a plane. After calculation, d... s =2.12μm 2 .

[0193] Furthermore, the average size of the inclusions in S4) in three-dimensional space is calculated by the following formula:

[0194] ;

[0195] Where, d 3D Let d be the average size of the inclusion in three-dimensional space. 3D =2.35μm.

[0196] Example 4

[0197] This embodiment provides a method for characterizing the three-dimensional average size of inclusions in steel based on two-dimensional data statistics, specifically including the following steps:

[0198] S1): Prepare the steel sample to be characterized;

[0199] S2): Place the prepared steel sample into an automated scanning electron microscope for observation;

[0200] S3): Statistically measure the mean and variance of the size of inclusions on the detection plane;

[0201] S4): Calculate the average size of the inclusions in three-dimensional space.

[0202] Furthermore, the preparation of the steel sample to be characterized in step S1) includes the following steps:

[0203] S1.1) Cut the steel sample to be characterized into a cube of 15 mm;

[0204] S1.2) The cut cube is placed into a hot mounting machine to create a circular sample with a diameter of 30 mm and a height of 20 mm.

[0205] S1.3) The mounted sample was polished using an automatic polishing machine, using 60, 240, 400, 800 and 1200 grit sandpaper in sequence, with dripping water for cooling and lubrication during polishing;

[0206] S1.4) The ground sample was polished using an automatic polishing machine, and polished with 6μm and 0.5μm polishing liquids in sequence;

[0207] S1.5) After polishing the sample, quickly remove the sample, rinse it with clean water, wipe the surface with anhydrous ethanol to remove residual polishing liquid and impurities, and then dry it.

[0208] Furthermore, step S2), which involves placing the prepared steel sample into an automated scanning electron microscope for observation, includes the following steps:

[0209] S2.1) Place the prepared steel sample into the sample chamber of the automated scanning electron microscope, and then evacuate it to below 10°C. -5 pa;

[0210] S2.2) Power on the filament of the automatic scanning electron microscope to stabilize the voltage to 15kV;

[0211] S2.3) Use backscatter mode to adjust focus, brightness, and contrast until the field of view is clear;

[0212] S2.4) Set the scanning area to 39.2 mm². 2 ;

[0213] S2.5) Start scanning, record and save the scan data. The scan data should at least include information on the location and size of the inclusions.

[0214] S2.6) After the scan is completed, the number of valid inclusions N is 714;

[0215] S2.7) Repeat the grinding and polishing process, and perform automatic scanning electron microscopy (SEM) scanning of inclusions, setting the scanning area to 39.2 mm² again. 2 The data of the inclusions from the rescanned sample were added to the data from the previous scan. After the second scan, the total number of inclusions was 1502.

[0216] Furthermore, the mean and variance of the size of inclusions on the statistical detection plane in step S3) includes the following steps:

[0217] S3.1) The mean size of inclusions on the detection plane is calculated using the following formula:

[0218] ;

[0219] Where, d m To detect the average size of inclusions on a plane, d i To determine the size of the i-th inclusion, N is the number of effective inclusions detected. After calculation, d... m =3.35μm.

[0220] S3.2) The variance of the size of inclusions on the detection plane is statistically calculated using the following formula;

[0221] ;

[0222] Where, d s To detect the variance of inclusion dimensions on a plane. After calculation, d... s =6.32μm 2 .

[0223] Furthermore, the average size of the inclusions in S4) in three-dimensional space is calculated by the following formula:

[0224] ;

[0225] Where, d 3D Let d be the average size of the inclusion in three-dimensional space. 3D =2.95μm.

[0226] Example 5

[0227] This embodiment also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described in Embodiment 1.

[0228] Example 6

[0229] This embodiment also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0230] Example 7

[0231] This embodiment also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the method described in Embodiment 1.

[0232] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for characterizing the three-dimensional average size of inclusions in steel based on two-dimensional data statistics, characterized in that, include: Obtain the inclusion size data of the steel sample on the two-dimensional detection plane; Based on the inclusion size data, the statistical mean and statistical variance of the inclusion size on the two-dimensional detection plane are calculated; Then, based on the statistical mean and the statistical variance, the average size of inclusions in steel in three-dimensional space is calculated using a preset theoretical model that reflects the mathematical relationship between two-dimensional cross-sectional statistics and three-dimensional spatial dimensions.

2. The method according to claim 1, characterized in that, The specific process for obtaining inclusion size data of steel samples on a two-dimensional detection plane includes: Cut and mount the steel sample to prepare a standard specimen; The observation surfaces of the standard specimen are successively ground and polished to obtain the prepared steel sample; The prepared steel sample was scanned using an automated scanning electron microscope to identify and measure the cross-sectional dimensions of each inclusion.

3. The method according to claim 2, characterized in that, The prepared steel sample was scanned using an automated scanning electron microscope to identify and measure the cross-sectional dimensions of each inclusion, specifically including: The prepared steel sample was placed into the scanning electron microscope sample chamber and evacuated to a predetermined low pressure. The electron microscope filament is energized and stabilized to the predetermined operating voltage, and the backscatter mode is selected for imaging adjustment; Set a scanning area of ​​no less than the predetermined minimum area on the detection plane of the steel sample, start the scan and record information including the location and size of the inclusions; After the scan is completed, the number of valid inclusions is counted; If the number of effective inclusions does not reach the predetermined statistical threshold, the steel sample inspection surface is re-ground and polished, and supplementary scanning is performed in the same or different areas until the total number of effective inclusions exceeds the predetermined statistical threshold.

4. The method according to claim 1, characterized in that, The specific process for calculating the statistical mean and statistical variance of the inclusion size on the two-dimensional detection plane based on the inclusion size data includes: The statistical mean is the arithmetic mean of the cross-sectional dimensions of all valid inclusions; the statistical variance is the arithmetic mean of the squares of the differences between each dimension and the arithmetic mean.

5. The method according to claim 1, characterized in that, The formula for the pre-defined theoretical model reflecting the mathematical relationship between two-dimensional cross-sectional statistics and three-dimensional spatial dimensions is as follows: ； where d m is the statistical mean of the inclusion size on the plane of detection, d s is the statistical variance of the inclusion size on the plane of detection, and d0is the average size of the inclusions in three-dimensional space.

6. The method according to claim 5, characterized in that, Each observed inclusion cross-sectional profile is equivalent to a circle, and the diameter of this equivalent circle is used as the cross-sectional size data.

7. The method according to claim 6, characterized in that, The process of constructing the pre-defined theoretical model reflecting the mathematical relationship between two-dimensional cross-sectional statistics and three-dimensional spatial dimensions includes: Based on the assumption that the inclusions are spherical and uniformly distributed in the steel, the conditional expectation and conditional variance of the two-dimensional diameter of an inclusion with a given three-dimensional diameter observed on a random detection plane are obtained. Based on the assumption that the three-dimensional diameter of the inclusion follows a log-normal distribution, the mathematical relationship between the mean, variance and log-normal distribution parameters of the three-dimensional diameter is obtained. Based on the uniform distribution assumption, conditional expectation, and conditional variance, the conditional probability distribution of the diameter of the inclusion actually intercepted by the detection plane, as well as its first and second moments, are obtained. Based on the conditional expectation, conditional variance, first moment, and second moment, a conversion relationship between the arithmetic mean and variance of the two-dimensional observations and the average size of the three-dimensional space is established through full probability analysis.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method according to any one of claims 1-7.

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