CN110334664B - Statistical method and device for alloy precipitated phase fraction, electronic equipment and medium - Google Patents

Statistical method and device for alloy precipitated phase fraction, electronic equipment and medium Download PDF

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CN110334664B
CN110334664B CN201910615228.4A CN201910615228A CN110334664B CN 110334664 B CN110334664 B CN 110334664B CN 201910615228 A CN201910615228 A CN 201910615228A CN 110334664 B CN110334664 B CN 110334664B
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不公告发明人
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Abstract

Compared with the prior art, the technical scheme provided by the invention successfully enables the operation steps to be automatically executed completely through a pre-programmed application program by combining the alloy SEM image and the gray threshold method, and eliminates long time consumption and human errors caused by manual operation by experience in the prior art. When the precipitated phase fractions corresponding to a plurality of SEM images need to be counted, the automated process can be performed with higher efficiency by a batch processing technique. The invention also discloses a statistical device of the alloy precipitated phase fraction and electronic equipment, and has the beneficial effects.

Description

Statistical method and device for alloy precipitated phase fraction, electronic equipment and medium
Technical Field
The invention relates to the technical field of metal material precipitated phase fraction statistics, in particular to a method and a device for alloy precipitated phase fraction statistics, electronic equipment and a computer-readable storage medium.
Background
The alloy precipitated phase plays an important role in strengthening the metal material. Taking a high-temperature alloy as an example, the high-temperature alloy is also called a "superalloy", which is a metal material capable of working for a long time at a high temperature of more than 600 ℃ and under a certain stress. The alloy mainly depends on a precipitated phase with high volume fraction, so that excellent high-temperature strength and good comprehensive high-temperature mechanical properties such as fatigue resistance, creep resistance and the like are obtained. Therefore, such alloys are widely used in core components of aircraft engines such as turbine disks and turbine blades.
In order to ensure that equipment made from such alloys can operate efficiently and stably in these high temperature, high pressure environments, a good understanding of the properties of such alloys is necessary. Taking the nickel-based superalloy consisting of a matrix phase and a precipitated phase as an example, the properties of the alloy, such as high-temperature strength, fatigue resistance, creep resistance and the like, have been proved to be closely related to the fraction of the precipitated phase in the industry, namely the fraction of the precipitated phase of the nickel-based superalloy is an important parameter for evaluating the performance of the alloy. In addition, the statistic of precipitated phase fraction has important significance for quantitative description of the alloy structure, prediction of the alloy performance, establishment of alloy component-process-structure-performance relation and the like.
The conventional technique for counting the fraction of precipitated phases in an alloy is to manually introduce an Image obtained by Scanning Electron Microscope (SEM) into Image processing software (generally, Image J), manually adjust the threshold of each SEM Image so that the shadow portion and the precipitated phase are approximately overlapped, and calculate the area ratio of the total SEM Image occupied by the shadow portion after the adjustment is completed to obtain the fraction of precipitated phases. Because each SEM image is different, the trial adjustment can be carried out only by operators through self experience, and the result tends to be unknown and unstable due to human factors, the statistical efficiency is low (more times of trial is needed), and the counted precipitated phase fraction is influenced by human errors, so that the accuracy is not high.
Therefore, how to obtain the precipitated phase fraction of the alloy through statistics more accurately and efficiently is an urgent problem to be solved by those skilled in the art.
Disclosure of Invention
The invention aims to provide a method and a device for counting alloy precipitated phase fractions, electronic equipment and a computer-readable storage medium, and aims to improve the efficiency and accuracy of counting the precipitated phase fractions.
In order to achieve the above object, the present invention provides a statistical method for the precipitated phase fraction of an alloy, the statistical method comprising:
obtaining an SEM image of a target alloy, and converting the SEM image into a gray scale image;
counting the frequency of pixel points corresponding to each gray value in the gray map to generate a gray histogram;
when the target alloy consists of a matrix phase and a precipitated phase, determining a gray threshold value for dividing a gray interval to which the matrix phase and the precipitated phase belong by using a gray threshold value method;
counting the number of pixel points in the corresponding precipitation gray scale interval;
and calculating the ratio of the number of the pixel points to the total number of the pixel points in the SEM image to obtain a precipitated phase fraction.
Optionally, determining a gray level threshold for dividing the gray level interval to which the matrix phase and the precipitate phase belong by using a gray level threshold method includes:
selecting the gray value with the maximum frequency number in the gray histogram as a first gray value;
selecting a gray interval with a preset gray difference with the first gray value as an alternative interval to obtain a left alternative interval and a right alternative interval;
respectively counting the sum of frequency counts corresponding to all gray values in the left candidate interval and the right candidate interval, comparing the frequency counts of the left candidate interval and the right candidate interval, and marking the candidate interval with larger frequency count sum as a target candidate interval;
selecting the gray value with the maximum frequency in the target candidate area interval as a second gray value;
judging whether the gray difference between the second gray value and the first gray value is equal to the preset gray difference or not;
if yes, determining a gray level threshold value for dividing a gray level interval to which the matrix phase and the precipitated phase belong through a tangent method in the gray level threshold value method;
and if not, determining a gray level threshold value for dividing the gray level interval to which the matrix phase and the precipitated phase belong by the minimum threshold value method in the gray level threshold value methods.
Optionally, determining a gray level threshold for dividing the gray level interval to which the matrix phase and the precipitate phase belong by using a tangent method in the gray level threshold methods includes:
making a straight line between the vertex corresponding to the first gray value and the vertex corresponding to each gray value in the target candidate interval, and marking the straight line as a first straight line family;
selecting a straight line in the first straight line family, wherein the straight line enables the vertex distance between the intersection point and the first gray value to be minimum, and the straight line is selected as a tangent line; wherein the intersection point is a point at which each straight line in the first straight line family uniquely intersects with the y-axis;
taking the gray value of the vertex in the target candidate interval corresponding to the tangent as a third gray value;
determining a gray level interval between the first gray level value and the third gray level value as a tangent point alternative interval;
drawing a straight line by using the slope of the tangent line and the vertex corresponding to each gray value in the tangent point alternative interval, and marking the straight line as a second straight line family;
selecting a vertex corresponding to the straight line with the minimum y-axis intercept in the second straight line family as a tangent point;
and taking the gray value corresponding to the tangent point as a gray threshold value for distinguishing the gray intervals to which the matrix phase and the precipitated phase belong respectively.
Optionally, determining a gray level threshold for dividing the gray level interval to which the matrix phase and the precipitate phase belong by using a minimum threshold method in the gray level threshold methods includes:
taking a value with the smallest frequency between the first gray value and the second gray value as a valley value;
and taking the gray value corresponding to the valley value as a gray threshold value for dividing the gray intervals to which the matrix phase and the precipitated phase respectively belong.
Optionally, the statistical method for the alloy precipitated phase fraction further includes:
rewriting the gray value of each pixel point in the gray interval to which the precipitated phase belongs to be 0;
and rewriting the gray value of each pixel point in the gray interval to which the matrix phase belongs to 255 to obtain a rewritten gray image.
Optionally, after obtaining the rewritten gray scale map, the method further includes:
rewriting the color of the precipitated phase in the rewritten gray scale map into blue by using a JET color system;
and rewriting the color of the matrix phase in the rewritten gray scale image into yellow by using the JET color system to obtain a rewritten color image.
Optionally, when the SEM image is a depth-dependent SEM image obtained by shooting from the depth direction of the surface of the target alloy, the method further includes:
in a gray value matrix forming a gray level image, comparing the corresponding gray level of each pixel point with the size of the gray level threshold value row by row or column by column to obtain a comparison result;
counting the percentage of the pixel points of the precipitated phase in each row or each column according to the comparison result, and generating a scatter diagram of the precipitated phase fraction changing with the depth according to the percentage;
and smoothing the scatter diagram by using a moving average method to obtain a curve of precipitated phase fraction changing along with distance.
Optionally, the statistical method for the alloy precipitated phase fraction further includes:
when the target alloy is a nickel-based single crystal superalloy and the precipitated phase of the target alloy is subjected to raft transformation, respectively counting according to the rewritten gray-scale map to obtain the average length of the precipitated phase in the transverse direction and the average length of the precipitated phase in the longitudinal direction;
calculating to obtain a raft parameter according to the ratio of the transverse average length to the longitudinal average length, and quantitatively describing the raft degree of the corresponding precipitated phase according to the raft parameter.
In order to achieve the above object, the present invention further provides a statistical apparatus for the precipitated phase fraction of an alloy, the statistical apparatus comprising:
the SEM image acquisition and gray scale image conversion unit is used for acquiring an SEM image of a target alloy and converting the SEM image into a gray scale image;
the gray histogram generating unit is used for counting the frequency of the pixel points corresponding to each gray value in the gray map to generate a gray histogram;
a gray threshold value determination unit for determining a gray threshold value for dividing a gray interval to which each of the matrix phase and the precipitate phase belongs, by using a gray threshold value method, when the target alloy is composed of the matrix phase and the precipitate phase;
the counting unit of the number of the pixel points of the precipitated phase is used for counting the number of the pixel points in the corresponding precipitation gray scale interval;
and the precipitated phase fraction calculating unit is used for calculating the ratio of the number of the pixel points to the total number of the pixel points of the SEM image to obtain a precipitated phase fraction.
Optionally, the grayscale threshold determining unit includes:
a first gray value determining subunit, configured to select a gray value with the largest frequency in the gray histogram as a first gray value;
the left and right alternative interval determination subunit is used for selecting a gray interval with a preset gray difference with the first gray value as an alternative interval to obtain a left alternative interval and a right alternative interval;
the target candidate interval determining subunit is configured to count a sum of frequency counts corresponding to each gray value in the left candidate interval and the right candidate interval, compare the frequency counts of the left candidate interval and the frequency counts of the right candidate interval, and mark the candidate interval with the larger frequency count sum as the target candidate interval;
a second gray value determining subunit, configured to select a gray value with the largest frequency in the target candidate region interval as a second gray value;
a gray difference determination subunit, configured to determine whether a gray difference between the second gray value and the first gray value is equal to the preset gray difference;
a tangent method processing subunit, configured to determine, by using a tangent method in the grayscale threshold methods, a grayscale threshold for dividing the grayscale interval to which the matrix phase and the precipitate phase belong when the grayscale difference between the second grayscale value and the first grayscale value is equal to the preset grayscale difference;
and the minimum threshold method processing subunit is configured to determine, by using a minimum threshold method in the gray threshold methods, a gray threshold for dividing the gray interval to which the matrix phase and the precipitate phase belong when the gray difference between the second gray value and the first gray value is not equal to the preset gray difference.
Optionally, the tangent processing subunit includes:
a first straight line family obtaining module, configured to make a straight line between a vertex corresponding to the first gray value and a vertex corresponding to each gray value in the target candidate interval, and mark the straight line as a first straight line family;
a tangent line selecting module, configured to select, as a tangent line, a straight line in the first straight line family having a minimum distance between the intersection point and a vertex corresponding to the first gray value; wherein the intersection point is a point at which each straight line in the first straight line family uniquely intersects with the y-axis;
a third gray value determining module, configured to use a gray value of a vertex located in the target candidate interval and corresponding to the tangent as a third gray value;
the tangent point candidate interval selection module is used for determining a gray interval between the first gray value and the third gray value as a tangent point candidate interval;
the second straight line family obtaining module is used for making a straight line by using the slope of the tangent line and the vertex corresponding to each gray value in the tangent point alternative interval and marking the straight line as a second straight line family;
the tangent point selecting module is used for selecting a vertex corresponding to the straight line with the minimum y-axis intercept in the second straight line family as a tangent point;
and the tangent method gray threshold value determining module is used for taking the gray value corresponding to the tangent point as a gray threshold value for distinguishing the gray intervals to which the matrix phase and the precipitated phase belong respectively.
Optionally, the minimum threshold processing subunit includes:
a valley value determining module, configured to use a value with the smallest frequency between the first gray value and the second gray value as a valley value;
and the minimum threshold method gray threshold value determining module is used for taking the gray value corresponding to the valley value as a gray threshold value for dividing the gray intervals to which the matrix phase and the precipitated phase belong respectively.
Optionally, the statistical device for the alloy precipitated phase fraction further includes:
a precipitated phase gray value rewriting unit for rewriting the gray value of each pixel point in the gray interval to which the precipitated phase belongs to 0;
and the matrix phase gray value rewriting unit is used for rewriting the gray value of each pixel point in the gray interval to which the matrix phase belongs to 255 to obtain a rewritten gray map.
Optionally, the statistical device for the alloy precipitated phase fraction further includes:
a precipitated phase color rewriting unit for rewriting a color of a precipitated phase in the rewritten gray scale map into blue by using a JET color system after obtaining the rewritten gray scale map;
and a matrix phase color rewriting unit configured to rewrite a color of the matrix phase in the rewritten gray scale image to yellow using the JET color system to obtain a rewritten color image.
Optionally, the statistical device for the alloy precipitated phase fraction further includes:
a comparison result obtaining unit, configured to compare, in a gray value matrix constituting a gray value image, the gray value corresponding to each pixel point with the gray threshold value row by row or column by column to obtain a comparison result, when the SEM image is an SEM image that changes with depth and is taken from the depth direction of the surface of the target alloy;
the scatter diagram drawing unit is used for counting the percentage of the pixel points of the precipitated phase in each row or each column according to the comparison result and generating a scatter diagram of the precipitated phase fraction changing along with the depth according to the percentage;
and the smoothing unit is used for smoothing the scatter diagram by utilizing a moving average method to obtain a curve of precipitated phase fraction changing along with distance.
Optionally, the statistical device for the alloy precipitated phase fraction further includes:
the transverse/longitudinal average length counting unit is used for respectively counting and obtaining the average length of the precipitated phase in the transverse direction and the average length of the precipitated phase in the longitudinal direction according to the rewritten gray scale map when the target alloy is the nickel-based single crystal superalloy and the precipitated phase is subjected to raft formation;
and the raft parameter calculation unit is used for calculating to obtain raft parameters according to the ratio of the transverse average length to the longitudinal average length so as to quantitatively describe the raft degree of the corresponding precipitated phase according to the raft parameters.
In order to achieve the above object, the present invention also provides an electronic device, including:
a memory for storing a computer program;
a processor for implementing the statistical method of the alloy precipitated phase fraction as described above when the computer program is executed.
In order to solve the defects of the prior art, the statistical method of the alloy precipitated phase fraction provided by the invention comprises the following steps: firstly, converting an SEM image of a target alloy into a gray map, then extracting the frequency corresponding to each gray value in the gray map to obtain a gray histogram, then determining a gray threshold value which can be used for dividing a matrix phase gray interval and a precipitated phase gray interval by using a gray threshold value method according to the characteristic that the frequency representing the precipitated phase and matrix phase gray values is normally distributed in the respective gray intervals, and obtaining the precipitated phase fraction by simple statistics after determining the precipitated phase gray interval according to the gray threshold value. Compared with the prior art, the technical scheme provided by the invention successfully enables the operation steps to be automatically executed completely through a pre-programmed application program by combining the alloy SEM image with the gray threshold method, and eliminates long time consumption and human errors caused by manual operation through experience in the prior art. When the precipitated phase fractions corresponding to a plurality of SEM images need to be counted, the automated process can be performed with higher efficiency by a batch processing technique.
The invention also provides a device for counting the alloy precipitated phase fraction and electronic equipment, which have the beneficial effects and are not repeated herein.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It is obvious that the drawings in the following description are only embodiments of the invention, and that for a person skilled in the art, other drawings can be obtained from the provided drawings without inventive effort.
FIG. 1 is a flow chart of a statistical method for the fraction of precipitated phases in an alloy according to an embodiment of the present invention;
FIG. 2 is a gray scale diagram provided by an embodiment of the present invention;
FIG. 3 is a gray level histogram provided by an embodiment of the present invention;
FIG. 4 is a gray level histogram labeled with gray level threshold values provided on the basis of FIG. 3;
FIG. 5 is a rewritten gray scale image provided on the basis of FIG. 3;
FIG. 6(a) is a scatter plot provided by an embodiment of the present invention;
FIG. 6(b) is an image obtained by performing a smoothing process based on FIG. 6 (a);
FIG. 7 is a schematic diagram illustrating how much the raft is changed according to an embodiment of the present invention;
FIG. 8 is a flowchart of a method for determining a gray level threshold using a gray level threshold method according to an embodiment of the present invention;
fig. 9 is a gray histogram showing a left candidate interval and a right candidate interval according to an embodiment of the present invention;
FIG. 10 is a gray level histogram showing the bimodal features of the left candidate interval and the right candidate interval according to an embodiment of the present invention;
FIG. 11 is a gray level histogram of a unimodal feature showing a left candidate bin and a right candidate bin provided by an embodiment of the invention;
FIG. 12 is a flowchart of a method for determining a gray level threshold using a minimum threshold method in a gray level threshold method according to an embodiment of the present invention
FIG. 13 is a flowchart of a method for determining a gray level threshold using a tangential gray level thresholding method according to an embodiment of the present invention;
FIG. 14 is a schematic diagram of a tangential method for determining gray scale threshold values corresponding to the scheme shown in FIG. 13;
fig. 15 is a schematic diagram of error magnitudes between gray level threshold values respectively calculated in different manners and actual gray level threshold values according to an embodiment of the present invention;
fig. 16 is a block diagram of a statistical apparatus for precipitated phase fraction of an alloy according to an embodiment of the present invention.
Detailed Description
The invention aims to provide a method and a device for counting alloy precipitated phase fractions, electronic equipment and a computer-readable storage medium, and aims to improve the efficiency and accuracy of counting the precipitated phase fractions.
For the purpose of clearly explaining the objects, technical solutions and advantages of the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Example one
Referring to fig. 1, fig. 1 is a flowchart of a statistical method for the fraction of precipitated phases of an alloy according to an embodiment of the present invention, which includes the following steps:
s101: obtaining an SEM image of a target alloy, and converting the SEM image into a gray scale image;
the step aims to read the digital information of the SEM image obtained by shooting the target alloy through a scanning electron microscope, and convert the original SEM image into a gray scale image for facilitating subsequent threshold value selection. The grayscale map obtained by the grayscale processing conversion is obtained by R, G, B weighted average of the color SEM images. The gray scale image for display is typically stored with a non-linear scale of 8 bits per sampled pixel, so that 256 levels of gray scale are possible. The grey scale map obtained after conversion can be seen in fig. 2.
The SEM image information is stored in RGB three-dimensional digital form, and can be read by a computer. In order to facilitate the selection of the gray threshold in the subsequent steps, the method converts the SEM image in a three-dimensional digital form into a one-dimensional gray image, and particularly can realize the conversion in a weighted average mode.
The SEM image in the three-dimensional digital form is converted into the one-dimensional gray scale image, so that the calculation speed can be improved, and the SEM image can be segmented by using a gray scale threshold. The SEM image expression information only has structural information expressed by different gray scales, so that the image information is not lost when the SEM image expression information is converted into a one-dimensional gray scale image.
S102: counting the frequency of the pixel points corresponding to each gray value in the gray map to generate a gray histogram;
the abscissa of the gray level histogram generated in the step represents 256 gray level values of 0-255, and the ordinate represents the frequency of the pixel point corresponding to each gray level value, namely the gray level histogram reflects the distribution characteristics respectively representing the frequency of the gray level values of the alloy matrix phase and the precipitated phase, and the distribution characteristics are the basis for distinguishing the precipitated phase and the matrix phase by using a gray level threshold method. The resulting grey level histogram can be seen in fig. 3.
For example, the resolution of the gray-scale map is 800 × 600, the gray-scale map has 480000 pixels in total, that is, 480000 is the result of adding all the frequencies of the pixels corresponding to the 256 gray-scale values in the gray-scale histogram, and assuming that 100 pixels having a gray-scale value of 150 are in total in the gray-scale map, the ordinate corresponding to the vertex of the histogram whose abscissa is 150 will be expressed in the gray-scale histogram as 100.
S103: when the target alloy consists of a matrix phase and a precipitated phase, determining a gray threshold value for dividing a gray interval to which the matrix phase and the precipitated phase belong by using a gray threshold value method;
in addition to S102, the present step is directed to processing the gray level histogram obtained in the previous step by a gray level threshold method for an alloy consisting of only a matrix phase and a precipitate phase to obtain a gray level threshold value that can be used to distinguish a matrix phase gray level interval from a precipitate phase gray level interval, which may also be referred to as a critical point of two gray level intervals. Due to the definition of its critical point, the precipitated phase gray scale interval and the matrix phase gray scale interval will be located on one side of the gray threshold, respectively. For example, when the gray scale value corresponding to the pixel point representing the precipitated phase is larger than that of the matrix phase, two corresponding gray scale intervals will be distributed in the gray scale histogram in a manner that the gray scale interval of the matrix phase is shifted to the left and the gray scale interval of the precipitated phase is shifted to the right.
The purpose of obtaining the gray threshold value can be realized by utilizing a gray threshold value method because the precipitated phase and the matrix phase in the SEM image have obvious gray difference; and moreover, the gray values corresponding to the pixel points representing the precipitated phase and the matrix phase are subjected to normal distribution. Reflecting the above characteristics by the gradation histogram causes the portion representing the precipitated phase and the matrix phase to appear as two "peaks" approximately following the normal distribution, and the range of each "peak" corresponds to the gradation interval of the matrix phase and the precipitated phase. Therefore, the precipitated phase and the matrix phase can be separated only by finding a proper separation point between the two peaks.
Fig. 4 shows specific positions of the gray threshold on the basis of fig. 3, and it can be seen that the gray threshold marked in fig. 4 is just a dividing point between the left side "peak" and the right side "peak".
S104: counting the number of pixel points in the interval of separating out the corresponding gray scale;
s105: and calculating the ratio of the number of the pixel points to the total number of the pixel points in the SEM image to obtain a precipitated phase fraction.
On the basis of S103, S104 is to count the number of pixels in the precipitated corresponding gray scale interval, and obtain the precipitated phase fraction as the final result by taking the number of pixels in the precipitated phase gray scale interval calculated in S104 as a numerator and the total number of pixels in the SEM image as a denominator.
The precipitated phase fraction corresponding to the SEM image can be obtained already through the above steps. In order to be compared with the original SEM picture to check the accuracy of the segmentation of the grey threshold picture, an image which can correspond to a conclusion needs to be given. Therefore, in order to express the precipitated phase significantly, the precipitated phase and the matrix phase may be distinguished by using a gray scale threshold, and then the two phases may be rewritten in accordance with the gray scale value. For example, the gray scale values of the pixels in the gray scale section to which the precipitated phase and the matrix phase belong may be rewritten to 0 and 255, respectively, to obtain a rewritten gray scale map with high contrast (see fig. 5, and fig. 5 is a rewritten gray scale map obtained by rewriting the gray scale values of the precipitated phase and the matrix phase in fig. 2).
Furthermore, compared with a gray-scale image in which black and white are correspondingly displayed, the color image with bright color contrast is more attractive. Therefore, after obtaining the rewritten gradation pattern, the colors of the precipitated phase and the matrix phase in the rewritten gradation pattern can be rewritten into blue and yellow, respectively, using the JET color system. Of course, in different practical application scenes, the color combinations selected by the color map or the gray scale map are not limited, and the color combinations can be flexibly selected according to all possible special requirements in the practical application scenes.
Furthermore, on the basis of the scheme for rapidly and accurately determining the gray threshold value, the application expansion can be carried out, and the method specifically provides the expansion in two directions:
the application expansion is as follows: due to the influence of diffusion, high-temperature oxidation or the composition gradient of the alloy, the fraction of the precipitated phase of the alloy changes along with the change of depth or distance in a certain direction. During the research process of the alloy materials, quantitative description of the change is often needed. To this end, one implementation is as follows:
in a gray value matrix forming a gray level image, comparing the corresponding gray level of each pixel point with the size of a gray level threshold value row by row or column by column to obtain a comparison result;
counting the percentage of the pixel points of each line or each column of the precipitated phases according to the comparison result, and generating a scatter diagram of the precipitated phase fraction changing with the depth or the distance according to the percentage;
and smoothing the scatter diagram by using a moving average method to obtain a curve of precipitated phase fraction changing along with distance. The moving average method has the function of smoothing each scattered point which is originally distributed in a scattered way into a continuous curve so as to obtain corresponding phase fractions and highlight the change trend of the phase fractions at different positions.
Fig. 6(a) shows the generated scattergram, and fig. 6(b) shows the scattergram after the smoothing process.
And (5) application expansion II: in order to quantitatively describe the tissue raft degree of the nickel-based single crystal superalloy in the service process (raft refers to the raft structure of a rod body formed by evolution of an originally cubic precipitated phase of the nickel-based superalloy at a certain temperature and under a certain load), raft parameters can be calculated on the basis of gray threshold segmentation of the precipitated phase and a matrix phase. To this end, one implementation is as follows:
after the gray threshold value is obtained, respectively counting according to the rewritten gray graph to obtain the average length of the precipitated phase in the transverse direction and the average length of the precipitated phase in the longitudinal direction, and obtaining the raft parameters by calculating the ratio of the average length to the average length of the precipitated phase in the longitudinal direction so as to quantitatively describe the raft degree of the corresponding precipitated phase according to the raft parameters.
The process of calculating the raft degree is shown in fig. 7, where fig. 7 includes 5 gray-scale maps with the upper left corner marks (a), (b), (c), (d), and (e), which are obtained from different distances from the surface of the nickel-based superalloy, and a variation map which varies with the variation of the raft degree with the variation of the distance, where T represents the average length in the transverse direction, L represents the average length in the longitudinal direction, and S is the quotient of T and L.
Meanwhile, when the steps are realized by using scripts and application programs, the multitask parallel processing capability of the computer can be fully utilized to carry out batch processing, so that the work can be completed in the shortest time. Meanwhile, after batch processing, the original SEM images, the rewritten gray-scale images/rewritten color images, the precipitated phase fraction and other results can be automatically exported according to a certain format according to a preset result display template.
In order to solve the defects of the prior art, the technical scheme provided by this embodiment successfully enables the above operation steps to be automatically executed completely through a pre-programmed application program by combining the alloy SEM image and the grayscale threshold method, and eliminates long time consumption and human errors caused by manual operation through experience in the prior art. Meanwhile, when the corresponding precipitated phase fractions of a plurality of SEM images need to be counted, an automatic mode can be completed with higher efficiency through a batch processing technology.
Example two
Referring to fig. 8, fig. 8 is a flowchart of a method for determining a gray threshold by using a gray threshold method according to an embodiment of the present invention, and on the basis of the first embodiment, the embodiment provides a specific implementation manner for S103, including the following steps:
s201: selecting the gray value with the maximum frequency number in the gray histogram as a first gray value;
s202: selecting a gray interval with a preset gray difference with the first gray value as an alternative interval to obtain a left alternative interval and a right alternative interval;
referring to fig. 9, in fig. 9, the first gray scale value is 140, and the preset gray scale difference is set to 50, so that the gray scale value range of the left candidate interval is [0,90], and the gray scale value range of the right candidate interval is [190, 250 ].
S203: respectively counting the sum of frequency counts corresponding to all gray values in the left candidate interval and the right candidate interval, comparing the frequency counts of the left candidate interval and the right candidate interval, and marking the candidate interval with larger frequency count sum as a target candidate interval;
s204: selecting the gray value with the maximum frequency in the target candidate area interval as a second gray value;
in order to mark the positions of the matrix phase gray scale interval and the precipitated phase gray scale interval, the present embodiment determines a representative gray scale value through the four steps: a first gray value and a second gray value. The purpose is two: firstly, preparing for judging whether the corresponding gray histogram of the alloy SEM picture is a single-peak or double-peak characteristic in the next step S205; secondly, when the gray level histogram is judged to be the double-peak feature and S206 is executed, an alternative interval is provided for selecting the valley value.
In the gray-scale histogram, there is inevitably a highest peak corresponding to the precipitate phase or the matrix phase. Therefore, the highest peak can be directly found by a method of finding the maximum value of the global frequency, and the gray value corresponding to the highest peak is marked as the first gray value. Unlike the first gray value obtaining process, the second gray value obtaining process must be limited to a proper gray interval. Meanwhile, in view of the problem that the gray value which is closer to the first gray value and has higher frequency will interfere with the selection of the second gray value, in order to avoid the interference, the present application provides a method for obtaining a suitable gray interval for searching for the second gray value by presetting the gray difference, wherein one feasible method is as follows: and selecting an interval which is beyond the preset gray difference from the first gray value as an alternative interval (namely, searching for a second gray value in the alternative interval). In fact, according to different SEM images in actual situations, the candidate interval includes two cases, namely, a left candidate interval located on the left of two sides of the first gray scale value and a right candidate interval located on the right of the first gray scale value.
In the left candidate interval and the right candidate interval, the larger frequency sum generally corresponds to the gray scale interval to which the other phase belongs. Therefore, in most cases, the candidate interval with the larger frequency sum can be directly selected as the candidate interval for obtaining the second gray value. Taking fig. 9 as an example, it is obvious that the left candidate section has a larger frequency sum, and therefore the target candidate section in fig. 9 is the left candidate section.
S205: judging whether the gray difference between the second gray value and the first gray value is equal to a preset gray difference, if so, executing S207, otherwise, executing S206;
on the basis of S201 to S204, the present step is intended to determine which specific method is subsequently adopted to determine the gray threshold value by determining whether the gray difference between the second gray value and the first gray value is equal to the preset gray difference.
When the gray difference between the second gray value and the first gray value is equal to the preset gray difference, the second gray value is selected in the interval of the left (right) alternative interval, and the interval is monotonous, so that no obvious peak exists. Therefore, only one obvious peak exists in the gray level histogram at this time, and the gray level histogram shows a single peak characteristic (see fig. 10); on the contrary, there are two distinct peaks, which are characteristic of double peaks (see fig. 11).
S206: determining a gray level threshold value for dividing a gray level interval to which the matrix phase and the precipitated phase belong by a minimum threshold value method in gray level threshold value methods;
this step is established on the basis that the determination result of S205 is that the gray difference between the second gray value and the first gray value is not equal to the preset gray difference, which indicates that the gray histogram has an obvious double-peak feature. Because the shapes of two peaks under the double-peak characteristic are relatively equal, the minimum threshold method is more suitable to be adopted. As the name implies, this method first uses a value having the smallest frequency between the first gradation value and the second gradation value as a bottom value (corresponding to S301 in fig. 12), and uses a gradation value corresponding to the bottom value as a gradation threshold value for dividing the gradation sections to which the matrix phase and the precipitate phase belong (corresponding to S302 in fig. 12). In short, the frequency corresponding to the first gray value and the second gray value is used as two peak points of the double peak, and the gray value corresponding to the valley is a critical point between the two peak points, so that a gray threshold with higher accuracy can be simply and conveniently determined by the method when the double peak is characterized.
S207: determining a gray threshold value for dividing a gray interval to which the matrix phase and the precipitated phase belong by a tangent method in a gray threshold value method;
this step is established on the basis that the judgment result of the tangent method in S205 is that the gray difference between the second gray value and the first gray value is equal to the preset gray difference, which indicates that the gray histogram represents a single-peak feature, and therefore, a tangent method more suitable for the single-peak feature is adopted.
The unimodal characteristic refers to a condition that only one obvious characteristic peak exists in the gray level histogram due to serious overlapping of the gray level intervals corresponding to the precipitated phase and the matrix phase in the gray level histogram and too small volume fraction of one phase. And when the minimum threshold value method does not have a second obvious peak, the segmentation of the corresponding regions of the precipitated phase and the matrix cannot be accurately realized. In order to ensure that the determined gray level threshold is more accurate, the tangent method used by the application makes up for the defect, and the separation of the precipitated phase and the matrix phase is realized under the condition that the second obvious peak is not existed.
One specific implementation, including but not limited to, may be seen in the flowchart shown in fig. 13:
s401: making a straight line between a vertex corresponding to the first gray value and a vertex corresponding to each gray value in the target candidate interval, and marking the straight line as a first straight line family;
s402: selecting a straight line in the first straight line family, wherein the straight line enables the intersection point to be the minimum distance from the vertex corresponding to the first gray value, as a tangent line; wherein the intersection point is a point where each straight line in the first straight line family uniquely intersects with the y axis;
s403: taking the gray value of the vertex in the target candidate interval corresponding to the tangent as a third gray value;
s404: determining a gray level interval between the first gray level value and the third gray level value as a tangent point alternative interval;
s405: drawing a straight line by using the slope of the tangent line and the vertex corresponding to each gray value in the tangent point alternative interval, and marking the straight line as a second straight line family;
s406: selecting a vertex corresponding to the straight line with the minimum difference between the y-axis intercept and the first peak value in the second straight line family as a tangent point;
s407: and taking the gray value corresponding to the tangent point as a gray threshold value for distinguishing the gray intervals to which the matrix phase and the precipitated phase belong respectively.
As shown in the step of fig. 13, see fig. 14.
To show the difference of the accuracy of the finally calculated gray threshold in different ways, see the difference change diagram shown in fig. 15, the three gray histograms in the upper part of fig. 15 correspond to the moving distances 0, 30, and 70 respectively from left to right, the bimodal feature is gradually changed into the unimodal feature in an exemplary process, and the difference between the gray threshold determined by the minimum threshold method and the tangent method at different moving distances and the actual gray threshold is shown in the lower part. As can also be seen from fig. 15, the smaller the moving distance (the more obvious the double peak feature is), the closer the gray level threshold determined by the minimum threshold method is to the actual gray level threshold; the larger the shift distance (the more pronounced the single-peak feature), the closer the tangent-determined gray threshold value is to the actual gray threshold value.
Because the actual situation is complicated and cannot be illustrated by one list, a person skilled in the art can realize that many examples exist in combination with the actual situation according to the basic method principle provided by the invention, and the protection scope of the invention should be protected without enough inventive work.
EXAMPLE III
Referring to fig. 16, fig. 16 is a block diagram illustrating a structure of a statistical apparatus for alloy precipitated phase fraction according to an embodiment of the present invention, where the statistical apparatus may include:
an SEM image obtaining and grayscale image converting unit 100 for obtaining an SEM image of the target alloy and converting the SEM image into a grayscale image;
a gray histogram generating unit 200, configured to count frequency of pixel points corresponding to each gray value in the gray map to generate a gray histogram;
a gray threshold value determination unit 300 configured to determine, when the target alloy is composed of the matrix phase and the precipitate phase, a gray threshold value for dividing a gray range to which each of the matrix phase and the precipitate phase belongs, by using a gray threshold value method;
a precipitated phase pixel point number counting unit 400, configured to count the number of pixel points in a corresponding precipitated gray scale interval;
and the precipitated phase fraction calculation unit 500 is configured to calculate a ratio of the number of the pixel points to the total number of the pixel points of the SEM image, so as to obtain a precipitated phase fraction.
The gray threshold determining unit 300 may include:
the first gray value determining subunit is used for selecting the gray value with the maximum frequency number in the gray histogram as a first gray value;
the left and right alternative interval determination subunit is used for selecting a gray interval with a preset gray difference with the first gray value as an alternative interval to obtain a left alternative interval and a right alternative interval;
the target candidate interval determining subunit is used for respectively counting the sum of frequency counts corresponding to all gray values in the left candidate interval and the right candidate interval, comparing the frequency counts of the left candidate interval and the frequency counts of the right candidate interval, and marking the candidate interval with the larger frequency sum as the target candidate interval;
the second gray value determining subunit is used for selecting the gray value with the maximum frequency in the target candidate area interval as a second gray value;
a gray difference judging subunit, configured to judge whether a gray difference between the second gray value and the first gray value is equal to a preset gray difference;
the tangent method processing subunit is used for determining a gray threshold value for dividing the gray interval to which the matrix phase and the precipitated phase belong respectively by a tangent method in a gray threshold value method when the gray difference between the second gray value and the first gray value is equal to a preset gray difference;
and the minimum threshold method processing subunit is used for determining the gray threshold used for dividing the gray interval to which the matrix phase and the precipitated phase belong respectively by using the minimum threshold method in the gray threshold methods when the gray difference between the second gray value and the first gray value is not equal to the preset gray difference.
Wherein, this tangent line method processing subunit can include:
the first straight line family obtaining module is used for making a straight line between a vertex corresponding to the first gray value and a vertex corresponding to each gray value in the target candidate interval and marking the straight line as a first straight line family;
the tangent line selecting module is used for selecting a straight line which enables the vertex distance between the intersection point and the corresponding first gray value to be minimum in the first straight line family as a tangent line; wherein, the intersection point is the only intersection point of each straight line in the first straight line family and the y axis;
the third gray value determining module is used for taking the gray value of the vertex in the target candidate interval corresponding to the tangent as a third gray value;
the tangent point candidate interval selection module is used for determining a gray interval between the first gray value and the third gray value as a tangent point candidate interval;
the second straight line family obtaining module is used for making a straight line by using the slope of the tangent line and the vertex corresponding to each gray value in the alternative interval of the tangent point and marking the straight line as a second straight line family;
the tangent point selecting module is used for selecting the vertex corresponding to the straight line with the minimum y-axis intercept in the second straight line family as the tangent point;
and the tangent method gray threshold value determining module is used for taking the gray value corresponding to the tangent point as a gray threshold value for distinguishing the gray intervals to which the matrix phase and the precipitated phase belong respectively.
Wherein the minimum thresholding subunit may include:
the valley value determining module is used for taking the value with the minimum frequency between the first gray value and the second gray value as a valley value;
and the minimum threshold method gray threshold value determining module is used for taking the gray value corresponding to the valley value as a gray threshold value for dividing the gray interval to which the matrix phase and the precipitated phase belong respectively.
Further, the statistical device for the alloy precipitated phase fraction can further comprise:
a precipitated phase gray value rewriting unit for rewriting the gray value of each pixel point in the gray interval to which the precipitated phase belongs to 0;
and the matrix phase gray value rewriting unit is used for rewriting the gray value of each pixel point in the gray interval to which the matrix phase belongs to 255 to obtain a rewritten gray map.
Furthermore, the statistical device for the alloy precipitated phase fraction can further comprise:
a precipitated phase color rewriting unit for rewriting a color of a precipitated phase in the rewritten gray scale to blue by using a JET color system after obtaining the rewritten gray scale;
and a matrix phase color rewriting unit for rewriting the color of the matrix phase in the rewritten gray scale image into yellow by using a JET color system to obtain a rewritten color image.
Further, the statistical device for the alloy precipitated phase fraction can further comprise:
the comparison result obtaining unit is used for comparing the corresponding gray value of each pixel point with the gray threshold value row by row or column by column in a gray value matrix forming a gray value image to obtain a comparison result when the SEM image is taken from the depth direction of the surface of the target alloy and changes along with the depth;
the scatter diagram drawing unit is used for counting the percentage of the pixel points of each line or each row of the precipitated phases according to the comparison result and generating a scatter diagram of the precipitated phase fraction changing with the depth according to the percentage;
and the smoothing unit is used for smoothing the scatter diagram by using a moving average method to obtain a curve of precipitated phase fraction changing along with distance.
Further, the statistical device for the alloy precipitated phase fraction can further comprise:
the transverse/longitudinal average length counting unit is used for respectively counting and obtaining the average length of the precipitated phase in the transverse direction and the average length of the precipitated phase in the longitudinal direction according to the rewritten gray scale map when the target alloy is the nickel-based single crystal superalloy and the precipitated phase is subjected to raft formation;
and the raft parameter calculation unit is used for calculating to obtain raft parameters according to the ratio of the average length to the average length so as to quantitatively describe the raft degree of the corresponding precipitated phase according to the raft parameters.
This embodiment exists as an apparatus embodiment corresponding to the above method embodiment, and has all the beneficial effects of the method embodiment, and will not be described herein again.
Based on the foregoing embodiments, the present invention further provides an electronic device, which may include a memory and a processor, where the memory stores a computer program, and the processor may implement the steps provided by the foregoing embodiments when calling the computer program in the memory. Of course, the electronic device may also include various necessary network interfaces, power supplies, other components, and the like.
The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by an execution terminal or processor, can implement the steps provided by the above-described embodiments. The storage medium may include: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The embodiments are described in a progressive manner in the specification, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the method and its core concepts. It will be apparent to those skilled in the art that various changes and modifications can be made without departing from the principles of the invention, and it is intended that such changes and modifications also fall within the scope of the appended claims.
It is further noted that, in the present specification, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

Claims (8)

1. A statistical method for the fraction of precipitated phases of an alloy, comprising:
obtaining an SEM image of a target alloy, and converting the SEM image into a gray scale image;
counting the frequency of pixel points corresponding to each gray value in the gray map to generate a gray histogram;
when the target alloy consists of a matrix phase and a precipitated phase, determining a gray threshold value for dividing a gray interval to which the matrix phase and the precipitated phase belong by using a gray threshold value method;
counting the number of pixel points in the corresponding precipitation gray scale interval;
calculating the ratio of the number of the pixel points to the total number of the pixel points in the SEM image to obtain a precipitated phase fraction;
the method for determining the gray level threshold value used for dividing the gray level interval to which the matrix phase and the precipitated phase belong by using a gray level threshold value method comprises the following steps:
selecting the gray value with the maximum frequency number in the gray histogram as a first gray value;
selecting a gray interval with a preset gray difference with the first gray value as an alternative interval to obtain a left alternative interval and a right alternative interval;
respectively counting the sum of frequency counts corresponding to all gray values in the left candidate interval and the right candidate interval, comparing the frequency counts of the left candidate interval and the right candidate interval, and marking the candidate interval with larger frequency count sum as a target candidate interval;
selecting the gray value with the maximum frequency in the target alternative interval as a second gray value;
judging whether the gray difference between the second gray value and the first gray value is equal to the preset gray difference or not;
if yes, determining a gray level threshold value for dividing a gray level interval to which the matrix phase and the precipitated phase belong through a tangent method in the gray level threshold value method;
if not, determining a gray level threshold value for dividing the gray level interval to which the matrix phase and the precipitated phase belong by the minimum threshold value method in the gray level threshold value methods;
the method for determining the gray level threshold value used for dividing the gray level interval to which the matrix phase and the precipitated phase belong by the minimum threshold value method in the gray level threshold value methods comprises the following steps:
taking a value with the smallest frequency between the first gray value and the second gray value as a valley value; and taking the gray value corresponding to the valley value as a gray threshold value for dividing the gray intervals to which the matrix phase and the precipitated phase respectively belong.
2. The statistical method according to claim 1, wherein determining the gray level threshold for dividing the gray level interval to which each of the matrix phase and the precipitate phase belongs by a tangent method of the gray level threshold comprises:
making a straight line between the vertex corresponding to the first gray value and the vertex corresponding to each gray value in the target candidate interval, and marking the straight line as a first straight line family;
selecting a straight line in the first straight line family, wherein the straight line enables the vertex distance between the intersection point and the first gray value to be minimum, and the straight line is selected as a tangent line;
wherein the intersection point is a point at which each straight line in the first straight line family uniquely intersects with the y-axis;
the tangent is determined by a vertex corresponding to the first gray value and a vertex in the target alternative interval together;
taking the gray value corresponding to the vertex in the target alternative interval as a third gray value;
determining a gray level interval between the first gray level value and the third gray level value as a tangent point alternative interval;
sequentially making straight lines through vertexes corresponding to all gray values in the tangent point alternative intervals by using slopes with the same tangent line, and marking the straight lines as a second straight line family;
selecting a vertex corresponding to the straight line with the minimum y-axis intercept in the second straight line family as a tangent point;
and taking the gray value corresponding to the tangent point as a gray threshold value for distinguishing the gray intervals to which the matrix phase and the precipitated phase belong respectively.
3. The statistical method of claim 2, further comprising:
rewriting the gray value of each pixel point in the gray interval to which the precipitated phase belongs to be 0;
and rewriting the gray value of each pixel point in the gray interval to which the matrix phase belongs to 255 to obtain a rewritten gray map.
4. The statistical method of claim 3, after obtaining the rewritten gray scale map, further comprising:
rewriting the color of the precipitated phase in the rewritten gray scale map into blue by using a JET color system;
and rewriting the color of the matrix phase in the rewritten gray scale image into yellow by using the JET color system to obtain a rewritten color image.
5. The statistical method according to claim 1, wherein when the SEM image is a depth-dependent SEM image taken from the depth direction of the surface of the target alloy, the method further comprises:
in a gray value matrix forming a gray level image, comparing the corresponding gray level of each pixel point with the size of the gray level threshold value row by row or column by column to obtain a comparison result;
counting the percentage of the pixel points of the precipitated phase in each row or each column according to the comparison result, and generating a scatter diagram of the precipitated phase fraction changing with the depth according to the percentage;
and smoothing the scatter diagram by using a moving average method to obtain a curve of precipitated phase fraction changing along with distance.
6. The statistical method of claim 3, further comprising:
when the target alloy is a nickel-based single crystal superalloy and the precipitated phase of the target alloy is subjected to raft transformation, respectively counting according to the rewritten gray-scale map to obtain the average length of the precipitated phase in the transverse direction and the average length of the precipitated phase in the longitudinal direction;
calculating to obtain a raft parameter according to the ratio of the transverse average length to the longitudinal average length, and quantitatively describing the raft degree of the corresponding precipitated phase according to the raft parameter.
7. A device for counting the fraction of precipitated phases in an alloy, comprising:
the SEM image acquisition and gray scale image conversion unit is used for acquiring an SEM image of a target alloy and converting the SEM image into a gray scale image;
the gray histogram generating unit is used for counting the frequency of the pixel points corresponding to each gray value in the gray map to generate a gray histogram;
a gray threshold value determination unit for determining a gray threshold value for dividing a gray interval to which each of the matrix phase and the precipitate phase belongs, by using a gray threshold value method, when the target alloy is composed of the matrix phase and the precipitate phase;
the method for determining the gray level threshold value used for dividing the gray level interval to which the matrix phase and the precipitated phase belong by using a gray level threshold value method comprises the following steps:
selecting the gray value with the maximum frequency number in the gray histogram as a first gray value;
selecting a gray interval with a preset gray difference with the first gray value as an alternative interval to obtain a left alternative interval and a right alternative interval;
respectively counting the sum of frequency counts corresponding to all gray values in the left candidate interval and the right candidate interval, comparing the frequency counts of the left candidate interval and the right candidate interval, and marking the candidate interval with larger frequency count sum as a target candidate interval;
selecting the gray value with the maximum frequency in the target alternative interval as a second gray value;
judging whether the gray difference between the second gray value and the first gray value is equal to the preset gray difference or not;
if yes, determining a gray level threshold value for dividing a gray level interval to which the matrix phase and the precipitated phase belong through a tangent method in the gray level threshold value method;
if not, determining a gray level threshold value for dividing the gray level interval to which the matrix phase and the precipitated phase belong by the minimum threshold value method in the gray level threshold value methods;
the method for determining the gray level threshold value used for dividing the gray level interval to which the matrix phase and the precipitated phase belong by the minimum threshold value method in the gray level threshold value methods comprises the following steps:
taking a value with the smallest frequency between the first gray value and the second gray value as a valley value;
taking the gray value corresponding to the valley value as a gray threshold value for dividing the gray interval to which the matrix phase and the precipitated phase belong
The counting unit of the number of the pixel points of the precipitated phase is used for counting the number of the pixel points in the corresponding precipitation gray scale interval;
and the precipitated phase fraction calculating unit is used for calculating the ratio of the number of the pixel points to the total number of the pixel points of the SEM image to obtain a precipitated phase fraction.
8. An electronic device, comprising:
a memory for storing a computer program;
a processor for implementing the statistical method of the alloy precipitated phase fraction as claimed in any one of claims 1 to 6 when executing the computer program.
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