A method for finding the microstructural parameters of low-carbon steel using its metallographic images is proposed. It allows to determine the following parameters: the ratio of perlite to ferrite phases, the parameters of grains of crystallites and their mutual arrangement; the degree of granularity of the pearlite phases. The method is aimed at predicting the strength characteristics of steel samples and consists of several stages. The preprocessing step involves color reduction, refinement of the area of interest, noise filtering, illumination refinement and histogram equalization. The segmentation of the image is associated with the search for the size, area and convex shell of grains. The stage of finding the microstructural parameters is based on the stochastic gradient-based estimation of the parameters of the segmented objects. Examples of analysis of steel oil pipeline samples with a forecast of their strength characteristics are given.
Metallographic methods for detecting and determining the grain size of steels and alloys are established by GOST 5639 [
Numerous studies have shown the relationship between the parameters of the microstructure and the mechanical properties of
metals and alloys [5, 7-10, etc.]. The dependence of the strength characteristics of cold-rolled steels at the production stage on
the change in the microstructure was investigated in [
Image Processing, Geoinformation Technology and Information Security / R.G. Magdeev, A.G. Tashlinskiy
Shape and arrangement of grains in low-carbon and low-alloy steels are subjected to certain regularities associated with the
solidification of the metal and its transformation during processing and operation. In accordance with GOST 8233 [
One of the main geometric parameters of the microstructure of a metal is the grain size, which is its mean diameter. The size (minimum) grain size The average size ¯ is found as the average of all the changed grains. of the i-th grain is characterized by the arithmetic average of the longitudinal (maximum) size and the transverse
A correlation was found between the average grain size ¯ and the yield and strength limits, which are described by the
HallPetch dependence [
= 0 + √ ¯ , where - the yield strength; 0 of steel); - constant coefficient determined by the steel grade.
Large dispersion of grain sizes adversely affects the uniformity of mechanical and operational properties of products. To take
into account this circumstance, the spread parameter of the grains is used [
Over time, with sufficient external forces, the plastic deformation covers the entire volume of the polycrystalline. As a result, the grains get an elongated shape in the direction of the most intense flow of the metal. Simultaneously with the change in the shape of the grains during the deformation, the crystallographic axes of the individual grains rotate in the direction of the greatest deformation, which leads to anisotropy of the properties of the metal.
To control the microstructural characteristics at the stages of metal rolling, the Tretyakov method [
The degree of orderliness of orientations of the perlite grains in the investigated region of the steel microstructure is characterized by the directivity vector and the ordering coefficient. For a particular grain, the vector of orientation ⃗ dir = ⋅ exp(− ), i.e. the direction of the vector coincides with the direction of the longitudinal axis of the perlite grain (fig. 2). The general vector of the grain orientation is:, ⃗ dir = ∑ =1 ⃗ dir, and the ordering coefficient is: ord = | ⃗ dir|/( ¯ ), where - the number of grains is.
Other important characteristics of the metal microstructure affecting the mechanical properties of steel are the ratio of perlite to ferrite PF,%, and the degree of granularity of the pearlite phases grit,%. - the yield strength of the initial (in the production
The proposed technique for identifying microstructure parameters can be divided into three main stages.
Preliminary processing of images under study aimed at increasing the accuracy and reliability of finding the microstructural parameters of perlite grains. It consists of the following operations: color reduction of the image in order to simplify subsequent calculations area of interest extraction is aimed at excluding low-information areas of the image, filtering the image to compensate for high-frequency distortions caused by the peculiarities of the metallographic microscope path, brightness refinement compensating for uneven illumination of the microsection, and histogram equalization.
Segmentation on metallographic images of areas corresponding to perlite grains according to which their microstructural parameters are further located. It is achieved by the following procedures: segmentation, aimed at identifying areas of pearlite
Image Processing, Geoinformation Technology and Information Security / R.G. Magdeev, A.G. Tashlinskiy grains, mathematical morphology for eliminating internal discontinuities in grain images and excluding from the further analysis of small objects, isolating external boundaries and constructing convex shells of grains for the subsequent calculation of microstructural parameters.
Estimation of microstructural parameters of perlite grains, including the formation of adaptive templates for finding object
parameters, Gaussian filtration of convex shells of isolated grains and formed templates for the purpose of expanding the
working range of stochastic gradient descent procedures [
Below the implementation of the above steps of the methodology is briefly considered.
Image color reduction. In the formulated problem, the informative component of color is small, so vector-based (color)
images are advisable to translate into levels of gray [
Area of interest extraction is aimed at excluding from the further processing of low-information areas, the presence of which
is related to the specificity of the imaging by a metallographic microscope, which causes the image to be formed approximatel y
in the form of a circle. The analysis [
Image filtering is aimed at elimination of brightness distortions caused by the imperfections of the optical detectors of the
metallographic microscope. In images they appear as small (one - two pixels), but significant (up to 45% to neighboring pixels)
brightness increase. The nature of the appearance of distortions is due to optics and reflections during photography. To eliminate
their influence on the final result, nonlinear median filtration was used [
а) b)
Illumination refinement is used for lighting unevenness compensation. A typical example of distortion of this kind in metallographic images is a shadow. In this case, the image can be represented as: = ⋅ , where - an undistorted image, – illumination coefficient. One can obtain an approximate illumination map by applying a Gaussian filter with a large blur radius (about 5% of the highly informative image area). The restored image is looked for as: ^ = exp(log( ) − log(^)), which allows not only to align the image with the level of illumination, but also to perform gradient transformations [22].
Histogram equalization aligns the intensities with the aim of improving the quality of the display. To carry out the equalization, the conversion is performed: ekv( , ) = ( ( , )), where ( , ) – brightness value in the pixel with coordinates ( , ) of the original image, ekv( , ) – brightness value of the converted image, and ( ) is the single-valued monotonically increasing conversion function.
Fig. 3b shows examples of images after the preprocessing phase.
Image Processing, Geoinformation Technology and Information Security / R.G. Magdeev, A.G. Tashlinskiy 3.2. Perlite grains segmentation
At this stage, the problem of isolating individual perlitic spots is solved with a view to their further analysis. To solve this
problem, a growing areas method is used [
The problem of segmentation of the perlite spots is solved using the image binarization procedure based on the histogram analysis of the image, taking into account the sizes of the desired regions.
Morphological closing (in particular, with 5x5 kernel) is aimed at eliminating objects less than the specified window and filling the gaps that are inside the images of pearlite spots.
Individual perlite grain segmentation is based on the method of growing areas [
Perlite grain boundaries estimation. The boundaries of the selected objects are found via algorithms for the sequential
construction of contours, which are characterized by high speed, absence of discontinuities and "extra" boundaries with low
computational complexity. In particular, the recursive algorithm of the "beetle" was used [
Construction of convex shells of perlite grains. There are many algorithms for extracting a convex hull, for example, the algorithm of Chan, Kirkpatrick, Melkman [21], but Graham [22], Jarvis [23] and the so-called "quickhull" (QH) algorithms were most widely used [24]. Their effectiveness has been investigated for the problem on binary images of simple figures and pearlite spots [25]. On simple figures, all algorithms showed an adequate result with a slight difference in speed. On binary images of real objects - pearl spots obtained from images of microstructures of metal pipelines, the Jarvis algorithm and the QH algorithm distinguish the convex envelopes of the spot correctly, unlike the Graham error algorithm. In this case, the average time of the Graham algorithm was approximately 1.1 times less than the QH algorithm and 1.9 times less than the Jarvis algorithm (the experiment was performed on PC with AMD Athlon II X2 3GHz and 3GB RAM). Therefore, the method included the QH algorithm. Note that the computational complexity of the Graham algorithm does not depend on the number of vertices found and is proportional to log( ), where is the number of external points of the polygon (spot). The complexity of the Jarvis algorithm depends on the number of vertex spots and is proportional to qh, where ℎ is the number of common spot points and its convex hull, which in the worst case is 2. The computational costs of the QH algorithm is compounded by the complexity of constructing all subsets. At best, the problem is divided into two equally powerful subtasks, then the complexity of the algorithm is from 2 to 2. The advantage of the QH algorithm is also the possibility of parallel computations for all subsets.
Examples of isolated convex shells of pearlite spots are shown in Fig. 4, a. After the convex hulls are selected, their linear characteristics are calculated, which are then used to estimate the microstructural parameters.
In order to find the microstructural parameters of the spots, stochastic gradient descent-based estimation was used [
а)
b)
In order to increase the working range of the evaluation, the templates and convex hulls obtained for each object under study
are subjected to an approximate procedure [
Image Processing, Geoinformation Technology and Information Security / R.G. Magdeev, A.G. Tashlinskiy
As a model of possible deformations of a customized template, when it is adjusted to a convex hull, a model similar to the similarity model is used:
~ = 0 + (( − 0)cos − ( − 0)sin ) + ℎ , ~ = 0 + (( − 0)sin + ( − 0)cos ) + ℎ, where as the following adaptive parameters are used: scale factor , ellipticity coefficient , parallel shift ℎ¯ = (ℎ , ℎ ), - directional angle and the coordinates of the rotation center of the spot ( 0, 0) [26]. It should be noted that to ensure the work of stochastic gradient descent optimization procedures, it is necessary to estimate all the coefficients of the model, and to calculate the microstructural parameters it is sufficient to use just and . For each i-th spot with respect to the parameters of the adapted template, which has the maximum correlation with its convex hull, the following parameters are calculated: longitudinal size ; transverse size ; average size ; directional vector ⃗ dir and the form anisotropy coefficient (which coincides in this technique with the ellipticity coefficient). For example, Fig. 5 shows the histograms of the distribution of spots by the coefficient of anisotropy of the shape (fig. 5,a) and the directional angle (fig. 5,b). The left figure corresponds to the left microstructure of fig. 3,b, and the right one - the right. The selected type of histogram of grain directivity (from 0 to 180 degrees), due to the specific nature of the problem, makes it possible to identify the directions of growth of pearlite spots close to 0 (180) degrees.
Then the integral parameters of the grains are found: the number of grains, the ratio of perlite to ferrite, the granularity of the
pearlite phases, the general grain orientation vector, the average grain size, the grain size distribution, the degree of ordering of
the grain orientations, and the mean value of the anisotropic shape coefficient. In particular, for the left image of fig. 3, b, we
obtain: =41, PF=31,3%, grit=26,5%, ¯ =43, =37, ¯ end=0,44, | ⃗ dir|=696, =168, ord=0,39, and for the right one: =30,
PF=32,7%, grit=28,5%, ¯ =34,2, =23, ¯ end=0.40, | ⃗ dir|=718, =70, ord=0,70. From the obtained strength characteristics,
taking into account the data from [
It should be noted that the conducted studies showed that the average grain sizes, automatically found using the method
examined, and calculated according to the traditional methods of GOST 5639 [
As already noted, the practical actual task is to determine the changes in the strength characteristics of metals after a long period of operation. A particularly topical task is to determine the changes in the strength characteristics of metals, after prolonged use. The processes of changing the microstructure of metal structures during long-term operation are similar to the processes of cold rolling metals with a certain degree of deformation. We will give an example of the change in the microstructural characteristics of the steel of the 12GS pipeline after 40 years of explantation with its outer (fig. 6,a) and internal (fig. 6,b) surfaces. Histograms of the directivity vectors of microstructures are also shown there.
а) b)
Analysis of the data shows that all the parameters of the microstructure, other than the directivity, as well as the strength characteristics of the outer and inner surfaces of the pipeline metal differ slightly. It is essential to differentiate the orderliness of the microstructure grains, which on the one hand leads to hardening, but on the other hand to the brittleness of the metal and the
The reported study was supported by RFBR and Government of Ulyanovsk region (Russia), project № 16-41-732053.
Image Processing, Geoinformation Technology and Information Security / R.G. Magdeev, A.G. Tashlinskiy increase in the probability of the appearance of microcracks. Therefore, the forecast of the strength characteristics of the pipeline metal must take into account the directivity of the grains of both the external and internal surfaces.
A technique for determining the microstructural parameters of low-carbon steel is proposed. It allows to determine from metallographic images in real time the perlite to ferrite ratio, perlite grain, the general grain orientation vector, the average grain size, the grain size distribution, the degree of ordering of the grain orientations, and the mean value o f the anisotropic shape coefficient.
The technique can be arbitrarily divided into three stages: preliminary processing of the images under study, aimed at increasing the accuracy and reliability of finding microstructural parameters, determining the areas corresponding to perlite grains on the images, and actually evaluating the microstructural parameters of the grains. Preprocessing includes operations: color reduction, selection of the working area of processing, image filtering to compensate for high-frequency distortion caused by the peculiarities of the metallographic microscope path, compensation of uneven illumination of the microsection, histogra m equalization. Segmentation of perlite grains on the images is achieved by the following procedures: segmentation, aimed at identifying areas of pearlite grains, mathematical morphology for eliminating internal discontinuities in grain images and excluding from the further analysis of small objects, delineating outer boundaries and constructing convex shells of grains. Estimation of microstructural parameters includes the formation of adaptive templates for finding object parameters, Gaussian filtering of convex shells of segmented grains and formed templates for the purpose of expanding the working range of the required parameters, finding the microstructural parameters of the perlite grains and the degree of granularity of the pearlite phases.
The peculiarity of the technique is that the parameters of the templates are adaptive and adapt to the parameters of the spots represented by convex hulls. As an a priori information for finding the initial approximations of the parameters of the templ ates, the area of the selected convex envelope of the spot is used.
The proposed technique can be used to determine the strength characteristics of the metal at different stages of production and operation: from quality control at the plant to determining the remaining resource. Approbation of the technique on image s of microsections of oil and water pipelines of different service life has shown its high efficiency.
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