Prediction of the Destruction of Materials with Inhomogeneous Structures

Structural and metallurgical factors that cause the differences in the fracture resistance of steels and alloys are studied, which is necessary for predicting the destruction of media with an inhomogeneous structure. The prospects for digitalization of measuring the parameters of the structure and fracture surfaces using Big Data algorithms are considered.


INTRODUCTION
The prediction of the destruction of structures is largely determined by the complete evaluation of the quality of raw materials, which also concerns the assessment of their residual life. At their core, steel and alloys are a kind of medium the morphological heterogeneity of which can be quite large, especially in industrial production. The diversity of structures and their geometries makes it difficult to develop general approaches to identifying critical structural parameters that limit the properties of materials [1][2][3]. The heterogeneity of the morphological structure determines not only the spread of viscosity between products, but also the difference in the mechanisms of destruction within the same product (sample). To solve problems related to obtaining objective information about the behavior of a material in a structure, it is necessary to understand the mechanisms of destruction of media with an inhomogeneous structure. The standard measurement technique is not always sufficient to assess the destruction of such structures. This requires digital procedures for measuring the characteristics of structure inhomogeneity and destruction, and for comparing the obtained results. An essential condition for the successful application of this approach is the appropriate metrological support.
Metal properties are a result of a set of operations that are performed throughout the entire technological chain, from smelting to final heat treatment. However, the prediction of its strength, ductility, and toughness can be obtained by the data mining control of the technological process and the final product. This is also important for developing recommendations aimed at improving product quality. Data processing tools of passive observations, data mining, and Big Data [4] have become rapidly developing fields of applied statistics. However, the choice of algorithms for a specific production task requires an analysis of its content by a technologist, which implies knowledge of the mechanisms of evolution of structures and defects along the entire technological chain and the laws of destruction of the metal as a medium with an inhomogeneous structure. This suggests the possibility of measuring the structural and destruction parameters to directly compare them and, on this basis, isolate the critical components of the structure, which limit the heterogeneity in the metal quality. In this regard, it is obvious that one should know the laws of destruction of materials as the media with an inhomogeneous structure and the laws of their formation in accordance with various factors of treatment prehistory within the framework of industrial technology to be able to predict the destruction of materials [1].

THE EXTENT OF THE INHOMOGENEITY OF A MEDIUM WITH AN INHOMOGENEOUS STRUCTURE AND ITS DESTRUCTION
The formation of structural differences in nominally similar structures in steels is determined by the variety of scenarios of treatment prehistory (mechanisms responsible for the evolution of structures and defects) within the framework of industrial technology

STRENGTH AND PLASTICITY
and begins with the stage of metal smelting. According to the phase equilibrium diagram, the solidifying metal and the melt are different in composition. The growth of the first crystals from the surface to the ingot axis gives a difference in composition over its cross section (zonal liquation). Its extent depends on the phase diagram type, the solidification rate, and the direction of heat removal during crystallization, which are functions of the size and shape of the ingot or continuously cast billet.
The crystal grows from the melt as a dendrite, which can be up to 1-10 cm in size. The dendritic skeleton has two parameters: the distance Λ between the dendrite axes and liquation factor K = c max /c min , i.e., the ratio of the highest and lowest concentrations of the component (within the axes and in the interaxial regions of the dendrites). Depending on the sizes of the ingot and liquation zones in it, the step of the axes can be Λ 1 = 0.1-3 mm in the first-order dendrites and Λ 2 = 3-100 μm and even down to 400 μm in the second-order dendrites; generally, the average step (period) of dendrite axes on a random secant (Λ ≈ Λ 2 ) is used in practice. Dendritic liquation is determined by the speed w of the crystallization front and temperature gradient grad(T) at this front. From the surface to the axis of the ingot, temperature gradient grad(T) decreases and dendritic step Λ increases. Hence, the difference in the morphology of the dendritic structure is observed not only between liquation zones, but also within each of them.
Not only is the size of the dendrites important, but also the degree of dendritic liquation associated with it. The dispersion of dendrites limits the diffusion redistribution of impurities and reduces the inhomogeneity in the composition. The degree of liquation can be quite high; for example, the following degrees of liquation were found in ingots of alloyed structural steels with 0.1-0.4 wt % C: K Cr = 1.3-2.1; K Mn = 1.2-1.9; K Si = 1.3-1.7 [5]; and K Ni = 1.2-1.8 (forgings made of 38KhN3MFA-Sh steel). Liquation is enhanced by carbon that simultaneously redistributes after the main alloying elements (already after solidification), thereby leveling its thermodynamic activity, and diffuses into volumes with an excess of carbide forming elements (W, Mo, Cr, and Mn) and leaves volumes with an excess of a ferrite forming element (Si) [1].
Impurities and a sulfur-enriched low-melting segregated material are pushed back into the interaxial and interdendritic spaces of the ingot. Hence, the long-term consequences of liquation in the ingot are inhomogeneities in the geometry (size, shape, and location) of nonmetallic inclusions (NIs). The finer the dendrites are, the lower the liquation of sulfur is [1] and the finer the sulfides are. The statistics of the geometry of inclusions on the scale of a product (sample) can be characterized by a Bauman sulfur print. As an example, for a forging made of 38KhN3MFA steel, the measurements of the dark spot parameters (on a series of successive frames with an area of about 100 mm 2 , which were cut to the scale of the forging section in the horizontal, vertical, and diagonal directions) gave the following data about sulfide contamination over the forging section (central, intermediate, and peripheral zones of the forging): the density ρ is in the ranges from 1.15-1.50 to 0.60-0.90 and 0.60-0.97 pieces/mm 2 ; the volume fraction V ds of dark spots is from 3.5-5.0 to 1.5-2.7 and 0.9-2.0%; and the average diameter kd ds l ranges from 0.18-0.21 to 0.16-0.18 and 0.11-0.16 mm. The size distribution of dark spots is asymmetric (Fig. 1) [6] and reflects the behavior of the distribution of NIs in general, according to which the larger their size is, the less likely they are to appear within eyeshot. The shape of the distribution is important for estimating the effectiveness of using the average size parameters of NIs when comparing different samples from the results of measuring their geometry.
The correlation in the arrangement of inclusions, for example, segregation banding of brittle oxides due to their crushing during rolling, is a next important factor. The distribution of particles (in particular, sulfides) can be inhomogeneous because of zonal liquation or the formation of a more compact cluster in the volume of impure liquation localized in the interbranch regions of the dendrite at the final stage of crystallization. It is possible to distinguish a dense chain of points along a certain curve (with a known shape) from a random scattering of particles by conformal transformations of the plane [7]. Differences between random sets of points on the plane (or centers of particles that are small compared to distance r between them) can be estimated, for example, using the following algorithm for partitioning the plane into Voronoi polyhedra [8]: all points inside each of the polyhedra lie closer to its center than to the centers of all other adjacent polyhedra. This partitioning allows one to determine the nearest neighbors of each particle and to measure the distance between them. The left and right tails of such a distribution characterize the high probability of ductile fracture formation and favorable conditions for the development of plastic deformation, respectively. The difference in the arrangement of NIs can be quite large even within the same product. As an example, the average distances krl between particles within a forging made of 38KhN3MFA steel for two random fragments cut out from NI images (with the same area) were 447 ± 14 and 314 ± 12 μm. Not only are the average values different, but also the measurement samples as a whole vary (Fig. 2). According to the Kolmogorov-Smirnov criterion [9,10], λ exp = 12.98 > λ tabl = 1.95 with a risk of 0.001. Therefore, the difference between the samples is substantial. This difference can also contribute to the spread of toughness across the cross section of the forging.
The variable contents of alloying elements (as well as carbon together with them) in the cast structure lead to a difference in the critical rate of austenite cooling, as a result of which a different structure can be obtained within the dendrite axes and between them with the same rate of steel cooling. Hence, the effect of liquation on rolled products leads to the structural banding typical of medium carbon steel, i.e., to the martensite-bainite, bainite-pearlite, ferrite-pearlite, and carbide segregation bandings in high-carbon steel.
The arrangement of low-melting nonmetallic inclusions (sulfides and silicates) inside the dendrite cell and their flattening into filaments by rolling is another reason for the banding of the microstructure, which is also associated with liquation. Austenite is enriched with silicon at the point of contact with silicate, which is the reason that the thermodynamic activity of dissolved carbon is higher at this site and is displaced from it. This leads to the ferrite-pearlite banding, as a result of which ferrite lines appear in the structure with a silicate filament on the axis of the ferrite band.
The layer near the MnS filaments is enriched in manganese, because of which carbon is pulled in this layer, thereby leading to the formation of pearlite bands after cooling. The obtained result, i.e., alternating bands of ferrite and pearlite along the rolling direction, is eventually the same.
To describe the structure and morphology of fractures, the selection of informative parameters of their geometry is of great importance. Manual measurements are objectively limited by labor consumption, so the reference standards or verbal description predom-inate in regulatory documents. Therefore, it is necessary to know the mechanisms of deformation and destruction of inhomogeneous structures and the size distribution statistics of individual components of the structure. As an example, inclusions with a transverse size from 10 to 20 μm rather than from their entire size range observed in a light microscope (from 1 μm and above) are of interest when assessing the heterogeneity of the morphology of NIs in bearing steel. These are those large inclusions, the probability of which to be found the near-surface layer with the maximum contact stresses will be at a maximum. It is these NIs that will determine the large scale quality of the bearings, as opposed to larger particles that will cause the failure of the properties of individual bearings; however, such defects can be detected by the nondestructive testing methods.
During ductile fracturing of alloys, the detachment of NIs (ductile inclusions) from the matrix or their cracking (brittle) leads to the appearance of pores, while the plastic growth and merging of the latter provides the growth of a macrocrack. This leads to a pitted structure of a ductile fracture in the shape of halves of merged pores (often with an inclusion in the center). Under planar deformation conditions, the dependence of the fracture toughness K Ic on the transverse dimension d and volume fraction V of inclusions (identical and equiaxed) is expressed through the average (in three spatial dimensions) distance Λ ≈ d/V 1/3 between the particles [11].
However, the wide range of their sizes (from 1 to 10 6 μm) with an insignificant volume fraction of 0.01-0.1 vol % is a characteristic feature of nonme-  [8,11]. At the same time, there is no reason to presume that their arrangement will always be random; their clusters or regions with a reduced concentration may be formed due to the implementation of various scenarios of technological prehistory. This facilitates the initiation of ductile fracturing and the occurrence of plastic deformation.
Such a variety of differences in the contamination of steel with nonmetallic inclusions (along with the microstructure heterogeneity) leads to differences in the level of energy intensity of ductile fracture. A qualitative assessment of the morphology of satellite ductile fractures of this kind is usually not enough to identify the causes of such a scatter, for example, a more than two-fold increase in the difference in the toughness of steels, namely, 40Kh2N2MA, 09G2S, 16G2AF, 15Kh2NMFA, and 38KhN3MFA steels with a heterogeneous structure (tempering sorbite in   high-quality rolled products; ferrite-pearlite banding of different scales in the microstructure of sheet steels; a difference between the inhomogeneity in the morphology of NIs and the inhomogeneity of ferrite regions in steels, at which the pattern of the dendritic structure was preserved after small forging shrinkage) [8]. Differences in the structure of fractures could only be revealed by representative statistics of the results of measurement of the fracture parameters by two-and three-dimensional tools. These include the difference in the asymmetry coefficients of the empirical distributions of the number of pit neighbors, which are determined on the basis of partitioning the 2D images of fractures into Voronoi polyhedra, from the diameters and depths of pits, and from the thicknesses of bridges between adjacent pits according to 3D relief models obtained by stereophotogrammetry methods.
It is found that the fracture resistance is related to the fraction of bridges and their thickness at the break between adjacent pits. A decrease in their fraction from 0.50 to 0.27 is accompanied by a change in relative narrowing ψ from 40 to 80% and a change in the fracture toughness from 0.52 to 2.72 MJ/m 2 (the correlation coefficients R of linear dependencies were 0.81 and 0.96, respectively). In this case, the ν md /ν sl ratio between the fractions of bridges that were destroyed by the mechanisms of mesodetachment (ν md ) and slicing (ν sl ) varied in the range from 0.65 to 1.9, depending on the toughness level. The maximum values of viscosity corresponded to the destruction of the bridges along the line of shear stresses (destruction by slicing). The development of microplastic deformation of the metal matrix, which precedes the merging of adjacent pores, determines the work of crack propagation along the bottom of a macroscale brittle square, i.e., the brittle component in a fracture of toughness samples, which is surrounded by a viscous component along the perimeter (GOST 4543). The level of plasticity of the matrix itself also plays an essential role and leads to the observed correlation between fracture parameters and plasticity characteristic ψ.
The variation in the values of the characteristics of the distribution of structural inhomogeneities and their relationship with toughness shows that it is necessary to use a wider range of characteristics, in particular, those that estimate the statistics of their size distribution, to identify differences in the morphology of fractures.
The morphology of viscous fractures is directly related to the structure, for example, to the arrangement of NIs. Thus, the statistics of Voronoi polyhedra revealed a relationship between the location of pits in fractures (three samples cut from different places of a large forging made of steel 38KhN3MFA) and dark spots of the Bauman sulfur print [6]. This indicates the possibility of predicting ductile fractures based on the analysis of the steel structure.
To predict the fracturing of inhomogeneous structures, appropriate quantitative estimates of fracture resistance, primarily, cold brittleness and fracture toughness, are required. Existing approaches, for example, serial impact tests according to the Davidenkov method, usually indicate a substantial spread in toughness values in the ductile-brittle transition temperature range. As an example, the spreads in the values ΔKCU = KCU max -KCU min at temperatures of -40°C, -60°C, and -70°C for sheet steel 09G2S (according to the results of certification tests from about 1200 melt batches) were 200, 340, and 280 J/cm 2 , respectively. This is an indirect sign of the heterogeneity of the structures both at the scale of a sample and from sample to sample, which gives rise to a blurring of the cold brittleness threshold. In particular, the developed structural inhomogeneity in large forgings made of improvable 38KhN3MFA-Sh steel leads to a substantial spread in the toughness over the entire temperature range of testing, which is the reason that the cold brittleness threshold is blurred; thus, serial curves are satisfactorily described by a linear function (determination coefficient in the range of 0.84-0.92). This makes it difficult to assess the degree of influence of various structural anomalies on cold brittleness [1].
Micromechanical serial tests on microsamples with dimensions comparable to the scale of a structural inhomogeneity may be promising in the cases at which the criterion for the transition from ductile to brittle fracturing is a change in the peak amplitude of acoustic emission by at least an order of magnitude [12]. In particular, it was these kinds of tests that made it possible to demonstrate [13] that only the interaxial regions are prone to brittle fracturing in large forgings made of improvable 38KhN3MFA-Sh steel in the range from -130 to -100°C, while the dendrite axes are also prone to brittle fracturing at temperatures below -130°C. At the same time, a ductile fracturing anomaly is observed in the same forgings, namely, stone-like fracturing, i.e., fracturing along clusters of submicrometer-and micrometer-sized NIs precipitated along the boundaries of superheated austenite grains, which is not associated with cold brittleness.
The fracturing of a medium with an inhomogeneous structure is rather difficult to assess in terms of fracture mechanics, especially in the case of advanced plastic deformation when it is not possible to reliably estimate the critical stress intensity factor K Ic for planar strain. As an example, the choice of the maximum load value (point C on the load-displacement of the crack-edge diagram recorded during the test in accordance with GOST 25-506-85) is not always obvious when determining the following criteria for nonlinear fracture mechanics: critical crack opening (CCO) δ c for the deformation fracturing and the Cherepanov-Rice integral (J-integral) for the energy fracturing. If we proceed from the concept of the CCO as the max-imum opening at the mouth of a crack, at which its propagation begins, then it is obvious that only fracture monitoring is able to reliably identify the critical stages of static crack growth. The same approach can be logically attributed to the determination of the J-integral.
It is possible that it will be more correct to apply the classical concept [14] based on the idea that the opening of a crack occurs by rotating its edges relative to a certain center when determining the CCO. With this approach, it is possible to determine the δ c value with reference to the structure under provision that the geometry of opening and the kinetics of crack propagation are taken into account [15]. In particular, it is shown that the scatter of δ c values only within one position of the leading edge of a static crack (along the sample thickness), taking not only its curvature into account, but also its irregularity, which reflects the heterogeneity of the morphology of heterogeneous structures, can reach 10-20% or more for large forgings made of improvable 38KhN3MFA-Sh steel.
Understanding the mechanisms of destruction of a medium with a heterogeneous structure is important not only for predicting its resistance to destruction according to its present (post factum) structure, but also for developing the principles for designing the optimal configuration of structures and sizes (shapes) of its individual components for a given level of properties. This approach was implemented for determining the optimal composition of 17M6F5B moderately alloyed high-speed steel (with granular technology) for small shaped tools that cut hard-to-cut materials [16]. In the same way, heat-resistant intermetallic composites with a honeycomb structure, i.e., beads from nickel aluminides inside and refractory metal outside, were designed [17].
The hard alloys that serve as the surfacing of the working bodies of soil tillage agricultural machines are usually characterized by a complicated structure consisting of a sufficiently strong matrix, in which reinforcing particles (borides, carbides of various natures, etc.) are located [18]. Repeated exposure of the alloys to abrasive soil particles leads to the achievement of the ultimate strength of the matrix in local volumes of surfacing and to the appearance of cracks in them (destruction sites).
Comparison of the results of measuring the geometry of the structure and the morphology of fractures on the scale of surfacing layers [19] revealed the dependence of the critical degree of local strain of material interlayers that surround the reinforcing particles on the average thickness of the viscous interlayers and the asymmetry coefficient of the distribution of their thickness values. The geometric parameters of the structure at which the required level of critical deformation is reached and the destruction of the matrix begins can be determined from the obtained relation or the inverse problem of predicting the risk of premature failure of the surfacing layer can be solved using the available morphological types of hard alloy structures.

DIGITALIZATION OF MEASUREMENTS OF THE STRUCTURE AND DESTRUCTION PARAMETERS
To predict the failure of structural materials, the following three sources of information are used: images of structures and fractures, test results (mechanical and physical tests), and production control databases of the process and the final product. Until recently, the evaluation of images of structure and fracture surfaces mainly involved their comparison with reference images; however, now modern computing power and software make it possible to obtain fundamentally different information about their structure. However, its reliability will be determined by the level of metrological support of the image analysis procedure. On this basis, it is possible to predict the properties of an inhomogeneous structure from a description of the geometry of its components in comparison with the morphology of fractures.
Digital images of the structure and fractures consist of the brightness field z(x, y), i.e., a single-valued function of the coordinates on a frame plane in 256 shades of gray, on which light and dark regions correspond to certain components of the structure or the fracture. Separate points of the image, i.e., the pixels with their own level of brightness (gray scale), are most often combined into a rectangular matrix with a size of m × n.
Other things being equal (optical parameters and characteristics of the photosensitive matrix), the digital image quality is limited by contrast K, i.e., the ratio of the difference between the brightness B o of different image elements and the background brightness B b to one of these brightness values K = (B o -B b )/B b . Variation within the object-background transition zone in the primary digital image at 256 gray levels with the purpose of converting it into a binary one (a matrix of the 1-0 form, in which the element of the structure corresponds to 1 and the background corresponds to 0) can lead to a change in the geometry of individual elements of the same type (sizes, areas, and shapes) and to a change in their number as a result of crushing or merging several elements [20]. This can distort the statistics of measurements of the geometric characteristics of objects. As an example, measurements of the volume fraction of small inclusions are comparable only with a unified algorithm and settings for identifying the edge of particles. By changing the equipment (various modifications of the same automatic image analyzer), we obtained differences in the volume fractions of small particles by a factor of up to 2-3 and elongated inclusions by a factor of up to 4-5 on the same sections (fields of view) [1].
The existing variety of binarization algorithms, for example [21], indicates different approaches to choosing a threshold value. In particular, the use of common binarization algorithms, such as the methods of the mean and local mean, and the Otsu method [21], for the same images (fields of view) of typical structures (dendritic structures and ferrite-pearlite bandings in the microstructure) of NIs in 38KhN3MFA and 09G2S steels revealed a substantial difference in the results. Thus, the kdl max /kdl min ratio of the maximum and minimum average values (for three binary images obtained by this method) of transverse dimensions of dendrites differed by a factor of 5. This also corresponded to the difference in the number of dendrites by a factor of 2.7; the average step of perlite bands differed by a factor of more than 7, the number of NIs differed by a factor of 43, and their volume fraction V differed by a factor of nearly 30.
It follows from the above that a reasonable choice of the level (threshold) of binarization largely determines the reproducibility and comparability of the results of measuring image elements. In this regard, it turned out to be useful to plot the dependence of the area F of dendrites on their perimeter P with successive variation of the binarization threshold with a step corresponding to one gray level from 0 to 255 for images with a complicated hierarchical structure, such as a dendritic structure (Fig. 3a). The resulting C-shaped curve reflects the following nature of the change in the image morphology with a change in the binarization threshold: from an absolutely black picture (the gray level is zero) with its subsequent gathering into a single binary picture by adding components of the structure with the initially lighter colors.
The inflection point on the curve corresponds to the beginning of the transition to a gradual blurring of the dark component in the image, which completes with the formation of an absolutely white image. The linear character of the two components of the curve reflects the self-similarity of the structure images [22] obtained with a stepwise change in the contrast.
The nose-shaped segment of the curve corresponds to a change in the mechanism of binary image formation and the corresponding contrast level can be used as the binarization threshold value [23].
In those structures in which there are several components that differ in the level of brightness intensity, several inflections that will determine the individual contrast conditions for each of them may appear on the C-shaped curve (Fig. 3b). The use of this approach can provide step-by-step selection of groups of objects of an identical nature for their subsequent measurement.
It would be preferable to use local binarization algorithms for images of point-like objects, for example, NIs. In such cases, the decision on the level of binarization is made on the basis of an analysis of the brightness fields of particles, the background, and the particle-background transition zone. Obviously, the choice of the binarization procedure implies an individual adjustment for a certain type of structure by studying the structural patterns of its brightness field.
For the quantitative analysis of images in materials science, it is important to cut off the noise, the brightness intensity of which can correspond to the shades of gray of one or more structural components. However, their difference in size and shape is observed. A combination of erosion-dilation procedures that take into account the existing concepts about the nature of structures that are given in the images under consideration can be effective for this. As an example, an average distance of 1.6 × 0.1 mm between first-order axes was obtained by the random chord method over a length of 250 mm from the images of the preserved cast structure in large forgings made of tempered 38KhN3MFA steel in liquation zones with coarse equiaxed dendrites. Nodes that slightly resembled nuclei of first-order or, possibly, second-order axes were observed on them. Local measurements of the content of well segregated components in these regions did not reveal any regular patterns in their distribution. The presence of such components should not affect the results of estimating the structural features by ordinary visual observation. However, such artifacts can distort the results of determining the average values of transverse dimensions of dendrites or their step during large-scale automatic measurements of the geometry of a dendritic structure, for example, by the random chord method. This makes it necessary to filter artifacts in the image.
A similar situation is observed when measuring the geometry of NIs. The standard procedure according to GOST 1778 implies their observation at a magnification of 100×, while 1 mm in the image corresponds to 10 μm on the scale of the sample. The accompanying resolution of such a digital image is usually quite high (1 px ≈ 0.40-0.60 μm) and sets the lower limit of the recorded sizes of dark objects. However, a metallographer can only visually establish the measure of their compliance with NIs in disputable cases. To distinguish single objects from each other by the human eye in the image, their minimum size should be 0.1-0.3 mm. A larger value is already used for drawing small details on maps and technical plans; however, metallography is aimed not only at distinguishing an object, but also at identifying it. Therefore, possible contradictions in assessing the contamination of NIs in steel can be eliminated by limiting the minimum dimensions of the particle diameter to d ≥ 10 μm (or by confirming their nature in the case of considering the same fields of view at higher magnifications).
In some cases, the task of filtering consists in separating or selecting objects of different (same type) natures. As an example, the compactness of sulfur print spots, which is estimated from the decrease in their perimeter due to merging during dilatation (pixel-by-pixel sequential displacement with a step of 1 px of their contours in the direction of increasing the size of each spot), helped to reveal the predominant location of sulfides in large forgings from improvable 38KhN3MFA steel, i.e., interdendritic regions [13] However, only the Adobe PHOTOSHOP™ graphic editor has more than a dozen filters that implement the procedure of various dilation schemes, and only three or four of them allow one to apply the procedure taking the geometry of the arrangement of sulfur print spots into account (in interdendritic regions).
These filters were no longer so effective for image processing of a sulfur print in a sheet of 16G2AF steel (Fig. 4a), in which a weakly pronounced orientation of dark spots along the rolling direction was observed. It could be caused by coarse manganese sulfide particles elongated during rolling into the filaments with a diameter of about 2 μm and a total length of 100-300 μm or more, which are preserved in a slate-like fracture, i.e., sequences of alternating protrusions and depressions elongated along the rolling direction. The delamination along the interface between the filaments of manganese sulfides and adjacent bands of pearlite with the formation of elongated pores and their merging accompany a decrease in the toughness (Fig. 4b). However, only a combination of successive dilatation and filtering (with a step of 1 px) of dark spots on the binary image of the sulfur print, first, in  the direction of rolling and then in the direction perpendicular to it, made it possible to estimate the degree of elongation of dark objects and their predominant orientation in the direction of rolling. This means that it is possible to assess the risk of a slate-like fracture from the sulfur print. The need to evaluate the measurement scales that give reproducible results inevitably arises when measuring the parameters of structures of different scales and fractures from the image. This circumstance has long been reflected in the classification of structures and fractures in the requirements of regulatory documents for the minimum areas of observation objects, for example, thin sections. They remain relevant when working with digital images of structures and fractures, with which the choice of the minimum required volume of measurements that provides reproducibility of the results can be strictly justified. The achievement of the values of the geometric parameter of any structural component or a generalized characteristic of the morphology of the entire image invariant with respect to the subsequent increase in the volume of observation may be such a criterion. In particular, such an approach was applied for the metal of large forgings with a preserved pattern of the dendritic structure (Fig. 5), in which the minimum image area was established for each liquation zone. It can be estimated, for example, from volume fraction V d , i.e., the number of light objects (dendrites) per unit area (%), and from the anisotropy A of the macrostructure image, i.e., the ratio of the number of white dots in two mutually perpendicular directions. The minimum areas S of the image, starting from which the volume fraction V d of dendrites and their anisotropy A did not change substantially, were 130-190, 260-790, and 200-450 mm 2 (on the sample scale) for the peripheral, intermediate, and central zones of forgings, respectively. For each zone, such a frame area turned out to be 1.7 to 10 times larger than the area of working sections of standard toughness specimens and eight-fold tangential tension specimens of type III (a diameter of 10 mm), which already implies the possibility of a scatter in the strength, plasticity, and toughness values of the metal due to differences in the structural features from sample to sample.
This means that the prediction of material properties based on the results of standard tests may contain substantial risks associated with a significant scatter of experimental data due to the inhomogeneity of the structure.
As was established from measuring the parameters of the ferrite-pearlite microstructure of 09G2S steel with banding (at a magnification of 200×), an increase in the volume of measurements leads to changes in the asymmetry coefficient values from 1.0 to 2.6 and in the kurtosis from 4.7 to 10.4, and then to their stabilization starting from fields of view with an area of 0.5-4.3 mm 2 (on the sample scale). The sizes of such areas are determined by the scale of the heterogeneity of the microstructure, which can vary both along the thickness of the sheet and from sheet to sheet, as well as from batch to batch.
The scale of measurements is also important in assessing the morphology of fractures. Their digital processing at any observation scale (macroscopic, mesoscopic, and microscopic scales) is characterized by high labor consumption, which limits the scope of  measurements. This causes well-known difficulties in describing fractures, for example, in connection with attempts to apply the concept of fractal dimension D to an objective ranking of fractures of different morphology [24]. The obtained results turned out to be contradictory, since the D values on fractures of identical nature could differ and practically coincide, for example, for brittle and ductile fractures. Digitalization of measurements of the fracture surface parameters provided the rapid accumulation of the required array of reproducible results in a wide range of scales (from microscopic to mesoscopic ones), the processing of which did not reveal substantial differences in the fractal dimension values of fractures of different natures, such as the ductile, brittle, mixed, and stone-like fractures [25]. The values obtained in practice for the slope (fractal dimension D) of the logarithmic dependence of crack profile length L k measured with step δ k , the spread of which differed by more than two orders of magnitude, on the step value have no practical meaning apparently, since even if they coincide (under the provision that they are correctly defined), this does not mean that the destruction mechanisms will be identical. These results once again confirm the need to substantiate the scope of digital measurements that provide the reliability and reproducibility of the results.
Thus, the practice of developing and applying procedures to digital processing and measuring the parameters of structures and fractures shows the possibility of obtaining reproducible characteristics of their morphology, which reflect the nature of the objects under consideration. To accomplish this, it is important to make a reasonable choice of binarization and filtering criteria based on the physical laws of the formation of the image brightness field when processing them. In measurements, it is important to choose the representative volumes of measured objects, taking into account their statistical nature. From a direct comparison of the morphologies of structures and fractures it is possible to identify the critical components that determine their destruction.
This serves as a basis not only for improving existing technologies of synthesis of materials with the purpose of improving their quality, but also for developing fundamentally new materials (designing structures with specified properties) and for predicting the destruction of materials in structures [1-3, 13, 26, 27].

PREDICTING THE RESISTANCE TO FRACTURING ON THE BASIS OF PRODUCTION CONTROL DATA MINING
The early forecast of destruction of a material can be made even at the stage of its production by taking into consideration the relationship between the variation of the control parameters of the technology, including the chemical composition of the steel, and the characteristics of the material responsible for resistance to destruction. The metallurgical industry is equipped with tools for measuring and collecting data along the entire technological chain, including realtime monitoring. This substantially expanded the amount of information about the production technology and the final product quality. Previously, such an analysis was limited to the statistical substantiation of selective acceptance control; however, it was later extended to local monitoring of technological operations. Today, this is an analysis of the entire sequence of technological operations of the production cycle (end-to-end, i.e., from raw materials to the final product). The ultimate goal is to provide, on the basis of various procedures, the detection of production line weaknesses, the prediction of product quality, and its continuous management based on technology optimization. The prognosis is based on the analysis of various scenarios for the implementation of technological operations (within the tolerance zone of normative documentation). The main difficulty lies in proposing various substantiated (and, in principle, verifiable) hypotheses about various chains of events and technology trajectories (evolution of structures and defects), which lead to a wide variation in the quality of the metal.
Moreover, one should take the diversity of the statistical nature of the objects under consideration into account. In particular, the distributions of the control parameter values (composition and technology) do not belong to class of normal distributions in principle, since the formation of their tails is limited from below and above by the normative tolerance zone. As an example, asymmetric distributions are often observed due to the maintenance of the chemical composition at the upper or lower limits of the alloy grade, as well as bimodal distributions are encountered [28]. This limits the application of classical statistics. However, the main obstacle is the lack of a single space  of technology parameters, because of which the occurrence of parameter values in the the risk zone (for example, the phosphorus content at the upper limit) does not necessarily lead to negative consequences, just as their occurrence in a favorable zone does not guarantee a positive prognosis. There are usually many reasons for a decrease in the metal quality, and often this happens unexpectedly when all the technology parameters do not go beyond the tolerance zone (the so-called "sudden outbreaks of defects"). In the existing sequence of technological operations, process parameters ξ k (regimes) in the number of K ~ 100 parameters are measurable and partly controlled. At the output, a dozen and more quality parameters y i are recorded, and they have their own tolerance level d i (properties, structure, and fracture).
In the presence of branched and intricately related causes due to the effect of complicatedly interconnected factors, the traditional prognosis based on perturbation, i.e., the action of one of the technology parameters, is usually not efficient. For the prediction and subsequent control, it is necessary to describe the y i (ξ k ) dependence of the K-dimensional nonlinear type (the current technology is close to the optimum). For each of the N batches of the product (smelting batches, charges, and rolls), there are results of measuring regime parameters {ξ k } and properties y i , i.e., the process trajectories in the parameter space. A retrospective analysis of production control data arrays should give the shape and parameters of the y i (ξ k ) dependence.
The volume N implies mathematical restrictions on the choice of the method for identifying significant relationships between input and output parameters. If the batch is a melt (of a given brand and assortment), then N < 1000 as a rule [1]. Regression equation y i (ξ k ) in the vicinity of the optimum at K ≈ 100 ξ k parameters should contain about K 2 /2 cross terms c ks ξ k ξ s that describe the interaction of factors. Hence, the search for unknown parameters c ks is limited in principle, since K 2 /2 @ N, i.e., their number is much larger than the number of equations.
However, one can limit the problem itself. Given that both arguments ξ k and the functions, i.e., quality parameters y i , are usually roughly discrete, the regression can be replaced by a discriminant analysis. The search in the {ξ k } space can be performed only for the boundary between the risk area with y < d 0 and the area of successful outcomes of acceptable quality with y > d 0 (for example, below and above the average value for the sample of results of measuring quality parameter y i ). The minimum of the sum of two discrimination errors is given by the point x, at which relevant empirical distributions Φ 1 (x) and Φ 2 (x) are characterized by the largest difference [9]. Such nonparametric discrimination is invariant to the type of distributions and it can also be extended to multivariate distributions for considering possible correlations [29].
Complicated heuristic techniques of cognitive graphics (graphically identifying nonobvious dependences) turned out to be effective when searching for areas with a dominant type of dependence. As an example, two-dimensional mapping of the regions of existence of the y i (ξ k ) dependence objects in the form of dense point clouds on different ξ i -ξ m planes has become successful. In the case of the division of the cloud into two clouds, there is every reason to assume that the presence of areas of variation of technology parameters, which lead to a qualitative change in the behavior of the system, is an objective reason that causes the division. In general, this approach made it possible to assess the risks of anomalous ductile fracturing (stone-like fracture) in large forgings made of improvable 38KhN3FMA-Sh steel even within the framework of the technological process. It also makes it possible to formulate recommendations for its prevention by nonlocal adjustment of the consequences of negative disturbances at subsequent stages of the technological process within its tolerance zone [27].

CONCLUSIONS
It has been shown that the determination of destruction patterns of a medium with an inhomogeneous structure by using digital technologies makes it possible to predict the destruction of materials and evaluate their residual life and also makes it possible to formulate recommendations for improving the production technology for increasing the final product quality.
The metrologically supported digital measurements of the morphology of heterogeneous structures, fractures at the macroscopic, mesoscopic, and microscopic scales of observation and acoustic emission, which are based on the statistical nature of the objects under study, are required to predict the risk of failure of materials with an inhomogeneous structure.
Comparison of the morphologies of structures and fractures, and properties y for a given group of alloys or their states allows one to solve the inverse problem, i.e., to identify the critical components of the structure (or their groups and combinations), value x of which determines this property, and to find the y(x) dependence that predicts this property for structures of this type with different structural geometry.
An early prediction of the destruction of materials is possible even at the stage of their production when considering the relationship between the variation in the values of the control parameters of the technology and the characteristics of the material responsible for the resistance to destruction. The prognosis can be made using nonparametric statistics and using complex heuristic techniques of cognitive graphics, which involve understanding the patterns of technological