=Paper=
{{Paper
|id=Vol-2485/paper56
|storemode=property
|title=Determination of the Size-topological Parameters the Structure of Cast Iron
|pdfUrl=https://ceur-ws.org/Vol-2485/paper56.pdf
|volume=Vol-2485
|authors=Konstantin Makarenko,Ekaterina Zentsova,Alexander Nikitin
}}
==Determination of the Size-topological Parameters the Structure of Cast Iron==
https://ceur-ws.org/Vol-2485/paper56.pdf
Determination of the Size-topological Parameters the Structure
of Cast Iron
K.V. Makarenko1, E.A. Zentsova1, A.A. Nikitin1
makkon1@yandex.ru|kopilka.32@mail.ru|zzzalexzzz95@gmail.com
1
BSTU, Bryansk, Russian Federation
The methods of geometric identification and determination of the main size-topological parameters of the graphite phase in cast
iron are studied. The methods used in world practice to identify the form of graphite inclusions are considered. It is proposed to use
the methods of fractal geometry for the determination and identification of graphite inclusions in cast iron. A method for determining
the size-topological characteristics of the graphite phase in cast iron has been developed. To describe the non-uniformity of the
distribution, the lacunarity function was used. An example of determining the size-topological parameters of the graphite phase for
various types of cast iron is presented.
Keywords: graphite, inclusion, phase, cast iron, distribution, shape, size, quantity, fractal, lacunarity.
1. Introduction in
F Fi qi , (4)
During classification of graphite inclusions according to i 1
GOST 3443 – 87, comparative evaluation of real where Fi – the factor of graphite inclusions’ shape( for graphite
microstructures in relation to the reference images is taken into of spherical shape, F = 1, for vermicular shape F = 0,2…0,5,
account. Such method requires from the researcher certain skills depending on location of its colonies and their sizes); qi – the
and complicates the classification of graphite inclusions during volume proportion of graphite in each form in the cast iron
formation of mixed or transitional structures that refer to structure.
different classes of cast irons or form in different cross sections Such solution represents the simplified variant, suggested
of the item. by V.I. Litovka.
In national metallography, the analytical methods of I.P. Volchock [18] applied the graphite index which enables
determination of graphite inclusions’ shapes are developed. to determine simultaneously both the quantity and form of
There are two main approaches to determine the size- graphite. The index of graphite (Jgr) is calculated as a ratio of
topological parameters of the structure- with the dimensionless sum of maximal sizes ai, i – graphite inclusions to length L
factors of shape or the measuring of inclusions’ outline. The arbitrary secant, crossing them:
simplest of them was suggested by S.A. Saltykov [15] and this
J gr
ai . (5)
approach uses dimensionless factor of shape (F), designed for L
the evaluation that also includes graphite inclusion, in
accordance with the formula(1): The similar method was used by S.A. Shevchuck for the
evaluation of length of graphite inclusion in grey cast iron [16].
S (1)
F 3,545 , However, in spite of the analytical form of description,
P these methods are comparative and the classification of graphite
where S – the area of inclusion, P- the perimeter of inclusion inclusions with these methods is performed on the basis of the
For inclusions of ideal spherical shape F=1 subjective evaluation of the researcher.
O.V. Sotsenko [17] suggested to use apart from the The method of еру metallographic analysis, developed by
dimensionless factor of shape (FK), the measuring of the outline E. Epanchin [3] deserves special attention. For the
to determine the compactness of inclusions: determination of inclusions’ parameters in alloys, he used the
S (2) television microscope “Quantimetre” that was modified for the
F K ,
So calculation of inclusions’ area from the images, received in the
where So – the area of the circle, made around the inclusion. raster electronic microscope (REM). The use of the device
On the basis of this method, he developed the reference enabled to identify separate elements of graphite inclusions, not
scales, containing various shape modifications of graphite having being registered with other methods [2].
inclusions, present in cast iron. In modern conditions, when different analytical
The similar reference scale for shape identification in computerized complexes, designed for the metallographic
graphite inclusions after the modification and evaluation of researches, are getting more widespread, the problem of
their effect on physical-mechanical properties of cast iron was inclusions’ identification in the microstructure images is being
developed by V.I. Litovka [11]. For determination the degree of solved with the help of the specialized software [13], [6].
graphite spheroidization (DGS), he used the formula: While developing the software, different methods and
i n algorithms of calculation are used; herewith, the number of the
F N i i (3) studied parameters, related to the description of inclusions,
DGS i i1n 100%, increases several times. So, the programme Macros III (Carl
N
i 1
i Zeiss, Vienna, Austria) for the analysis of the evaluation of the
sphericity of graphite inclusions in the cast iron with spherical
where Fi – the magnitude of factor of graphite inclusions, graphite, uses more than 10 different parameters [8].
Ni – the number of graphite inclusions, included in i-group and Brazilian researchers, being engaged in the issues of the
having the factor of Fi – shape. identification of graphite inclusions in cast iron, give 5
For those cases, when in cast iron in the section plane, modifications of the calculation of one factor, applied for the
several different forms of graphite inclusions are observed evaluation of the degree of spherical inclusions [14]. Such
simultaneously, S.A. Saltykov suggested to use the factor of diversity of parameters and multiplicity of their modifications
shape that would take into account the proportions (fractions) of effects on the deviation of the results in the evaluation of the
each graphite shape [20],[7]: identical parameters, determined in different analytical systems.
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
Besides, often, the software, installed in foreign analytical
complexes, does not meet the requirements of GOST 3443-87
and that makes certain difficulties in their usage in the national
enterprises.
Meanwhile, there is another approach for solving the
problem of the identification of graphite inclusions in cast iron.
The approach is based on the researches, proving that the
increase of graphite inclusions in cast iron follows the laws of
fractal geometry [1, 5, 9, 10, 12, 19].
2. The Technique of the Conducting Research
As a source of the initial images for the analysis, the
standard scales of GOST 3443-87 and unetched sections,
different in structure and technology of cast iron production,
were used. Fig. 2. The graphical method of the determination of the
For the analysis of images of cast irons’ microstructure, the stochastic fractal dimension by the slope of the trend line.
programme ImageI was applied. Fractal dimensions were
determined with the help of the analytical module FracLac. The So, the studied structure is presented as a binary array,
module calculates the fractal dimension for binary images by which is divided into the cells of the given size, and for each
the grid method. cell, the evaluation of the individual elements of the structure is
Initially, in the process of operation of the segmentation in performed, the structure has a correlation with the array of the
the binary image, the programme distinguishes separate whole structure.
inclusions. Then, the computer scanning of each inclusion with
the help of the grid with a certain size of the cell is performed.
3. The Research Results
The scanning of the inclusion is performed several times. A descriptive characteristic in the multifractal formalism is
During each following stage of the scanning, the side of the grid a spectrum of generalized dimensions Dq. In the spectrum they
cell increases by one pixel according to the arithmetic distinguish a hausdorff (D0), informational (D1) and
progression. In the figure 1, separate stages of the scanning of correlational (D2) dimensions. For more accurate evaluation of
the longitudinal section of the laminar graphite inclusion, the geometrical objects under analysis, the function of the
observed in the section plane of grey cast iron, are presented. multifractal spectrum f() is used.
The number of stages is determined by the maximal size of The microstructure of the pre-eutectic cast iron was studied.
the grid cell. Thus, for the inclusion, presented in figure 1, the The microstructure of cast iron is presented by the dendritic
number of stages during the scanning by the cells of increasing matrix (fig. 3, a) with microfine eutectic interdendritic graphite
size was 46. At each stage, the number of cells, containing (fig. 3, b).
pixels of the image of (F) inclusion ant their size (), which is
calculated as a ratio of the cell square to the total area of the
image, is determined. These parameters are used in the
calculation of fractal dimensions (Dβ) according to the formula:
ln F (6)
D lim .
0 ln
The fractal dimension is determined by the slope of the
trend line, constructed by the method of the smallest squares in
the coordinates (–ln) - InF (fig. 2). While using the statistical
approach, the fractal dimension is stochastic (D), and for the а) b)
evaluation of the accuracy of its results, additionally, the Fig. 3. The Initial cast iron microstructure:
determination coefficient is defined (r2). For all of the
а – the dendrites of austenite (not etched), 80;
conducted experiments, the determination coefficient has shown
b– interdendretic graphite (not etched), 1000.
a high degree of correlation of the averaged trend line and
calculated parameters r2 [0,92; 0,99]. Multifractal parameterization for the evaluation of the
geometric parameters of the dendritic structure of the initial
austenite and eutectic graphite were performed on the binary
images (fig. 4).
а) b)
Fig. 4. The binary images of the microstructure,
Fig. 1. The results of the separate stages of the scanning of presented in the fig. 3: а – the dendrites of austenite;
graphite inclusion by the grid method. b – interdendretic graphite.
For the multifractal analysis of the images of the cast iron
microstructure, the program module FracLac was used that is
the plugin of the programme ImageJ. F()-spectra and spectra
Dq of the generalized Renyi dimensions were analyzied. The (KGf3) and the whole scale, belonging to the cast iron with the
results of the analysis are in the fig. 5. spherical graphite (ShGf1…ShGf5). To simplify the
identification of graphite inclusions, the color scale was used,
on which the separate stages of the fractal dimensions of the
inclusions’ shape had their own colors.
The examples of the use of fractal analysis for the
identification of graphite inclusions in cast irons of different
brands, are represented in the fig. 6.
b)
a)
c) d)
Fig. 5. The spectra of the generalized dimensions: a) b)
а – for the dendrites of austenite; b –for eutectic graphite
f()- spectra; c – for the dendrites of austenite;
d – for eutectic graphite
The presented graphs characterize both microstructures as
multifractal ones Dq Dq at q > q. The analysis of the
Hausdorff dimension D0 (dendr.austen) = 1,89 > D0
(eutect.graph) = 1,54 shows that the dendritic structure of the
austenite, having predominant fractal dimension, is the leading
c) d)
one in the structure formation of cast iron. The graphite phase
stands out in the interdendrertic intervals and in fact, fits within Fig. 6. The examples of the identification of graphite
the certain limits, dictated by the initial -phase, herewith the inclusions in the samples, 100: a - grey cast iron;
fractal dimension of the graphite phase as a geometric object b - malleable cast iron; c - cast iron with the vermicular
will be lower than the one of the dendrites of austenite. graphite; d - ductile cast iron.
The method of the determination of the fractal dimension
can be used for the analysis of the processes of the structure In the fig.6, b - the image of the microstructure of the ferrite
formation and for the evaluation of the processes of the phases’ malleable cast iron is presented. In the structure, the compact
evolution in new alloys. Except the general study of the images inclusions that belong according to the fractal dimensions, to
of the material microstructures, the fractal analysis can be used the fourth and fifth stages, predominate.
for the determination of the morphological parameters of the The structure of the sample from the cast iron with the
graphite phase, as these parameters can’t be determined vermicular graphite (fig.6, c) contains the inclusions of three
numerically by standard methods. Distribution and shape of stages of compactness, except the first two ones. The compact
graphite inclusions belong to such parameters. inclusions of the circular shape are identified in the local parts
of cast iron. The vermicular twisting shape of graphite
4. The Discussion of Results inclusions (VGf2) belongs to the third stage of the scale. In the
structure, the compact shape of graphite inclusions, belonging
Before the study of the microstructure of different cast
to the fourth stage of the compactness scale, predominates.
irons, the calibration measurements of the standard scales of the
The microstructure of the ductile cast iron, used for the
images, presented in appendix 3 to GOST 3443-87, were
fractal analysis, is shown in the fig. 6, d. The small inclusions
conducted. Such analysis enabled to match the fractal
of incorrect configuration, observed in the structure, have a
dimensions with the standardized shape of graphite inclusions.
compact shape, belonging to the fourth stage of the scale. Large
At first, the scale of the fractal dimensions of the inclusions,
inclusions of graphite are identified as spherical ones.
observed in the section plane, was accepted from D = 1, what
Except the shape of graphite inclusions, during the
corresponds to the segment, to D = 2 -the ideal circle in the computer analysis, the parameters, characterizing quantity, size
plane. During the study of the standard scales of the images of and distribution of the graphite phase in cast irons, can be
GOST 3443-87, the inclusions with the ideal circular shape numerically identified.
were not found, that’s why the upper value of the interval was The quantity of the graphite phase (Sgr) in cast iron is
decreased to D =1,9. The range of the fractal dimensions calculated from the ratio of the number of black pixels (Cgr),
covers all of the observed ones, that have been during the study characterizing the content of the graphite phase, observed in the
of graphite inclusions in cast irons (of GOST 3443-87). plane of the not etched section, to the total number of pixels of
The range of the fractal dimensions was divided according the image (Сim):
to the scales of GOST 3443-87 into five stages of the graphite С
“compactness”. The first stage [1,0…1,09] correspond to the S gr gr 100%. (7)
laminar acicular shape of graphite (PGf3); the second one Сim
[1,1…1,29] to the laminar rectilinear (PGf1); the third stage The size of graphite inclusions (Agr) is evaluated according
[1,3…1,49] - to the laminar swirling (PGf2) and nesting (PGf4), to the sum of the square of graphite inclusions (Si) to the total
and also to the vermicular twisting (VGf2);the fourth stage number of inclusions (n), segmented on the image of the
[1,5…1,69] - to the vermicular nodular (VGf1) and thickened microstructure:
i n
(VGf3), and to the structure of malleable cast iron- filamentary
(KGf1) and flocculent (KGf2); the last fifth stage [1,7…1,9] S i
Аgr i 1 . (8)
includes the compact shape of malleable cast iron inclusions n
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