=Paper=
{{Paper
|id=Vol-3896/short13
|storemode=property
|title=Computer assisted analysis of transgranular and intergranular micromechanisms of brittle fracture
|pdfUrl=https://ceur-ws.org/Vol-3896/short13.pdf
|volume=Vol-3896
|authors=Ihor Konovalenko,Pavlo Maruschak
|dblpUrl=https://dblp.org/rec/conf/ittap/KonovalenkoM24
}}
==Computer assisted analysis of transgranular and intergranular micromechanisms of brittle fracture==
https://ceur-ws.org/Vol-3896/short13.pdf
Computer assisted analysis of transgranular
and intergranular micromechanisms of brittle
fracture
Ihor Konovalenko, Pavlo Maruschak
Ternopil Ivan Puluj National Technical University, 56, Ruska Street, Ternopil, 46001, Ukraine
Abstract
Automated techniques dealing with the fractography analysis of fractures that occurred
in Magnesium Aluminate Spinel (MgAl2O4) are considered. Fractures were found to develop following
the mixed brittle fracture pattern, predominantly by chipping. The main relief elements include
chipping facets, which are formed under conditions of transgranular and intergranular fracture. Some
informative features that aid in describing micromechanisms of fracture are proposed. An image
recognition algorithm was applied, which allows detecting transgranular fracture sections on
fractograms and calculating their area. The algorithm includes the edge detection operations using
the Sobel method. It also uses a number of filters, which allow detecting the morphological features
inherent in the transgranular fracture in the image.
Keywords ⋆1
Fractogram, scanning electron microscopy, image recognition, edge detection, Sobel algorithm,
thresholding.
1. Introduction
Fractography analysis that provides for a high reproducibility of results has now become
possible owing to the computer assisted techniques for investigating images obtained by
scanning microscopy. To this end, statistically significant arrays of fracture components are
considered in order to make the identification of fracture micromechanisms of materials and
structures more reliable. In particular, this applies to brittle fractures of materials that are
formed under conditions characterized by a low energy intensity of fracture. In addition, the
comparative analysis of different areas is important, which is followed by identifying the factors
of microstructure embrittlement. In our case, brittle fracture describes a fracture surface
without macroplastic deformation, which occurs in the conventionally elastic zone of the
material deformation. At the same time, microplastic strains can localize at the microlevel, in
particular, at the crack tip. The rate of brittle fracture is much higher than that of ductile
fracture. This makes the former particularly dangerous and requirs additional research. Fracture
⋆
ITTAP’2024: 4th International Workshop on Information Technologies: Theoretical and Applied Problems, October 23-
25, 2024, Ternopil, Ukraine, Opole, Poland
1∗
Corresponding author.
†
These authors contributed equally.
icxxan@gmail.com (I. Konovalenko); maruschak.tu.edu@gmail.com (P. Maruschak)
https://orcid.org/0000-0002-2529-9980 (I. Konovalenko); 0000-0002-3001-0512 (P. Maruschak)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
occurs along the crystallographic planes (planes of chipping) in case of transgranular failure or
along grain boundaries in case of intergranular failure. Brittle fracture is particularly sensitive to
structural features that prevent plastic deformation under the loading conditions considered
(emission of brittle carbides, embrittlement of grain boundaries, structural and morphological
changes, etc.), or under a triaxial stress-strain state.
Therefore, the objective criteria that describe the permissible non-uniformity of the
structure based on the quantitative fractography analysis need to be developed. This will
provide for a deeper understanding of the material deformation patterns that occur at different
scale levels, especially when supported by the modern software for the analysis of images
obtained by scanning electron microscopy. Such algorithms are efficient because they consider
the hypotheses that suggest a relationship between the morphological features analyzed and the
physical-mechanical properties of materials, as well as the correctness of the methods for
recognizing and analyzing the morphological formations on the fracture surface.
This article aims at analyzing the morphology of brittle fractures in the images of fracture
surfaces of Magnesium Aluminate Spinel (MgAl2O4) in order to identify the trans granular and
intergranular micromechanisms of fracture.
2. The relationship between the morphological
features analyzed and the physical-mechanical
properties of materials
Deformation caused by shear in the sliding planes or cleavage planes, or on grain
boundaries is known to precede fracture of a polycrystalline material. A great many papers
describe and streamline the signs of transgranular and intergranular micromechanisms of
fracture. Being based predominantly on experimental data, they need to be systematized
because of their descriptive nature and morphological diversity. Given the above, a quantitative
fractography analysis requires a unified description of signs inherent in the micromechanisms
of fracture. In this regard, detecting and considering the non-uniformity of the fracture surface
at different scale levels appears critical. In addition, the concept of “multiscale” addresses the
need to consider the material deformation and fracture on the fractographic image along with
their reflections. And the fractographic image needs to be given a universal physical description
that will allow it to be used for investigating a wide class of materials and deformation rates.
Table 1
Micromechanisms of fracture and signs that describe the condition of the fracture surface
Micromechanism of Description of the Image of a surface fragment with a
fracture micromechanism of fracture certain the micromechanism of
fracture
Transgranular combines the elements of
fracture - chipping and quasi-
(transcrystalline) chipping, as well as provides
for the combination in
different ratios of the
fracture elements specified
and plastic strains localized,
which appear in the form of
lines on the fracture surface
of the grain
Intergranular occurs mainly along the
fracture - grain boundaries due to
(intercrystalline) their lower strength
compared to that of the
grain body. Fracture is
facilitated by impurities
segregated at grain
boundaries. Fracture has a
jet pattern – steps of
chipping that occurred due
to fracture of bridges
between brittle cracks that
propagated along
crystallographic planes.
A fractogram of a fracture surface contains important information about the nature of
deformation and characteristics of the fracture process, as well as other factors that affect the
strength of materials. Therefore, the fractogram analysis makes it possible to obtain valuable
information that allows improving the material studied and preventing its further fracture.
Samples of initial images are shown in Fig. 1, a, b. They are taken from the database of images
depicting fracture surfaces of Magnesium Aluminate Spinel (MgAl2O4) [7]. As is seen, fracture
patterns analyzed are caused by a mixed micromechanism of failure. Most clearly pronounced is
the transcrystalline jet fracture type that occurred by the chipping mechanism inherent in
brittle fracture. In addition, the fracture surface shows the elements of transgranular fracture,
that is, light wavy ridges, indicating a higher energy intensity of crack propagation. Thus,
fractograms present with two types of sections distinguished on the fracture surface. The first
type is flat and smooth sections that are usually characteristic of intergranular fracture. The
second type is wavy sections that correspond to the transgranular fracture of the material. In
order to automate the process of recognizing the above sections in the image, an algorithm was
developed, which receives a fractogram as an input and, by applying a number of
transformations, highlights the sections corresponding to the intergranular and transgranular
fracture. Next, the sections found are quantified by calculating their areas. In particular, this
allows us to conclude as to which type of fracture prevails for a certain specimen./To detect
intergranular and transgranular areas of fracture in images, an algorithm was used, which
consists of the stages of edge detection by Sobel method, thresholding, removal of small binary
objects, and detection of zones with a texture corresponding to two types of fracture sections.
a b
c d
e f
Figure 1. Initial images of a fracture surface (a,b); edges highlighted by using the Sobel
operator and filtering (c,d); superimposed masks of areas of intergranular fracture
3. Image processing algorithm
General process of image processing for segmentation of intergranular and transgranular
fractures is shown on Fig. 2.
Figure 2: Image processing steps to highline the intergranular fractures
Morphologically, the fracture surface (Fig. 1, a, b) is formed by a complex combination of
sections of intergranular and transgranular fracture, which are usually limited by clearly visible
edges of fractures or kinks. Moreover, the sections of transgranular fracture are also
characterized by a wavy topography, which contains ridges and depressions with a specific
texture. Therefore, the Sobel edge detection method was used as the first step of the recognition
algorithm [8]. Suppose the original image is represented by two-dimensional pixel array I 0.
Then Sobel operator uses a pair of 3×3 convolution kernels:
(1)
where G x and G y are horizontal and vertical gradients.
The convolution is performed by sliding the kernel over the image starting at the top left
corner and allows to highlight parts of the original image with gradients. The Sobel operator
performs a spatial gradient measurement on the image and thereby emphasizes areas of high
spatial frequency corresponding to the edges. At the same time, the gradient of the intensity
function is calculated at each point of the image. The operator uses two 33 pixels kernels
convolved with the input image to compute approximations of the horizontal G x and vertical
G y gradients. At each image point, the obtained gradient approximations are combined by
calculating gradient G and its direction θ :
(2)
After the edges are selected, the image will contain a significant number of small artifacts,
which impede further processing and the search for the sections of interest. This is explained by
the complex morphology of the initial fractogram. At the same time, such noises usually have a
much lower intensity than those found after applying the Sobel edge operator. To discard them,
thresholding was used with a limit that allows preserving all the important components of the
image and discarding a significant amount of noises.
Binary object filtering was applied to the image after thresholding. To do this, all
connected objects were found and those with a height and width of less than 3 pixels were
removed from further consideration. Figure 1, c, d shows the resulting images obtained after
pre-processing using the Sobel operator, thresholding and filtering.
The images presented in Fig. 1, c, d visualize large black areas that correspond to smooth
sections of intergranular fracture on the initial fractogram; as well as areas formed by quasi-
parallel white lines, which correspond to the zones of transgranular fracture in the fractogram.
Such sections are characterized by high morphological homogeneity and similarity in different
areas of the image.
Sections of transgranular fracture are characterized by a significant morphological non-
uniformity. To perform the automated detection of transgranular fracture sites, we applied to
the preprocessed images (Fig. 1, c, d) a set of filters with kernels containing parallel components
with different angles of inclination (from 0° to 150° with a step of 30°). This made it possible to
highlight the sections that contain parallel edges. Other sections in the image were attributed to
intergranular fracture. Images presented in Fig. 1, e, f show the sections of intergranular and
transgranular fracture detected by the method described above.
4. Analysis of MgAl2O4 fracture fractograms
The area occupied by sections of both types was calculated. Figure 3 shows the
distribution histograms of the areas occupied by sections of transgranular fracture on the
specimens studied. As seen from the histograms of the specimens, the sections of intergranular
fracture are, in general, significantly larger than those of transgranular fracture (the areas up to
2000 pixels prevail).
Figure 3: Distribution histogram of areas occupied by sections of transgranular fracture
The quantitative analysis of fracture areas suggests that the surface was formed by a
mixed micromechanism of fracture. However, in case of transcrystalline fracture, the terms
“ductile” and “brittle” do not always correspond to the micromechanisms considered. This
makes it difficult to attribute brittle fracture to either type considered. When investigating the
fracture surface, digital analysis was used to detect the signs of plastic deformation, waviness of
the fracture surface characteristic of transgranular fracture. Brittle fracture with the smoothed,
structureless surfaces is typical of intergranular fracture.
The advantage of the “computer-assisted” classification of crystallographic features is
that it allows identifying patterns of the fracture process itself [9]. In most cases, the chipping of
metals and alloys occurs as a result of the initiation and propagation of cracks in structurally
non-uniform (“weak”) places in the metal (grain boundaries weakened by impurities, non-
metallic inclusions, etc.) [10, 11]. In the first approximation, the ratio of the areas occupied by
the micromechanisms analyzed is a comparative characteristic, which describes the energy
intensity of fracture that occurs in polycrystalline bodies. It also characterizes the energy
absorbed by the material when the fracture is formed.
5. Conclusions
An algorithm for the image analysis is proposed, which makes it possible to recognize the
sections of transgranular fracture on fractograms. The algorithm takes into account the
morphological features of such sections and allows highlighting the connected sections and
calculating their area.
Fractography analysis of the fracture surfaces of specimens from Magnesium Aluminate
Spinel (MgAl2O4) suggests that its fracture occurred following the mixed brittle fracture pattern,
predominantly chipping.
The results of the fractography studies suggest the presence of sections, in which
different grains have the same character of fracture. There are also sections of brittle fracture
that propagates in a parallel direction, which changes sharply in the adjacent grain. The more
frequent are the changes in the direction of fracture, the more ductile the material. Steps of
branching on the fractures of the specimens studied also indicate the margin of the material
plasticity.
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