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Acta Materialia 255 (2023) 119073
Available online 17 June 2023
1359-6454/© 2023 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Full length article
In-situ quantitative tracking of micro-crack evolution behavior inside CMCs
under load at high temperature: A deep learning method
Rongqi Zhu
a
, Guohao Niu
b
, Zhaoliang Qu
b
,
*
, Panding Wang
b
,
*
, Rubing Zhang
c
,
Daining Fang
a
,
b
a
State Key Laboratory for Turbulence and Complex Systems & Center for Applied Physics and Technology, College of Engineering, Peking University, Beijing 100871, PR
China
b
Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100081, PR China
c
Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044, PR China
ARTICLE INFO
Keywords:
Micro-crack evolution behavior
CMCs
Quantitative tracking
Deep learning method
In-situ X-ray computed micro-tomography
ABSTRACT
Micro-cracks play an extremely signicant role in the failure of ceramic matrix composites (CMCs). In-situ
quantitative tracking of micro-crack evolution behavior remains a great challenge. In this study, a deep learning
micro-crack segmentation method based on the generative adversarial network was developed to quantitatively
characterize the micro-crack evolution behavior of CMCs under tensile load at high temperature with in-situ X-
ray computed micro-tomography (
μ
CT). This method realizes a precise and robust segmentation of the micro-
cracks in
μ
CT images with low gray contrast and image quality caused by noise and artifacts. The crack pa-
rameters including crack opening area, crack opening displacement and crack volume of each micro-crack were
obtained. For the most micro-cracks, the values of these parameters exhibited no obvious increase during the
loading process. Noticeable increasing of crack parameters occurred in some large micro-cracks at high load
levels. The evolution of each micro-crack was also tracked to further identify the critical damages dominating the
eventual failure. The four largest cracks exhibiting a more dramatic volume evolution were captured as the main
cracks. These main cracks all originated from the preexisting micro-cracks and were usually formed by the
coalescence of adjacent small micro-cracks with increasing tensile loads. The ultimate fracture was demonstrated
to take place near these main cracks.
1. Introduction
Ceramic matrix composites (CMCs) have become an ideal candidate
for hot end component materials in the next generation of gas turbines
with high thrust-weight ratios due to their excellent high-temperature
performance, high specic strength, and high fracture toughness
[1–3]. The outstanding properties of CMCs are attributed to their
intricately designed multi-scale microstructures [4,5]. However, these
same microstructures also give rise to a complex failure behavior.
Additionally, micro-defects that arise during manufacturing process can
also evolve and trigger more complicated situations for the failure in the
service environment, which can involve high temperatures, high pres-
sures and other challenging conditions. The failure behavior is intrin-
sically dependent on the evolution of microstructures and micro-defects.
Especially, the spatial distribution and quantitative information of
micro-cracks are critical in any analysis of failure mechanism.
Therefore, to gain in-depth insight into failure mechanism of CMCs, it is
necessary to conduct accurate analysis and quantitative tracking of the
micro-crack evolution behavior under load at high temperatures.
Many studies have focused on the micro-crack evolution behavior of
CMCs. The evolution of micro-cracks in CMCs under uniaxial tension
was examined by scanning electron microscopy. The information on
surface micro-cracks was obtained [6,7]. To obtain the information on
the micro-cracks inside CMCs, a method based on electrical resistance to
estimate crack length without visual observation was developed. But
this method is limited to the measurement of crack length during the
growth stage [8]. Acoustic emission (AE) was applied to locate cracking
sources and characterize micro-cracks evolution inside CMCs, allowing
for the quantication of the location, time, and quantity of cracking
during micro-crack evolution [7,9]. However, this method does not
provide a clear visualization of the morphology of micro-cracks, and
obtaining detailed information on micro-cracks such as crack length,
* Corresponding authors.
E-mail addresses: quzl@bit.edu.cn (Z. Qu), wangpanding@pku.edu.cn (P. Wang).
Contents lists available at ScienceDirect
Acta Materialia
journal homepage: www.elsevier.com/locate/actamat
https://doi.org/10.1016/j.actamat.2023.119073
Received 24 November 2022; Received in revised form 17 April 2023; Accepted 5 June 2023
Acta Materialia 255 (2023) 119073
2
crack opening displacement, and area is difcult. To gain further insight
into the micro-crack evolution mechanism, a more comprehensive and
visualized approach to obtain information on micro-cracks inside CMCs
is necessary.
X-ray computed micro-tomography (
μ
CT) has been gradually
considered as a powerful tool for visualizing and quantifying the internal
three-dimensional microstructure of materials, due to its increasing
spatial and temporal resolution [10–12]. By this way, the microstructure
and porosity of CMCs have been analyzed quantitatively [13–17].
Furthermore, in-situ
μ
CT has been employed to observe and investigate
micro-crack evolution behaviors inside CMCs under load at both
ambient [18–30] and high temperatures [5,31,32]. In the previous
studies, micro-crack evolution behaviors were studied qualitatively
without obtaining any quantitative information about micro-cracks [18,
28,29]. To gain a more comprehensive understanding of micro-crack
evolution behavior, micro-cracks were further extracted and quanti-
tively investigated using image segmentation tools based on traditional
segmentation algorithms such as grayscale thresholding and
region-growing algorithms [23,24,26,27,30]. A segmentation procedure
utilizing digital volume correlation (DVC) residuals was also applied to
quantitively characterize micro-cracks inside CMCs [19,20,25,31,32].
The displacement calculated by DVC was used to evaluate the residual
eld, which highlights the location of bad correlation induced by the
strong local kinematic uctuations. The residuals were subsequently
used to characterize the information on micro-cracks. This procedure is
restricted by the accuracy of the displacement eld calculated by DVC
and usually requires sophisticated calculation that may consume too
much time and labor, especially for the enormous amount of data pro-
vided by the in-situ
μ
CT experiments. The accuracy of both traditional
segmentation algorithms and the segmentation procedure based on DVC
residuals is easily affected by noise, artifacts, and low gray contrast. As
CMCs are mainly composed of elements with low atomic number, gray
value of micro-crack pixels is close to that of the surrounding phases,
which makes the identication of the micro-cracks from the complex
microstructures particularly difcult [17]. This difculty is com-
pounded by the fact that micro-cracks inside CMCs are typically thin and
show weak signals in
μ
CT images, often covering only a few pixels in
opening width. In this condition, the segmentation accuracy is highly
sensitive to image quality and more susceptible to noise and artifacts.
Considering the complexity of the loading, noise and artifacts are more
common in the images obtained from in-situ
μ
CT tests. This poses a
greater challenge for the segmentation of numerous and randomly
distributed micro-cracks inside CMCs. Although the image segmentation
tools based on traditional segmentation algorithms and the segmenta-
tion procedure based on DVC residuals are powerful enough in
micro-crack segmentation, segmenting extremely tiny micro-cracks with
low gray contrast in low-quality images containing noise or artifacts is
still a challenge. Moreover, the tracking of micro-cracks is also impor-
tant to real-time monitor the damage state of the CMCs and identify the
source of the critical damages. Unfortunately, few studies have focused
on the tracking of micro-cracks inside CMCs. Thus, there is a need to
develop a method that enables automatic segmentation, quantitative
analysis, retrieval and tracking of micro-cracks inside CMCs.
Recently, with the development of deep learning method, great
progress has been made in the computer vision eld, such as image
classication [33], object detection [34] and image segmentation [35].
Beneting from the strong feature extraction capability of deep learning
method, some convolutional neural network (CNN) models based on
FCN [36], Unet [37–40] and Deeplab v3+[41] were proposed to detect
cracks in the images of concrete buildings and pavement. In this way, the
cracks could be precisely segmented at the pixel level. Inspired by the
above successful applications, deep learning method provides a prom-
ising application for the segmentation of micro-cracks inside CMCs.
However, deep learning models designed for detecting cracks in images
of concrete buildings and pavement have limitations when applied to
CMCs with complex multi-scale microstructures. The weak features of
micro-cracks and low image quality caused by noise and artifacts further
pose new challenges for the segmentation of micro-cracks based on
existing deep learning methods. Therefore, a deep learning model
specially designed for the automatic segmentation, quantitative anal-
ysis, retrieval and tracking of micro-cracks inside CMCs is required.
In the present study, we proposed a novel deep-learning-based
method for quantitatively characterizing the micro-crack evolution
behavior of CMCs with in-situ
μ
CT. The complete information on each
micro-crack was obtained and tracked during the loading process at high
temperature. The failure mechanism was subsequently discussed based
on the micro-crack information. This study provides a new way to
quantitatively analyze and automatically track the micro-crack evolu-
tion behavior inside CMCs.
Fig. 1. (a) Dimensions and optical image of SiC/SiC specimen. (b) In-situ
μ
CT apparatus with a laboratory X-ray source at elevated temperatures.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
3
2. Experimental
2.1. Materials and specimen
Two-dimensional plain-weave SiC/SiC composites were prepared by
chemical vapor inltration (CVI) process. SiC fabric was stacked with a
fabric layer orientation of 0
/90
. Boron nitride interface layer with the
thickness of 0.3
μ
m was rstly deposited on the bers with boron tri-
chloride (BCl
3
) and ammonia (NH
3
) as gas sources. Then, methyltri-
chlorosilane (CH
3
SiCl
3
, MTS) was used to deposit the SiC matrix and
carried by bubbling hydrogen in gas phase. The molar ratio of H
2
to MTS
was 10. SiC matrix was deposited at a reduced pressure of 5 kPa around
1100 ◦C. Argon was used as the dilute gas to slow down the chemical
reaction rate during the deposition. The as-prepared composite panels
were machined into specimens, as shown in Fig. 1(a). Following
machining, a thin protective layer of SiC were further coated on the
specimens using the CVI process to cover the machined edges.
2.2. In-situ tensile test with
μ
CT at high temperature
In-situ tensile test was performed by an in-situ
μ
CT apparatus with a
laboratory X-ray source at elevated temperature, as shown in Fig. 1(b).
More details about the apparatus and experimental procedure were
described in our previous study [42]. In this study, the test was con-
ducted under a vacuum environment at a temperature of 1000◦C. Ten-
sile loads were applied stepwise in a load-controlled mode until the
specimen fractured. The
μ
CT scan was conducted at each load step. Each
scan consisted of 1000 exposures for 3 s and was collected over a 360◦
rotation of the specimen. A resolution of 7.94
μ
m/pixel with a full eld
view of 16.3 ×16.3 mm
2
in the observing plane of the object was
adopted. More detailed parameters of the
μ
CT scans are descripted in
Table 1. The fracture morphology was also scanned after the tensile
tests. The obtained CT data were subsequently reconstructed to obtain a
set of slices using a ltered back projection algorithm by VGStudio Max
3.0 software. The obtained slices were then processed and visualized by
Avizo 2020.1 software.
2.3. SEM test for fracture morphology
An additional scanning electron microscope (SEM) test was per-
formed on the fracture specimen with Zeiss Sigma 300 to investigate
more detailed fracture morphology and verify the results from
μ
CT after
the tensile tests.
3. Results of in-situ tensile test with
μ
CT at high temperature
Before the tensile test,
μ
CT test was conducted to characterize the
internal structures of the SiC/SiC specimen in unloaded state. Fig. 2(a)
Table 1
Detailed parameters of
μ
CT scans in the high temperature in-situ
tensile test.
Tube current 150 kV
Tube voltage 160
μ
A
Power 24 W
Source object distance 57 mm
Source detector distance 1443 mm
Collected projections 1000
Exposure time per projection 3 s
Total acquirement time 50 min
Angle of scanning 360˚
Fig. 2. (a) A slice of CT image with matrix, voids, weft and warp tows marked by arrows. (b) The gray-level distribution of CT image, which is divided into three
regions based on two thresholds indicating the gray-level ranges of voids, bers and matrix, respectively. (c) (3D) rendering volume for region of interest extracted
from specimen with different phases marked by arrows. (d)-(f) Matrix, bers and voids extracted from (c), respectively.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
4
shows a typical slice of CT images where the bers, matrix, and voids are
still distinguishable despite the low gray contrast. The gray-level dis-
tribution of CT image is presented in Fig. 2(b). To segment the different
phases, including bers, matrix, and voids, a greyscale threshold method
was adopted. The minimum entropy principle was used to determine the
thresholds of segmentation that separate the gray levels into several
regions indicating the gray distribution of different phases. More
detailed information about the segmentation of different phases is pro-
vided in the Appendix. A. The three-dimensional (3D) rendering of the
region of interest extracted from specimen is shown in Fig. 2(c). Three
different phases, include matrix, bers and voids, are segmented and
displayed in Fig. 2(d)-(f). The horizontal ber tows (warp tows) and
vertical ber tows (weft tows) intersect each other in an orthogonal
woven conguration and are surrounded by deposited matrix. Large
voids are mainly located between adjacent ber tows.
During the tensile test, the load and displacement data were recor-
ded, and the load- displacement curve is plotted in Fig. 3. The insets
show a typical photograph of the experiment and an illustration of the
loading conguration. Solid circles indicate
μ
CT acquiring points at
different tensile loads, including the initial load, 600, 1000, 1400, and
1700 N. It is worth noting that, in the initial step, a small preload (~80
N) is applied to ensure the stability of the specimen during the
μ
CT scan.
It was noticed that some load drops occurred during the constant
displacement (holding) period at each scan. These load drops are the
common phenomenon in the interrupted in-situ X-ray computed to-
mography experiments, primarily due to the relaxation of the testing rig.
The nal fracture occurred as the tensile load increased to 2000 N,
giving the ultimate tensile strength of 222 MPa. Fracturing of specimen
Fig. 3. Load-displacement curve, with insets showing the experiment photo-
graph and loading conguration.
Fig. 4. Microstructure evolution of the SiC/SiC specimen with increasing tensile load. Top: 3D rendering volume including crack propagation region marked by
circles, and bottom: slices at the position of dotted box in the top row.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
5
at the peak-load indicates a typical brittle fracture behavior.
Fig. 4 shows the microstructure evolution of the SiC/SiC specimen
with increasing tensile load. Micro-crack evolution behavior was
observed in several regions of the specimen during the tensile loading.
The micro-crack evolution behavior is categorized into two types. On
one hand, preexisting micro-cracks propagated and grew, as marked by
the red circles and arrows in Fig. 4. On the other hand, new micro-cracks
appeared and propagated, as shown by the yellow circles and arrows in
Fig. 4. Micro-cracks were mostly located in the warp tows and matrix
and propagated along the planes perpendicular to the loading axis.
As mentioned earlier, the gray contrast of the different phases in the
μ
CT images for CMCs is generally low which can also be found in 3D
rendering volume and slices in Fig. 4. This makes the segmentation and
extraction of the micro-cracks from the complex microstructure a chal-
lenging problem. Particularly, some micro-cracks with small size are
imperceptible and difcult to distinguish manually by conventional
image segmentation methods. To obtain more comprehensive and
detailed information on the micro-crack evolution behavior, a segmen-
tation method for the micro-cracks is needed and will be introduced in
the next section.
4. Deep learning-based micro-crack segmentation method
With the rapid development of deep learning technology, some CNN
based models, such as Unet [35], Segnet [43] and Deeplab net [44–47],
have achieved excellent performance in image segmentation task. This
provides a promising application for the segmentation of micro-cracks in
μ
CT images for CMCs. In this section, a new and customized network
was designed for the micro-crack segmentation. The pipeline of the deep
learning includes training data preparation, network training and
evaluation.
4.1. Training data preparation
Some original
μ
CT slices with the pixel resolution of 1100 ×280,
obtained from different loading steps of in-situ tensile test, were selected
as the training data. The training data consisted of two types of images:
one with slices including micro-cracks, and the other with slices without
micro-cracks. For the rst type, the micro-cracks were manually labeled
with the assistance of a local interactive threshold segmentation
method. In the labeled images, the pixels corresponding to micro-cracks
were assigned a value of one, while the remaining pixels were set to
zeros. These images were then cropped into the size of 128 ×280 to
reduce the computational burden during network training after the
image labeling. The micro-crack pixels were visually marked by green
color, as presented in Fig. 5. These labeled images were taken as the
ground truth image during the training process. As the micro-crack la-
beling was a time-consuming and labor-cost mission, a data augmenta-
tion technique using horizontal and vertical image ipping was
implemented to increase the amount of training data, in which the ori-
entations of the slices may have been reversed. In total, over 700 images
were obtained after the data augmentation process. The data set was
then randomly split into a validation set and a training set with a ratio of
1/9, which were used for network validation and training, respectively.
Finally, the gray values of each original image were normalized into the
range from 0 to 1.
4.2. Neural network architecture
4.2.1. Baseline model
As shown in Fig. 5, the micro-cracks in the
μ
CT slices are generally
thin and difcult to discern. Hence, a network with high sensitivity to
small features is necessary to capture the tiny and weak features in the
Fig. 5. Examples of micro-crack labeling in
μ
CT slices: left column showing original images and right column showing labeled images in which the micro-crack pixels
are marked in green. (For interpretation of the references to colour in this gure legend, the reader is referred to the web version of this article.)
R. Zhu et al.
Acta Materialia 255 (2023) 119073
6
μ
CT slices. Among the various image segmentation networks, a deeplab
v3+network proposed by Chen et al. [46] has achieved an excellent
performance in segmenting small objects. Some critical elements of the
network may account for its advantages, as follows:
(1) Atrous convolution, as shown in Fig. 6(a), is the sparse form of the
conventional convolution. It has a larger eld-of-view compared
to convolution, making it advantageous for capturing multiscale
image features. While a large eld-of-view can also be achieved
by down-sampling operation repeated down-sampling can reduce
resolution of image features, leading to the ignoring of small
details. The atrous convolution maintains a balance between
receptive eld and feature resolution, which is ideal for seg-
menting micro-cracks.
Fig. 6. Critical elements of deeplab v3+network include (a) artous convolution, (b) depthwise separable convolution and (c) atrous spatial pyramid pooling. (d)
Detailed architecture of the modied deeplab v3+network.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
7
(2) Depthwise separable convolution, as shown in Fig. 6(b), is a
critical element in the deeplab v3+network that reduces a large
number of parameters while maintaining similar network ca-
pacity. This operation speeds up calculation and increases the
efciency of the network.
(3) Atrous spatial pyramid pooling, as shown in Fig. 6(c), employs
several parallel atrous convolutions with different sampling rates
to capture feature at several ranges. In this way, multiscale in-
formation can be acquired appropriately, which is necessary in
the micro-crack segmentation task.
(4) Encode-decode structure, as shown in Fig. 6(d). The encode
module is used to learn and process a high-level feature while the
decode module is employed to gradually retrieve segmentation
details. This conguration enables effective high-resolution
segmentation.
In this study, the deeplab v3+network was adopted as a baseline
model for the segmentation. However, some modications were made to
the original network to adapt it to our work. The number of convolution
layers was reduced to adapt to the scale of this segmentation problem,
and the rate of atrous convolution was reduced to obtain features with
higher resolution. The number of down-sampling and up-sampling op-
erations were also decreased to prevent skipping over thin micro-cracks.
A detailed architecture of the network is presented in Fig. 6(d).
As the proportion of micro-crack pixels is small compared to that of
the non-crack pixels, using a balanced cross entropy loss function is
necessary. The conventional cross entropy loss function may guide the
network to output an "all zeros" segmentation, which still yields a high
accuracy in terms of the segmentation of the entire image by accurately
segmenting non-crack pixels. Hence, to magnify the contribution of the
minority object pixels, a balance factor is used in the balanced cross
entropy loss function. The function expression is given by:
loss = − βtlogp− (1−t)log(1−p),(1)
where β is the balance factor, which was set as 100 in this study. t takes
the value of 1 or 0, which denotes a given pixel as a crack pixel or non-
crack pixel. p, ranging from 0 to 1, is the probability of a given pixel to be
a crack pixel predicted by the network. The Adam optimizer with a
learning rate of 0.0001 was used to train the network. Batch size of
single training iteration was set as 8. The training work was imple-
mented in Tensorow2.0 with Python on the platform equipped with an
Intel i7–10,700 CPU and a Nvidia 3090 GPU. The total training epoch
was 83, and the train time was 5 h. The loss function curve is shown in
Fig. 7. Once the training of the network is completed, the application of
the network for crack detection is convenient and efcient, which takes
only a few tens of milliseconds to process a single image.
Micro-crack segmentation results obtained from the modied deep-
lab v3+network are shown in Fig. 8. To compare the performance, a
traditional segmentation method based on Top-Hat and local thresh-
olding segmentation algorithms embedded in Avizo software was
adopted to segment the micro-cracks. However, the results of the
traditional segmentation method are relatively poor, as the micro-cracks
were hardly identied. Unet, which is a commonly used segmentation
network for micro-cracks in concrete, was also applied for comparison
with our proposed networks. Due to the repeated down sampling and up
sampling in the network architecture, the thickness of the micro-cracks
Fig. 7. Loss function during training the baseline and GAN model.
Fig. 8. Micro-crack segmentation results obtained from different methods. Green indicates the pixels that are correctly segmented, while red indicates the pixels that
are incorrectly segmented. (For interpretation of the references to colour in this gure legend, the reader is referred to the web version of this article.)
R. Zhu et al.
Acta Materialia 255 (2023) 119073
8
segmented by Unet is larger than that of the target micro-cracks, and
some weak sections of micro-cracks could not be distinguished. Fortu-
nately, the modied deeplab v3+network was able to successfully
identify and segment the majority of micro-cracks. However, some noise
pixels, which do not belong to crack, were still recognized as the micro-
crack pixels incorrectly. Besides, the gray distribution of the micro-
cracks is usually not uniform, and the gray level in some sections of
the micro-cracks is similar to that of the surrounding non-crack phase.
Thus, some continuous micro-cracks were identied as several discon-
nected parts.
4.2.2. Micro-crack segmentation method based on the generative
adversarial network (GAN)
To realize more accurate identication and segmentation of micro-
cracks, a new network based on generative adversarial model [48]
was proposed, called crack detecting GAN, as shown in Fig. 9(a). Typi-
cally, GAN consists of generator and discriminator network. The
generator network generates data from original input. Then the
discriminator network absorbs generated data and targeted real data
together to distinguish them as far as possible, which further prompts
the generator to output a more realistic data during this competitive
process. The real micro-cracks look continuous and natural, but the
discontinuity and random noise may destroy the delity of a
micro-crack. This GAN structure is used to guide the generated cracks to
be continuous and noise-free to achieve a realistic effect. The proposed
crack detecting GAN utilized the previous modied deeplab v3+
network as a generator, while a patchGAN classier was employed as a
discriminator which was enlightened by the pixel2pixel GAN [49].
Compared to the classical GAN, the patchGAN assesses the generated
crack structure in the scale of patches rather than the whole image. In
other words, the discriminator outputs the result with the M ×N shape
rather than a single value. Therefore, this discriminator tries to classify
whether each M ×N patch in an image is real or fake. By this way, the
discriminator architecture would restrict the attention to the local in-
formation of the images, which helps to identify high-frequency struc-
tures such as micro-cracks. To provide a clearer illustration, Fig. 9(b)
presents the implementation of PatchGAN. The patches in the output
refer to the identication result for corresponding parts in the input
images. The size of the corresponding part is determined by the
eld-of-view of the patch.
The aim of the GAN is to obtain desired data appears realistic using
the generator. The discriminator exactly provides the driving force for
training the generator to generate more desired outputs. The purpose of
discriminator is to maximize the difference between generated data and
real data, while the generator strives to minimize the difference.
Therefore, in mathematics, the overall object function of the GAN can be
Fig. 9. (a) Network architecture of the proposed crack detecting GAN. The interpretations of symbols, such as “Conv”, “DSCB” and “⊕” refer to Fig. 6(c). (b)
Illustration of the PathGAN discriminator. Each patch in the PathGAN is responsible for classifying whether the corresponding part of the input image is real or fake.
Table 2
The values of the pixel-wise metrics for the quantitative evaluation.
PA IoU Precision Recall F
1
Score
Tradition segmentation
method
98.17% 7.74% 10.37% 23.47% 14.38%
Unet 99.48% 52.99% 56.31% 89.97% 69.27%
Modied deeplab v3+99.77% 69.62% 85.97% 78.55% 82.09%
Crack detecting GAN 99.91% 86.90% 94.81% 91.24% 92.99%
R. Zhu et al.
Acta Materialia 255 (2023) 119073
9
Fig. 10. (a) The CT rendering volume of the part used for validation. (b) The front view of the CT volume in (a) with crack region marked by a dash box and micro-
cracks pointed by arrows. (c) CT slices in the planes in which the micro-cracks are located, as marked in (a). (d) SEM image of the same microstructure in (a) with the
same crack region and micro-cracks marked by a dash box and arrows. (e) The segmentation results of SEM image and CT images in the crack region. (f) Crack width
measured in segmented result of CT and SEM.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
10
expressed as:
lossGAN =min
θmax
ϕ(Ex∼pr(x)[logD(x;ϕ)] + Ez∼p(z)[log(1−D(G(z;θ);ϕ))]),
(2)
where D and G denote the discriminator and generator, respectively. ϕ
and θ are the parameters of D and G, respectively. x and z are the real
labeled date and original input data, respectively. E denotes the expec-
tation value. As the GAN is an unsupervised network, it is necessary to
add a delity constraint to guarantee the accuracy of the segmentation.
In this study, the balanced cross entropy loss function given by Eq. (1)
was chosen as a delity function. Then, the object function can be
rewritten as:
lossTotal =min
θmax
ϕ(Ex∼pr(x)[logD(x;ϕ)] + Ez∼p(z)[log(1−D(G(z;θ);ϕ))])
−λ(βtlog(p) + (1−t)log(1−p)),
(3)
where λ is a factor that controls the weight of delity term in total loss.
In this study, λ was set as 100.
The generator and discriminator of the crack detecting GAN were
trained alternately. Before the crack detect GAN was formally trained,
the generator of the crack detect GAN was pre-trained by the way
described in the previous section. To achieve stable training of the crack
detecting GAN, the discriminator was trained three times while the
generator was trained once in each training epoch, making the
discriminator a little stronger than the generator. The same hardware
conguration in the previous section was adopted, and the total training
time was 7 h. The loss function curve is shown in Fig. 7. After training,
the time taken to process a single image is in the order of millisecond.
The micro-crack segmentation results obtained from the proposed
crack detecting GAN are also shown in Fig. 8. Compared with the results
obtained from Unet and the modied deeplab v3+network, the pro-
posed crack detecting GAN achieved a higher segmentation accuracy
and crack sensibility with less noise and better delity.
4.3. Evaluation
To quantitatively evaluate micro-crack segmentation results ob-
tained from different networks, some widely used pixel-wise metrics in
image segmentation were adopted. The metrics include pixel accuracy
(PA), intersection over union (IoU), precision, recall and F1 score. The
expressions are given by:
PA = (TP +TN)/(TP +FP +FN +TN ),(4)
IoU =TP/(TP +FP +FN),(5)
Precision =TP/(TP +FP),(6)
Recall =TP/(TP +FN),(7)
F1Score =2(Precision⋅Recall)/(Precision +Recall),(8)
where TP, FP, TN and FN represent the number of true positive (true
crack), false positive (false crack), true negative (true non-crack) and
false negative (false non-crack) pixels, respectively. An additional un-
seen data consisting of 55 images were used to perform the evaluation.
The value of the pixel-wise metrics for different networks were calcu-
lated according to Eqs. (4)-(8) and are listed in Table 2. For the crack
detecting GAN, the value of PA, IoU, Precision, Recall and F
1
Score are
99.91%, 86.90%, 94.81%, 91.24% and 92.99%, respectively. The crack
detecting GAN outperforms the other two networks in all of the selected
metrics. These results indicate that the crack detecting GAN can more
Fig. 11. Three-dimensional morphology evolution of micro-cracks with increasing tensile loads.
Fig. 12. Illustration of the COA and COD for a micro-crack.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
11
accurately identify and segment the micro-cracks in CMCs than the other
two methods.
To further validate the segmentation method proposed in this paper,
an addition comparation between high-resolution SEM images and the
CT images was performed. The SEM images with the resolution of
0.7299
μ
m/pixel were collected from the fractured part of the specimen.
Fig. 10(a)-(d) shows the high-resolution SEM image and the corre-
sponding CT results in the same microstructure. Two exposed micro-
cracks, which are marked by arrows and dash boxes in Fig. 10(a)-(d),
were captured in the SEM image as well as the CT results. These micro-
cracks were used for the validation subsequently. It is noteworthy that
the surface of the fractured specimen in the SEM image is rugged, and
the two micro-cracks are located in different depths along the y axis.
Therefore, two CT slices in different planes were extracted to presented
the different micro-cracks, respectively, as shown in Fig. 10(a) and (c).
Before the segmentation, the position of SEM image in the xz plane was
aligned by the common features in CT and SEM images to ensure con-
sistency. A gray difference-based method was applied to segmentation
Fig. 13. (a) and (b) Crack opening displacement eld and crack opening area distribution at different loading steps.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
12
the micro-cracks in high-resolution SEM images. More details about the
method are provided in the Appendix. B. Fig. 10(e) shows the segmented
results in the crack region of CT by different network models and the
segmented results of SEM. Compared to the CT result, SEM resolved the
micro-cracks more rened with higher resolution. Among the results
from three different network models, the result of proposed Crack
Detecting GAN presents higher delity, in which the crack length,
orientation and basic trend of crack width variation are most consistent
with the SEM result. Fig. 10(f) shows the quantitative comparison of the
cracked width measured from in z direction at different x positions be-
tween SEM result and CT results. The proposed method exhibited better
performance than the other methods. However, the widths of micro-
cracks measured from CT results are usually lager than those obtained
from SEM result due to the limited resolution of CT, which prevents the
resolving of crack width with the scales smaller than the voxel size.
Increasing the resolution of CT scans would help to reduce these errors.
5. Discussion
5.1. Micro-crack identication and extraction
The proposed crack detecting GAN was utilized to identify and
extract the micro-cracks from all the slices collected from in-situ tensile
tests with
μ
CT at high temperature. The detailed information on the
micro-cracks at different loading steps was obtained. By stacking the
segmented slices, the three-dimensional morphology evolution of micro-
cracks inside CMCs with increasing tensile loads is shown in Fig. 11. In
the initial unloaded state, the preexisting micro-cracks arising from
manufacturing process are randomly distributed inside the specimen. As
the tensile loads increase, these preexisting micro-cracks propagated
and new micro-cracks appeared. The orientations of the micro-cracks
are usually perpendicular to the loading axis and parallel to the weft
tows. In the previous loading steps with lower load levels, the micro-
cracks are usually tiny. However, when the tensile load was increased
to 1400 N, large micro-cracks emerged. Meanwhile, plenty of small
micro-cracks sprouted around the large micro-cracks. At the last loading
step, the large micro-cracks propagated and merged with adjacent
micro-cracks, forming larger micro-cracks which lead to the ultimate
failure.
5.2. Quantitative analysis of micro-cracks
To perform a more detailed analysis of the evolution behavior of
micro-cracks, the complete information for each micro-crack was
quantitatively evaluated. As the critical parameters for the character-
ization of cracks crack opening displacement (COD), crack opening area
(COA) and crack volume (CV) of each micro-crack were measured from
the segmented results. To clarify, in this work, the COD, COA and CV are
dened as below:
(1) The crack opening displacement (COD) is dened as the height of
micro-cracks along the direction of loading. For a given micro-
crack, the COD is a distributed quantity in the xy plane which
is perpendicular to the direction of loading.
(2) The crack opening area (COA) is dened as the projected area of
micro-crack in the xy plane. For a given micro-crack, the COA is a
single value.
(3) The crack volume (CV) is dened as volume of voxels occupied by
the micro-cracks. For a given micro-crack, the CV is a single
value.
Fig. 12 illustrates the denition of COD and COA. By counting the
voxels of micro-crack, the CV of each micro-crack can be easily
measured. A self-made Python procedure was used to measure the COA
and COD of each micro-crack. Firstly, the segmented result from neural
network was binarized to distinguish the background and micro-crack
component. Then, each separated part of the component was labeled
by different numbers indicating the different micro-cracks. For each
micro-crack, the COA was obtained by counting the non-zero projections
in the xy plane. In the positions where there was a non-zero projection,
the COD was obtained by measuring the height (i.e., distance along the
loading direction) of the micro-crack at that position. This was done by
Fig. 14. Statistical analysis of micro-cracks: (a) COA, (b) CV, (c) MCOD-Single for a given micro-crack, (d) total CV, total crack count, and MCOD-All for all micro-
cracks. In (a), (b) and (c), the scatter point indicates the value of each micro-crack and histogram indicates average value of all micro-cracks with the error bar
denoting the distribution ranging from 10% to 90%.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
13
counting the non-zero elements along the direction of loading in that
position.
Fig. 13(a) illustrates the COD eld distribution of micro-cracks inside
CMCs at different loading steps. The value of COD is visualized by a
gradient color map. Due to the limited resolution of the micro-computed
tomography (
μ
CT) scans, it is generally difcult to detect an increase
within the scale of one voxel (7.9
μ
m). Therefore, the small increase of
COD within one voxel is neglected. The crack opening displacement
(COD) for the majority micro-cracks usually presented a small value
during the loading process, with an average of 1–3 voxels. For the most
micro-cracks, there was no obvious variation in COD during the loading
process. The noticeable increase in COD appeared in several regions
because of the emergence of several large micro-cracks at the last
loading step. This could be explained by the fact that the driving forces
of the most micro-cracks for continuous growth are usually limited and
the growth of micro-cracks is usually impeded by the blunting in micro-
cracks, bridging with bers and the other factors. The signicant
opening and propagation of micro-cracks generally occurs in several
local regions of the specimen, which are usually determined by various
complicating factors, such as the microstructure, dispersion of the
properties, the geometry of micro-cracks, and so on. The COA
distribution of micro-cracks is shown in Fig. 13(b). The majority of
micro-cracks exhibited small COA values until the point of nal failure.
However, the noticeable variation in COA occurred at the 1400 and
1700 N loading steps for several large cracks. Notably, at the loading
step of 1700 N, the micro-cracks with large COAs usually have large
CODs simultaneously, as displayed in Fig 13(a). The increasing in COA
was found to be more obvious than that in COD, indicating that the
micro-cracks tend to propagate along the plane perpendicular to loading
axis. This behavior can be attributed to the orthogonal weave congu-
ration of CMCs, in which the opening of micro-cracks located in weft
tows is usually constrained by the warp tows, while the micro-cracks still
keep propagating in the perpendicular plane because of stress concen-
tration in crack tips. Additionally, the width of large micro-cracks in the
direction of the y-coordinate axis is relatively smaller than the length in
the direction of the x-coordinate axis. As the y-coordinate axis is parallel
to the stacking direction, the micro-cracks tend to propagate within a
single ply rather than to adjacent stacks.
To provide further quantitative information on micro-cracks, statis-
tical analysis of micro-cracks was conducted. Statistical results of COA,
crack volume (CV) and maximum crack opening displacement for each
given micro-crack (MCOD-Single) are shown in Fig. 14(a), (b) and (c),
Fig. 15. The volume evolution of new micro-cracks appearing in (a) initial, (b) 600 N loading step, (c) 1000 N loading step, (d) 1400 N loading step, and (e) 1700 N
loading step. Main cracks are marked out by blue dotted boxes. Insets are inserted to illustrate the location and shape of corresponding main cracks. To highlight the
main cracks, the brightness and size of symbol increases with increasing the crack volume and the curves are plotted with transparency in different degree according
to crack volumes. The volume evolution of micro-cracks with small size is plotted by dash line. (For interpretation of the references to colour in this gure legend, the
reader is referred to the web version of this article.)
R. Zhu et al.
Acta Materialia 255 (2023) 119073
14
respectively. It is worth to note that the values of MCOD-Single in Fig. 14
(c) are displayed as the integer multiples of pixel size due to the limited
resolution. The statistical results of total crack volume, total crack count
and maximum crack opening displacement for all micro-cracks (MCOD-
All) in each step are shown in Fig. 14(d). From Fig. 14, the loading
process can be divided into two stages. The rst stage includes the initial
step, 600 N step and 1000 N step. In this stage, the mechanical response
of CMCs was almost elastic, and no obvious damage evolution was
observed. The COA and CV only exhibited minor changes, and the values
of total crack volume and total crack count hardly increased. The second
stage comprises 1400 N step, 1700 N step and subsequent loading pro-
cess. In this stage, micro-cracks with large opening area and volume
appeared with increasing tensile loads. The values of the total crack
volume and total crack count also increased rapidly, indicating the
emergence of considerable and critical damage in the specimen.
Therefore, once the critical damage occurred, the following damage
evolution became overwhelming. Movie S1 in the supplementary
material provides more explicit depictions of the complete evolution of
micro-cracks.
5.3. Micro-crack tracking and failure prediction
To gain a thorough insight into the origin and evolution of micro-
cracks and to further identify the critical damages that dominate even-
tual failure, the volume evolution of each micro-crack was tracked
during the tensile test. The tracking procedure was performed by a self-
made code based on the position of micro-cracks, as depicted below. In
each step of the loading process, the different micro-cracks were labeled
with a unique serial number. Then, the micro-cracks of each step were
overlapped with the previous step in the same position. The labels of the
overlapped micro-cracks in two adjacent steps were connected with
each other. In this way, the labels of a given micro-crack were connected
step by step, and the evolution of micro-cracks during the loading pro-
cess could be tracked subsequently.
Fig. 16. The evolution of main cracks at different loading steps: (a) the location of main cracks inside the specimen, (b) the evolution of each main crack.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
15
As new micro-cracks continually appear during the tensile process,
the information of micro-cracks was tracing back from the loading steps
at which they rst appeared. The volume evolution of new micro-cracks
appearing at initial, 600 N, 1000 N, 1400 N, and 1700 N steps are shown
in Fig. 15(a), (b), (c), (d) and (e), respectively. Merging of the small
cracks was a general phenomenon during the loading process, expressed
as the intersection of the curves, as annotated by the red dash circles in
Fig. 15. When the tensile loads ranged from 0 to 1000 N, the number of
new micro-cracks was relatively small and the volume of micro-cracks
remained at a low level. As the tensile load increased to 1400 N, a lot
of new micro-cracks appeared. The volume of the new micro-cracks
promptly increased in the subsequent step. At 1700 N, four cracks,
which are distinguished with the other cracks by the larger volume, are
marked out by blue dash boxes and called main cracks. As shown in
Fig. 15(a), the four main cracks all originated from the preexisting
micro-cracks. Some of them subsequently coalesced with the adjacent
small micro-cracks with increasing tensile loads, as presented in Fig. 15
(a), (c) and (d).
The four main cracks were individually extracted and named Crack
1, Crack 2, Crack 3 and Crack 4. The evolution of main cracks at different
loading steps are shown in Fig. 16. It is found that Crack 1, Crack 2 and
Crack 3 are approximately located in a plane perpendicular to the tensile
axis, as presented in Fig. 16(a). The plane was eventually found to be
close to the fracture surface. With the exception of Crack 4, other main
cracks were formed by the convergence of several small micro-cracks
which generated during the loading process. New micro-cracks also
tended to appear near the preexisting micro-cracks and converge to form
main cracks. It is noted that disastrous damages are usually originated
from the preexisting micro-cracks, which has also been reported in the
previous work [21,24]. Thus, reduction of micro-defects in the fabri-
cating process is essential to prevent the premature failure of CMCs.
Besides, based on the micro-crack tracking procedure, the more detailed
information on the main cracks at different loading steps were also
given. For a more explicit visualized version of this information, please
refer to the Movie S2 in the Supplementary material.
Fig. 17. Fracture analysis based on
μ
CT: (a) fracture morphology, (b) distance between micro-cracks and fracture surface at different loading steps. The volume and
opening area of micro-cracks are indicated by different sizes and colors of the symbols, (c) distribution of main cracks relative to the fracture surface.
R. Zhu et al.
Acta Materialia 255 (2023) 119073
16
5.4. Fracture morphology and failure mechanism
Fracture part was scanned by an off-site
μ
CT after the tensile tests.
The fracture morphology is shown in Fig. 17(a). It is found that the
fracture surface is jagged. Fiber pull-outs and ber exposure were
observed in the longitudinal and horizontal ber tows, as presented by
the yellow arrows. There were different causes resulting in the exposure
and pull-outs of bers in the horizontal and longitudinal tows. On one
hand, in the longitudinal tows, the propagation of transverse cracks in
the matrix would lead to the debonding of the interface between bers
and matrix. Once the bers fracture, the broken part would be pulled out
from the matrix. On the other hand, in the horizontal tows, the fracture
of bers usually occurred after the fracture of longitudinal tows. Once
the carrying capacity of the longitudinal tows was lost, the tensile load
in the longitudinal tows would be transferred to the horizontal tows,
resulting in shear stresses in the horizontal bers and matrix, which
cause debonding of the interface and tearing between bers. In this
stage, the transverse cracks deected and became longitudinal cracks.
However, the longitudinal cracks were hardly captured because of their
small opening and rapid fracture of specimen after the failure of
longitudinal tows. The distances between micro-cracks and fracture
surface were calculated and shown in Fig. 17(b). Large micro-cracks
appeared and converged near the fracture surface with increasing ten-
sile loads. Then ultimate fracture exactly happened in the position
where the large micro-cracks clustered. The distribution of main cracks
relative to the fracture surface is displayed in Fig. 17(c). Three of the
main cracks are located very close to the fracture surface and are proved
to be the fatal damages inducing the failure of the specimen. The top
views of the distribution are also given in Fig. 17(c), and some longitude
ber tows adjacent to main cracks are marked out by dash orange cir-
cles. It is noticed that the main cracks were originally located in matrix
or horizontal tows and propagated in the matrix and horizontal tows
with increasing tensile loads. Once the main cracks propagated to the
interface between longitudinal and horizontal tows, they deected and
expanded to adjacent matrix and horizontal tows, as annotated by the
blue dash arrows in Fig. 17(c). It implies the damage of matrix and
horizontal ber tows accounts for the failure of specimen.
SEM images of fracture morphology are also shown in Fig. 18. The
pull-out bers in longitudinal tows and exposed bers in horizontal tows
were observed, as similarly presented in the Fig. 17(a). From Figs. 17(a)
Fig. 18. SEM images of fracture morphology.
Fig. A2.1. (a) The high-resolution SEM images with the crack region marked by white dash box. (b) The gray-level distribution of crack region in SEM image, which
is divided into two regions indicating the gray-level ranges of crack and non-crack based on a gray threshold. (c) The gray values along the z direction of the orange
dash line in (a), in which the crack region is determined by the searching for the range with the gray levels below the gray threshold. (For interpretation of the
references to colour in this gure legend, the reader is referred to the web version of this article.)
R. Zhu et al.
Acta Materialia 255 (2023) 119073
17
and 18, two fracture modes of longitudinal ber tows were observed.
The rst fracture mode is a transverse fracture with bers breaking and
the second fracture mode is fracture with bers pulling out, as pointed
by the arrows and dash boxes. For the rst fracture mode, an overly high
bonding strength between interphase and bers hinders the debonding
and sliding of bers, which prevents the dissipation of energy and leads
to low toughness [50].
6. Conclusions
In the present study, an in-situ quantitative characterization of micro-
crack evolution at high temperature under load was achieved through
the
μ
CT and a deep-learning-based crack detection method. Compared
to the traditional segmentation method and the existing image seg-
mentation neural network, the proposed micro-crack segmentation
method based on a novel GAN achieved a more accurate and robust
segmentation of the micro-cracks. The thin and weak micro-cracks were
efciently and precisely captured in the
μ
CT images despite the noise
and a low gray contrast. By this mean, the micro-crack evolution
behavior of CMCs was quantitatively analyzed and tracked. The quan-
titative information of critical micro-crack parameters including CV,
COA and COD was obtained. At low load levels, there was no obvious
crack evolution observed with increasing tensile loads, and the COA and
COD of micro-cracks maintained a low value. At high load levels, rapid
evolution of damage occurred, with the sharp increase in the micro-
crack number and the total CV, and noticeable variation in COA and
COD due to the emergence of several large micro-cracks. The tracking of
the micro-cracks further revealed that the main cracks all originated
from the preexisting micro-cracks induced by the manufacturing pro-
cess. The formation of the main cracks was usually accompanied by the
coalesce of adjacent micro-cracks. The nal fracture of specimen was
demonstrated to exactly occur in the place where main cracks clustered.
Furthermore, the proposed method is limited to the CMCs and can
also be applied for other complicated materials and situation. Especially,
for research of time-dependent damage mechanisms that mainly focus
on the dynamic evolution of micro-cracks, the scanning time of
μ
CT
must be shortened to achieve a stronger time-resolved capability, which
may result in drastically reduced image quality. The proposed method
may provide a reliable way to capture information of micro-cracks
during the dynamic process.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inuence
the work reported in this paper.
Acknowledgements
The authors would like to acknowledge the support of National
Natural Science Foundation of China [Nos. 12027901, 12172048] and
the National Science and Technology Major Project [2019-VII-
0007–0147, 2017-VI-0020–0093].
Supplementary materials
Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.actamat.2023.119073.
Appendix A: Segmentation of CT images
A greyscale threshold-based method was adopted to segment the different phases in the CT images, including bers, matrix, and voids. The
minimum entropy principle was used to determine the thresholds of segmentation that separate the gray levels into several regions indicating the gray
distribution of different phases. The entropy of the whole gray distribution is dened as
E= − ∑
N
i=0
pilog2(pi),(A1.1)
where N is the number of grayscales, pi is the probability of occurrence of the ith gray level. To obtained the two thresholds of three different phases, a
two-step selection process was adopted. In the rst step, the threshold between voids and solid phases was determined by searching for the threshold
value that minimizes the total entropy of voids region and solid phases EV&S
min
T1EV&S= − ∑
T1
i=0
pilog2(pi) − ∑
N
i=T1+1
pilog2(pi),(A1.2)
where T1 is the threshold between voids and solid phases. In the second step, the threshold between bers and matrix is searched in the interval (T1,
N]to minimize the total entropy of the bers and matrix EF&M
min
T2∈(T1,N]EF&M= − ∑
T2
i=T1
pilog2(pi) − ∑
N
i=T2+1
pilog2(pi),(A1.3)
where T2 is the threshold between bers and matrix.
Appendix B: Crack segmentation of SEM image
A gray-based method was applied to segmentation the micro-cracks in high-resolution SEM images, as presented in Fig. A2.1(a). Two main steps
are conducted in the method. Firstly, a gray threshold of the crack region in SEM image is approximatively selected by minimum entropy principle to
separate the gray levels into two regions indicating the gray distribution of crack and non-crack:
min
TEC&NC = − ∑
T
i=0
pilog2(pi) − ∑
N
i=T+1
pilog2(pi),(A2.1)
R. Zhu et al.
Acta Materialia 255 (2023) 119073
18
where EC&NC is the entropy, N is the number of grayscales, pi is the probability of occurrence of the ith gray level, T is the threshold between crack and
non-crack phases. Fig. A2.1(b) shows the gray-level distribution of crack region in SEM image with the gray levels separated into two regions by the
threshold. Then, the range of z positions for the micro-cracks in each x position is determined by searching for the region below the gray threshold
calculated in previous step. The searching starts from the position with the minimum gray value and proceeds towards the two ends until any gray
values within the region exceed the gray, as shown in Fig. A2.1(c). The segmentation process is nally implemented by a python code.
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