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Numerical modeling of cracking behavior in Cr
coating for ATF cladding under three-point
bending
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ICETMS 2021
Journal of Physics: Conference Series 2076 (2021) 012088
IOP Publishing
doi:10.1088/1742-6596/2076/1/012088
1
Numerical modeling of cracking behavior in Cr coating for
ATF cladding under three-point bending
Mingduo Yuan1, Ziyan Pan1, Zhenyu Zou1, Weijian Zhang1, Mingyue Du1, Jishen
Jiang1*, Xianfeng Ma1*
1Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen
University, Zhuhai 519082, Guangdong, China
*Corresponding Authors email: jiangjsh3@mail.sysu.edu.cn (Jiang J);
maxf6@mail.sysu.edu.cn (Ma X)
Abstract: In-situ three-point bending tests and finite element modeling based on the cohesive
zone model were developed to study the stress evolution and cracking behavior of the Cr
coated Zr-4 alloy for accident tolerant fuel claddings. The initiation and propagation of
micro-cracks were captured by in-situ observation and predicted by the numerical simulation.
The results showed that vertical cracks first initiated from the coating surface and propagated
to the Cr/Zr4 interface. Under larger bending strain, interfacial cracks began to initiate from the
vertical crack tips driven by large local stress concentration.
1. Introduction
After the Fukushima nuclear accident, great attention has been focused on developing the accident
tolerant fuel (ATF) materials to improve the accident resistance of the nuclear materials under both
design-basis accident conditions and beyond-design-basis conditions [1-3]. Surface coatings on the
fuel claddings were regarded as one of the most favorable methods. Among different kinds of ATF
coatings, Cr coating was proved to be one of the optimal consideration due to its superior oxidation
and corrosion resistance, irradiation resistance, etc. [4-6]. However, the mechanical properties of the
Cr coated-Zr cladding system were seldom investigated, although they played a crucial role in the
application of the Cr coatings.
The mechanical properties of the Cr coated Zr4 substrates are evidently related to the cracking
behavior, including both surface cracking and interfacial cracking of the Cr coating [7]. Under the
external loading, vertical cracks may appear in the Cr coating. Under the continuous loading, these
cracks will propagate into the substrate or deflect to the interface to form interfacial cracks. The crack
path is high dependent on the fracture toughness of the coating and the interfacial strength of the
coating- substrate. When the interfacial adhesion is weak, interfacial cracks will be formed from the
vertical crack tips driven by local stress concentration. When the interfacial adhesion is strong enough,
vertical cracks in the Cr coating will penetrate into the substrate, leading to the failure of the coated
sample [7]. Therefore, the cracking behavior can reflect the mechanical properties of the coated
sample. In our previous work [8,9], evolution of surface cracks were successfully captured by in-situ
tensile tests. However, interfacial cracks might be initiated under large deformation. The initiation and
propagation of interfacial cracks and the competition between the interfacial and vertical cracks were
unclear. Thus, the effective experimental method and numerical model should be developed to study
the cracking behavior of the ATF coatings.
ICETMS 2021
Journal of Physics: Conference Series 2076 (2021) 012088
IOP Publishing
doi:10.1088/1742-6596/2076/1/012088
2
In this work, in-situ three-point bending tests were developed to capture the cracking behavior of
the Cr coated Zr-4 substrate. A finite element model (FEM) based on the cohesive zone model (CZM)
was built to study the stress evolution and crack propagation of the Cr coating. The cracking modes of
the Cr coating samples were further investigated.
2. Materials, experimental test, and finite element modeling
The Zr-4 substrate was machined into cuboid three-point bending samples, the geometry of which was
shown in figure 1(a). After polishing and cleaning processes, Cr coatings were deposited on the Zr-4
substrate by magnetron sputtering technique. As shown in figure 1(b), the thickness of the
as-deposited Cr coating was about 15μm, and no original micro-voids or micro-cracks appeared.
Figure 1. (a) Geometry of the three-point bending sample, unit: mm, (b) cross-sectional morphology of
the as-deposited Cr coated Zr-4 substrate, (c) In-situ mechanical test setup equipped with a
high-magnification optical microscope, (d) view of the mechanical loading system.
As shown in Figure 1(c), in-situ three-point bending tests were carried out at room temperature on
a mechanical testing system equipped with a high magnification optical microscope. The sample was
fixed in the loading system by applying small preloading, as shown in Figure 1(d). During the bending
test, the micro-deformation and crack evolution of the Cr coating-Zr4 substrate could be observed by
the optical telescope in real time. Three-point bending tests were performed under a
displacement-control mode at a constant rate of 510-3 mm/s. The bending test was suspended for
several times to capture the images of the cracking in the coated sample.
ICETMS 2021
Journal of Physics: Conference Series 2076 (2021) 012088
IOP Publishing
doi:10.1088/1742-6596/2076/1/012088
3
Figure 2. Finite element model of the three-point bending test.
To model the stress and crack evolution of the Cr coated sample, a two-dimensional FE model was
built in ABAQUS, and the geometry and meshes were shown in Figure 2. The geometry was the same
as the test sample, and the meshes in the middle region near the coating were refined to obtain enough
calculating precision. The Cr coating was regarded as elastic material and the substrate was regarded
as elasto-plastic material. The mechanical parameters could be found in Ref. [8,10]. To model the
vertical crack in the Cr coating and the interfacial crack between the coating and the substrate, the
cohesive elements in zero thickness were inserted in the FE models, as shown in figure 2. The
damage-based CZM assumes that once the cohesive element reaches a critical value, damage will
occur and accumulate under continuous loading. Once damage value reached one, crack will be
initiated. Detailed description could be found in Ref. [8,10]. In the CZM, the fracture strength 𝜎
and
the fracture toughness 𝐺
for both the Cr coating and the interface should be determined first. Due to
lack of published data, parameter sensitivity analyses were carried out, and finally for the Cr coating,
𝜎
and 𝐺
were set as 150 MPa and 200 J/m2, respectively, and for the interface, 𝜎
and 𝐺
were
set as 150 MPa and 100 J/m2, respectively.
3. Results and discussion
3.1. In-situ observation
Figure 3 shows the cracking behavior of the Cr coated Zr-4 substrate under three-point bending based
on in-situ observation. Vertical cracks were first generated in the Cr coating driven by local tensile
stress. As the loading continued, vertical crack density increased and finally entered a plateau stage,
which is consistent with the in-situ tensile test [8]. It is worth noting that at large deflection, interfacial
cracks began to initiate from the vertical crack tips, which were driven by the large local interfacial
peeling stress and shear stress. However, even under severe deformation, spallation of the Cr coating
did not occur, which reflects the good interfacial adhesion of the coating.
ICETMS 2021
Journal of Physics: Conference Series 2076 (2021) 012088
IOP Publishing
doi:10.1088/1742-6596/2076/1/012088
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Figure 3. In-situ observation on the cracking behavior the Cr coated Zr-4 substrate under different
deflection, d: (a) d=0 mm, (b) d=0.6 mm, (c) d=0.9 mm, (d) d=1.3 mm.
3.2. Finite element results
As shown in the experimental results, both vertical and interfacial cracks appeared under bending. The
initiation and propagation of the cracks were believed to be driven by the local stresses. Figure 4
displays the stress and vertical crack evolution based on the FE calculation. It is shown that damage
appeared in the coating layer when the deflection, d, reached 0.04 mm. The damage led to local stress
degradation in the Cr coating. When d reached 0.260 mm, vertical crack began to initiate from the
coating surface and then propagate vertically to the interface. Note that the stress around the crack
released greatly. Namely, the presence of crack leads to stress redistribution. Under continuous loading,
the crack opened greatly and the stress concentration in front of the crack tip became more significant.
The large stress in the substrate beneath the coating might lead to crack penetration into the substrate.
Besides, the interfacial crack initiated from the crack tip was also modeled. The FE results shown
in Figure 5 (a) is consistent with the experimental result shown in Figure 5(b). The initiation of the
interfacial crack greatly released the local stresses around the vertical crack tip. As the bending loading
increased, the crack began to propagate along the interface. Based on the experimental and FE results,
the cracking behavior followed a similar trend in those typical brittle coating-ductile substrate system
under external loadings. The brittleness of the Cr coating might be related to the microstructure and
the large residual stress generated during deposition process. Once the microstructure of the Cr coating
is optimized and the residual stress is eliminated by some special deposition process and
heat-treatments, the mechanical properties of the Cr coating would be improved and different fracture
modes would be expected.
ICETMS 2021
Journal of Physics: Conference Series 2076 (2021) 012088
IOP Publishing
doi:10.1088/1742-6596/2076/1/012088
5
Figure 4. Numerical results of the stress and crack evolutions of the Cr coated sample under
three-point bending: (a) d=0.04 mm, (b) d=0.260 mm, (c) d=0.266 mm, (d) d=0.800 mm.
Figure 5. (a) Numerical result and (b) experimental result of the interfacial crack.
4. Conclusions
In-situ three-point bending tests and finite element simulation based on the cohesive zone model were
developed to study the stress evolution and cracking behavior of the Cr coated Zr-4 substrate for
accident tolerant fuel claddings. The initiation and propagation of both vertical and interfacial cracks
were captured by in-situ observations and predicted by the finite element calculation. The results
showed that vertical cracks were first generated in the coating and then propagated to the interface.
ICETMS 2021
Journal of Physics: Conference Series 2076 (2021) 012088
IOP Publishing
doi:10.1088/1742-6596/2076/1/012088
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Under larger bending strain, interfacial cracks began to be formed from the vertical crack tips driven
by large local stress concentration. However, even under severe deformation, spallation of the Cr
coating is still not observed, which reflects good interfacial adhesion of the present Cr coating.
Acknowledgements
This project was supported by the Guangdong Major Project of Basic and Applied Basic Research
(2019B030302011), National Natural Science Foundation of China (Grant No. 52005523, U2032143,
11902370), International Sci & Tech Cooperation Program of Guangdong Province
(2019A050510022), Key-Area Research and Development Program of Guangdong Province
(2019B010943001, 2017B020235001), China Postdoctoral Science Foundation (2019M653173 and
2019TQ0374), Guangdong Education Department Fund (2016KQNCX005), and Fundamental
Research Funds for the Central Universities (19lgpy304).
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