Applied Ocean Research 116 (2021) 102880

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Applied Ocean Research

journal homepage: www.elsevier.com/locate/apor

Experimental study on the compression mechanical behaviour of steel pipes

with mechanically induced pitting corrosion
Yang Yang a, *, Tianyu Xu a, Jingyuan Qin a, Zheng He b, Qiao Yu a, Juan Su c, Xiaofeng Zhou d
a
School of Naval Architecture & Ocean Engineering, Dalian University of Technology, Liaoning, China
b
School of Civil Engineering, Dalian University of Technology, Liaoning, China
c
COOEC, Offshore Oil Engineering Co., LTD, Tianjin, China
d
Technique Center of Tianjin Pipe (Group) Corporation, Tianjin, China

A R T I C L E I N F O A B S T R A C T

Keywords: Pitting damage severely degrades the mechanical properties of the main force-bearing member of a circular tube;
Offshore platform pipe it can also change its failure mode. Offshore high-strength seamless steel pipes with steel grade X52Q certified by
Mechanically induced pitting corrosion ABS were selected for a pressure test and research. The constraint conditions of one hinged end and one fixed end
Corrosion damage degree
were adopted to investigate the effect of the bending moment of the nodes so that any section of the circular tube
Compression mechanical properties
Failure mode
can be subjected to the superposition of axial force and bending moment. Pitting craters were generated using
Local stress concentration mechanical processing methods; the effect of pitting parameters such as diameter, depth, and distribution on the
mechanical properties and failure modes of circular pipes was explored. Pitting corrosion damage caused local
stress concentration and the local cross-section weakening of the tube. In addition to the decline of the bearing
capacity under the action of axial compression load, the failure mode of the pitting corrosion damage tube also
showed differences. Increased local damage caused by the increase in the diameter of the pitting corrosion was
likely to cause plastic hinges on the pits of the tube, and this changed stress conditions, failure modes, and failure
locations of the components. An increase in the depth of the pitting craters resulted in a significant drop in the
overall load-bearing capacity caused by local buckling. The location of pitting corrosion had negligible effect on
the mechanical performance of the tube; the end distribution was more unfavourable than the centre distribu­
tion. The stress–strain distribution characteristics of the pitting area of the specimen were considerably different,
and the stress concentration on the inner side of the pitting corrosion were serious and uneven. The results of the
experimental analysis and several numerical examples indicated that pitting corrosion causes the pressure-
bearing circular pipes with lower strength buckling to more likely suffer from an instability failure.

local corrosion (Huang et al., 2010) because of the influence of local

defects and stress concentration; the bearing capacity of pitting
1. Introduction damaged components is often lower than that of uniformly corroded
components with equal mass loss. Simultaneously, the ductility of
International Standardization Organization Standard (ISO) (2017), pitting components is considerably reduced because of the effect of local
corrosive environments are categorised into five grades. amongst them, stress concentration. Therefore, the effect of pitting corrosion on struc­
the marine corrosive environment is the worst, and corrosion loss tural safety is likely to be higher than that of uniform corrosion (Hebor
related to this accounts for about 1/3 of the total corrosion loss globally and Rieles, 2002). The legs and struts of the platform not only have to
(Zhang et al., 2017a). The structure of the offshore platform is subjected bear about 60% of the weight of the entire platform and act as a force
inevitably to long-term adverse effects such as sun exposure, salt spray, transmission path; it faces adverse effects of spray erosion and alter­
wave impact, time-varying environmental temperature and humidity, nating wet and dry (Sun et al., 2015). Thus, the corroded mechanical
and marine microbial erosion. Corrosion types of steel offshore plat­ properties of pile legs and struts are subjected to pressure or bending,
forms are diverse (Dewanbabee and Das, 2013), and they are divided and they play a vital role in the safety of the entire platform.
into large-area uniform and local corrosions. Although the loss of steel It is easy to form unevenly distributed pits in the marine corrosive
caused by uniform corrosion is considerably greater than that of the

* Corresponding author.
E-mail address: yyang@dlut.edu.cn (Y. Yang).

https://doi.org/10.1016/j.apor.2021.102880
Received 13 July 2021; Accepted 11 September 2021
Available online 25 September 2021
0141-1187/© 2021 Elsevier Ltd. All rights reserved.
Y. Yang et al. Applied Ocean Research 116 (2021) 102880

Nomenclature Di inner diameter of pipe mm

Do external diameter of pipe mm
α deflection of pipe mm DDR Diameter-depth ratio of pits
γ corner at the top of pipe ◦ DOP degree of pitting corrosion
ΔA sectional area loss of critical section mm2 E elasticity modulus MPa
ΔV corroded volume mm3 fy yield strength MPa
Φ pipe size (external diameter D0 × thickness of pipe t0) mm l length of pipe mm
μ Poisson’s ratio r2 goodness of fit
ε strain mm− 1 Si number of the ith strain gauge
εn nominal strain mm− 1 SLR sectional loss rate
σ stress MPa t depth of pit mm
σn nominal stress MPa t0 thickness of pipe mm
σt true stress MPa V0 original volume of an intact stiffened plate mm3
A0 cross-sectional area loss of critical section mm2 VLR volume loss rate
d diameter of pit mm

environment because of the uneven physical and chemical properties of failure modes of round pipes are highly sensitive to pitting corrosion that
the surface of the steel component. With an increase in the corrosion causes local defects (International Organization for Standardization
time, the radius and depth of the pits gradually expand and deepen; (ISO) et al., 2017). Local buckling usually occurs when a short and thick
further, even through holes are formed (Saad-Eldeen et al., 2012). Me­ round tube is compressed. The buckling shape is a waist-drum shape-­
chanical properties of the round tube are severely affected once adjacent distributed along the ring direction-that shows the failure form of local
pits corrode to form through-type pits (Lin et al., 2013). The main instability (Cao et al., 2016). A slender tube undergoes overall buckling
characteristic parameters of pitting corrosion are diameter, depth, accompanied by local buckling when it is compressed (Ahn et al., 2016).
shape, and distribution (Zhang et al., 2016). According to the measured Overall elastic instability often occurs when the slenderness ratio of the
data, the diameter of the corrosion pits of marine engineering structures round tube is large (Wang and Melchers, 2017). The slenderness ratio
is generally 20–80 mm (Chen and Wang, 2005). The diameter-to-depth and diameter-thickness ratio of steel pipes are the factors that determine
ratio of pits is 1/10–1/6 (Zhang et al., 2017b). The shape of pitting the failure mode of steel pipes (Wang et al., 2016). However, pitting
corrosion can be approximated by cylindrical, conical, and hemispher­ corrosion considerably changes the failure location and failure path of
ical simulations (Hou et al., 2016). When the corrosion volume is the the round pipe components because of the uneven local stress of the
same, the shape of the pitting corrosion crater has a slight effect on the components. The increase in the diameter and depth of the pit degrades
mechanical properties of the component (Yao et al., 2018). A difference the ultimate bearing capacity of the member and increases the possi­
in the distribution of the pitting corrosion crater can lead to changes in bility of local buckling greatly (Nakai et al., 2004). Pitting corrosion has
the damage location and form of the component; this in turn affects the little effect on the failure mode of components; however, it causes
mechanical properties and failure modes of the component (Yao et al., components at the critical point of strength failure and instability failure
2018) (Fig. 1). The round pipes of the offshore platform in the splash and to enter the instability failure earlier (Wang et al., 2015). Compared
tidal range zones are subject to the effects of alternating wet and dry with the diameter and depth, the distribution of pitting corrosion will
conditions, splashing waves, and erosion by ocean currents. Often, large cause the damage location of component to change (Wang et al., 2016).
areas of pitting corrosion appear in the middle section of the tube Considering the tube node can constrain the linear displacement and
(Zhang et al., 2010) (Fig. 1). part of rotational displacement, it is a semi-rigid constraint (Wang and
The round pipe is used as the main force member of the jacket Cui, 2007). The restraint stiffnesses of different pipe nodes on circular
platform because its force performance is considerably better than other pipe members are distinguished by factors such as the node structure
cross-sectional forms and its resistance in the water is smaller. The force and stiffness of other connecting members. Nodal constraints are
of the round pipe support member is complex, i.e. an axial force; how­ simplified as consolidation or hinged connections when studying the
ever, it is subjected to the action of the bending moment, shear force, mechanical behaviour of circular pipe members.
and water pressure (Xu and Wan, 2010). They are approximated as The circular tube is restrained by one hinged end and one fixed end
slender rods with axial or eccentric compression because of the small to study the compressive performance of marine engineering steel pipe
bending moment and shear force on the pipe members of offshore members with pitting corrosion damage; simultaneously, it considers
platforms (Wang and Ajit Shenoi, 2019). The pressure properties and the effect of the bending moment transmitted by the circular tube node.
A special seamless steel pipe for the offshore engineering structure with
steel grade X52Q was selected for the experiment to simulate the me­
chanical behaviour of the main support pipe of the platform structure as
realistically as possible. The pitting craters of the experiment compo­
nents were generated by mechanical processing methods to obtain the
influence law of the pitting diameter, depth, and distribution accurately.
Changes in mechanical properties such as the ultimate bearing capacity
and buckling form of steel pipes with the main pitting corrosion pa­
rameters were studied via compressive experiments on steel pipes with
different pitting damages. Stress and strain distribution characteristics
of the corroded area were studied via numerical simulation analysis, and
the local buckling mechanism of the component were revealed. Corre­
lation between the bearing capacity and buckling mode of pitting
Fig. 1. Locally corroded offshore platform column (Fang et al., 2014); (a) Local
damaged components and evaluation index of typical corrosion degree
corrosion of offshore platforms; (b) Details of the local corrosion of column. was studied, and the effect of pitting damage degree on the mechanical

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

behaviour of steel pipe components was analysed. Table. 1

Configuration of pitting craters in the steel pipe specimens.
2. Materials and methods Specimen Pitting t d/ Pitting Number of
Location /mm mm distribution pitting craters
2.1. Material and parameters of round tube D20T6E* 6 20 Even 48
distribution
The compressive load of the platform main pipe-the main support D40T6E 6 40 Even 48
distribution
and force transmission member of the offshore platform structure-can
D60T6E 6 60 Even 48
reach thousands or even tens of thousands of tons (Mohd et al., 2015). distribution
The platform pipe member can be considered an axial or eccentric D30T3E 3 30 Even 48
force-bearing member because the shear force transmitted by the node is distribution
considerably smaller than the axial force or bending moment. The D30T6E 6 30 Even 48
distribution
high-strength seamless steel pipes commonly used in offshore engi­
D30T9E 9 30 Even 48
neering with the steel grade X52Q certified by ABS were selected as the distribution
test objects to simulate the pressure performance of the main pipe of the D20T6C** 6 20 Centre 36
offshore platform as realistically as possible and by considering the
specifications of the finished offshore steel pipes. The steel pipes were
provided by China Tianjin Pipe Group Co., Ltd., which is the main D20T6O*** 6 20 One side 36
supplier of CNOOC Offshore Construction Division. X52Q steel is used in
the construction of marine engineering structures and pipelines, and its
nominal stress–strain relationship curve is shown in Fig. 2. The nominal D20T6B**** 6 20 Both sides 36
stress data were processed to approximate the true stress–strain rela­
tionship and key mechanical parameters of the steel to simulate the
mechanical properties of steel pipes later, according to the relationship *
: D20T6E = Evenly distributed pitting on total pipe, the diameter of pit d =
σ t = σ n (1 + εn ); here, σt, σn and εn represent real stress, nominal stress, 20 mm, and the depth of pit t = 6 mm.
and nominal strain, respectively. **
: D20T6C = Evenly distributed pitting on the centre of pipe only, d = 20
The overall failure mode of the platform main pipe is often closely mm, t = 6 mm.
related to its length-diameter ratio (Samadani et al., 2009), whereas the ***
: O = Evenly distributed pitting on one side only.
****
local failure mode is more closely related to its diameter-thickness ratio : B = Evenly distributed pitting on both sides.
(Mohd et al., 2015). Although the design ranges of the length–diameter
and diameter-thickness ratios are not provided in the code, they are set pieces for each parameter is set to one to avoid inaccurate results caused
to be between 5 and 20 and 30–60, respectively, to provide full play to by experimental dispersion and processing errors. If the experimental
the load-bearing capacity of the member while reducing the possibility result has a large deviation, specimens with the same parameter need to
of overall buckling and local buckling of the circular tube member be added. The detailed size and physical photo of specimens are illus­
(Guedes Soares et al., 2009). Further, considering the conditions of the trated in Fig. 3. A sufficient numerical simulation analysis will be added
experiment equipment and the safety issues such as pressure instability given the currently limited number of experimental samples.
caused by pitting corrosion damage, a type of offshore structural steel Although there are certain differences in the shapes of pits obtained
pipe of Φ168.3× 10 mm is selected in the test; the length of the steel pipe via mechanical drilling and formed by seawater corrosion, this differ­
is 800 mm (length-diameter ratio of the round pipe member is about 5). ence has a very small effect on the mechanical properties of components
as long as the degree of corrosion is similar (Yao et al., 2018). A me­
2.2. Pitting parameters chanical drilling method can thus more effectively ensure the size and
location of the pits used in the test to obtain the pits. The pitting shape
The main parameters of pitting corrosion include pitting diameter, has little effect on the mechanical properties of the specimen or
depth, distribution, and shape. The first three have the most significant component because of the same degree of corrosion (Paik et al., 2003a).
effect on the mechanical properties of the specimen (Saad-Eldeen et al., Simultaneously, cylindrical pits can more easily ensure processing and
2011). The test specimens were divided into three groups (a total of 9 alignment accuracy compared to that using the spatial curved surface of
specimens) to study the influence of the above three parameters sepa­ conical and hemispherical pits; further, their stress concentration is
rately; the detailed parameters of the specimens are summarised in more obvious. Therefore, cylindrical pits are used to simulate pitting
Table 1. corrosion. The bottom and sides of the etched hole are treated with
When the experimental results are reasonable, the number of test rounded corners to reduce the stress concentration caused by
machining. Hammering is used to eliminate residual stress caused by
machining corrosion pitting craters. Considering the various factors of
the service period, marine environment, and maintenance, the diameter
of the corrosion points of ships and offshore platforms is between 25 and
80 mm (Paik et al., 2003b); the diameter–depth ratio is about 1/10–1/6.
According to this range, the diameter of the corrosion pitting craters d in
the test is 20–60 mm, and depth t is between 3 and 9 mm. There will be
cases where corrosion pitting craters are distributed in the middle of the
pipe or are full because steel pipe corrosion often starts at the welded
joints (Paik et al., 2004). In the experiment, four distribution forms of
corrosion pitting craters distributed on one side of the end of the round
pipe, on both sides of the end, in the middle, and those evenly distrib­
uted are investigated, as shown in Fig. 4(a), (b), (c) and (d). The details
of the pitting corrosion parameters of each component are summarised
in Table 2.
Fig. 2. Tensile stress–strain curve of Steel X52Q.

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

Fig. 3. Details of pipe specimen crater; (a) Details (unit: mm); (b) Specimen; (c) Pitting specimen; (d) Details of a pit; (e) Machine drilling pit.

Fig. 4. Distribution forms of the pitting craters.

Table. 2
Measured average value of the geometrical dimensions of the specimen (mm).
Specimen Length l Inner diameter of steel pipe Di Steel pipe thickness t0 Outer diameter of steel pipe D0 Pit diameter d Pit depth t

Intact 806.0 147.4 10.3 168.1 – –

D20T6E 798.8 147.6 10.4 168.4 19.6 6.0
D40T6E 805.5 147.7 10.7 168.5 39.7 6.1
D60T6E 805.0 147.8 10.6 169.1 59.4 5.9
D20T6C 804.5 147.7 10.6 168.4 19.7 6.2
D20T6O 806.3 148.3 10.5 168.5 19.8 6.1
D20T6B 807.7 147.7 10.5 168.5 19.8 6.3
D30T3E 809.5 148.1 10.5 169.1 29.7 3.0
D30T6E 803.8 147.3 10.7 168.7 29.7 5.9
D30T9E 806.5 147.8 10.6 169.1 29.6 9.1
Max imperfect 1.2% 0.7% 7% 0.4% 2% 5%

2.3. Test device and strain gauge layout conservative and the node bending moment transmission cannot be
considered. Therefore, the top end of the round tube is provided with a
2.3.1. Test setup and initial imperfections spherical hinge and the bottom end is set as a fixed restraint to consider
A YAW-5000 electro-hydraulic servo pressure testing machine with a the end restraint effect properly and reasonably (Fig. 5(b)).
maximum bearing capacity of 5000 kN is used to perform axial The linear displacement of the upper end of the steel pipe is con­
compression tests on the steel pipes (Fig. 5(a)). In the experiment, strained; however, the angular displacement is not limited. The lower
displacement control is employed for applying a compressive load to the platform of the testing machine is the loading end, and the lower end of
round pipe. If the upper and lower ends are set as fixed constraints, the the steel pipe is fixed to the lower platform through a fixture; its hori­
result is not safe, and the actual node cannot achieve the consolidated zontal displacement and angular displacement are restrained. The load
state of restraint to consider the effect of the bending moment of the level and axial compression deformation are recorded by the sensor of
node. If the upper and lower ends are hinged, the result is too the testing machine; the sampling time is 1 s. The size of each test piece

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

Fig. 5. Test setup; (a) Test machine; (b) Schematic diagram of test machine.

Fig. 7. Load vs. axial shortening curves of intact steel pipe.

is slightly different because of the mechanical errors in production and
cutting. Vernier callipers were used to measure the diameter, wall
In the initial loading stage, the strain at each position of the circular
thickness, and length of the pipe at different positions and the diameter
tube in the elastic working state increases linearly with an increase in
and depth of the corrosion point. The average values are summarised in
the load, and the strain change at each position is the same (Fig. 8).
Table 2.
Plastic deformation occurs almost simultaneously at all positions of the
component. Although there are certain differences in the deformation,
2.3.2. Strain gauge layout
the development trend of the strain at each point is similar; they are all
A total of 14 strain gauges are set on the surface of each steel pipe
under compression. Further, this shows that the stress and strain dis­
along the pipe axis to study the change law of the overall deformation of
tributions of each part of the intact specimen are continuous. The middle
the circular pipe and the local strain of the pitting craters during the
position of the component where strain gauge 6 is located quickly rea­
compression process. As shown in Fig. 6(a), 8 strain gauges (S1–S8) are
ches the compressive deformation limit; then, the strain remains almost
symmetrically arranged at the upper, middle, and lower three places on
the surface of the pipe because the steel pipe is symmetrical along the
main axis. Further, there are 4 approaches to pitting crater distribution,
and 6 strain gauges (S9–S14) are arranged in each way, as shown in
Fig. 6(b–e), respectively. A 16-channel DH3816N static strain tester is
selected for real-time strain monitoring.

2.4. Compression test of uncorroded round pipe

The undamaged steel pipes were subjected to uniaxial compression

tests to analyse the compressive performance of components damaged
by pitting corrosion. The yield load (2.35 × 103 kN) of the intact steel
pipe is very close to the ultimate load (2.42 × 103 kN); however, the
axial compression displacement (33.95 mm) that corresponds to the
ultimate load is almost six times the yield displacement (5.97 mm), as
indicated in Fig. 7. After reaching the ultimate load, the steel pipe still
maintains a certain bearing capacity. Uncorroded steel pipes demon­
strate obvious strength failure characteristics, and the components un­
Fig. 8. Load vs. strain curves of intact steel pipe.
dergo axial compression and lateral bending.

Fig. 6. Layout of strain gauges on tested specimens and around pitting craters.

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

unchanged until the overall bearing capacity of the component de­

creases. This is the position where the overall bending deflection of the
component is the largest, and therefore, it is not subjected to only axial
pressure but also to the tensile force caused by bending. The tensile and
compressive forces cancel each other without increasing the strain point
as the load increases. The compressive deformation in the same ring
position adjacent to a slightly larger (strain gauges 5) deformation limit
reached quickly. The compression deformation of the same circumfer­
ential position of strain gauges 3 and 4 under the highest load increase
because it is on the concave side of the overall bending of the compo­
nent. The data of the two strain gauges on the top of the component
show a similar rule; the deformation on the curved convex side does not
increase considerably, whereas the concave-side deformation increases
at all times. In the initial stage of the loading, the deformation law at the
bottom of the component is similar to that above. However, as the load
increases, the bending moment at the lower fixed end increases, and the
bending tensile stress at the location of strain gauge 8 increases faster
than the compressive stress; therefore, compression deformation at 8
points decreases and the curve increases in the opposite direction.
The above-mentioned law can be confirmed through photos of the Fig. 10. Schematic of parameters.
compression process of steel pipes (Fig. 9). Points 6, 5, 2, and 7 are
located on the curved convex side, and points 1, 3, 4, and 8 are located
on the concave side. Point 8 is raised slightly in the final stage of the
loading. As the loading displacement increases, the bending deflection
of the middle and upper part of the steel pipe increases gradually, and
local buckling and bulging appear on the concave side. According to the
measurement method shown in Fig. 10, the maximum deflection α of the
intact steel pipe in the ultimate state is 34 mm; the maximum rotation
angle γ of the spherical joint is 11.7 ◦ The intact steel pipe exhibits
strength failure characteristics of overall bending with local buckling,
and this performance is closely related to constraint conditions.

3. Analysis of the effect of pitting corrosion parameters

3.1. Effect of pitting diameters

Fig. 11. Failed pipes with different pitting diameters.

Fig. 11(a), (b), (c) and (d) shows that the bending shapes of the three
uniformly distributed pitting round pipes D20T6E, D30T6E, and the large damage area of a single pit; the folds along the ring of the tube
D40T6E are like those of the uncorroded components. The component is are connected. These factors cause the circular tube to rotate around this
bent to one side, and maximum deflection occurs in the upper middle position, i.e., the pitting corrosion connecting zone forms a plastic hinge.
part of the component. The difference is that the location of pitting The failure mode of the compressed round pipe is unlike the other
corrosion is prone to local buckling, and this is characterised by local components. After bending, the upper and lower round pipes are in a
bumps; further, it becomes more obvious as the diameter of the pitting straight line, the deflection of the component is increased, and the top
corrosion increases. The failure modes of the three specimens are corner is not large.
consistent; they are all strength failures accompanied by local buckling Fig. 12(a), (b), (c) and (d) shows that the strain change pattern at
and overall bending. Fig. 11 shows that the final shape of the D60 each position of the member with the smallest pitting diameter
specimen is obviously different from other specimens. Further, there are (D20T6E) is relatively close, and it is like the intact member. The
obvious local buckling and folds in the pit after compression owing to bearing capacity level is slightly lower than that of the intact member.
Indeed, the component is less affected by pitting damage, and the stress
and strain distributions of the component are still relatively uniform.
With an increase in the pitting diameter, the bearing capacity level of the
component drops significantly. The strain changes of D20, D30, and D40
are relatively close, and the strain at each position of the component is
not considerably different in the initial stage. After reaching the yield
load, the strain change at each position of the component shows a sig­
nificant difference; the larger the pitting diameter, the more obvious is
the difference. A significant compressive strain does not increase or even
rapidly decreases in many parts of the component because of the bulging
caused by local buckling. Thus, the force at this point is the super­
position of the axial pressure at both ends of the component and the
tensile force caused by the local bulge. The number of points where the
strain decreases continue to increase as the pit diameter increases; this
means that locations where bulging occurs are increasing. Before
reaching the yield load, the bottom of the D60 member exhibited a large
plastic deformation. Further, after reaching the yield load, local strains
Fig. 9. Compression history of intact steel pipe. at most positions of the component were reduced and oscillated back

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

Fig. 12. Load vs. strain curves of pipe with different pit diameters.

and forth. The top spherical hinge only rotates slightly (3.7 ◦ ) because of degenerates from two-fold statically indeterminate to first-order stati­
the appearance of the plastic hinge, and the tube above the plastic hinge cally indeterminate. When the pitting diameter increases to a certain
is subjected to the axial force and hardly bends. The maximum side shift extent, the failure mode of the component will be unstable.
of the component occurs at the position of the plastic hinge, which is
higher than the maximum side shift of the round pipes with other pitting
3.2. Effect of pitting depths
diameters. The appearance of plastic hinges will reduce the number of
structural constraints that are extremely detrimental to the safety of the
The failure modes of the three specimens with the same pitting
structure; they should be avoided in actual engineering.
diameter and different depths are all strength failures. Weak locations
Fig. 13 that the four types of circular tube members with different
appear in the upper and middle pits of the component because of the
pitting diameters are strength failures; however, the failure modes of the
combined effects of constraint conditions and pitting damage (Fig. 14
specimens are very different. D20 and D40 round pipes show failure
(a), (b) and (c)). As the corrosion depth increases, the local bulging
modes of overall bending accompanied by local buckling. D20 and D40
phenomenon of the specimen becomes increasingly obvious; however,
round pipes show failure modes of overall bending accompanied by local
the diameter is not very large and it is difficult to communicate. The
buckling. The failure mode of the D60 round tube is manifested as a
failure mode and shape of the circular tube with a 3 mm deep pitting
plastic hinge caused by local buckling; the bearing capacity of the
crater are controlled by constraint conditions because the stiffness of the
component is not high. With an increase in pitting damage, the failure
circular tube section is not considerably weakened. The final state of this
mode of the circular tube gradually evolved from overall bending to
round tube is strength failure accompanied by partial depression and
local plastic hinge deformation. The force mode of the circular tube
overall bending. No local bulging occurs because the thickness of the
specimen after pitting damage is still large. The pitting crater with a

Fig. 13. Load vs. axial shortening curves of pipes with different pit diameters. Fig. 14. Failed pipes with different pitting depths.

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

depth of 9 mm significantly weaken the stiffness of the circular tube

section; the circular tube exhibits serious local bulging and insignificant
overall bending. The combined influence of pitting damage and
boundary conditions becomes the controlling factor of the final failure
state of the round tube. The remaining cross-section of the tube with a 9
mm pitting crater is very thin. When pitting craters are compressed, a
local buckling phenomenon that bulges outwards because of the folds is
formed. The remaining section at the 3 mm pitting crater is thicker;
therefore, it has a certain bearing capacity without wrinkles. During the
compression process, the upper and lower cross-sections of the pitting
craters are squeezed to the inside to form a depression local buckling
phenomenon. The cross-sectional loss of the circular tube caused by the
pitting crater with a 6 mm depth is between the above two, and local
buckling is also observed between the two, with no depressions and
bulges. It appears as a failure form of overall bending dominated by
constraint conditions.
Fig. 16. Load vs. axial shortening curves of pipes with different pit depths.
Before reaching the yield load, the strain change law of each position
of the specimen is relatively close (Fig. 15(a), (b) and (c)). The yield load
and corresponding strain levels decrease as the corrosion depth in­ specimen is overall bending with local inward buckling; the T6 specimen
creases. The local compressive strain of the circular tube with a 3 mm- is the overall bending and the T9 specimen is the drum-shaped local
deep pitting corrosion is reduced greatly, which implies the strain at this buckling. Although the damage degree of the circular tube with a 3 mm
point is the superposition of the component compressive strain and local deep pitting corrosion is relatively small, its local buckling shape is
tensile strain. Further, there are few places where the superimposed inwardly concave, and the bearing capacity of the circular tube drops
strain of the circular tube with a 6 mm deep pitting corrosion appears; sharply. The final deformation capacity of the specimen is smaller than
this implies that there are few places where the component has local the circular tube with 6 mm deep pitting. With an increase in corrosion
protrusions or depressions. The maximum compressive strain at each depth, the deformability of the round pipes shows a downward trend.
point of a circular tube with a 9 mm deep pitting corrosion varies The deformation and load-bearing capacity of the specimens with
greatly, by even up to 10 times or more; this means the unevenness of overall bending are higher than those of the specimens with local
internal force and deformation at each point caused by pitting corrosion buckling; the specimens with pitting corrosion are more likely to un­
damage is more obvious. dergo local buckling.
The elastic stage of each tube coincides in the load–displacement
curve shown in Fig. 16. The yield load and ultimate load decrease with 3.3. Effect of pitting distributions
an increase in pitting depth. The post-buckling curve of the circular tube
has a certain difference because of the difference between the local Fig. 17(a), (b) and (c) shows that local buckling occurs at the
buckling form and final failure state. The failure mode of the T3 corrosion points under the action of compressive load regardless of

Fig. 15. Load vs. strain curves of pipe with different pit diameters.

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

compressive stress and local buckling tensile stress. Local buckling not
only leads to a decrease in the load-bearing capacity and ductility of the
component, but it also changes the weak position of the component. The
test results of several pitting distribution positions indicate that the local
buckling is the most serious when the corrosion points are distributed at
one or both ends of the specimen; the weak position is located in the
pitting area adjacent to the spherical hinge. Further, the local buckling is
slightly smaller when pitting corrosion is distributed in the middle of the
specimen or evenly distributed, and the weak position is located in the
pit area of the middle section of the specimen. The pitting corrosion
distributed in the middle part has the least influence on the bearing
capacity and deformability of the component (Fig. 19); the mechanical
properties of the component are not lower than that of the noncorrosive
component. The pitting corrosion distributed on both sides or one side
Fig. 17. Failed pipes with different pitting distributions. has similar effects on the mechanical properties of the components; they

where the corrosion points are densely distributed in the circular pipe.
This implies the location of local buckling is not only determined by
constraints, but the degree of pitting damage plays a decisive role. Like
the bending form where the corroded spots are all over the member, a
round tube member with corroded spots in the middle of the specimen
undergo overall bending with local buckling. The deformation of pits
distributed on one or both sides of the component is similar; the
component only has certain rotation and partial buckling near the
spherical hinge position, and the rest remain close to a straight line.
The strain change law at each point of the component is relatively
consistent when the pitting corrosion is located in the middle of the
specimen; this indicates that pitting corrosion has little effect on the
stress and strain of the specimen (Fig. 18(a), (b) and (c)). When pitting
corrosion is located on one or both sides of the component, compressive
strain at a certain position of the component rapidly decreases after
reaching a certain value. This implies there is a depression or protrusion
at this point, and that the strain is simultaneously affected by the overall Fig. 19. Load vs. axial shortening curves of pipes with different pit locations.

Fig. 18. Load vs. strain curves of pipe with different pit diameters.

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

all reduce the load-bearing and deformation capacities of the compo­ obtaining the stress and strain distribution law of all positions in the
nents. In actual engineering, corrosion is often distributed near the node corrosion area through the test method. The solid unit C3D8R con­
area (end of the component) due to the sudden change in the section at forming to the von Mises criterion is used for simulating the pressure
the joint and the weaker anti-corrosion performance of the welding heat- behaviour of the circular pipe. The true stress–strain relationship curve
affected zone. This implies pitting corrosion has a greater effect on the of X52Q is used as the material constitutive model (Fig. 21) wherein the
deformation capacity, bearing capacity, and failure mode of the yield strength is 480 MPa, elastic modulus is 238 GPa, Poisson’s ratio is
component. 0.30, mesh size is 5 mm, and the arc length method is selected as the
nonlinear iterative method. The size of the specimen, boundary condi­
tions, and distribution of pitting corrosion are simulated and completely
3.4. Analysis of the local stress and strain of pitting-corroded tube consistent with the test member. The circular tube D30T6E is considered
as an example for comparing the numerical and test results. The initial
3.4.1. Strain distribution law in pitting area defect is realised by introducing the first-order buckling mode; the initial
The detrimental effects of pitting corrosion on the mechanical defect size is the measured defect of the specimen. As shown in the
properties of components are attributed to stress concentration and Fig. 21, the load–displacement curve, failure mode, and deformation
cross-section discontinuity. As shown in Fig. 20, the strain distribution diagram of the specimen obtained via numerical calculation are in good
around the pitting area was compared when the test component reached agreement with the test results. Therefore, the numerical simulation
the buckling load and the ultimate load to analyse the stress and strain methods and results are considered credible.
distribution law of the pitting area. Most components have large internal The strain change in the pitting area has a considerable effect on the
strains in the pitting craters (the average value of the black area is local buckling position and deformation form of the component; it is
-0.028, the average value of the grey area is -0.023), followed by the likely to affect the weak position and failure mode of the component.
stresses of adjacent points outside the pit ring (the average value of the Therefore, the stress distribution in the pit area is analysed with the
orange area is -0.022, and the average value of the yellow area is loading process to clearly understand the strain change mechanism of
-0.022). Finally, the adjacent points (the average value of the blue area is the pitting area (Fig. 21). The internal stress level of the pitting corrosion
-0.004, the average value of the green area is -0.002) on the outer side of continues to increase with an increase in the loading level. Although the
the pitting craters have the smallest stresses. The strain level at each pit diameter of D60T6E is twice that of D30T6E, the maximum stress at
location of the pit area shows a downward trend as the diameter of the the pit of D60T6E is nearly 25% lower than that of D30T6E under the
pit increases. After the diameter increases, the local stress concentration same load level. Meanwhile, stress distribution at the pitting corrosion
weakens gradually, and the pitting corrosion transitions to uniform of D60 is more uniform, which is consistent with the previous analysis, i.
corrosion. An increase in the pitting depth did not lead to an increase in e., the larger the diameter of the pitting damage, the closer it is to the
the stress level at the pits. When the depth is small, the stress level is low impact characteristics of the uniform corrosion damage. Fig. 22 shows
because of the remaining cross-sectional area at the pit. In contrast, that the stress in the pitting corrosion is larger than the surrounding
when the pit depth is large, the remaining section quickly exhibits area; however, the distribution is not uniform. The remaining thickness
plastic deformation and causes local stress redistribution. Therefore, the of the pits is very thin and it easily bulges and dents because of local
strain at the pit does not increase significantly (Fig. 20). The strain in the buckling under axial compression; this is also the cause of uneven stress
pit is relatively high when the pitting corrosion is distributed in the local and strain in the pits.
position of the component because the partial cross-section of the Although the local stress concentration at the pitting corrosion of
specimen where the corrosion points are distributed has abrupt changes; D30T6E is considerably higher than that of D60T6E, the local damage
further, the stress distribution of the entire component is uneven. The caused to the specimen is not sufficient to cause greater local buckling;
strain is higher because of the greater stress in the pitting area. Mean­ therefore, the final failure mode of the specimen is not changed. Indeed,
while, the strain level outside the longitudinal pit is very low and the pitting damage with a small diameter can hardly cause changes in me­
strain level outside the ring pit is high; this shows that the pit has a chanical properties such as the bearing capacity and failure mode of the
relatively large compression deformation in the circumferential direc­ specimen under uniaxial force. Pitting damage with a larger diameter
tion and the longitudinal outer region of the pit has local tensile strain can cause local buckling and the transformation of failure modes such as
attributed to the compression. The strain in the pitting pits distributed in plastic hinges because of the large damage surface. Thus, when the
the local parts of the component is greater than the strain in the pits all component is subjected to fatigue load, the local high stress caused by
over the surface of the component. The strain in the pitting area in the the small diameter pitting damage will easily cause the component to
failure state is equal to or higher than the strain in the pit under the show fatigue cracks or even break at the pitting corrosion.
ultimate load.
3.5. Effect of corrosion degree on ultimate bearing capacity of round pipe
3.4.2. Stress distribution law of pitting area
ABAQUS (6.14) is used for additional numerical analysis owing to Pitting diameter, depth, and distribution location can only reflect a
the limited number of experimental specimens and the difficulty in certain aspect of the corrosion degree of the component. The correlation
between the compressive bearing capacity of pitting round pipes and the
evaluation indexes of commonly used corrosion degrees is analysed to
evaluate the effect of pitting damage of round pipes more comprehen­
sively, and DDR refers diameter-depth ratio of pits (Table 3).
Owing to the limited number of experiments, the ultimate bearing
capacity and corresponding corrosion index of a total of 50 numerical
models were additionally analysed, as summarised in Table 4. Under the
condition of the equal length of the components, the UL approximately
shows a linear downward trend with an increase in the corrosion degree
(Fig. 23). Further, the relationship with the SLR (sectional loss rate) is
the closest (r2= 0.91). The consistency of the VLR (volume loss rate) is
Fig. 20. Comparison of strain variation around pitting crater (For interpreta­ also high; however, the dispersion of the data increases significantly
tion of the references to color in this figure, the reader is referred to the web with an increase in the degree of corrosion. The ultimate bearing ca­
version of this article). pacity of the component does not agree well with the DOP (degree of

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

Fig. 21. Numerical model calibration.

Fig. 22. Stress distribution around pitting crater.

pitting corrosion) regardless of the degree of corrosion. This shows that

Table. 3
the load-bearing capacity of compression members damaged by equal-
Bearing capacity and corrosion damage degree of specimens in test or
length pitting is closely related to the degree of maximum cross-
simulation.
sectional damage. The volume loss rate and DOP reflect the overall ef­
Specimens UL/kN YL/kN DOP/% VLR/% SLR/% DDR/% fect of pitting damage on the component, which includes not only the
Intact 2424.00 2344.88 0 0 0 0 broken section, but also the non-destructive section. Therefore, the re­
D20T6C 2429.28 2134.84 2.64 1.66 14.08 3.33 sults are not in good agreement.
D20T6O 2235.44 2121.40 2.64 1.66 14.08 3.33
D20T6B 2245.09 2144.10 2.64 1.66 14.08 3.33
D20T6E 2163.68 2126.56 3.52 2.22 14.08 3.33
3.6. Mechanical model of failure of pitting-corroded tube under
D40T6E 2046.46 2019.91 14.32 8.19 25.20 6.67
D60T6E 1996.77 1830.51 32.55 15.83 30.39 10.00 compression
D30T3E 2283.49 2266.44 8.00 2.27 9.32 10.00
D30T6E 2182.10 2062.14 8.00 4.83 20.37 5.00 Fig. 24 shows that although the 800 mm-long D60T10E has a very
D30T9E 1818.74 1741.94 8.00 7.39 30.02 3.22
high degree of pitting damage, the round tube is still strength-damaged.
In contrast, the 1000 mm-long round tube is not damaged by pitting
corrosion; however, instability damage is observed. The partial
depression of the unstable circular pipe is serious, and the component is

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

Table. 4 near-instability strength failure. Thus, the failure types of pitting

Ultimate load (UL) and corrosion damage degree of specimens in simulation. corroded round pipes with a moderate slenderness ratio under
Specimens (SLR-VLR-DOP) UL /kN Specimens (SLR-VLR-DOP) UL /kN compressive load can be divided into three categories: strength failure
without or with slight local buckling (Class I), plastic hinge caused by
D20T2E (4.34–0.71–2.64) 2372.98 D40T5E (20.27–6.67–14.32) 2118.40
D20T3E (6.76–1.08–2.64) 2355.11 D40T6E (25.20–8.19–14.32) 2046.46 large local buckling (Class II), and instability damage (Class III).
D20T4E (9.17–1.46–2.64) 2332.43 D40T7E (29.92–9.71–14.32) 1899.11 The mechanical model of the Class I failure type of a round pipe can
D20T5E 2307.74 D40T8E 1778.45 be simplified as one end being embedded and the other end being hinged
(11.58–1.84–2.64) (34.75–11.22–14.32) (Fig. 25(a)). The deflection curve of the component is shown in the
D20T6E 2163.68 D40T9E 1668.37
(14.08–2.22–2.64) (39.58–12.74–14.32)
figure; the maximum deflection of the component occurs near the hinge
D20T7E 2238.11 D40T10E 1432.31 point and the concave position of the component is prone to local
(16.41–2.59–2.64) (48.79–15.28–14.32) buckling. According to the mechanical model, local buckling mostly
D20T8E(18.82–2.98–2.64) 2197.35 D42T6E (25.91–8.93–15.72) 1985.07 occurs in the upper depression and left side of the bottom fixed end
D20T9E 2147.06 D44T6E (26.68–9.68–17.25) 1971.10
because of the bending moment. When the pitting diameter is small, the
(21.24–3.35–2.64)
D22T6E 2234.31 D46T6E 1935.50 cross-section of the component is not considerably weakened even if the
(15.25–2.64–4.31) (27.39–10.44–18.86) pitting depth is large, and the area of high stress is small. Meanwhile, the
D24T6E 2227.62 D48T6E 1907.20 component is more likely to have a Class I failure mode, and pitting
(16.51–3.12–5.13) (28.03–11.21–20.53) corrosion has little effect on the unidirectional force performance of the
D26T6E 2185.99 D50T5E (22.58–5.16–22.28) 1979.53
(17.73–3.66–6.02)
component. However, the large depth of pitting corrosion leads to a
D28T6E 2189.34 D50T6E (28.62–6.67–22.28) 1882.50 higher level of concentrated stress, and it can be inferred that compo­
(18.92–4.23–6.99) nents are prone to stress corrosion cracking at the pitting location under
D30T3E (9.32–2.27–8.00) 2283.49 D50T7E (34.65–8.19–22.28) 1752.38 reciprocating loads.
D30T4E 2269.31 D50T8E (40.69–9.71–22.28) 1617.65
The class II failure type round pipe can be approximately simplified
(12.85–3.12–8.00)
D30T5E 2218.20 D50T9E 1486.85 to the mechanical model shown in Fig. 25(b). The upper circular tube is
(16.47–3.98–8.00) (46.72–11.22–22.28) a compression member hinged at both ends because of the existence of
D30T6E 2182.10 D50T10E 1111.16 plastic hinges; the deformation of this section of the circular tube is a
(20.37–4.83–8.00) (61.38–12.74–22.28) straight line. The lower round tube is subject to the constraint of one end
D30T7E 2093.66 D52T6E 1862.53
fixed and the other hinged. Although the plastic hinge has a certain
(23.71–5.68–8.00) (29.09–12.77–24.10)
D30T8E 2027.43 D54T6E 1842.12 bending rigidity, it is lower than that of the other parts of the member.
(27.33–6.54–8.00) (29.51–13.55–25.99) The plastic hinge is the position of the maximum deflection of the
D30T9E 1818.74 D56T6E 1818.27 component, and it has a large angle of rotation. When the pitting
(30.02–7.39–8.00) (29.84–14.32–27.95)
diameter is large, it is easy for the component to form a plastic hinge at
D30T10E 1793.80 D58T6E 1796.21
(36.42–8.57–8.00) (30.09–15.08–19.98) the pitting corrosion even if the pitting depth is not large because the
D32T6E 2136.39 D60T6E 1996.77 local buckling deformation is large and the buckling deformation of
(21.26–5.42–9.13) (30.26–15.83–32.55) adjacent pits are connected. Further, the plastic hinges change the stress
D34T6E 2079.95 D60T7E 1572.70 state of the structure and reduce the number of constraints. Although the
(22.22–6.10–10.30) (37.50–19.25–32.55)
cross-section of uniformly corroded components is weaker, the cross-
D36T6E 2073.77 D60T8E 1403.17
(23.22–6.77–11.55) (44.74–22.65–32.55) section is uniformly distributed, the internal force and deformation of
D38T6E 2042.71 D60T9E 1260.29 the tube are evenly distributed, and it is not easy to form a local plastic
(24.17–7.47–12.87) (51.98–26.06–32.55) hinge. Although the uniformity of the cross-section of large-diameter
D40T4E 2223.52 D60T10E 797.10
pitting components is close to uniform corrosion, it remains uneven.
(15.44–5.16–14.32) (74.25–34.76–32.55)
This causes an uneven local stress and strain distribution of the com­
ponents, which leads to the appearance of plastic hinges.
bent along the depression. This implies that although pitting corrosion The class III failure type round pipe has a large slenderness ratio. The
can change the failure shape and load-carrying capacity of a compressed failure mode is transformed into overall buckling failure, wherein the
tube, its failure mode does not influence the main controlling factor. The strength-to-yield ratio is small and the bearing capacity level is
failure mode of the compressed tube is controlled by the slenderness extremely low. The gradual appearance of pitting corrosion on surface of
ratio of the tube. However, the appearance of pitting corrosion makes the round pipe leads to a considerable increase in the possibility of
the round tube more prone to instability failure when it is under the instability damage. Compared with Class II local buckling, there is no

Fig. 23. Influence of corrosion degree on the ultimate bearing capacity of components.

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Y. Yang et al. Applied Ocean Research 116 (2021) 102880

Fig. 24. Comparison of failure modes.

Fig. 25. Bending deformation and mechanical model of pitting corrosion and compressed pipe.

significant difference in the appearance of the overall buckling tube. that the evaluation index of the corrosion degree is determined. The
However, after the occurrence of Class II local buckling, the bearing main conclusions of the research are as follows:
capacity of the circular tube does not drop significantly. The change in (1) The experiments and numerical analysis results indicate that
the load and displacement is similar to that of the overall bending tube. pitting corrosion significantly reduces the ultimate bearing capacity and
The difference is that the bearing capacity of the overall buckling tube deformation capacity of the component although it has little effect on
decreases sharply, and the specimen bend quickly around the plastic the axial stiffness of the component. An increase in diameter can reduce
hinge, which causes damage to the specimen. Further, the diameter of the compressive strain in the pitting area and weaken the local
the circular tube does not change significantly during local buckling, concentrated stress of the structure so that the component transitions
and the deformation of the specimen is concentrated at the location from local corrosion to uniform corrosion. An increase in depth makes
where local buckling occurs. While the overall buckling specimen has a the local stress concentration of the component more serious, and it has
large area of depression, the diameter of the circular tube is greatly a greater effect on the bearing and deformation capacity of the
reduced, which results in a plastic hinge. component than on the diameter. Pitting corrosion distributed in the
middle position has the least influence on the load-bearing and defor­
4. Conclusion mation capacities of the component, while the pitting corrosion
distributed on one or both sides of the component have a greater effect.
Axial compression tests were conducted on circular pipes with (2) The failure mode of round pipe components is determined by its
different diameters, depths, and distributions of mechanically machined slenderness ratio and constraint conditions, and the effect of pitting
pitting corrosion with one-end hinged and one-end fixed to study the corrosion is very limited. When the failure mode of an intact round pipe
influence of pitting corrosion damage on the pressure properties and is strength failure, pitting corrosion causes local buckling which does not
failure modes of circular pipes. The influence mechanism of pitting lead to the instability failure of the entire component. The experiment
corrosion on the compressed circular pipe is analysed by comparing the and numerical analysis results indicate that almost all local buckling
failure modes and main mechanical parameters of each component, and occur at the location of the pitting corrosion. A change in pitting
the pressure mechanical model of the pitting circular pipe is proposed. corrosion caused by the failure mode of the round tube occurs under two
The experiments and appropriate numerical simulations results indicate scenarios: When the area of local damage caused by pitting corrosion is

13
Y. Yang et al. Applied Ocean Research 116 (2021) 102880

too large, it becomes a weak position of the specimen and forms a plastic Fang, Y.Z., Peng, Y.L., Yang, J.F., Gu, Q., Jiang, T., Jiang, H.Y., 2014. Experimental study
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addition, mechanical polishing is selected to generate pitting corrosion Wang, R.H., Fang, Y.Y., Dou, P.L., 2015. Research on ultimate bearing capacity of pile-
in this article, which has a certain gap with the formation of pitting column platform leg with pitting damage. Ocean Eng. 33 (03), 29–35.
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Declaration of Competing Interest Wang, X., Melchers, R.E., 2017. Long-term under-deposit pitting corrosion of carbon
steel pipes. Ocean Eng. 133, 231–243.
Wang, R.H., Ajit Shenoi, R., 2019. Experimental and numerical study on ultimate
The authors declare that they have no known competing financial strength of steel tubular members with pitting corrosion damage. Mar. Struct. 64,
interests or personal relationships that could have appeared to influence 124–137.
the work reported in this paper. Wang, Y.W., Cui, W.C., 2007. Research status and prospect of ship structural reliability
considering the influence of corrosion. J. Ship Mech. 2 (11), 307–320.
Xu, Q., Wan, Z.Q., 2010. Finite element method for shell with pitting corrosion. J. Ship
Acknowledgement Mech. 14 (1), 84–93.
Yao, Y., Yang, Y., He, Z., Wang, Y.P., 2018. Experimental study on generalised
constitutive model of hull structural plate with multi-parameter pitting corrosion.
This research was financially supported by the National Natural Ocean Eng. 170, 407–415.
Science Foundation of China (Grant No. 51979036). Zhang, J., Shi, X.H., Soares, C.G., 2017a. Experimental analysis of residual ultimate
strength of stiffened panels with pitting corrosion under compression. Eng. Struct. 12
(1), 70–86.
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