Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth
Polyethylene pipes are widely used in water supply, gas, and sewage systems due to their excellent mechanical properties. A slow crack growth is the primary fracture mechanism for the pipes under long-term internal pressures. If the creep loading is treated as a special case of fatigue loading, the...
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irk-123456789-1739972020-12-29T01:26:35Z Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth Luo, W.B. Liu, Y.P. Yin, B.Y. Li, Y. Liu, X. Научно-технический раздел Polyethylene pipes are widely used in water supply, gas, and sewage systems due to their excellent mechanical properties. A slow crack growth is the primary fracture mechanism for the pipes under long-term internal pressures. If the creep loading is treated as a special case of fatigue loading, the slow crack growth kinetics of polyethylene is defined in fatigue fracture tests at different stress ratios and extrapolated to creep crack kinetics. Linear elastic fracture mechanics concepts became the basis for predicting the creep lifetime of pressure-tight pipes subjected to various hoop stresses from extrapolated (synthetic) creep crack growth curves, and the prediction is in good agreement with the standard extrapolation, in accordance with ISO 9080. Полиэтиленовые трубы широко применяются в водоснабжении, системах газоснабжения и канализации благодаря их высоким механическим свойствам. Медленный рост трещин является основным механизмом разрушения полиэтиленовых труб под длительным внутренним давлением. Рассматривая нагружение при ползучести как особый случай усталостного нагружения, кинетика медленного роста трещин в полиэтиленовом материале определяется путем испытаний на усталостное разрушение при различных коэффициентах асимметрии цикла напряжений и экстраполируется на кинетику трещин ползучести. Исходя из теории линейноупругой механики разрушения долговечность при ползучести полиэтиленовой трубы под давлением, подверженной действию различных окружных напряжений, прогнозируется на основе синтетической кривой роста трещин ползучести, и прогнозы хорошо согласуются со стандартной экстрополяцией в соответствии с ISO 9080. 2018 Article Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth / W.B. Luo, Y.P. Liu, B.Y. Yin, Y. Li, X. Liu // Проблемы прочности. — 2018. — № 5. — С. 107-114. — Бібліогр.: 12 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/173997 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел Luo, W.B. Liu, Y.P. Yin, B.Y. Li, Y. Liu, X. Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth Проблемы прочности |
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Polyethylene pipes are widely used in water supply, gas, and sewage systems due to their excellent mechanical properties. A slow crack growth is the primary fracture mechanism for the pipes under long-term internal pressures. If the creep loading is treated as a special case of fatigue loading, the slow crack growth kinetics of polyethylene is defined in fatigue fracture tests at different stress ratios and extrapolated to creep crack kinetics. Linear elastic fracture mechanics concepts became the basis for predicting the creep lifetime of pressure-tight pipes subjected to various hoop stresses from extrapolated (synthetic) creep crack growth curves, and the prediction is in good agreement with the standard extrapolation, in accordance with ISO 9080. |
| format |
Article |
| author |
Luo, W.B. Liu, Y.P. Yin, B.Y. Li, Y. Liu, X. |
| author_facet |
Luo, W.B. Liu, Y.P. Yin, B.Y. Li, Y. Liu, X. |
| author_sort |
Luo, W.B. |
| title |
Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth |
| title_short |
Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth |
| title_full |
Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth |
| title_fullStr |
Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth |
| title_full_unstemmed |
Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth |
| title_sort |
creep lifetime assessment of pressure-tight pe100 pipes based on a slow fatigue crack growth |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2018 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/173997 |
| citation_txt |
Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow Fatigue Crack Growth / W.B. Luo, Y.P. Liu, B.Y. Yin, Y. Li, X. Liu // Проблемы прочности. — 2018. — № 5. — С. 107-114. — Бібліогр.: 12 назв. — англ. |
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Проблемы прочности |
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2025-07-15T10:52:17Z |
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2025-07-15T10:52:17Z |
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| fulltext |
UDC 539.4
Creep Lifetime Assessment of Pressure-Tight PE100 Pipes Based on a Slow
Fatigue Crack Growth
W. B. Luo,
a,b,1
Y. P. Liu,
a
B. Y. Yin,
a
Y. Li,
a
and X. Liu
a,b,2
a College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan, China
b Hunan Key Laboratory of Geomechanics and Engineering Safety, Xiangtan University, Xiangtan,
China
1 luowenbo@xtu.edu.cn
2 liux@xtu.edu.cn
Polyethylene pipes are widely used in water supply, gas, and sewage systems due to their excellent
mechanical properties. A slow crack growth is the primary fracture mechanism for the pipes under
long-term internal pressures. If the creep loading is treated as a special case of fatigue loading, the
slow crack growth kinetics of polyethylene is defined in fatigue fracture tests at different stress ratios
and extrapolated to creep crack kinetics. Linear elastic fracture mechanics concepts became the
basis for predicting the creep lifetime of pressure-tight pipes subjected to various hoop stresses from
extrapolated (synthetic) creep crack growth curves, and the prediction is in good agreement with the
standard extrapolation, in accordance with ISO 9080.
Keywords: slow crack growth, creep lifetime, stress intensity factor, stress ratio, polyethylene
pipe.
Introduction. Polyethylene (PE) is widely used in gas and water supply pipes, due to
its excellent mechanical properties. The long-term failure behavior of PE is of essential for
the lifetime and safety assessment of these PE pipes [1–5]. It is generally accepted that the
long-term failure behavior of pressurized PE pipes can be separated into three common
regions depending on the hoop stress in pipes as illustrated in Fig. 1 [1, 4]. In region A for
relatively high-stress levels, the pipe failure is mainly caused by the ductile deformation,
resulting in a large plastic region. In region B for medium and low hoop stress levels, the
pipe failure is manifested as a quasi-brittle slow crack growth (SCG), which is preceded by
the crack initiation stage, SCG failures usually happen during a relatively long period. In
region C, the pipe failure is mainly caused by the aging process, polymer degradation, and
stress corrosion cracking, showing stress independence.
© W. B. LUO, Y. P. LIU, B. Y. YIN, Y. LI, X. LIU, 2018
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 5 107
Fig. 1. Schematic illustration of the failure behavior of pressure-tight PE pipes.
1. Fundamental Model. Taking into account the actual pressure of PE pressure-tight
pipe, SCG is the critical failure mechanism of pressurized PE pipes and refers to the most
relevant damage in the pipes. Based on this fact, the range of the plastic zone is very small
and only presents in the vicinity of the crack tip. Therefore, SCG can be described with
linear elastic fracture mechanics (LEFM). In LEFM, the stress distribution near the mode I
crack tip is represented by the stress intensity factor K [6]:
K F a� � � , (1)
where � is the remote tensile stress, a is the crack length, and F is the dimensionless
geometric factor which can be estimated numerically or can be found in the literature for
some simple geometries. For a single-edged crack with a b� 0.6, in which b is the width
of the specimen, whereas the geometric factor F is derived via Eq. (2) [7]:
F
a
b
a
b
a
b
a
� � �
�
�
�
�
�
�
�
�112 023 1055 2171 3038
2 3
. . . . .
b
�
�
�
4
. (2)
For pipes with an initial crack on the inner wall surface, considering the influence of
the crack shape change during the crack propagation, the geometric factor F under internal
pressure loading is reduced to the following form [2]:
F
a
s
a
s
a
s
� �
�
�
�
�
�
�
�
�
�
03417 00588 00319 01409
2
. . . .
�
�
3
, (3)
where s is the pipe wall thickness.
The crack growth behavior under static loading, namely creep crack growth (CCG)
behavior, of polymer materials, is usually defined by a curve of da dt versus K in the
double logarithmic coordinate system, as shown in Fig. 2. The curve can be subdivided into
three regions: in region I, there exists a threshold value for K , below which the creep crack
is arrested, and for K above the threshold value, the CCG rate decreases with the rising K .
In region III, the creep crack grows in an acceleration mode with increased K . In region II,
the crack exhibits a stable growth: the log-log relationship between da dt and K possesses
a linear correlation, which can be expressed by the power law of Paris and Erdogan [8]:
W. B. Luo, Y. P. Liu, B. Y. Yin, et al.
108 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 5
Fig. 2. Scheme of the crack growth rate curve under static loading [2].
da
dt
CK m
� , (4)
in which, the parameters C and m are material constants.
According to creep and long-term fracture approach, the crack growth process under
static loading is a very long-term period ranging from several years to several decades.
Thus, an accelerated characterization method is necessary [9–12]. According to [1], fatigue
crack growth (FCG) tests under various stress ratios can be used to quickly predict the
creep failure lifetime of PE pipes under static loading as illustrated in Figs. 3 and 4. The
critical point in this extrapolation approach is that the creep loading of a material can be
considered as a special case of fatigue loading when the stress ratio R � 1. In Fig. 3, for the
fatigue tests of PE specimen with an initial crack, R is the ratio of the minimum load to
maximum one. In the case of static loading condition, R is equal to 1. According to the
extrapolation methodology in Fig. 4, the FCG curves at different R are acquired through
corresponding fatigue tests (left diagram) and transformed into the K Rmax � curves (right
diagram); then, the maximum stress intensity factors at various constant crack growth rates
are extended to R � 1 (static loading) via appropriate mathematical methods (right
diagram); finally, the extrapolation results are transformed back into the kinetics diagram to
generate a “synthetic” CCG curve (left diagram). Furthermore, the material parameters C
and m under static loading can be determined and used for lifetime prediction of
pressure-tight pipes using Eq. (5) by considering the relevant stress intensity factors of a
growing crack in a pipe with an initial crack on its inner surface:
t
CK
daf m
a
a f
� �
1
0
, (5)
where a0 is the initial crack length and a f is the crack length at failure.
2. Experiment. The dumbbell-shaped tensile specimens with a 2 mm long
prefabricated crack are cut from the PE100 pipes for water supply, which are provided by
Akan Enterprise Group (Shanghai) Co. Ltd. The shape and geometrical dimensions of the
specimen are shown in Fig. 5, and the specimen thickness is 4 mm. Fatigue tests are carried
out on a CARE-M3000 dynamic electromagnetic force test machine at 20�C (see Fig. 6). A
Rapid Analysis of the Creep Lifetime ...
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 5 109
Fig. 3. Crack tip stress field for static and cyclic loads at various R-ratios [1].
sinusoidal tension is applied to specimens under a force-controlled mode with a maximum
tensile force of 500 N, namely, 12.5 MPa, and various stress ratios (R � 0.1, 0.2, 0.3, and
0.4) at a frequency of 8 Hz. The crack profiles are sequentially recorded in the real
time-scale by a CCD camera and automatically identified by a MATLAB image processing
program developed by the authors. Figure 7 shows an example of the FCG process for
R � 0.1 and the corresponding crack tip/lip images, with which the crack lengths and
growth rates are determined by the image processing.
110 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 5
W. B. Luo, Y. P. Liu, B. Y. Yin, et al.
Fig. 4. Methodology to generate synthetic SCG curves for static loading based on cyclic tests [1].
Fig. 5. The geometry of the test specimen (unit: mm).
Fig. 6. Experiment system.
3. Results and Discussion. It can be seen from Fig. 7 that the crack grows gradually
and then suddenly loses its stability at some instant when the crack grows to approx. a half
width of the specimen, resulting in the total fracture. The fatigue lifetime t f and crack
length a f at fracture are listed in Table 1. The time to failure increases markedly with the
ascent of R-ratio. Nevertheless, it is noteworthy that the crack-tip plastic zone is very small
so that the LEFM is applicable for the crack growth analysis.
Figure 8 presents the fatigue crack length variation with time for R-ratios of 0.1, 0.2,
0.3, and 0.4, respectively. It can be also seen in Fig. 8 that the crack grows very slowly and
the shape of curves is just like a “stair” at the initial stage. It is obvious that the FCG is
ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 5 111
Rapid Analysis of the Creep Lifetime ...
T a b l e 1
The Fatigue Lifetime and the Crack Length at Fracture
R t f , s a f , mm
0.1 14,790 3.9754
0.2 24,960 3.7983
0.3 84,990 4.0554
0.4 170,520 2.9426
Fig. 7. FCG process and the corresponding crack tips/lips for R � 0.1.
Fig. 8. FCG curves for various stress ratios R.
discontinuous, which reveals that there is an incubation time for crack nucleation and
merging before the crack growth. After about 10,000 s or 80,000 cycles, the cracks begins
to grow more and more rapidly until a sudden failure.
From Fig. 8, crack growth rates (da dt) are calculated, and the corresponding stress
intensity factors (K max ) are determined via Eqs. (1) and (2). Figure 9a shows the da dt
versus K max curves for R-ratios of 0.1, 0.2, 0.3, and 0.4. It is seen that for a given K max ,
the crack growth rate decreases with the ascent of R-ratio. The obtained crack kinetic
curves in region II demonstrate that the relationship of da dt versus K max is approximately
linear in the log-log scale, following the power via Eq. (4). Hence, these crack kinetic
curves in Fig. 9a are linearly extrapolated to higher K max for each R-ratio, and the K max
values at given crack growth rates, such as 10 5� , 10 4� , and 10 3� mm/s, are obtained for
each R-ratio and plotted in Fig. 9b. It is obvious that the K max needed to keep constant
crack growth rate increases linearly with the rising log R, and the K max values for the
three constant crack growth rates at R � 1 are determined by extrapolation. These
extrapolation data are then re-plotted in Fig. 9a to produce the synthetic crack growth
kinetics, namely the CCG law. It can be seen that the extrapolations are in good agreement
with the power law of Eq. (4) with C � �
�192 10 7. and m� 3.61.
112 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 5
W. B. Luo, Y. P. Liu, B. Y. Yin, et al.
a
b
Fig. 9. Crack kinetics of PE100 at different R-ratios and extrapolation of “synthetic” CCG curve (a);
extrapolation of R-ratio dependence of SIF to R � 1.0 (b).
The creep failure time of the pressure-tight pipe is estimated for various hoop stress
values, as shown in Fig.10. Since there are no experimental failure time data for hoop
stresses below 10 MPa at room temperature due to the long time expectation up to several
decades, Fig. 10 only shows the long-term hydrostatic strength data, which exhibit a ductile
failure mode (Region A), up to 104 h. These were obtained from the internal pressure tests.
According to ISO 9080, the standard extrapolation method based on time-temperature
superposition is used to predict the ductile-brittle transition knee and the quasi-brittle
failure time under SCG mechanism (Region B), as shown by dashed lines in Fig. 10. The
prediction of the failure time via Eqs. (3) and (5) with two determined parameters C and
m is also given by the solid line in Fig.10. Here, a PE100 pipe with standard dimension
ratio (SDR) of 11 and diameter of 160 mm is considered, and the typical size of the initial
crack a0 in pipe is preset to be 0.1 mm, as observed experimentally in [4]. The predictions
in Fig. 10 for PE100 at 20� by the proposed method based on the LEFM concept and FCG
accelerated characterization are in good agreement with those provided by ISO 9080
standard extrapolation method.
Conclusions. In this study, the crack growth kinetics of PE material is investigated
under cyclic loads at various R-ratios. For the determination of the crack growth kinetics, a
method of measuring crack length is developed based on digital image technology. An
extrapolation concept for the assessment of CCG is applied for one kind of PE pipe. With
the “synthetic” CCG curve, lifetime prediction based on LEFM is possible. The result of
this study shows the residual service life of a PE pipe with an initial 0.1 mm-long crack is
estimated to exceed 50 years when the hoop stress is lower than 5.6 MPa,, and the validity
of the proposed extrapolation method is verified.
Acknowledgments. This work was supported by the National Natural Science
Foundation of China (11572275) and the Hunan Provincial Innovation Foundation for
Postgraduate, China (CX2017B309).
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Rapid Analysis of the Creep Lifetime ...
Fig. 10. Hoop stress vs. time to failure curves determined via internal pressure tests (dots) and
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Received 05. 03. 2018
W. B. Luo, Y. P. Liu, B. Y. Yin, et al.
114 ISSN 0556-171X. Ïðîáëåìè ì³öíîñò³, 2018, ¹ 5
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