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On the Prediction of Long-term Creep-Failure of GRP Pipes
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1
On the Prediction of Long-term Creep-Failure of GRP Pipes
in Aqueous Environment
R. M. Guedes1, Alcides Sá2, Hugo Faria2
1Departamento de Engenharia Mecânica e Gestão Industrial, Faculdade de Engenharia
da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal 2INEGI, Instituto de Engenharia Mecânica e Gestão Industrial, Portugal
Abstract
The aim of this work was to study the long-term failure of GRP (Glass Fiber Reinforced
Polymer) pipes under the influence of moisture absorption. These pipes are used in
water transportation which has an important effect on the mechanical properties of the
polymeric matrix. The GRP pipes are usually tested under ring deflection or internal
pressure conditions. This study presents and analyzes experimental creep-rupture data
obtained from standard test methods under ring deflection conditions. This loading
configuration simulates in laboratory the conditions verified in a sub-soil installation.
The creep testing was carried out under constant dead weight on unconditioned and
preconditioned samples in a submerged condition. The diametrical deflection of
samples was measured periodically and the time to failure of each sample was recorded.
The main purpose of this work was to determine the short and long-term rupture
energies of GRP pipes and assess the influence of moisture preconditioning on those
values. The observed failure mode was always the same. It was concluded that the
energy at failure decreases with time. The influence of the preconditioning on the creep-
rupture of GRP pipes was considered negligible. Different time-dependent failure
models were described and used for long-term extrapolation of the experimental data.
The maximum strain at failure decreased about 12% from 0.1 to 1000 hours of creep
testing. Furthermore data extrapolation to 50 years predicts a reduction of strength of
about 60%, founded on the most conservative time-dependent failure criterion.
Keywords: GRP pipes; Creep rupture; Mechanical testing; Fracture; Energy.
2
1. Introduction
In recent years materials that possess high specific strength and specific modulus were
developed to fulfil the need for advanced lightweight structures. Fibre reinforced
plastics (FRP) have these characteristics, and are being used as primary as well as
secondary load carrying members in civil engineering structures. Consequently, the
development of testing procedures to predict the lifetimes of materials in extreme
service environments is becoming a high priority.
The problem tackle in this paper deals with durability issue which is usually associated
to different important fields of research. Those include viscoelastic effects, damage
initiation and propagation, environmental effects and glass-fiber stress corrosion. The
last case has been well studied and several models, based on fracture mechanics, have
been presented to model the propagation of a stress-corrosion crack in a glass fibre and
predict the time to failure in different environments [1-10].
High-performance polymer composites exhibit a time-dependent degradation in
modulus (creep or stress relaxation) and strength (creep rupture) as a consequence of the
viscoelasticity of the polymer matrix [11, 12]. One of the most important aspects of
long-term durability and dimensional stability of these materials is their long-term creep
behaviour. Prediction of long-term integrity of any polymeric composite structure
depends on the viscoelastic properties of these materials [11-13]. However, long-term
properties prediction of GRP pipes remains a difficult task because extensive long-term
mechanical tests on the components are required [14].
Yet the structural applications of composite materials in civil construction are becoming
more important. One major application is on rehabilitation in renewal of the structural
inventory, to repair or strengthen. The success of these applications has promoted the
development of new solutions based on FRP (Fiber-Reinforced Polymers). Although
these new products may promise a better mechanical performance on a long-term basis,
the lack of a historical record leads to overdesigned structures. The main reason is
because durability factors, usually determined after long-term experimental tests,
depend on each material system.
On the other hand the full comprehension of internal material changes from microscopic
scale up to the full structure length is far from being well known. The interaction
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between of different mechanisms acting at different scale levels is extremely complex
and not yet fully understood.
Glass fibre reinforced plastic pipes are composite constructions consisting of short
and/or long glass fibre and thermoset materials such as unsaturated polyester or
vinylester as their main components. These pipes are normally produced through
centrifugal casting and/or filament winding of long fibres. GRP pipes are an alternative
to traditional pipes in metallic materials where corrosion, weight and environmental
effects limit the use of this kind of materials. For this reason they are being widely used.
Their good specific mechanical properties deserve a special attention in several
applications. GRP pipes have applications in pressure pipeline as well as in drainage
sewerage piping systems. In these applications the pipe is in contact with various fluids
that, in some cases may have aggressive effects on the material components of the pipe
[12-15]. GRP pipes are frequently used in water transportation and it is widely
recognized that water as a pronounced effect on the mechanical properties and on the
structure of fibre reinforced polymer materials [16-20]. One of the most important
factors which affect the creep behaviour of these materials is moisture. Water penetrates
the resin and attacks the matrix, the reinforcement and the interface of several
composite materials [21]. Some of the hygrothermal aging effects are reversible like the
effect on Tg (reversible when the material dries) and others are not like the plasticization
of the matrix and post-cure reactions [18].
Farshad [22] performed diametrical compression creep tests on GRP pipes. Prior to
creep testing in submerged conditions the samples were conditioned in water at ambient
temperature. During the testing period, diametrical deflection of samples was measured
and the time to failure of each sample was recorded. The long-term tests showed that,
for the pipes tested, the strength corresponding to 1000 testing hours was about 60% of
the short-term strength. Moreover, extrapolation of the data to 50 years showed a
reduction of strength by about 55%.
Nishizaki [20] studied the effects of water on the durability of pultruded glass-fibre
reinforced polymers (GFRP) with vinylester resin for applications in normal air
conditions. Deterioration tests, including both immersion and atmosphere conditions at
various temperatures, were conducted to investigate the deterioration characteristics of
pultruded GFRP after being permeated by water. The bending strength of the GFRP was
reduced. The reductions in bending strength were larger in a 60ºC water immersion
4
condition compared to both 60ºC moist-atmosphere condition and a 40ºC water
immersion condition.
The purpose of the present work was to determine and compare lifetimes of GRP pipes
under various loading levels. The observed failure mode was always the same, fiber
breakage, and always localized in the same region. This fact allowed the calculation of
the local failure energy from the experimental data. This failure energy decreased as
lifetime increased and the influence of preconditioning was considered negligible.
Different time-dependent failure criteria were used to model the GRP lifetimes with
reasonable success. Data extrapolation to 50 years predicts a reduction of strength by
about 60%. Furthermore maximum strain at failure decreased about 12% from 0.1 to
1000 hours of creep testing.
2. Time-dependent failure criteria
As the computing power capabilities improve more complex micro-mechanical
models can be solved to predict the creep and creep rupture of real polymers and
polymer matrix composites. These local and direct analyses of the defects initiation and
growth have shown promising results [23]. This type of analysis has the advantage to
allow a deeper understanding of the mechanisms responsible for the rupture and the
creep-rupture. Nevertheless the global and homogeneous analysis, simpler to formulate
and solve, is still more appropriated for practical applications. One of the first
theoretical attempts to include time on a material strength formulation was developed
by Reiner and Weissenberg [24] for viscoelastic materials. Briefly, the Reiner-
Weissenberg criterion [24] states that the work done during the loading by external
forces on a viscoelastic material is converted into a stored part (potential energy) and a
dissipated part (loss energy). The criterion says that the instant of failure depends on a
conjunction between distortional free energy and dissipated energy, a threshold value of
the distortional energy is the governing quantity.
Let us assume that the unidirectional strain response of a linear viscoelastic material,
under arbitrarily stress σ(t), is given by the power law as,
( ) ( ) ( )0 1 0
0
nt t
t D t D dσ ττε σ τ
τ τ∂ −= + ∂
∫ (1)
5
where D0, D1, n are material constants; and τ0 represents the time unity (equal to
1second or 1hour or 1day, etc.).
The free stored energy, using Hunter [25] formulation, is given by
( ) ( ) ( ) ( ) ( ) ( ) 2 1 21 20 1 1 2 0 0
0 1 2
1 1 2
2 2
nt t
s
tW t t t D t D d d
σ τ σ ττ τε σ σ τ ττ τ τ
∂ ∂ − −= − − ∂ ∂ ∫ ∫ . (2)
The total energy is defined as,
( ) ( ) ( )
0
t
tW t dε τ
σ τ ττ
∂=
∂∫ . (3)
Accordingly these time-dependent failure criteria [26] predict the lifetime under
constant load, as a function of the applied load σ0 and the creep strength under
instantaneous condition σR:
Reiner-Weissenberg Criterion (R-W), states that ( ) 20
2s R
DW t σ≤ ,
11 10
0 1
1 11
2 2
nnf nn
t D
Dτ γ = − −
. (4)
Maximum Work Stress Criterion (MWS), states that ( ) 20
2t R
DW t σ≤ ,
1 1
0
0 1
1 11
2
nf n
t D
Dτ γ
= −
. (5)
Maximum Strain Criterion (MS), states that ( ) 0 Rt Dε σ≤ ,
1 1
0
0 1
11
nf n
t D
Dτ γ
= −
. (6)
Modified Reiner-Weissenberg Criterion (MR-W), states that ( ) ( )0
2t R
DW t tσ σ ≤
,
11 10
0 1
1 11
2 2
nnf nn
t D
Dτ γ = − −
. (7)
where 2 20 Rγ σ σ= .
Another possible approach is based on the kinetic rate theory of fracture. Based on this
Zurkov [27] used a simple relationship to predict lifetime of several different materials
(except for very small stresses) in terms of a constant stress level σ,
6
( )0 0expft t U kTγσ= − . (8)
where t0 is a constant on the order of the molecular oscillation period of 10-13s, k is the
Boltzmann constant, T is the absolute temperature, U0 is a constant for each material
regardless its structure and treatment and γ depends on the previous treatments of the
material and varies over a wide range for different materials.
3. Materials
The GRP pipes used on the experimental program were produced by centrifugal casting.
The pipes are composed by unsaturated polyester reinforced with fibreglass filled with
sand. The mechanical properties provided by the manufacturer are described on Table I.
Accordingly with the manufacturer the pipe wall is made up of three different major
layers, each one possessing different properties according to its functions. Moreover the
pipe wall is composed by an inner layer which provides the chemical resistance, by a
mechanical resistant layer, and a top coat. The specimens used in creep tests are
depicted in Figure 1.
Burn-off tests were made according to the standard procedure NP 2216 1988 on 10
specimens removed from the pipes in order to analyse the components and the structure
of the specimens. The structure of the pipes is heterogeneous and it is constituted by
roving, random matt, polyester resin and sand according to the values displayed on
Table II. Ten plies were observed each one composed by a sub-layer of roving in the
hoop direction and another sub-layer of random matt as depicted in Figure 2. The matrix
is composed of a mixture of polyester resin with sand particles of small size distributed
uniformly.
The glass transition temperature (Tg) of the composite was measured, using a DMTA
machine of the Polymer Laboratories®, as 106.5ºC (±3.4ºC) for the unconditioned
specimens. The glass transition temperature was identified as the peak of loss modulus
measured at 1Hz. The measured glass transition temperature of the conditioned
specimens in water at 50ºC was 100.8ºC (±8.7ºC).
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4. Methods
Prior to testing, samples were stored at room temperature of 20–25 °C and 50% relative
humidity. Care was taken to prepare and maintain the pipe samples free of scratches. A
number of selected specimens were conditioned in a container filled with tap water. The
hoop edges were not protected to prevent water ingress.
The creep tests were carried out following to the European standard EN 1227:1997 [28].
This standard is used to determine the long-term ultimate relative ring deflection under
wet conditions on glass-reinforced thermosetting plastics (GRP) pipes. The
experimental creep tests were carried out applying a dead weight to the specimen
submerged in water at room temperature. The deflection was measured periodically and
the failure time recorded. The test set-up is depicted in Figure 3a and 3b.
Creep tests were preformed on 18 unconditioned specimens using several load levels
(10 to 14 KN) [28]. Creep tests were also performed on specimens preconditioned in
water at 50ºC. After the preconditioning the specimens were tested in the same
conditions, i.e. submerged in water at room temperature. In Table III are listed all the
specimens tested, with the load level and the applied preconditioning conditions.
The deflection was measured with a deflection dial gauge with a precision of ±0.01mm.
Since the load was applied with a beam bar there were no local indentations to account
for.
5. Data reduction schemes
The observed failure mode was always the same, fibre breakage, and always in the same
points, as shown in Figure 4. This is in strict accordance with the theoretical analysis
[29] which predicts the higher tensile stress in such points. Therefore these points were
considered the critical points where the failure always takes place, under ring deflection.
Consequently all the stress-strain analysis developed is focused in those points.
Furthermore it is assumed that the material is linear viscoelastic until failure to keep the
calculations simple.
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In this particular case, a very flexible structure, large defections occur well before
failure takes place. Therefore the circumferential elastic modulus E, function of the
applied load P and the maximum deflection W of a pipe with an average radius R and
with a thickness h, must be calculated taking into account the geometrical nonlinearity
[29]:
max
max
Eσε
= , (9)
where
( )2
1 121max P
bR h Rσ
π
= ± +
,
( )( )2
4
8max
hWRRW
επ ξ
≅ ±− +
with ( ) ( )22 21208 128
9
WW
Rξ π α π ≅ − + −
and α π= ,
which reduces to the linear relationship when 0α = . In Figure 5 is depicted the strain
calculated using the linear and the non-linear relationships against the strain measured,
using an electrical strain gauge. One should note that the strain gauge fail before the
pipe collapsed. It is clear that the non-linear relationship must be used, almost from the
beginning, to obtain the correct maximum strains from the maximum deflection.
The strain gauges were only used in static testes. They were placed in the tensile
stresses sides where the maximum strain was verified, i.e. along the loading line. This
was done to check the accuracy of the equation (9).Five specimens were tested with
strain gauges with a good repeatability.
During the creep test the load is prescribed as constant and the maximum deflection
( )W t becomes time dependent as well the modulus ( )E t which can be obtained from
the previous elastic solution assuming a linear viscoelastic behavior and applying the
Elastic-Viscoelastic Correspondence Principle [30] as
( ) ( )max
max
E tt
σε
= . (10)
In fact this is not the real relaxation modulus but the reciprocal of creep compliance.
The relaxation modulus can be obtained using the simple approach suggested by Park et
al. [31]. However in this case the differences were negligible. Finally the creep
compliance is given by
9
( ) ( ) 0 10
1n
tD t D D
E t τ
= = +
, (11)
where D0, D1, n are material constants; and τ0 represents the time unity (equal to
1second or 1hour or 1day, etc.). This expression is usually designated as the power law
and allows the creep compliance representation of many polymers and polymer based
composites materials in a time scale of practical interest [32].
6. Experimental results
In this section the creep and lifetimes results are presented. The objective is to assess the
long-term prediction methodologies and the hygrothermal effects due to the
preconditioning. Since the material presents initial stiffness variability, of ±0.61 GPa for
unconditioned specimens and ±0.75GPa for the conditioned specimens in water at 50ºC,
the creep compliance was normalized to the initial value D0 calculated at 0.01hours
which corresponds to initial creep deflection. This was done to compare more easily the
creep data.
Creep tests
Unconditioned specimens
The measured average initial modulus of the unconditioned specimens was 10.48
(±0.61) GPa. The circumferential normalized creep compliance of some unconditioned
specimens against the power law equation is depicted in Figure 6.
Specimens preconditioned at 50ºC
The average initial circumferential modulus of the preconditioned specimens in water at
50ºC was 10.05 (±0.75) GPa. The circumferential normalized creep compliance of some
specimens preconditioned against the power is depicted in Figure 7. It seems reasonable
to assume that the creep compliance of the preconditioned specimens follow the same
power law used to describe the creep compliance of the unconditioned specimens.
Although some objections may be pointed against this assumption, it has the advantage
to simplify the subsequent calculations and analysis.
10
Lifetime results
The creep tests were initiated using a loading rate as slow as necessary to obtain the
desired creep load in 3 min (±0.5 min). Under creep loading conditions the short-term
(<0.1 h) failures take place at stress levels close to 165MPa.
Therefore the reference value of the creep strength was chosen to be165MPa. In Figures
8 and 9 are represented the maximum applied stress and the strain at failure,
respectively, against the lifetime. Three preconditioned specimens, indicated by arrows,
did not fail after 5000 hours when the test was stopped.
The Zurkov type relationship [27] fits reasonably the experimental data with a squared
correlation coefficient of 0.72. The “low” value of the correlation coefficient reflects the
scatter of the creep rupture data, which is typical of creep rupture in general. The data
extrapolation for 50 years gives a maximum stress limit of 103 MPa. This represents a
strength reduction of 37% compared against the reference strength (165MPa). Although
slightly different curves were determined for the unconditioned and preconditioned
specimens as depicted in Figure 8, the influence of the preconditioning on lifetime was
considered negligible. The main effect was a drop of 4% in the initial modulus. A
decrease on the maximum strain at failure was detected, 12% after 1000 hours and, by
extrapolation, 17% after 50 years.
7. Discussion of results
Both conditioned and unconditioned creep specimens were tested under the same load
and environment conditions. When comparing the instantaneous modulus (elastic) and
the creep compliance we can conclude that the preconditioning caused a 4% drop of the
elastic modulus but did not affect the viscoelastic behaviour. Nevertheless the reduced
number of preconditioned specimens tested as well the applied reduced stress range is
no sufficient to draw definitive conclusions.
The lifetime expressions previously summarized depended on the viscoelastic properties
and on the creep strength under instantaneous condition. Moreover these expressions
depend on the rate between the viscoelastic and elastic compliance parameters (D1/D0).
From the creep tests this ratio was determined as 0.030. However, for the lifetime
11
prediction, it was verified that the ratio D1/D0 should be larger, i.e. 0.08. One
explanation for this can be attributed to the linear viscoelastic assumption. Since the
stress state is not uniform, the stress influence over the creep compliance is averaged
when linear viscoelastic behaviour is presumed. Therefore one should expect higher
creep compliance values at the critical points, since the stress acts as an accelerator
factor on the viscoelastic behaviour [32]. The creep strength under instantaneous
condition was determined to be 165MPa. The viscoelastic parameters are summarized in
Table IV.
If we consider the normalized rupture free energy as
20
2
ff
R
ww
D σ= , (12)
and the normalized applied stress as
00
R
σσσ
= , (13)
then it is possible to rewrite all the previous criteria in an non-dimensional form.
Reiner-Weissenberg Criterion (R-W):
1fw = . (14)
Maximum Work Stress Criterion (MWS):
( )2 102 1 2n n
fw σ −= + − . (15)
Maximum Strain Criterion (MS):
( ) ( )20 02 1 2 2n n
fw σ σ= − + − . (16)
Modified Reiner-Weissenberg Criterion (MR-W):
0fw σ= . (17)
If we plot the experimental data against the theoretical values, calculated using the
values in Table IV, it became quite clear that the R-W criterion is not appropriated for
the present case, as depicted in Figure 10.
In Figure 11 are depicted the theoretical lifetime predictions against the experimental
results. As it was expected from the previous analysis the R-W criterion is not well
suited for this case. All the other models follow quite well the experimental data. Table
V summarizes the lifetime predictions for each theoretical approach. The maximum
strain criterion is more conservative when compared against the other models.
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In this case it seems appropriate to apply the MS criterion. The criterion can be
rewritten as follows
1
max 0 0
0 1 0
f nt D
D
ε στ σ −=
. (18)
Now using the MS criterion and considering a 50 year (438,000 hours) lifetime
prediction we obtain 79MPa and 68MPa for εmax=0.0160 and for εmax =0.0135,
respectively, see also Figure 12. These lifetime predictions imply a creep strength
reduction between 52 and 59 %, respectively.
Before closing this section something more has to be said about the preconditioned
effect. Although the preconditioning in water at 50ºC appeared to be irrelevant some
extra phenomena may occur. One phenomenon developed at high temperatures is the
post-curing process and the other is the acceleration of the ageing effect. In both cases
the outcome would be an increase of stiffness and strength. This in part would
compensate the stiffness decrease due to the water uptake. However neither the post-
curing process nor the ageing effect were measured or taken into account in this study.
8. Conclusions
Creep tests were performed on GRP pipes in order to determine the long-term creep
compliance and creep-rupture. It was observed that preconditioning in water at 50ºC
had a small influence on the initial stiffness of GRP pipes, a decrease of about 4%.
Furthermore the creep and creep-rupture behaviour in aqueous environment of
preconditioned and unconditioned GRP pipes under lateral deflection was very similar.
Not quite surprisingly Zurkov [27] type relationship was able to fit the entire lifetime
experimental data with a reasonably correlation. Other lifetime models based on
different time-dependent failure criteria, which depend on the viscoelastic properties
and on the creep strength under instantaneous conditions, were briefly presented and
successfully applied, with the exception of Reiner-Weissenberg criterion. Moreover it
was verified that the maximum strain criterion was the most conservative criterion of
all. On that ground and considering a 50 year lifetime, a strength reduction of about
60% was predicted.
Acknowledgements
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The research hereby presented was supported by Fundação para a Ciência e Tecnologia
(Ministério da Ciência e do Ensino Superior) through project POCTI/EME/47734/2002.
The authors acknowledge the support of Dr. João Rodrigues (INEGI) who performed
and analyzed all the burn-off tests.
References
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Figure Captions
Figure 1 – Creep specimens.
Figure 2 – Detail of the ply reinforcement composed of roving in the hoop direction and
random matt.
Figure 3 – Creep test apparatus; a) during load calibration and b) submerged in a tank
during creep tests.
Figure 4 – The GRP pipe failure mode under ring deflection.
Figure 5 – Comparison between the measured strain and the strain calculated using
linear and non-linear relationships.
Figure 6 – Normalized creep compliance of GRP pipes under ring deflection, without
preconditioning.
Figure 7 – Normalized creep compliance of preconditioned GRP pipes under ring
deflection.
Figure 8 – Lifetime GRP pipes under ring deflection versus the maximum applied
stress.
Figure 9 – Lifetime GRP pipes under ring deflection versus the maximum strain at
failure.
Figure 10 – Normalised free energy at failure versus normalised stress for the
experimental data and theoretical models.
Figure 11 – Experimental lifetime and theoretical predictions for GRP pipes under ring
deflection.
Figure 12 – Lifetime prediction of GRP pipes under ring deflection using the maximum
strain criterion, considering two extreme values.
17
List of Tables
18
Table I – Properties of the pipes provided by the manufacturer.
EHoop (MPa) ERadial (MPa) ELongitudinal (MPa)
10547 3808 3808
19
Table II – Relative composition of GRP pipes for mass content (%).
Constituents Average values Standard deviation
Polyester (matrix) 35.65 0.41
Roving 10.41 1.51
Matt 12.66 0.88
Sand 41.28 2.54
20
Table III – Creep specimens with the correspondent load and preconditioning.
Specimen Nº Preconditioning Load (N)
C36 No 12196
C46 No 11831
C47 No 12087
C55 No 12400
C56 No 12400
C38 No 10643
C50 No 10380
C52 No 10431
C39a No 12719
C48 No 12830
C49 No 12692
C51 No 13638
C57 No 13088
C39b No 13970
C45 No 14420
C58 No 13988
C53 No 11411
C54 No 11139
C88 50ºC during 4920 hours + 3000 hours at dry air 11096
C89 50ºC during 4920 hours + 3000 hours at dry air 11096
C92 50ºC during 4920 hours + 3000 hours at dry air 11353
C90 50ºC during 7112 hours 9865
C91 50ºC during 7112 hours 10567
C93 50ºC during 10800 hours 9084
C94 50ºC during 10800 hours 10059
C95 50ºC during 10800 hours 11358
21
Table IV – Viscoelastic properties and strength under instantaneous conditions.
D1/D0 D1/D0* n σR
MPa 0.030 0.080 0.200 165 *Value used for lifetime prediction
22
Table V – Lifetime theoretical predictions.
Failure Criteria
Maximum Stress 1000 h 1 year 50 years
R-W 146 138 119 MR-W 130 116 86 MSW 129 117 93 MS 125 110 79
23
List of Figures
24
12mm
R250mm
300mm
Figure 1 – Creep specimens.
25
Figure 2 – Detail of the ply reinforcement composed of roving in the hoop direction and
random matt.
26
(a) (b)
Figure 3 – Creep test apparatus; a) during load calibration and b) submerged in a tank during creep tests.
27
Figure 4 – The GRP pipe failure mode under ring deflection.
28
0
50
100
150
200
250
300
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04
Strain
Str
ess
(MP
a)
Strain gauge
Linear calculation
Non-linear calculation
Strain gauge failure
Pipe failure
Figure 5 – Comparison between the measured strain and the strain calculated using
linear and non-linear relationships.
29
0.90
1.00
1.10
1.20
0.01 0.1 1 10 100 1000 10000
Time (hours)
Cre
ep C
ompl
ianc
e C
(t)/
C0 Not Precond.( ) 1
0 0 0
1n
D t D t
D D τ
= +
11 0 0 00.030, 0.20, 1h, 110475MPaD D n Dτ −= = = =
Figure 6 – Normalized creep compliance of GRP pipes under ring deflection, without
preconditioning.
30
0.90
1.00
1.10
1.20
0.01 0.1 1 10 100 1000 10000
Time (hours)
Cre
ep C
ompl
ianc
e C
(t)/
C0
Precond.( ) 1
0 0 0
1n
D t D t
D D τ
= +
11 0 0 00.030, 0.20, 1h, 110050MPaD D n Dτ −= = = =
Figure 7 – Normalized creep compliance of preconditioned GRP pipes under ring
deflection.
31
60
100
140
180
0.01 0.1 1 10 100 1000 10000 100000 1E+06
Time to Failure (hour)
Str
ess
(MP
a) Not Precond
Precond.
Zurkov (Not Precond.)
Zurkov (Precond.)
15624.09
00
e , 1 hour, 0.72ftσ
τ ρτ
−
= = =
15324.87
00
e , 1 hour, 0.72ftσ
τ ρτ
−
= = =
Figure 8 – Lifetime GRP pipes under ring deflection versus the maximum applied
32
0.000
0.004
0.008
0.012
0.016
0.020
0.01 0.1 1 10 100 1000 10000 100000
Time (hour)
Max
. Str
ain
at F
ailu
re
PrecondNot Precond
0.0108
2max 0
0
0.0154 , 1 hour, 0.257tε τ ρ
τ
−
= = =
Figure 9 – Lifetime GRP pipes under ring deflection versus the maximum strain at
failure.
33
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
Normalised Stress
Nor
mal
ised
Fai
lure
Fre
e E
nerg
y
Experim.R-WMR-WMSWMS
Figure 10 – Normalised free energy at failure versus normalised stress for the
experimental data and theoretical models.
34
60
100
140
180
0.01 0.1 1 10 100 1000 10000 100000 1E+06
Time to Failure (hour)
Str
ess
(MP
a)
Not Precond
Precond.R-W
MR-W
MSW
MS
Figure 11 – Experimental lifetime and theoretical predictions for GRP pipes under ring
deflection.
35
60
100
140
180
0.01 0.1 1 10 100 1000 10000 100000 1E+06
Time to Failure (hour)
Str
ess
(MP
a)
Not Precond
Precond.
εmax=0.0135
εmax=0.0160
Figure 12 – Lifetime prediction of GRP pipes under ring deflection using the maximum
strain criterion, considering two extreme values.
