Thin-Walled Structures 131 (2018) 347–359
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Thin-Walled Structures
journal homepage: www.elsevier.com/locate/tws
Full length article
Evaluating mechanical performance of GFRP pipes subjected to transverse
loading
T
⁎
Roham Rafiee , Mohammad Reza Habibagahi
Composites Research Laboratory, Faculty of New Sciences and Technologies, University of Tehran, North Karegar St., Tehran 1439957131, Iran
A R T I C LE I N FO
A B S T R A C T
Keywords:
Composites
Pipes
Theoretical modeling
Finite element analysis
Experimental analysis
Transverse loading
The main objective of this research is to investigate the damage progression and the failure mechanism of GlassFiber Reinforced-Plastic (GFRP) pipes subjected to compressive transverse loading. An experimental study is
performed to observe the level of diametric deflection where failure takes place under transverse loading and
also to monitor experienced failure mode. Then, conducted experimental study is simulated in commercial finite
element software taking into account both interlaminar and intralaminar failure modes, simultaneously.
The degree to which the pipe can withstand diametric deflection without experiencing any failure mode is
extracted. Then, appropriate in-plane failure criteria are chosen for identifying the onset of in-plane failure mode
while cohesive approach is employed for identifying the initiation of delamination as the out-of-plane failure
mode. Results of numerical simulation reveal that the liner is debonded from its adjacent hoop layer at 27%
diametric deflection which is in a reasonable agreement with experimentally observed 31%. Moreover, the
magnitude of the reaction force at 5% diametric deflection is obtained as 1242 N which is in a good agreement
with experimentally measured 1225 N. Therefore, a satisfactory level of accuracy is achieved in constructed
model implying on the appropriate modeling of damage progression. Finally, a parametric study is conducted to
investigate the influence of various effective parameters on the pipe resistance level against transverse loading
wherein neither in-plane nor out-of-plane failure is experienced.
1. Introduction
Glass-Fiber Reinforced Polymer (GFRP) pipes are increasingly utilized in the infra-structure industries because of various benefits including but not limited to light weight, strength, corrosion resistance,
extended durability against environmental issues and mechanical
loadings. Moreover, the design architecture of GFRP pipes can be tailored and thus a wide range of properties suitable for various applications is achievable. The unique characteristics of GFRP pipes have inspired the confidence for their applications in various oil, gas, water
and waste-water piping systems.
From installation point of view, GFRP pipes are classified into
aboveground and underground or buried pipes. Dictated by normative
standards, GFRP pipes are practically examined from various aspects
under the quality control program. The main design constraints of
GFRP pipes are categorized into internal failure pressure, longitudinal
tensile strength, circumferential tensile strength and apparent pipe
stiffness [1,2]. Buried pipes tend to ovalize under the effect of installation and service loads and thus the pipe stiffness parameter becomes more prominent for designing buried pipelines.
⁎
The pipe stiffness indicates the degree to which the pipe can tolerate
ovality under transverse loading without experiencing any failure. Pipe
stiffness defines the ability of pipe to withstand not only against external transverse loading but also negative internal pressure [3].
Classified as an structural property, the apparent pipe stiffness
(Kpipe) is proportional to the elastic modulus of pipe along circumferential/hoop direction (EH) and cubic power of cross section thickness
and it is inversely proportional to the cubic power of the pipe diameter
(D3) [4]:
EH I
E I
= 53.77 H3 = Kpipe
0.14877R3
D
(1)
where I is the second moment of area in the longitudinal direction per
meter length (I/L) with respect to the pipe neutral axis. The schematic
presentation of pipe stiffness is presented in Fig. 1.
Revealing the resistance of the pipe against transverse loading, the
pipes shall have sufficient strength to withstand certain amount of decrease in vertical diameter without any indication of structural damage
as evidenced by visible damage or interlaminar separation.
Consequently, as a key factor in designing buried pipes, the mechanical
Corresponding author.
E-mail address: Roham.Rafiee@ut.ac.ir (R. Rafiee).
https://doi.org/10.1016/j.tws.2018.06.037
Received 10 March 2018; Received in revised form 24 June 2018; Accepted 28 June 2018
Available online 17 July 2018
0263-8231/ © 2018 Elsevier Ltd. All rights reserved.
Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
Fig. 1. Description of pipe stiffness [5].
structural layers to increase the pipe thickness as a cost-effective
method for pipe stiffness enhancement.
Except theoretical studies on the stress analysis of GFRP pipes
subjected to this specific load case, no study has been conducted on
evaluating failure of GFRP mortar pipes. Moreover, the influence of
winding angle and also the core layer on whether postponing or expediting the occurrence of delamination as the most dominant failure
mechanism have not been studied.
The analysis of pipe mechanical response to transverse loading is a
vital task establishing the confidence toward the safe performance of
GFRP mortar pipes in underground applications. The main objective of
this paper is to evaluate the influence of GFRP mortar pipe ovalisation
on its structural integrity by means of finite element (FE) modeling.
Firstly, an experimental study is conducted on a GFRP mortar pipe as a
case study to determine the pipe resistance to diametric deflection
against external transverse loading. Then, the FE model of a GFRP
mortar pipe is built and subjected to the same loading condition of
experimental program. Both intralayer and interlayer failure are taken
into account at the same time and the damage progression is analyzed.
Validating the constructed model, the obtained results from FE modeling and also experimental observation are compared. Finally, a
parametric study is performed to evaluate the influence of fiber volume
fraction, winding angle, core thickness and the sequence of wounded
layers on both in-plane failure and also delamination of the pipe against
transverse loading.
performance of layered GFRP pipes against compressive transverse
loading is required to be analyzed.
In contrast with other conducted investigations focusing on the
mechanical behavior of GFRP pipes subjected to internal hydrostatic or
axial loading [6–35] very limited studies have been done on analyzing
the performance of GFRP pipe subjected to transverse loading [36–42].
Xia et al. [36] presented two methods to analyze the stresses and
deflections of multi-ply cylindrical pipes under transverse loading
conditions. They conducted an experimental investigation too and
compared it to the results of theoretical calculations. They noticed that
the values obtained from the experimental results fall between the
values reported by theoretical calculations. Guedes [37] presented a
method to analyze the stresses and deflections of transversely isotropic
laminated cylindrical pipes, under transverse loading conditions. He
developed an approximate 2D solution based on the assumption that
the ratio of each ply thickness to its middle surface radius is negligible
compared to unity. He has also analyzed underground GFRP pipe under
transverse loading. He noticed that the relation between the maximum
deflection and the maximum hoop strain was no longer linear as predicted by the small deformation theory. So a simple approach using
deformation components based on finite deformations theory was
proposed in his study [38]. Farshad and his co-worker [39,40] reported
the results of long-term test on glass reinforced plastic pipe ring samples
under wet conditions in their contribution. Samples were subjected to a
range of diametric compression forces by series of loading devices. The
creep test was carried out under constant dead weight in a submerged
condition. Faria [41] focused on the experimental and numerical analyses of GFRP pipes under ring compressive loading. short- and longterm experimental tests as well as numerical simulations were performed to investigate the occurrence of delamination. Tse et al. [42]
developed closed-form solutions for the spring stiffness of mid-surface
symmetric, filament wound, composite circular ring under unidirectional loading. A 3D finite element analysis has also been applied to
their study. Results show that FEA prediction of stiffness is always
higher than the theoretical result. Furthermore, relations between the
spring stiffness and the winding angles and geometry of the composite
ring are considered and discussed in their study.
A lack of sufficient investigations on evaluating the mechanical
performance of GFRP pipes under transverse loading is loudly noticeable in literature [43]. As a normal practice among industrial producers
of GFRP pipes for the purpose of producing thicker and also economical
pipes, an impregnated sand layer with resin is incorporated in between
Fiber-Reinforced Polyester (FRP) layers as a core layer. These GFRP
pipes are referred to as GFRP mortar pipes [1]. From installation point
of view, thicker pipes are required for underground applications. On the
other hand, the required layers of GFRP which can sufficiently and
appropriately accommodate internal pressure, results in a thin pipe
cross-section. Therefore, a sand/resin layer is incorporated into the
2. Experimental study
According to ASTM D2412-02 [3], the resistance of the pipe against
compressive transverse loading is examined using an experimental
procedure known as parallel-plate loading.
2.1. Materials and test specimens
A GFRP mortar pipe with diameter of 500 mm is chosen as a case
study in this research. A small piece of pipe with the length of 300 mm
was cut from the full length of a GFRP mortar pipe as the test specimen.
The pipe was produced using discontinuous filament winding process.
The wall construction of the investigated GFRP mortar pipe consists of
liner layer and structural plies. The inner layer is called liner and it is
produced on cylindrical mould. This layer comprises stitched glass fiber
(450 g/m2), surface mat (30 g/m2) and unsaturated polyester resin with
the approximate thickness of 1.51 mm. The liner prevents structural
layers to be in direct contact with the fluid inside the pipe. As a GFRP
mortar pipe, the structural plies contain hoop and cross FRP layers and
also a core layer. A bundle of E-glass direct roving containing 42 strands
with the bandwidth of 180 mm is impregnated with unsaturated
polyester resin and then wound around the liner layer fabricating hoop
348
Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
where F is applied compressive load per length at 5% diametric deflection denoted by ∆y . Substituting the amounts of measured load and
diametric deflection values into Eq. (1), the pipe stiffness is obtained as
163.3 KPa.
In the next stage, the test continued by increasing the applied
compressive load to the deflected specimens till the 10% and 20%
diametric deflections and no evidence of failure is observed.
The loaded specimen and testing apparatus at different stages of 5%,
10% and 20% diametric deflections are shown in Fig. 3.
Although the test is required to be terminated at the diametric deflection of 20% in accordance with ASTM D2412-02 [3], the test continued by increasing the amount of applied compressive loading. It was
observed that in 31% of diameter deflection, delamination occurred at
the interface of liner and adjacent hoop layer and immediately after
that all layers separated from each other. It should be mention that the
value of compressive force at this stage was measured as 7078 N. This
stage is illustrated in Fig. 4 and the initiation of delamination is evident
by naked eye.
Table 1
Mechanical properties of constitutive materials in investigated GFRP mortar
pipe.
Young's modulus [GPa]
Shear modulus [GPa]
Poisson's ratio
Tensile strength [MPa]
Compressive strength [MPa]
Density [gr/cm3]
Weight fraction [%]
Glass fiber
Polyester resin
Silica sand
70
26.89
0.22
1970
–
2.56
59.5%
3.5
1.32
0.33
78
130
1.15
31.1%
10
3.5
0.39
–
–
2.65
9.4%
The weight of pipe was measured as 160.3 kg after complete accomplishment of
curing process.
and cross FRP layers. The weight of roving in gram per kilometer is
known as TEX which is 2400 for the used E-glass direct roving in
production process [18]. The core layer is an impregnated sand filler
with unsaturated polyester resin ply placed between the FRP layers as a
sandwich-like structure. The ply configuration of the investigated pipe
is [90/ ± 60.19/Core/ ± 60.192/90]. The total thickness of the pipe
is measured as 6.07 mm and the thickness of each cross (i.e. ± 60.19),
each hoop and core layers are 0.88, 0.38 and 1.16 mm, respectively.
Mechanical properties of the constitutive materials employed for the
production of the pipe is presented in Table 1 according to the datasheet of materials suppliers. Characterization of the constituent contents of investigated pipe is performed according to the procedure G
and method I of ASTM D 3171 [44]. Three samples were taken from the
pipe and the weight fractions of the fiber, resin and sand were measured
and reported in Table 1.
Cross section of the aforementioned pipe and its corresponding dimensions is schematically illustrated in Fig. 2.
3. Finite element modeling
In this section, the conducted experiment in the preceding section is
simulated numerically using Abaqus/CAE commercial finite element
(FE) package [45].
3.1. Model preparation
Following the geometrical specifications reflected under Section
(2.1), a cylindrical model with the average diameter of 500 mm and
length of 300 mm is constructed using continuum shell elements [44].
8-node general-purpose hexahedron continuum shell element is used
for the model. In continuum shell modeling the entire 3-D body is used
as the geometrical model and just displacement DOF is provided [45].
Generally, continuum shell elements capture more accurately the
through-thickness response of laminated composite structures, thus
they are suitable for investigation of delamination between layers.
In this model, each layer is defined separately as an independent
cylindrical part with different thickness. The inner diameter of each
layer is considered the same as the outer diameter of the previous layer.
These concentric cylinders are assembled together using tie constraint
to form GFRP pipe in this model. Since in this technique each layer is
modeled independently, surface-based cohesive behavior can be defined properly in the interface of adjacent layers. It is noteworthy to
mention that while all structural FRP layers and also liner ply are
constructed using continuum shell element, the specific sand/resin core
layer is modeled using 3-dimensional 8-node brick element (C3D8R) to
be able to capture the out of plane stresses of the core.
Two parallel steel plates are also built with dimensions
(length×width×thickness) of 500 mm × 300 mm× 100 mm. 8-node
linear brick (C3D8R) elements are used for modeling these steel bearing
plates. The interaction between steel plates and outer surface of GFRP
pipe is defined using tie constraint. Specifically, suitable tangential and
normal behaviors are defined between layers to investigate post-failure
behavior.
Mechanical properties of liner, structural FRP and core layers used
in FE modeling are presented in Table 2. As it can be seen from Table 2,
isotropic behavior is assumed for both liner and core layers, while FRP
layers are treated as transversely isotropic material. The employed
micromechanics formulations to calculate mechanical properties of FRP
and core plies are presented in Appendix A. Moreover, the procedure of
calculating required volume fractions as the input of micromechanics
equations using measured constituents weight fraction is described in
Appendix B.
where XT , XC , YT , YC and S are longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse
compressive strength and shear strength for FRP layers. Non-linear
2.2. Test procedure
The pipe specimens are placed in a calibrated compression testing
machine equipped with two parallel, smooth and flat steel plates. The
specimens were carefully centered laterally in-between the parallel
plates in a manner that its longitudinal axis is located parallel to the
plates. The upper bearing plate was moved downward till a contact is
established between the plate without applying more load than required amount for holding the specimens. The specimens were compressed diametrically between two parallel bearing plates at a controlled rate of 12.5 ± 2.5 mm. The test temporarily stopped when the
diametric deflection reached the 5% of the diameter as the first phase of
experiment. Deflected specimens were visually inspected and no
cracking, rupture or wall delamination has been observed. The corresponding applied load at this stage was recorded as 1225 N. So, the
experimentally measured pipe stiffness (PSexp) is obtained using following formulation [3]:
PSexp =
F
Δy
(2)
Fig. 2. Cross section of layers with corresponding dimensions.
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Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
5% diametric deflection
10% diametric deflection
20% diametric deflection
Fig. 3. Different stages of Parallel-plate loading test on a GFRP mortar pipe specimen (By courtesy of ALH Co., Iran).
Fig. 4. Interplay-debonding (delamination) at 31% diametric deflection.
Table 2
Mechanical properties of constructing layers for investigated GFRP mortar pipe.
Ex [GPa]
Ey [GPa]
ν
G [GPa]
XT [MPa]
YT [MPa]
XC [MPa]
YC [MPa]
S [MPa]
FRP (hoop/cross) layers
Core layer
Liner layer
41.498
13.73
0.267
4.85
1167.87
33.43
583.93
53.718
65
8.4
7.1
0.39
3.02
78
0.3
2.73
78
150
150
–
–
Fig. 5. Value of the reaction force versus total number of elements.
geometry feature of the software is turned on to capture the encountered large deformation as one of nonlinear sources. Avoiding the
dependency of the results to the mesh density, a convergence study is
carried out on the reported reaction force for the non-linear model and
proper mesh density is chosen as illustrated in Fig. 5.
Total number of elements are 4720. All elements are square- and
cubic-shaped elements. The constructed FE model is presented in Fig. 6.
plane and out-of-plane failure modes are outlined in this section.
3.2.1. Intralaminar damage
Progressive damage modeling based on the concepts of continuum
damage mechanics is used to evaluate the intralaminar damage mechanism in the FRP layers.
Hashin failure criteria are used to identify the initiation of in-plane
damage in FRP layers. Five different damage initiation mechanisms are
evaluated using below formulations [46]:
3.2. Damage modeling strategies
Both interlayer and intralayer failure modes are intended to be
monitored. The employed strategies for taking into account both in350
Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
Fig. 6. FE layer by layer modeling technique.
2
2
⎛ σY ⎞ + ⎛ σS ⎞ = 1
⎝S⎠
⎝ YT ⎠
⎜
(3a)
The growth of each damage variable for particular mode is related
to the computed equivalent displacements using following expression
[47]:
(3b)
dI =
⎟
2
2
⎛ σY ⎞ + ⎛ σS ⎞ = 1
⎝S⎠
⎝ YC ⎠
⎜
⎟
2
2
⎛ σx ⎞ + ⎛ σS ⎞ = 1
⎝S⎠
⎝ XC ⎠
⎜
2
⎜
2
δft , eq = LC
2
+ εxy
2
δfc, eq = LC −εxx
(3e)
Eqs. (3a)–(3e) account for fiber tension, fiber compression, matrix
tension, matrix compression and in-plane shear failure modes, respectively.
As mentioned earlier, isotropic behavior is assumed for sand/resin
core layer, so maximum principal stress criterion is used to investigate
damage initiation in this layer. It is noteworthy to mention that in case
of failure this layer is totally removed from calculations. This is done by
reducing the mechanical properties of the failed core ply (i.e. Young's
modulus and Poisson's ratio) to the lowest possible values (almost zero)
avoiding numerical instability in FE analysis.
Damage evolution is characterized by progressive degradation of
material stiffness. After identifying damage initiation, the mechanical
properties of the failed ply are degraded by applying further loading.
Prior to the damage initiation, material is linearly elastic and the
stiffness matrix of the failed ply is updated using below formulation
[47]:
dft )(1
(5)
−
−
−
dmc)
2
+ εxy
(8c)
δmc, eq = LC
εyy
2
2
+ εxy
(8d)
2GIC
σI0, eq
(9)
3.2.2. Interlaminar damage (delamination)
As it was explained before, cohesive zone modeling technique is
employed for identifying the occurrence of delamination. Generally,
there are two strategies to implement cohesive zone modeling in FE
analysis: surface-based cohesive behavior or cohesive element.
Formulation and governing equations in both strategies are the
same and the implementation procedure is different. In surface-based
cohesive behavior, adhesion between adjacent layers is defined as an
interaction through a zero-thickness interface, while in cohesive element method, a material with specific mechanical properties thickness
is defined between layers. The first strategy is more convenient and also
preferred when the thickness of the adhesive is considerably low.
Recalling from Eq. (1), the pipe stiffness accounting for the relation
between diametric deflection and compressive transverse load is proportional to the cubic power of the pipe thickness. Consequently, increasing the pipe thickness by defining cohesive elements in-between
the layers can considerably violate the overall mechanical behavior of
the pipe. Moreover, the investigated GFRP pipe is produced using filament winding method and thus the thickness of the resin as the adhesive material between adjacent layers is significantly less than the
thickness of other layers and also they are very hard to be measured
accurately. Consequently, in the current study, surface-based cohesive
behavior is chosen for modeling delamination.
Cohesive zone is characterized by a constitutive law establishing a
(6b)
dmt)(1
2
is the equivalent stress at the onset of damage and GIC is
where
representative of critical energy release rate for mode I failure. Lc is
characteristic length based on the element geometry and formulation.
(6a)
dfc )(1
εyy
σI0, eq
where df , dm and ds show the state of fiber damage, matrix damage and
shear damage, respectively and expressed as below [47]:
dmt ; σyy ≥ 0
dm = ⎧ c
⎨ dm ; σyy ≺0
⎩
(8b)
δmt , eq = LC
δIf, eq =
(4)
t
⎧ df ; σxx ≥ 0
⎨ dfc ; σxx ≺0
⎩
(8a)
Also,
stands for fully damaged equivalent displacement and
obtained as below [47]:
where D reflects the current state of damage and obtained as below
[46]:
D = 1 − (1 − df )(1 − dm) νxy νyx > 0
(7)
δIf, eq
(1 − df ) Ex
(1 − df )(1 − dm) νyx Ex
0
⎡
⎤
1⎢
⎥
(1 − df )(1 − dm) νyx Ex
(1 − dm) Ey
0
⎢
⎥
D
−
D
d
E
0
0
(1
)
s
s
⎣
⎦
ds = 1 − (1 −
εxx
(3d)
σx
=1
XC
df =
I ∈ {ft , fc, mt , mc }
represents the equivalent displacement at failure onset and it
where
is obtained as below [47]:
(3c)
⎟
C=
δI , eq (δIf, eq − δI0, eq)
δI0, eq
⎟
⎛ σx ⎞ + ⎛ σs ⎞ = 1
⎝S⎠
⎝ XT ⎠
δIf, eq (δI , eq − δI0, eq)
(6c)
351
Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
Fig. 7. : Bi-linear traction-displacement law (left), interface strength directions (right).
where; t denotes thickness of adjacent layer, E3 represents through
thickness Young modulus and α is a parameter much larger than unity.
Quadratic-stress criterion is utilized to distinguish the initiation of
delamination [53]:
correlation between the traction vector and the resultant interfacial
separation. Traction-separation laws can be categorized as either initially elastic or initially rigid. The traction is initially zero at zero separation for the case of initially elastic rule. The traction increases with
growing separation till a maximum value and then it starts diminishing
and reaches zero at a finite displacement. In the case of initially rigid
cohesive laws, the surfaces subjected to separation remain in contact till
a critical traction is reached and then the traction decreases to zero with
increasing separation. The initially elastic cohesive law has some
drawbacks over the initially rigid models, since it is unphysical and
suffering from mesh dependency. Various initially rigid cohesive
models are developed to overcome the mesh dependency pertaining to
initially elastic laws [48,49], but they come with their own set of
complications and more preferred to the case of dynamic fracture
analysis [50,51]. For the purpose of this study, initially elastic cohesive
law is utilized and a convergence study is performed in term of element
size to overcome the difficulty of mesh-dependent results.
Bi-linear traction-displacement law is utilized as the constitutive
law of the cohesive zone. The employed constitutive laws of the CZM
are shown in Fig. 7 wherein δ 0 and δ f imply on corresponding separation at onset of delamination and full separation, respectively.
Prior to the initiation of delamination, the relation between traction
and separation is mathematically expressed using below equation [45]:
δ
K
K K
t
⎧ n ⎫ ⎡ nn ns nt ⎤ ⎧ n ⎫
t = ts = ⎢ Kns Kss Kst ⎥ δs = Kδ
⎨t ⎬ ⎢
⎥⎨ ⎬
⎩ t ⎭ ⎣ Knt Kst Ktt ⎦ ⎩ δt ⎭
2
(1−D ) tn, t ≥ 0 ⎫
tn = ⎧
⎨
t
⎩ , no − damage ⎬
⎭
ts = (1−D ) ts
tt = (1−D ) tt
Kss (tt ) =
D =
(14)
∫δ
δmf
o
m
Teff dδ
GC − Go
(15)
where Teff and δm are effective stress and maximum separation, respectively. Go represents the elastic energy at damage initiation. GC
represents critical fracture energy and it is obtained using energy-based
Benzeggagh-Kenan (B-K) criterion in this study [54]:
(11)
αG23
tply
(13)
where tn , ts and tt are the contact stress components predicted by the
elastic traction-separation behavior for the current separations without
damage.
D is defined as the scalar damage variable in contact points and it
governs the delamination propagation as the rate of cohesive stiffness
degradation. D has a initial value of zero at onset of delamination and it
evolves gradually and reaches unity at full separation. Following formulation is used to evaluate energy based mix-mode damage variable
[45]:
The nominal traction vector in 3-D model consists of three components: tn is in normal direction while ts and tt are in shear directions.
Corresponding separations are δn, δs and δt. Pure shear separation does
not give rise to normal cohesive force and vice versa. Therefore, normal
and shear stiffness components are not coupled and only Knn, Kss and Ktt
must be defined. Penalty stiffness members are calculated using following equations [52] and their values are inserted in Table 3.
Knn
2
ton, tos and tot are interlaminar strength components in normal and tangential directions, respectively. Interlaminar strength components are
taken from the nominal values measured experimentally by supplier of
the resin and inserted in Table 3. Qd represents delamination failure
index. The interfacial failure or delamination initiates, once Qd reaches
unity in a cohesive zone between two adjacent layers. Then gradual
degradation process starts on the basis of linear softening law and it
continues until the complete separation. After initiation of delamination, the tractions of cohesive zone start to degrade as below [45]:
(10)
αE3
=
tply
2
⎧ ≺tn ≻ ⎫ + ⎧ ≺ts ≻ ⎫ + ⎧ ≺tt ≻ ⎫ = Q
d
o
o
o
⎨
⎨
⎨
⎩ tn ⎬
⎭
⎩ ts ⎬
⎭
⎩ tt ⎬
⎭
(12)
η
G
Gnc + ⎜⎛Gsc − Gnc ⎟⎞ ⎧ S ⎫ = GC
⎩ GT ⎬
⎭
⎝
⎠⎨
GS = Gs + Gt
GT = Gn + GS
Table 3
Interface cohesive properties.
Properties
Values
3
Normal penalty stiffness (N/mm )
Shear penalty stiffness (N/mm3)
Normal strength tno (MPa)
1.5 × 10
6 × 105
32.76
Shear strength tso , tto (MPa)
19.1
Normal critical fracture energy Gnc (N/mm)
0.01
Shear critical fracture energy Gsc , Gtc (N/mm)
B-K exponent η
0.025
6
(16)
where Gn, Gs and Gt stand for normal toughness, shear toughness along
the first and second shear directions, respectively. η is B-K exponent.
This criterion is specifically useful when the critical fracture energies
are the same along the first and second shear directions. The interface
cohesive properties are shown in Table 3.
Fig. 8 is a schematic representation of mix-mode response in cohesive interactions.
2
352
Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
matrix tensile mode is the dominant damage mechanism in this layer.
Summarizing the sequence of failure events observed numerically in
the investigated GFRP mortar pipe under compressive transverse
loading, firstly the liner is debonded from its adjacent hoop layer at
27% diametric deflection. Then, matrix cracking takes place in the
outermost layer of the pipe at 30% of diametric direction followed by
debonding of core from the next cross layer at 33%.
5. Parametric study
The satisfactory agreement between the reported results for the
occurrence of delamination and experimental observations established
out confidence toward the proper modeling procedure. Therefore, in
this section, the influence of various effective parameters on the interlayer and also intralayer failure of a GFRP mortar pipe under compressive transverse load is investigated. The effective parameters
chosen for parametric study include fiber volume fraction, the winding
angle of cross plies, the thickness of core and liner layers and also layup sequence. In the next sections, one parameter is varied while all
other are kept fixed.
Fig. 8. Illustration of mix-mode behavior in cohesive zone modeling.
4. Results and discussion
5.1. Core thickness
After defining suitable in-plane damage mechanism and surfacebased cohesive behavior between different layers of investigated GFRP
mortar pipe, non-linear numerical analysis is carried out under displacement control conditions. Both interlaminar and intralaminar damages are taken into account in the FE analysis, simultaneously.
Prior to analyzing the occurrence of failure, a displacement of
− 25 mm is applied to the upper plate in y direction resembling 5%
diametric deflection status while the other plate is restricted from any
movement. The magnitude of the reaction force at 5% diametric deflection is obtained as 1242 N. The reasonable agreement between obtained reaction force from FE analysis and experimentally measured
1225 N validates modeling process.
In the next stage, the displacement of the upper plate gradually
increases to − 200 mm (40% of pipe diametric deflection) and the
magnitude of delamination failure index (Qd) is monitored as the output
of non-linear FE analysis. Fig. 9 shows the contour plots of delamination
failure index of the cohesive interface between liner and adjacent hoop
layer at four different diametric deflections. It can be seen from Fig. 10
that delamination initiated from the free edged and it propagates along
the specimen length.
The increasing trend of delamination failure index (Qd in Eq. (12))
versus the percentage of diametric deflection for the liner and adjacent
hoop layer and also for Core and next cross layer are presented in
Fig. 10. Results show that in 27% diametric deflection delamination
occurs at the interface of liner and adjacent hoop layer and it starts
from the free edges. This result is in a acceptable agreement with experimental observations reported in Section (2). Further increase in
loading results in the occurrence of delamination between core layer
and adjacent cross ply ( ± 60.19°) at 33% diametric deflection.
As it can be seen, failure index of delamination evolves from zero to
the maximum value of unity and then it remains constant, since the
phase of delamination propagation starts at this point.
The magnitudes of maximum principal stress in liner and also core
layers are also checked at different diametric deflection to investigate if
failure happens in these layers. As it has been reported in Table 2,
strength of sand/resin core layer is considered the same as the value for
pure resin as a conservative approach. Results are presented in Table 4
and 5. It can be inferred from presented results in Table 4 and 5 that
none of them fails before experiencing delamination failure in the
current pipe configuration.
Furthermore, FEA results show that the outermost cross layer
(− 60.19°) is the most critical layer from intralayer damage point of
view. Fig. 11 shows different the in-plane damage variables for this ply
at the diametric deflection of 30%. It is evident from the results that
Effect of core layer on the occurrence of delamination failure is
studied in this section. Five different values for core thickness are
chosen for the investigated pipe. Fig. 12 shows that increasing the core
thickness will be led to experiencing delamination failure between core
and adjacent cross ply at the lower level of diametric deflection. It does
not have any influence on delamination between liner and hoop layers.
It is worth mentioning that increasing the thickness of core does not
influence the diametric deflection level wherein liner is debonded from
the next hoop layer.
Moreover, the influence of core thickness on its maximum principal
stress is also studied and the results are depicted in Fig. 13. As it was
expected, increasing core thickness will induce higher stresses in this
layer revealing more susceptibly of this layer to in-plane failure. But, in
all cases, in-plane failure will not happen before delamination failure
mode. For instance, a 5-mm core layer experiences failure at the diametric deflection of 37% after the occurrence of delamination at 24%.
5.2. Fiber volume fraction
Practically, the volume fraction of fiber in FRP layers is often place
between 50% and 60% in industrial filament winding process. In this
section fiber volume fractions of 50%, 52%, 54%, 56%, 58% and 60%
are chosen. Fiber volume fraction has significant effect not only on the
mechanical properties of the FRP layers but also on the thickness of
them. The dependency of the mechanical properties and thicknesses of
the FRP plies to the fiber volume fractions are presented in Appendices
A and C.
As it is evident from reflected equations in Appendix (A) increasing
fiber volume fraction will reduce transverse tensile strength and increase transverse modulus of FRP layers. As a result, it will induce
higher levels of transverse stress in FRP layers. It can be inferred from
Fig. 14 that increasing fiber volume fraction will cause matrix cracking
in the outermost − 60.19° layer at lower diametric deflection levels.
Consequently, increasing fiber volume fraction in FRP plies has a negative side effect on the structural failure of GFRP mortar pipes subjected to compressive transverse loading. Although increasing fiber
volume fraction will improve the strength of the pipe along fiber direction, it will results in a premature failure when matrix cracking is a
dominant in-plane failure mode instead of fiber breakage/buckling
mode of failure. This is an important finding should be taken into account in the structural design stage of the GFRP pipes.
It should be mentioned that changing volume fraction of FRP layers
does not have any tangible effect on the occurrence of delamination as
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Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
Fig. 9. The status of delamination failure index in quadratic-stress criterion for the CZM between liner and adjacent hoop layer at different diametric deflection.
interlaminar failure mode.
5.3. Winding angle in cross plies
Qd
In order to study the influence of cross-ply winding angle on the
failure of a GFRP pipe under compressive transverse load, five different
winding angles of 52.5°, 55°, 57.5°, 60.19° and 65° are selected. These
values are widely used for the production of industrial-scale GFRP pipes
using discontinuous filament winding technology. According to the
presented equations in Appendix C, winding angle also affect the
thickness of FRP layers. Fig. 15 illustrates variations of overall pipe
thickness versus various fiber volume fractions for different winding
angles.
Keeping the fiber volume fraction as a constant value of 57.14% and
core thickness as a constant value of 1.16 mm, Fig. 16 shows that increasing winding angle postpones delamination at the interface of core
layer and adjacent cross ply for the investigated GFRP mortar pipe.
It is noteworthy that, increasing winding angle also increase the
magnitude of pipe stiffness and it will also postpone in-plane failure in
GFRP pipe.
Percentage of diametric deflection (%)
Fig. 10. Overall diagram of delamination initiation and propagation for different interfaces.
Table 4
Hoop stress distribution in liner.
Diametric deflection
5%
10%
15%
20%
25%
27%
30%
Hoop stress (MPa)
5.11
10.3
15.35
20.2
25.1
30.42
30.89
5.4. Liner thickness
Thickness of this layer is reduced from 1.51 mm to 0.5 mm as a
normal practice in industrial centers. Results show that liner thickness
does not have substantial effect on the failure of a GFRP pipe under
compressive transverse loading.
Table 5
Maximum principal stresses in core layer.
Diametric deflection
5%
10%
15%
20%
25%
30%
Maximum principal
stress (Tensile)
Maximum principal
stress (compressive)
7.89
15.17
21.87
27.01
31.8
35.6
− 8.86
− 17.15
− 25.5
− 34.4
− 42.3
− 50.16
5.5. Lay-up sequence
Four different ply configurations are considered for the investigated
GFRP pipes without changing the overall combination of hoop, cross
and core layers and also their populations. These four stacking sequence
are outlined as below:
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Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
Fig. 11. In-plane damage variables at 30% diametric deflection for the outermost layer (− 60.19°).
Fig. 12. delamination diametric deflection versus core thickness.
Fig. 13. Maximum principal stress versus volume fraction for different core
thicknesses.
A)
B)
C)
D)
[90/ ± 60.19/core/ ± 60.192/90]
[ ± 60.19/90/core/90/ ± 60.192]
[ ± 60.19/90/core/ ± 60.192/90]
[ ± 60.19/90/core/ ± 60.19/90/ ± 60.19]
Results show that, configurations B, C, and D tend to delaminate at a
lower levels of diametric deflection at the interface of core layer and
adjacent layer. The reason is mainly due to mismatch in Poisson's ratio
between the core layer and the hoop layers. Mismatch of plies properties causes a high interlaminar shear stress in the interface of layers.
Therefore, configuration (A) tends to be a more resistant design against
These ply configurations are compared to determine the most resistant configuration to interlaminar failure against transverse loading.
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Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
Diametric deflection (%)
6. Conclusion
Mechanical behavior of a GFRP mortar pipe with ply configuration
of [90/ ± 60.19/Core/ ± 60.192/90] under compressive transverse
loading is studied. Firstly, the resistance of the pipe to diametric deflection is investigated experimentally and the level of diametric deflection where failure begins is extracted. Then, FE analysis is conducted to simulate the aforementioned test conditions evaluating
intralayer and interlayer failures. Progressive damage modeling based
on the concepts of continuum damage mechanics is used to examine the
intralaminar damage mechanism in the FRP layers. Surface-based cohesive behavior is also utilized to capture the initiation and propagation
of delamination between the layers. A good agreement between FE
results and experimental observation is observed. Progress of damage is
studied and various diametric deflection levels which will be led to
debonding of the layers and also in-plane failure are numerically
identified.
After validating the modeling procedure, a parametric study is
conducted to examine the influence of fiber volume fraction, winding
angle, thickness of core layer and liner layer and lay-up sequence on the
inerlayer/intralayer failure of a GFRP mortar pipe under compressive
transverse loading. It is observed that increasing core thickness will
expedite both in-plane failure and delamination in the pipe. Increasing
fiber volume fraction will be led to the occurrence of in-plane failure in
the outermost FRP layer at the lower levels of diametric deflection as a
result of reduction in transverse strength of FRP layers. In contrast,
increasing winding angle of FRP layers will postpone delamination at
the interface of core layer and adjacent cross ply. Thus, the negative
side effect of increasing fiber volume fraction can be compensated by
adjusting winding angle in cross layers. Moreover, results show that
thickness of liner layer does not have any sensible effect on the failure.
Finally, the influence of lay-up sequence on the delamination failure of
GFRP mortar pipe subjected to compressive transverse loading is analyzed examining different combinations of ply configurations whilst the
whole numbers of hoop, cross and core layers are kept fixed.
Fiber volume fraction (%)
Fig. 14. Influence of fiber volume fraction on the intralaminar failure of outermost cross layer (− 60.19°).
Diametric deflection (%)
Fig. 15. pipe thickness versus fiber volume fraction for different winding angles.
Acknowledgement
The authors acknowledge the financial support provided by the
Iranian National Science Foundation (INSF) under contract 96008676.
Winding angle (°)
Fig. 16. The level of diametric deflection resulting in delamination between
core and cross ply versus winding angle of the cross ply.
delamination under compressive transverse loading.
Appendix A. Calculating mechanical properties of different layers
Following micromechanics equations are employed for FRP and sand/resin core layers [55–57]:
EX = Ef V fFRP + Em VmFRP
EY = Em
(1 + 2ηT V fFRP )
(1 −
ηT V fFRP )
(A1)
, ηT =
Ef / Em − 1
Ef / Em + 2
(A2)
νX = νf V fFRP + νm VmFRP
(A3)
Gm
ES =
1−
V fFRP
(1 − )
Gm
Gf
(A4)
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Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
(V score )0.67Em
Ecore =
(
1 − (V score )0.33 1 −
)
(V score )0.67Gm
Gcore =
νcore =
Em
Es
(
1 − (V score )0.33 1 −
Gm
Gs
)
+ (1 − (V score )0.67) Em
(A5)
+ (1 − (V score )0.67) Gm
(A6)
Ecore
−1
2Gcore
(A7)
where Ef, Em, Gf and Gm are representative of fiber modulus, matrix modulus, fiber in-plane shear modulus and matrix in-plane shear modulus as
presented in Table 1, respectively. EX, EY, ES and νX stand for longitudinal, transverse, in-plane shear moduli and major Poisson's ratio, respectively.
Strength of FRP layers are obtained using below empirical formulation:
E
XT = Xf ⎜⎛V fFRP + VmFRP m ⎞⎟
Ef ⎠
⎝
(A8)
XC = 0.5XT
(A9)
XC = 0.5XT
(A10)
YC =
VmFRP X ′m
(A11)
where Xf , Xm , X ′m stands for fiber tensile strength, matrix tensile strength and matrix compressive strength respectively as per Table 1.
The in-plane shear strength is also of FRP layers is also selected as 65 MPa for all cases as an average of shear strength for unidirectional FRP
layers with different fiber volume fraction
on the basis of experimental observations. Due to the negligible value of in-plane shear stress component in comparison with longitudinal/
transverse stress component, this assumption is a rational compromise in modeling.
Strength of sand/resin core layer is considered the same as the value for pure resin as a conservative approach.
Appendix B. Calculating volume fractions of constituents
Reflected volume fraction of fiber (V fGFRP ) and resin (VmGFRP ) of FRP layers and also sand volume fraction (V score ) of core layer in Eq. (A1) to (A11)
are computed using below formulation based on the measured weight fractions which were reported in Section (2.2):
V score =
ρsAreal
ρs
.
1
tcore
(B1)
3
where tcore is the thickness of sand/resin layer. The density of sand, i.e. ρs , is also 2.65 gr/cm .
ρsAreal is the areal density of sand layer obtained as:
ρsAreal =
Wspipe × mpipe
(B2)
πDL
where mpipe, D and L represents the mass of pipe, average diameter of pipe and the length of pipe. The length of investigated pipe was 12 m and Wspipe
represents measured weight fraction of sand in pipe which is reported in Section (2.2).
The measured weight fraction in Section (2.2) consists of dedicated resin volume fractions of both FRP and sand/resin layers which should be
considered separately in micromechanics equations. The volume fraction and weight fraction of resin in core layer is obtained using below equations:
Vmcore = 1 − V score
Wmcore =
(B3)
Vmcore ρs
core
V s ρs + Vmcore ρm
(B4)
where ρm denotes resin density. The amount of resin in core layer is then obtained as:
mmcore =
Wmcore mpipe Wspipe
1 − Wmcore
(B5)
Then, the mass of incorporated resin in FRP layers are obtained as below:
mmFRP
= Wmpipe mpipe − mmcore
(B6)
where Wmpipe
stands for the measured weight fraction of resin in pipe and reported in Section (2.2). Having in hand dedicated mass of matrix in GFRP
layers, volume fraction of matrix in FRP layers is calculated using dedicated weight fraction of matrix in FRP layers as below:
WmFRP =
mmFRP
mmFRP
+ Wfpipe mpipe
(B7)
FRP
W FRP ⎛ W f
W FRP ⎞
+ m ⎟
VmFRP = ⎜⎛ m ⎟⎞/ ⎜
ρm
⎝ ρm ⎠ ⎝ ρf
⎠
(B8)
where ρf denotes fiber density which is 2.56 gr/cm . Finally, volume fraction of fiber in FRP layers are obtained as:
3
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Thin-Walled Structures 131 (2018) 347–359
R. Rafiee, M.R. Habibagahi
V fFRP = 1 − VmFRP
(B9)
Appendix C. Calculating thickness of FRP and core layers
tcross =
ρAC =
Wf =
ρFRP × wf
(C1)
NS T
BSinθ
thoop =
ρAH =
2 × ρAC
(C2)
ρAH
ρFRP × wf
(C3)
NS T
B
(C4)
Vf ρf
(Vf ρf + Vm ρm )
(C5)
ρFRP = (Vf ρf + Vm ρm )
(C6)
where tcross and thoop are thickness of cross and hoop piles, respectively. ρAC and ρAH stands for areal density of cross and hoop plies. Wf denotes
weight fraction of fiber. ρFRP is the density of FRP layers. ρf , ρm and θ represents the density of roving, the density of resin and the winding angle of
ply measured from longitudinal axis of the pipe. Vf , Vm and T represents fiber volume fraction, resin volume fraction and the TEX of roving. NS is
number of strands in the roving bundle and B stands for the roving bundle band width which is 42 and 180 mm, respectively.
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