Kabir, Md,Fawzia, Sabrina,Chan, Tommy, Gamage, J.C.P.H ...€¦ · 1 Experimental and Numerical...
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Kabir, Md, Fawzia, Sabrina, Chan, Tommy, Gamage, J.C.P.H., & Bai, J.(2016)Experimental and numerical investigation of the behaviour of CFRPstrengthened CHS beams subjected to bending.Engineering Structures, 113, pp. 160-173.
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https://doi.org/10.1016/j.engstruct.2016.01.047
1
Experimental and Numerical Investigation of the Behaviour of CFRP Strengthened CHS Beams Subjected
to Bending M. H. Kabir a,, S. Fawzia a*, T.H.T. Chan a, J.C.P.H. Gamage b, J.B. Bai c
a School of Civil Engineering and Built Environment, Faculty of Science and Engineering, Queensland
University of Technology, 2 George Street, Brisbane, QLD 4000, Australia, Email: [email protected] b Department of Civil Engineering, University of Moratuwa, Sri Lanka.
c Laboratory MSS/MAT, CNRS UMR 8579, Ecole Centrale Paris, 92295 Chatenay Malabry, France
Abstract
This paper presents the results of an experimental and numerical program to investigate the
circular hollow section (CHS) beams, strengthened using Carbon Fibre Reinforced Polymer
(CFRP) sheets. The circular hollow shaped steel beams bonded with different CFRP layer
orientations were tested under four-point bending. The mid-span deflection, service load and
failure load were recorded. The LHL (where L, first inner longitudinal layer, H, second hoop
layer and L, third outer longitudinal layer) and LLH (where L, first inner longitudinal layer,
L, second longitudinal layer and H, third outer hoop layer) layer oriented strengthened beams
perform slightly better than HHL (where H, first inner hoop layer, H, second hoop layer and
L, third outer longitudinal layer) layer oriented strengthened beams. The LHL and LLH layer
oriented treated beams showed very similar structural behaviour. Numerical analyses were
then conducted on the CFRP strengthened steel CHS beams. The validity of the models has
been assessed by comparing the failure loads and mid-span deflections. The effects of various
parameters such as bond length, section types, tensile modulus of CFRP, adhesive layer
thickness and adhesive types have been studied.
Keywords: CHS; CFRP; strengthened; layer orientation; numerical investigation; bending
Nomenclature
ARK630 araldite K630
BL bond length
COV coefficient of variance
df orthotropic ply damage parameter in fibre direction
dm orthotropic ply damage parameter transverse to fibre direction
2
ds orthotropic ply damage parameter in shear direction
Ea elastic modulus of adhesive
Ei elastic modulus of fibres in i direction
Exp experiment
FE finite element
G with GFRP
Ga shear modulus of the adhesive
Gcmax maximum fracture energy
Gn fracture energy in normal direction
Gs, Gt fracture energy in shear directions
Gij shear modulus
GT1C or GC
1C mode I Fracture energy in fibre direction
GT2C or GC
2C mode II Fracture energy in transverse direction
ID identification
Knn elastic stiffness of the adhesive in normal direction
Kss, Ktt elastic stiffness of the adhesive in shear directions
LCFRP length of bonded CFRP
Le effective span
MBr MBrace saturant
Nuij poisson’s ratio
OD outer diameter
PFE ultimate load determined from FE analysis
PL point load
Ps(cs) service load of the strengthened beams
Ps(s) service load of the unstrengthened beams
Pu(cs) ultimate load of the strengthened beams
Pu(s) ultimate load of the unstrengthened beams
Pult ultimate load from experimental test
SKD330 sikadur 330
SL or ST ultimate in-plane strength shear directions respectively
t thickness
tn nominal stress normal mode only
ts, tt nominal stresses shear directions
tn0 peak value of nominal stress in normal direction
3
ts0, tt0 peak values of nominal stress in shear directions
T0 thickness of the adhesive
Ui linear displacement in i direction
US unstrengthened
URi rotation in i direction
XT or XC ultimate in-plane strength in fibre direction
YT or YC ultimate in-plane strength in transverse direction
δn normal separation
δs, δt separation in shear directions
εn strain in normal direction
εs, εt strain in shear directions
εn0 peak nominal strain in normal direction
εs0, εs
0 peak nominal strain in shear directions
1. Introduction
In some especial cases such as compression, torsion and bending in all directions, aesthetic
demand, corrosion resistance due to absent of sharp edge and fire protection capability by
pouring water inside the tube, the tubular shape hollow members perform better than other
open sections [1]. Therefore, the application of such members has been increasing
dramatically for building various onshore and offshore structures. In offshore structures,
circular hollow section is mainly used to form jacket structures which sometimes subjects to
bending due to wave force [2]. A large number of such structures are sometimes found
structurally inadequate due to design errors, loss of material properties, exposure to severe
environments, or increase in service loads. This degradation phenomenon draws a great
attention to the engineers for strengthening or rehabilitation of metallic structures.
There are many advantages of using CFRP materials for strengthening and rehabilitating of
bridges and structures. The high durability and fatigue endurance, superior strength-to-weight
ratio, costs saving through labour savings, flexibility to form all kind of shapes of these
materials enable them to compete easily with other traditional strengthening materials in this
field [3-5]. After having the initial success of using CFRP to concrete structures [6-8], the use
of CFRP composites for strengthening and rehabilitating work has been prolonged to timber
and masonry and more recently also metallic structures. Several field applications of
composites materials have been reported in [9, 10], where mostly steel bridges have been
4
strengthened using adhesively bonded CFRP composites. A satisfactory number of
experimental works have been conducted to strengthened open and close steel sections using
various numbers and orientations of CFRP layers [2, 11-25]. Their results have shown that the
combination of two materials, CFRP and steel, has found to increase strength, stiffness,
ductility and structural performance of strengthened systems. Some of the studies also have
shown that the number and the orientation of CFRP layers affect the strength of the sections
primarily when they are subjected to compression and bending. From the durability point
view, the current study has used LHL layers orientation (where L is the longitudinal layer and
H is the hoop layer) of CFRP to strengthened CHS member and tested under bending. The
reasons of selecting LHL layers and treating the surface with primer have been clearly
mentioned in one of the authors’ published works [26]. The experimental works are
considered to be satisfactory, and yet, not many numerical studies have been done yet for
adhesively bonded CFRP structures to simulate the real experimental works. Considering time
and cost of the experimental testing, finite element (FE) techniques offer the opportunity to
develop a numerical model, which would accurately predict the failure or damage mechanism
of the structures in a relatively short time. The complicated composite behaviour of the
structures has been simulated by several researchers under bending, tension and impact
loadings [10, 13, 27-33]. Their studies dealt with mainly hollow columns, H and I shape steel
beams, double strap joints and orthotropic damage models. Various techniques of material
models were deployed. It was reported that the damage mechanism mainly depends on the
model of composites and adhesives. According to aforementioned literatures, continuum shell
for CFRP composites and cohesive model for adhesive are able to predict real damage of the
structures with delamination of CFRP. There are no research has been found yet to present the
numerical model of CFRP strengthened circular hollow steel members under bending. It is
common that the strength capacity varies from section to section for circular steel hollow
members. Hence, it is very urgent to do more numerical models for different types of section
to minimise cost and time and to guide the engineers. To overcome this gap in knowledge,
this paper aims to investigate the numerical simulations with various types of parameters of
CFRP strengthened circular hollow section members under bending. The results from
numerical simulations have been validated with experimental findings.
5
2. Experimental Investigation
2.1. Material properties
The modulus of elasticity, tensile strength and tensile strain of steel, CFRP and GFRP were
determined experimentally by coupon test. The material properties for these three materials
are listed in Table 1.
2.2. Test specimens
The test specimens including total of ten steel tubes with circular cross-sections of 101.6 mm
outer diameter and 4.0 mm thickness were cut into required size. The length of the circular
member was chosen 1300 mm and the effective span was considered 1200 mm for a four-
point bending test. Fig. 1 shows the schematic diagram of the test set-up with all dimensions
being in mm.
2.3. Specimen preparation
It is very important to have a properly prepared surface of the steel substrate for the success of
steel/CFRP strengthening system. Solvent cleaning, grit blasting, sand blasting and surface
grinding are the most common methods to prepare steel surface [12, 23, 34-38]. Among these,
grit or sand blasting method has been proven to be most effective method to get uniform high
energy surface [12, 23, 34, 36, 38]. A uniform high energy surface indicates that the energy
exerted by the surface will be almost similar on the whole area to be bonded with CFRP
patch. When a substrate, steel tube in this study, has a high surface energy, it tends to attract
other material (adhesive and CFRP) significantly. As a result, a perfect bond between
substrate and CFRP patch is achieved. The surface preparation generally involves cleaning,
followed by removal of weak layers and then re-cleaning [39, 40]. The current study was
involved a large amount of surface to be prepared. Therefore, the relatively cheap and locally
available sand blasting method was deployed. The garnet abrasive system (grit no. 30/60) was
used for sandblasting. The grit size varies from 600 to 250 micron which results the average
size of the grit 0.425 mm and it was between the range used by Teng et al [23]. Then the sand
blasted surface was cleaned by washing with acetone to remove the weak layer, deposited
dust particles and grease [41]. At this stage, two strain gauges were attached to specially
cleaned surface on top and bottom of steel beam at mid-length where the maximum bending
moment occurred to record the compressive and tensile strains.
The acetone cleaned surface of the eight specimens was then treated with adhesion promoter
prior to applying epoxy adhesive and allowing it to dry for approximately 1 hour. Then the
6
two part impregnated epoxy adhesive was mixed according to manufacturer guidelines [42]
and applied on primed steel surface during its pot life. The CFRP sheet was cut into the
required dimensions oriented longitudinally, horizontally and longitudinally to the length of
the beam was directly applied on top of the adhesive layer. For two identical specimens (S3A-
1), an additional Glass Fibre Reinforced Polymer (GFRP) layer oriented longitudinally was
embedded in adhesive before applying CFRP sheet. The embedded GFRP layer acts as a
barrier to protect galvanic corrosion when exposed to wet environment. A rib roller was run
immediately to press the fabric along the fibre direction against the substrate until visual signs
of adhesive were observed bleeding through the fabrics. It helps the fabrics to form a plate
after getting desired shape. The whole procedure was done on the wet surface which implies
the top surface of the lower layer remained still sticky. To achieve a uniform and high quality
bond, masking tape was wrapped around the circumference of the CFRP wrapped area and
kept for a period of at least 24 hours (Fig. 2a). Then the masking tape was removed and the
finished specimens (Fig. 2b) were cured for about two weeks under ambient temperature to
ensure full curing.
2.4. Test set-up and instrumentation
A 230 kN controlled MTS actuator was used to do the tests of the CHS beams. All the tests
were performed under four-point bending with simply supported condition. Fig. 3 shows the
test set-up with apparatus. The load was applied as a displacement control ‘static compression
load’ at a constant rate and was continued up to failure of each specimen. Two string pots
were placed at the centre of the beams to measure the average mid-span deflection of the
specimens. Two additional LVDTs were mounted on top of the supports to measure support
displacement. The actual deflection of the beams was determined by deducting support
displacement from mid-span displacement.
3. Experimental Results
Two specimens were tested for each group and the difference of service and ultimate load
between them was very close. The service load was taken at deflection Le/250 in accordance
with AS 3600 [43] for all members not supporting articulated brittle partitions and failure
loads for all the beams. The ultimate load was considered as the maximum load taken by the
beams during four-point bending test. Since the differences of service and ultimate loads
between two identical specimens were very marginal, the worst case scenario for both loads
has been discussed for each group in the results section as well in the finite element section.
7
3.1. Failure modes of the tested beams
Fig. 4 shows the failure modes of the tested unstrengthened and strengthened beams with
various layers orientation. Typical ductile modes of failure were displayed by all the
specimens during testing. It can be seen that (Fig. 4) the failure occurred to both LHL and
LLH layer oriented beams due to local buckling of the tubular hollow section in the
compression zone near the loading points where the crushing of fibre layers was found as
well. Though the failure occurred to both beams due to local buckling of the section near the
loading points in the compression zone, the load-strain (tensile strain of steel section at mid
length of beam) curves (see Fig. 5) show that the full capacity of the section was utilized
during failure. It was also noticed that a minor debonding occurred at tension face of both
ends. It may happen due to high stress concentrations at ends. The CFRP composites in
tension face remained intact. However, the failure modes for the strengthened beams with
HHL layers orientation were totally different and it failed due to complete rupturing of CFRP
at middle of tension face and yielding of steel at middle of tension face as well. The fibres at
compression face also crushed and steel also yielded. No end de-bonding was found for HHL
layers oriented beams until failure. This change of failure mode is interesting. However, it can
be said that this different failure mode may happen due to replacing one longitudinal layer by
one hoop layer of CFRP composites.
3.2. Failure load
Table 2 shows the service and failure loads for all the beams. The corresponding ratios of
service and ultimate loads of the strengthened specimens Ps(cs) and Pu
(cs) relative to
unstrengthened steel beam Ps(s) and Pu
(s) tested under bending are also shown (Table 2). It can
be seen that the ratios of service and ultimate loads for LHL layers oriented strengthened
beams is higher than that of HHL layers oriented beams.
The three layers of CFRP configuration with various layer orientation helps to increase the
ultimate strength through the effective use of the longitudinal fibre strength and restraining
action of hoop-oriented fibres as shown in Fig. 6. The strengthened techniques (LHL, HHL
and LLH) adopted in the current study for compact section were able to increase ultimate load
to maximum of 33.0%, 37.0%, 30.0% and 33.0% for LHL, LHL (embedded GFRP), HHL and
LLH respectively in oriented beams compared to the unstrengthened beam. Similarly, the
load resistance at service has increased about 45.0%, 53.0%, 42.0% and 50.0% for LHL, LHL
(embedded GFRP), HHL and LLH respectively. It is interesting to see that the GFRP
8
embedded LHL layer oriented beam shows higher ultimate and service load than the LHL
layer oriented beam without embedded GFRP. It may have happened due to additional
sectional properties contributed by the embedded GFRP layer. However, a previous study
conducted by Haedir et al. [17], shows maximum strength gain at ultimate state is about 3%
for compact tubular section (OD = 33.81 mm, t = 2.70 mm similar CFRP used in the current
study) strengthened using HHL combination of CFRP and tested under four-point bending. In
another study [2], the maximum increment of ultimate load was 27% for strengthened
compact tubular hollow steel member (OD =168.5, t = 4.9 mm and CFRP used is Tyfo with
average tensile strength of 500 MPa and tensile modulus of 62500 MPa respectively, where in
the combination of CFRP were used as LLH and tested under four-point bending condition.
Therefore, strength increment for strengthened beam without embed GFRP was found 6%
more than the previous study. This higher strength capacity may have appeared due to bond
enhancement which may be contributed by pre-treated surface and uniform pressure exerted
by wrapped masking tape during initial curing stage.
The beams S5B-1 and S6B-2 which had LHL and LLH fibres orientation were slight stronger
than the beam S6B-1 with HHL layers of CFRP composites. It may have appeared due
presence of less number of longitudinal layer in HHL layers oriented beam. It is interesting to
see that both beams S5B-1 and S6B-2 perform similar way in term of load enhancement.
Finally the GFRP embedded LHL layers oriented beam performed better than all other beams
with the highest strength gain.
3.3. Mid-span deflection
The load-deflection responses of unstrengthened and strengthened beams with various fibres
layer orientations are shown in Fig. 7. It can be seen that all the strengthened beams with
various layer orientations display higher stiffness than that of unstrengthened beam B2
starting from around 40 kN load until the end of the test. This stiffness increment is the good
agreement with that measured experimentally by Seica and Packer [2] for CFRP strengthened
HHL fibres oriented compact tubular members tested under bending.
It is observed that (Fig. 7) the strengthened beams with various fibre layer orientations display
similar deflection trend and linear-elastic behaviour until around 78 kN load is attained and
then the deflection trend alternates to inelastic behaviour. The identical deflecting trend is
further continued up to 100 kN load for LHL and LLH layer oriented beams S5B-1, S3A-1
and S6B-2. It is noted that the beams S5B-1, S3A-1 and S6B-2 show stiffer behaviour than
9
beam S6B-1 in the plastic zone until the first sudden drops of stiffness where the sudden
debonding or rupture of CFRP composites occurs. However, the first sudden drop of stiffness
for beam S6B-1 delays and then it shows higher deflection than LHL and LLH layers oriented
beams. The LHL and LLH layers oriented beams S5B-1 and S6B-2 without embedded GFRP
show negligible difference in stiffness after a final noticeable drop of stiffness till to the
recorded values of deflection. In addition, the LHL layers oriented beam S3A-1 with
embedded GFRP shows a slight stiffer behaviour in elastic zone and this variation becomes
more evident at higher load in higher deflection. This may have happened due to additional
strength provided by embedded GFRP.
4. Finite element model
Finite element (FE) models were developed using the commercially available finite element
package ABAQUS version 6.12-2. The models were with the same configurations of the
tested beams as given in Fig. 8, where U is the linear displacement, and UR denotes the
rotation. Firstly, the FE models were validated by experimental results and later the effects of
different parameters such as the bond length, section variation, CFRP modulus of elasticity,
adhesive thickness, types of adhesives and loading conditions were studied. The Newton-
Raphson incremental iterative solution method was used to determine the response of the
beams.
4.1. Element types and mesh density
Various types of elements are available in the finite element package, ABAQUS software.
Four materials including steel, adhesive, CFRP and GFRP patches are modelled as four
different part instances. Three different types of elements are used to designate these part
instances since CFRP and GFRP patches are considered as similar type of element
(continuum shell). The steel tube component is modelled using 8-node 3-D solid element
(C3D8H), hybrid with constant pressure while the adhesive layers between the fibre layers are
modelled using the eight-node three-dimensional cohesive elements COHD8 that are useful in
modelling adhesives, bonded interfaces, gaskets and rock fracture [44]. The CFRP and GFRP
patches are meshed with an 8-node quadrilateral in-plane general-purpose continuum shell,
reduced integration with hourglass control, finite membrane strains (SC8R). This type of
element is capable of predicting CFRP failure [32, 45]. In addition, the continuum shell
element allow a full three dimensional model and they are more attractive in computation than
the standard brick elements because of capturing through-the-thickness shear stress without
using one element per layer [45, 46]. Finally, the three dimensional thick shell geometry leads
10
to improve accuracy in resolving contact problems. The computational time was reduced by
introducing 10 mm mesh for steel tube, 4 mm mesh for adhesive layers and 10 mm mesh for
CFRP and GFRP respectively. The connections between steel surface and adhesive surface
and between adhesive surface and CFRP composite surface are achieved by tie constraints.
Steel tube and CFRP composite are considered as master surface and adhesive is considered
as slave surface for tying purpose.
4.2. Steel tube model
The steel tube is modelled as a classical elastic-plastic metal with isotropic hardening. The
experimental stress-strain curve of the steel was adopted in FE model to represent the material
behaviour.
4.3. Adhesive model
It is very important to model adhesive layers appropriately between steel and CFRP patch or
between CFRP patch itself to capture the delamination of bond laminate. The cohesive zone
model (CZM) approach adopted to model the constitutive behaviour of adhesive layers. The
cohesive elements are more realistic and practical to model the behaviour of adhesive joints,
interfaces in composites and any situation where the integrity and strength of interfaces may
be of interest [44]. Cohesive elements are also capable of simulating damage and
delamination in composites [31, 32, 47]. Hence, in this study, the adhesive layers are
modelled as cohesive elements with fracture mechanics constitutive definitions. A triangular
traction-separation cohesive law with linear softening is used to characterize the material
behaviour of the adhesive because of having very thin layers of adhesive in composites. In
this case the macroscopic material properties are not relevant directly and it obvious to derive
concepts from fracture mechanics [44]. The mixed mode cohesive law considers all the three
components of stresses, which are one normal component and two shear component. These
components are denoted by tn, ts and tt respectively, while the corresponding separations are
presented by δn , δs and δt respectively.
It is assumed that the cohesive elements behave linear-elastically until the initiation of
damage [48, 49]. The elastic behaviour can be written as
(1)
=
t
s
n
tt
ss
nn
t
s
n
KK
K
ttt
δδδ
000000
11
It can be said that Knn will be equal to the initial slope of the bond-separation model for mode
I loading and can be expressed by
(2)
where Ea is the elastic modulus of adhesive determined by coupon test and To is the original
thickness of the adhesive layer.
Kss and Ktt are assumed to be the same, and should be equal to the initial slope for mode II
loading [48] and they can be written as
(3)
where Ga is the shear modulus of the adhesive. Due to absence of experimental data, a simple
relation may be used for the initial approximation of shear modulus. Although this relation is
developed for homogeneous isotropic materials. The relation can be expressed as
(4)
where ν is the Poisson’s ratio of adhesive.
The initial stiffness parameters, Knn, Kss, and Ktt can not be measured directly through the
experiment; however the eqs. 3 and 4 also give a reasonable initial approximation for K.
Therefore, in order to find a reasonable estimation of K, various numerical simulations with
different K values need to be compared to the experimental results [47]. The stiffness of the
cohesive elements should be large enough to provide reasonable stiffness but also not so large
to cause oscillations in interfacial traction of the element. In the current study reasonable
approximations are made for undetermined properties of materials to match the results with
experimental results and these values were constant for all specimens. These approximations
are made for stiffness parameters (Knn, Kss, and Ktt) and fracture energies (Gn, Gs and Gt) of
adhesives as shown in Table 3.
The cohesive elements are able to represent the failure of adhesive include crack initiation and
propagation. The damage criteria has been clearly presented by Teng et al. [50]. There are
four built-in failure criteria for damage initiation under traction separation law in ABAQUS
library. These are maximum nominal stress criterion, maximum nominal strain criterion,
0TEK a
nn =
65.0
0
3
==
TGKK a
ttss
( )ν+=12EaGa
12
quadratic nominal stress criterion and quadratic nominal strain criterion. The first two criteria
assume that the adhesive damage initiate when the maximum nominal stress or strain reaches
the maximum capacity of the adhesive. These criteria can be represented as
(5)
(6)
The last two criteria consider the combination effect of stresses and strains and it is assumed
that the damage initiate when a quadratic interaction function involving the nominal stresses
or strain ratios reaches a value of one. These criteria can be represented as
(7)
(8)
It has been reported that under mixed-mode loading, the adhesively bonded joints are
subjected to complex state of stress (normal stress and shear stress) and these stresses
contribute to adhesive failure [50, 51]. Therefore, the current study considers the mixed mode
failure criteria which is the quadratic traction damage criterion (QUADS) as shown in eq. 7
for both mode I and mode II loading. To define this QUADS damage criterion in ABAQUS,
nominal stress (tn) in normal mode only, nominal stress (ts) in first shear direction and
nominal stress (tt) in second shear direction are required as input values. In the current study,
nominal stress in normal mode and shear directions are considered similar. The other three
parameters, 0nt
0st and 0
tt are the peak values of the nominal stress in normal, first and second
shear directions of adhesive layer which are generated by ABAQUS during running of the FE
model. Nominal strain values can be found from coupon test.
4.4. CFRP model
In adhesively-bonded composite materials, the failure generally occurs either in the patching
materials or the bonding materials, or both. The ABAQUS software is able to capture the
damage and failure of the fibre reinforced polymer composites by using the available
materials model in it as discussed in sub-section 4.1. By implementing this material model in
ABAQUS, the damage initiation and propagation of an elastic-brittle material with an
12
0
2
0
2
0 =
+
+
t
t
s
s
n
n
tt
tt
tt
12
0
2
0
2
0 =
+
+
t
t
s
s
n
n
εε
εε
εε
1,,max 000 =
t
t
s
s
n
n
tt
tt
tt
1,,max 000 =
t
t
s
s
n
n
εε
εε
εε
13
isotropic behaviour such as unidirectional normal modulus carbon fibre reinforced polymer
(CFPR) fabrics can be achieved [52]. The material model for CFRP fabrics depends on
continuum damage mechanism and in-built Hashin damage criteria in ABAQUS [44]. In
Hashin damage model, the plasticity of the CFRP is always neglected and damage is detected
and characterised based on material stiffness reduction. The damage of the CFRP layer
initiates due to four main failure criteria, namely: fibre rupture in tension, fibre bucking in
compression, matrix cracking under transverse tension and shearing, and matrix crushing
under transverse compression [47]. Damage propagates when the fracture energy (damage
variable) in any of the four mentioned criteria reaches its maximum value (Gcmax) which can
be specified as an input parameter as longitudinal tensile and compressive fracture energy,
transverse tensile and compressive fracture energy in ABAQUS. Once damage initiates, three
non-negative in-ply parameters, df, dm and ds reduce the ply stiffness numerically in fibre,
transverse and shear direction respectively, until the final failure point is reached [47]. Hence,
to provide a more accurate validation of the numerical model with experimental results, the
CFRP composite damage is considered in the current study. The parameters used in
ABAQUS to facilitate Hashin damage criteria are longitudinal tensile and compressive
strength which represent ultimate tensile and compressive strength (XT and XC) of CFRP in
fibre direction, transverse tensile and compressive strength which represent ultimate tensile
and compressive strength (YT and YC) of CFRP in transverse direction.
5. Material properties in FE analysis
The tensile strength, strain and modulus of elasticity for steel, CFRP and adhesive are taken
form experimental data. The steel tubes had an average yield stress of 327 MPa, an ultimate
strength of 383 MPa and the modulus of elasticity was about 214 GPa confirmed by coupon
test. The properties for all the other elements used in FE model are listed in Tables 3 to 6. The
tensile tests of the CFRP composites patch were performed and peak failure strength and
tensile modulus were directly input to the FE model. The compressive strength of CFRP patch
was considered a 20% of the average tensile strength. For the interlaminar damage model, the
fracture energies associated with the various damage mechanism and all other properties used
in FE were initially approximated for numerical computations [27, 31, 45, 47, 53]. To
determine the undetermined damage properties of adhesive and CFRP at structural level, the
numerical models were run several times until the best validation were achieved.
14
6. Validation of the numerical model
The numerical simulation has been carried out based on the above FE model and the results
obtained from numerical analysis were standardized against the corresponding experimental
data. The ultimate load, load-deflection curves and failure mode of the unstrengthened and
composite beams having various layers orientation executed by FE models are compared with
the experimental results.
6.1. Ultimate load
A clear comparison of the experimentally measured ultimate load and those executed from FE
analyses for unstrengthened and strengthened control beams can be seen in Table 7. It can be
seen that the (PFE/Pult) ratios of ultimate load determined from FE analyses and experimental
tests varies from 0.97 to 1.03 which are very close to unity. Moreover, the COV of ultimate
load are very minimal and it varies from 0.002 to 0.022. Thus, it can be said that the
numerical models have been validated reasonably by showing very close values of ultimate
loads to that of the experimental values.
6.2. Mid-span deflection
Figs. 9-11 show the comparison between load vs deflection measured experimentally and
numerically for the unstrengthened and strengthened beams. It can be seen that the numerical
results and experimental data match very well until failure of the beams. Nonetheless, the load
drops are observed experimentally in Figs. 10 and 11 which are common for CFRP
strengthened steel structures [2, 54]. The current FE model developed using ABAQUS
software is not able to show this sudden drop of load which agrees with the model presented
by Teng et al. [50]. This sudden drop may have happened due to fracture of CFRP composite
which has not been depicted in the current model.
6.3. Failure mode
The failure modes of FE analyses models are found similar with the tested unstrengthened
beams and strengthened beams with LHL and LLH layer orientation of CFRP as shown in
Fig. 12. However, the failure mode of HHL layer oriented strengthened beam monitored
experimentally is slightly different from failure mode predicted experimentally. This is
because the experiment was done by deflection control of the MTS actuator and the test was
continued up to the end level of actuator. For HHL layer oriented beam, the failure mode was
captured at the end of test but the failure occurred at earlier stage of loading. Therefore, the
15
excessive bending can be seen in Fig. 12 for HHL layer oriented tested beam. Although, this
layer combination is not considered for later parametric study in this paper.
7. Parametric study
It is common that some strengthening parameters such as bond length, type of tubular section,
CFRP modulus of elasticity, adhesive thickness and adhesive type may have effects on the
strength of the strengthened beams. To understand the effects of these parameters, a range of
parametric study has been conducted using the corresponding validated FE models. The
parametric study is performed for LHL layer oriented strengthened beam only. The LHL layer
combination performs slightly better than HHL layer combination in terms of strength and
stiffness. The LHL and LLH layer combination show very similar structural behaviour. In
structural application under bending, both LHL and LLH layer combination can be used.
However from theoretical point of view, under tension the outer L is stronger than outer H
layer and hence H layer may elongate more than L layer. At this situation, the H layer may
allow more moisture infiltration especially when it goes in wet environment. In the case of FE
analysis, it can be seen that (see Table 7) the LHL layer oriented strengthened beam shows
higher ultimate load than other layer oriented beams, although the difference is not
significant. Therefore, the LHL layer combination is proposed in the current study for
considering durability in wet environment.
7.1. Bond length
Based on the test set-up (Fig. 8), the bond length is considered from loading points to the
supports points. This is one of the most important strengthening parameters that could be
much more easily changed in civil engineering practise and could affect the cost of the
project. The main objective of this section is to find the structurally sound but cost effective
bond length and this bond length will be continued for further parametric studies. The effects
of bond length are shown in Figs. 13 to 15 and Table 8.
It can be seen that (Fig. 13) as the bond length increases the strengthened beam become stiffer
and the degree of stiffness is more prominent in plastic zone and is less prominent in elastic
zone. It can also been seen that (Fig. 14) the debonding effect is becoming more evident with
decreasing of bond length. It means that the stress intensity decreases near the debonding area
with the increase of bond length as can be seen in Fig 15.
16
The loads of the beams at failure for different bond lengths are shown in Table 8. It can be
seen that the bond failure load increases with the increase of bond length and reaches to
maximum at 300 mm bond length. In addition, as the bond length increases from 100 to 300
mm, it is found that the relative load increment is minimal when the bond length approaches
to maximum length. Based on these observations from FE results, it can be concluded that the
increase in bond length is one of the most effective measures to enhance bond failure
resistance capacity of CFRP strengthened steel circular hollow beams. This parametric study
has been conducted to find out the cost effective bond length with reasonable strength
increment. Therefore, 200 mm bond length is selected as cost effective bond length with
reasonable strength increment based on the available dimension of CFRP, although the
effective bond length can be considered as 250 mm as shown in Fig. 13.
7.2. Section types
In this section ten different sections with various diameter-thickness ratios available in
Australia are studied using FE results for LHL layers oriented strengthened beams without
embedded GFRP. The effects of welded end plate are also discussed.
Fig. 16 shows the effect of welded plate at end on failure mode of the strengthened beams
having two different section properties. In case of the larger section (OD =165.0, t = 5.4 mm),
the strengthened beam without welded plate fails by local buckling of the wall at the supports,
while the beams with welded plate at end fails by local buckling of the tube wall near or
below the loading points which is similar to experimental failure mode for LHL layers
oriented beam as shown in Fig. 4. On the other hand, failure modes are similar for beams
having smaller section (OD =101.6, t = 4.0 mm) with and without welded plate at end.
Therefore, it can be said that for smaller section welded end plate is not mandatory whereas
welded end plate is mandatory for larger section to overcome local buckling at support.
It is interesting to see that (Table 9) the strength increment for different sections compared to
corresponding unstrengthened sections is not equal although the wrapping scheme and the
material properties are similar. It varies from 3.35% to 28.80% for strengthened beams
without out welded plate at ends. It can be seen that the strength increment is not significant
(3.25% and 4.26%) for sections with higher diameter and without welded plate at ends. It may
happen due to complete collapse of the tube section at supports before utilizing the full
contribution of CFRP as shown in Fig. 16a. In the case of strengthened beams with welded
plate at ends, the strength increment varies from 7.08% to 28.13%. Therefore, from these
17
observations, it can be concluded that the percentage of strength increment for a particular
section cannot be used for other sections having different outer diameter and thickness.
Hence, the proposed FE model is capable of predicting strength increment for different
sections strengthened using LHL layers oriented CFRP composites when the material
properties are known.
Table 9 also shows the variation of strength increment for strengthened beams with and
without welded plate at ends. It can be seen that this variation is significant for cross-sections
having diameter ranges from 165.0 mm to 140.0 mm. However, for the cross-sections having
diameter ranges from 114.0 mm to 90.0 mm show negligible difference in strength increment.
Hence, it can be said that the effect of welded end plate is negligible for cross-sections with
smaller sections available in the market. The circular hollow section (OD =101.6, t = 4.0 mm)
with and without welded plate at ends used in the current study shows almost the same
strength increment. Therefore, to minimise cost and time, the experiment was conducted for
the sections without welded plates.
7.3. Tensile modulus of CFRP composites
One of the important parameters is the tensile modulus of the CFRP composites. The material
technology has been improving rapidly and the elastic modulus of composite material could
be increased dramatically in the coming years. Therefore, three different tensile moduli up to
552 GPa have been investigated numerically. Fig. 17 shows the effect of CFRP modulus on
stiffness of the strengthened beams. The tensile moduli are considered 150, 210 and 552 GPa
respectively. It can be seen that the stiffness and ultimate load increase as the modulus of the
CFRP composites increase.
7.4. Adhesive layer thickness
Fig. 18 illustrates the effect of adhesive layer thickness on stiffness and ultimate load of the
strengthened beams for three different thicknesses of adhesives. The MBrace saturant
adhesive is used in this study with similar properties for different thickness of adhesive. The
strengthened beams are analysed numerically by introducing 0.20, 0.35 and 0.50 mm thick
adhesive layers respectively. It can be seen that the strengthened beam with higher adhesive
thickness shows higher stiffness and ultimate load. This increase in stiffness and ultimate load
for various thicknesses of adhesive layers is agreed with that measured numerically by Luo et
al. [55] for bonded steel-concrete composite beams, although the influence of adhesive layer
18
thickness was relatively small. It may happen due to higher sectional properties such as cross-
sectional area and moment of inertia contributed by the thicker layers of adhesive.
7.5. Types of adhesive
Another parameter of interest is types of adhesive. Various types of adhesive are available in
the market, however depending on the availability of material properties for FE analysis, three
types of adhesives are chosen in this study. The load-midspan deflection response for
different types of adhesive is shown in Fig. 19. It can be seen that the araldite K630 shows
higher stiffness than MBrace saturant and Sikadur 330. Sikadur 330 shows intermediate level
of stiffness. It may appear due to higher elastic modulus which leads to higher stiffness
parameters of adhesive as FE input.
8. Conclusions
In this paper, the structural behaviour of CFRP strengthened tubular steel members for
various layers orientations have been investigated experimentally first. The presented
experimental results of CFRP strengthened circular hollow steel beams are very promising. A
full three-dimensional finite element model has been developed in the numerical analysis of
both unstrengthened and strengthened beams. A range of parametric studies have also been
conducted. From the study conducted, the following conclusions can be drawn:
• Two different types of failure modes were observed for strengthened beams depending on
layer orientations. The LHL and LLH layers oriented beams failed by showing local
buckling of the tube wall near the loading points. However, the HHL layers oriented beams
failed by complete rupturing of CFRP and yielding of steel at tension face.
• The effects of CFRP fabrics on service and ultimate loads were remarkable. In particular
the maximum load resistance at service and failure were found about 53.0% and 37.0%
respectively. The effect of layer orientation on failure load was not significant and LHL and
LLH layers oriented treated beams performed slightly better than HHL layers oriented
treated beam.
• The effect of bonded CFRP fabrics on elastic stiffness of the beams was negligible at lower
level of load (until about 36 kN load). While at higher load, a significant increase in plastic
and elastic stiffness was observed for all the strengthened beams compared to
unstrengthened beam. The LHL and LLH layers oriented strengthened beams without
embedded GFRP showed very similar elastic and plastic stiffness until failure while LHL
layers oriented beam with embedded GFRP showed slight higher stiffness. The HHL layers
19
oriented beam showed more ductility and significant decrease in plastic stiffness until the
failure of LHL and LLH layers oriented beams.
• The proposed finite element model produces estimation of the ultimate load, midspan load-
deflection curves and failure mode for unstrengthened beam and strengthened beams with
various layers orientation of CFRP in good agreement with the experimental results.
• Parametric study shows that the proposed 200 mm bond length is reasonable in terms of
cost and strength. The section dimensions such as outer diameter and thickness play an
important role on strength increment of CFRP strengthened CHS steel beams. It is
suggested to use welded steel plate at the end for larger section of CHS beams. The section
chosen in this study was perfect in terms of strength increment. The CFRP with higher
tensile modulus and adhesive with higher thickness, perform better under bending by
increasing stiffness and ultimate load. Similarly the adhesive with high tensile modulus and
high stiffness parameters (K) performed better in terms of ultimate load and stiffness.
• The analysis, design and prediction of moment-curvature behaviour of CFRP strengthened
CHS beams are being conducted by the authors. The results will be compared in future
study with those reported in the literature on the same topic [56-58].
Acknowledgement
The authors would like to thank, Queensland University of Technology (QUT) for providing
support to carry out the work reported in this paper. The authors also wish to thank the high
performance computer facility and IT staff in Science and Engineering Faculty at QUT for
their assistance in carrying out this research.
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23
Figure Caption:
Fig. 1. Schematic diagram of test set-up (all dimension are in mm) [24, 26]
Fig. 2. Curing (a) with, (b) without masking tape at ambient condition
Fig. 3. Experimental set-up
Fig. 4. Failure mode of the tested beams
Fig. 5. Experimental and numerical load-strain curves of LHL layer oriented beam (Typical)
Fig. 6. Ultimate load for unstrengthened and strengthened beams
Fig. 7. Experimental load-displacement response for unstrengthened and strengthened beams
Fig. 8. Geometry for the composite beam for FE model
Fig. 9. Numerical and experimental load-displacement response for unstrengthened beam
Fig. 10. Numerical and experimental load-displacement response of LHL layer oriented strengthened beams (a) without, (b) with embedded GFRP
Fig. 11. Numerical and experimental load-displacement response of (a) HHL and (b) LLH layer oriented strengthened beams
Fig. 12. Comparison of failure modes between test and FE analysis
Fig. 13. Numerical load-displacement response of LHL layer oriented strengthened beams for various bond lengths
Fig. 14. Debond of CFRP at bottom ends from FE model
Fig. 15. Stress variation in the 1st layer of adhesive between loading point and end, (a) BL =100 mm, (b) BL= 200 mm, (c) BL=250 mm (d) BL=300 mm
Fig.16. Failure mode of beams determined numerically having different cross-section without and with welded end plate
Fig.17. Numerical load-displacement response of LHL layer oriented beam for various modulus of elasticity of CFRP
Fig. 18. Numerical load-displacement response of LHL layer oriented beam for various adhesive thickness
Fig. 19. Numerical load-displacement response of LHL layer oriented beam for various types of adhesives
24
Fig. 1.
(a) (b)
Fig. 2.
Fig. 3.
25
Fig. 4.
Fig. 5.
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.0180
20
40
60
80
100
120
Load
(kN)
Strain (mm/mm)
S6B-2_Exp_LLH S6B-2_FE_LLH
26
Fig. 6.
Fig. 7.
Fig. 8.
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
B2_US S5B-1_LHL S3A-1_LHL_G S6B-1_HHL S6B-2_LLH
27
Fig. 9.
(a) (b)
Fig. 10.
(a) (b)
Fig. 11.
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
B2-Exp B2-FE
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
S5B-1-Exp_LHL S5B-1-FE_LHL
0 10 20 30 40 500
20
40
60
80
100
120Lo
ad (k
N)
Deflection (mm)
S3A-1-Exp-G_LHL S3A-1-FE-G_LHL
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
S6B-1_Exp_HHL S6B-1_FE_HHL
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
S6B-2_Exp_LLH S6B-2_FE_LLH
28
Test: Unstrengthened FE: Unstrengthened
Test: Strengthened (LHL and LLH) FE: Strengthened (LHL and LLH)
Test: Strengthened (HHL) FE: Strengthened (HHL)
Fig. 12.
Fig. 13.
Debond at BL =100mm Debond at BL =200mm Debond at BL =250mm Debond at BL =300mm
(a) (b) (c) (d)
Fig. 14.
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
S5B-1-FE-BL-100 S5B-1-FE-BL-200 S5B-1-FE-BL-250 S5B-1-FE-BL-300
29
Fig. 15.
(a) OD=165.0, t=5.4 mm, without welded plate (b) OD=165.0, t=5.4 mm, with welded plate
(c) OD=101.60, t=4 mm, without welded plate (d) OD=101.60, t=4 mm, with welded plate
Fig. 16.
30
Fig. 17.
Fig. 18.
Fig. 19.
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
S5B-1-FE_E=1.50xE11 S5B-1-FE_E=2.10xE11 S5B-1-FE_E=5.52xE11
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
S5B-1-FE_To=0.20 mm S5B-1-FE_To=0.35 mm S5B-1-FE_To=0.50 mm
0 10 20 30 40 500
20
40
60
80
100
120
Load
(kN)
Deflection (mm)
S5B-1-FE-MBr S5B-1-FE-ARK630 S5B-1-FE-SKD330
31
List of Tables:
Table 1 Material properties of steel, CFRP and GFRP Steel tube CFRP GFRP
Elastic modulus (GPa) 214 205 55 Tensile strength (MPa) 327 2760 1065 Yield stress (MPa) 383 - - Tensile strain (mm/mm) 0.029 0.014 0.019
Table 2 Test details, beam resistance at service and failure and failure mode of the tested beams
Beam ID
No of beam
Wrapp -ing
Scheme
Service load at Le/250 (kN)
Ps(cs) /
Ps(s)
Ultimate load (kN)
Pu(cs) /
Pu(s) Failure mode
B2_US 2 - 44.10 50.30
- 76.75 78.40
- A
S5B-1 2 LHL 64.00 66.00
1.45 101.70 102.00
1.33 B
S3A-1 2 LHL 67.32 72.50
1.53 104.90 106.70
1.37 B
S6B-1 2 HHL 62.50 62.80
1.42 100.32 99.65
1.30 C
S6B-2 2 LLH 66.00 69.00
1.50 102.00 104.00
1.33 B
A for Ductile failure, B for Local buckling of wall, crushing of CFRP and debonding at ends, C for Rupture of CFRP & yielding of steel at bottom, no debonding at ends.
Table 3 Material properties of adhesives
Parameters
Adhesive types Mbrace Saturant
Araldite K630 Sikadur 330 [44]
Value Value value Ea (Pa) 2.86 x 109 6.5 x 109 4.82 x 109 tn (Pa) 46 x 106 33 x 106 31.28 x 106 ts (Pa) 46 x 106 33 x 106 31.28 x 106 tt (Pa) 46 x 106 33 x 106 31.28 x 106 Knn (N/mm3) 2.8 x 1013 6.07 x 1013 4.72 x 1013 Kss (N/mm3) 1.4 x 1013 3.03 x 1013 2.36 x 013 Ktt (N/mm3) 1.4 x 1013 3.03 x 1013 2.36 x 1013 Gn (N/m) 1000 1000 1000 Gs (N/m) 1250 1250 1250 Gt (N/m) 1250 1250 1250
32
Table 4 Orthotropic elastic properties of the fibre-reinforced epoxy Fibre types E1 (Pa) E2 (Pa) G12 (Pa) G13 (Pa) G23 (Pa) Nu12 CFRP 205 x 109 25 x 109 1 1 3.0 x 109 0.33 GFRP 55 x 109 1 1 1 6.7 x 109 0.33
Table 5 Orthotropic damage initiation properties of fibre-reinforced epoxy Fibre types XT (Pa) XC (Pa) YT (Pa) YC (Pa) SL (Pa) ST (Pa) CFRP 2760 x 106 552 x 106 1 1 50 x 106 1 GFRP 1065 x 106 213 x 106 1 1 50 x 106 1
Table 6 In-plane fracture energies for fibre-reinforced epoxy Fibre types GT
1C (N/m) GC1C (N/m) GT
2C (N/m) GC2C (N/m)
CFRP 91600 79900 1 1 GFRP 58000 50600 1 1
Table 7 Comparison of ultimate load between experimental and finite element analysis results
Beam ID
Experiment Finite element analysis
PFE /Pult COV Pult (kN) PFE (kN) B2 76.75 79.20 1.03 0.022 S5B-1 101.70 102.00 1.00 0.002 S3A-1 104.90 101.78 0.97 0.021 S6B-1 99.65 98.60 0.99 0.007 S6B-2 102.00 99.00 0.97 0.021
Table 8 Ultimate load at different bond length
Bond
Length(mm)
Ultimate
load
(FE)
Relative
increment of
ultimate load
(kN)
Relative
increment
of bond
length
(mm)
BL =100 93.09 0.00 0
BL =200 102.00 8.91 100
BL =250 106.88 4.88 50
BL =300 107.50 0.62 50
33
Table 9 Numerically determined ultimate load of unstrengthened and strengthened beams for various sections
Thickness (mm)
Ultimate Load (kN) Load increment
Outer Diameter
(mm)
Unstrengthened Strengthened
DS/t
Without welded plate
Welded plate at
end
Without welded plate at
end
Welded plate at
end
Without welded plate at
end
Welded plate at
end
165.0 5.4 30.6 219.50 265.70 228.85 284.50 4.26% 7.08%
165.0 5.0 33.0 203.00 247.00 209.80 271.80 3.35% 10.04%
140.0 5.4 25.9 202.00 202.00 230.00 235.90 13.86% 16.78%
140.0 5.0 28.0 187.60 187.50 216.00 221.60 15.14% 18.19%
114.0 5.4 21.1 134.88 134.66 161.85 162.50 20.00% 20.67%
114.0 4.5 25.3 113.90 113.90 139.00 139.60 22.04% 22.56%
101.6 5.0 20.3 98.84 98.68 120.50 120.55 21.91% 22.16%
101.6 4.0 25.4 79.20 81.12 102.00 103.00 28.80% 26.97%
90.0 6.0 15.0 93.00 93.00 111.55 112.00 19.95% 20.43%
90.0 4.0 22.5 64.00 64.00 82.40 82.00 28.75% 28.13%