Paper- H. Al-Zubaidy- Finite Element Modelling of CFRP-Steel Double (1).pdf

8/16/2019 Paper- H. Al-Zubaidy- Finite Element Modelling of CFRP-Steel Double (1).pdf

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Finite element modelling of CFRP/steel double strap joints subjected

to dynamic tensile loadings

Haider Al-Zubaidy a,c, Riadh Al-Mahaidi b,⇑, Xiao-Ling Zhao a

a Department of Civil Engineering, Monash University, Clayton, VIC 3800, Australiab Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Hawthorn, VIC 3122, Australiac Kerbala University, Kerbala, Iraq

a r t i c l e i n f o

Article history:

Available online 14 December 2012

Keywords:

CFRP sheet

Double-strap joints

Steel plate

FE modelling

Dynamic loadings

a b s t r a c t

This paper reports the numerical simulation of both CFRP/steel double strap joints with 1 and 3 CFRP lay-

ers per side at quasi-static and three dynamic tensile loading speeds of 3.35, 4.43 and 5 m/s. Simulations

are implemented using both the implicit and explicit codes respectively using non-linear finite element

(FE) package ABAQUS. In these analyses, failures of both CFRP sheet and adhesive are considered and a

cohesive element is utilised to model the interface. The developed FE models for both types of joints were

validated by comparing their quasi-static anddynamic findings with those obtained from previous exper-

imental program. This comparison includes four different variables such as the ultimate joint strength,

effective bond length, failure pattern and strain distribution along the bond length. It was found that

FE models proved to be able to predict all these parameters for both quasi-static and dynamic analyses

and their prediction matched well with test results.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years, the outstanding outcomes of strengthening and/

or upgrading concrete structures using the technique of adhesively

bonded carbon fibre reinforced polymer (CFRP) have attracted the

engineers’ attention to employ the same method for metal struc-

tures. However, in general, conducting experimental tests has

many drawbacks. These include cost, time, difficulties and limita-

tions in testing full scale members and the difficulties in imple-

menting a parametric study on different variables. These

shortcomings highlight the importance of developing finite ele-

ment models which are capable of predicting the behaviour of

the strengthened and/or upgraded structures. Therefore, finite ele-

ment analysis (FEA) has attracted an increasing demand to analyse

adhesively bonded joints since the composite materials have be-come common materials of strengthening and/or upgrading.

Some numerical studies have been successfully carried out to

predict the static and dynamic behaviour and strength of adhe-

sively bonded joints of similar and dissimilar substrates under dif-

ferent loading conditions. Under static tensile loading, the

behaviour and strength of CFRP composite adhesively bonded steel

plates were examined in [1–6]. Other studies numerically analysed

joints of similar adherends such as steel/steel [7], aluminium/alu-

minium [8] and composite/composite [9–11]. In addition, finite

element analysis of CFRP composite bonded to simply supported

steel beams under bending were also reported in Refs. [12–14]

and analysis for continuous beams were reported in [15]. However,

the strength and behaviour of structural joints such as the single

lap joints and T-joints, which were manufactured using rigid and

elastic adhesives, were experimentally investigated and compared

under static and impact loading [16]. On the other hand, compared

to static loading, the dynamic behaviour and strength of adhesively

bonded joints attracted limited attention in numerical studies.

These investigations included joints of different substrates such

as steel/steel [17], aluminium/aluminium [18] and composite/

composite [19]. Numerical prediction of the dynamic strength

and behaviour of joints of CFRP sheet bonded to steel plates has

not been reported in the literature. To cover this gap in knowledge,

this paper aims at investigating the numerical simulation of CFRP/double strap joints at quasi-static and the three dynamic loading

speeds of 3.35 m/s, 4.43 m/s and 5 m/s using both implicit and ex-

plicit codes in ABAQUS. Results of numerical simulations are com-

pared with experimental findings.

2. Summary of laboratory work

A total of 160 CFRP/steel double strap joints were prepared and

tested at quasi-static and three dynamic loading speeds of 3.35,

4.43 and 5 m/s and this number included two types of joints with

1 and 3 CFRP layers per side. These joints were formed by bonding

normal modulus CFRP sheet to steel plate using Araldite 420

0263-8223/$ - see front matter 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.compstruct.2012.12.003

⇑ Corresponding author.

E-mail address: [email protected] (R. Al-Mahaidi).

Composite Structures 99 (2013) 48–61

Contents lists available at SciVerse ScienceDirect

Composite Structures

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p s t r u c t

http://dx.doi.org/10.1016/j.compstruct.2012.12.003mailto:[email protected]://dx.doi.org/10.1016/j.compstruct.2012.12.003http://www.sciencedirect.com/science/journal/02638223http://www.elsevier.com/locate/compstructhttp://www.elsevier.com/locate/compstructhttp://www.sciencedirect.com/science/journal/02638223http://dx.doi.org/10.1016/j.compstruct.2012.12.003mailto:[email protected]://dx.doi.org/10.1016/j.compstruct.2012.12.003


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adhesive (Huntsman Duxford, UK). In this experimental program,

on average, two or three CFRP/steel samples were tested for both joints with 1 and 3 CFRP layers. Of these, 62 joints were produced

with 1 CFRP layer per side and 98 joints with 3 CFRP layers. Details

of manufacturing these joints, test procedure and experimental re-

sults can be found in the authors’ previous study [20]. A schematic

view of the specimen’s geometry and instrumentation used the

experimental program is shown in Fig. 1.

3. Finite element model

Based on dimensionality, it is well known that numerical simu-

lation can be conducted using either 2-D or 3-D modelling and

each has certain advantages and shortcomings. Even though 2-D

modelling is much easier to simulate and the analysis does not re-

quire very powerful computers, its results are always less accurate,particularly when analysing large-scale structures. Conversely,

more precise results are expected from 3-D modelling, although

this is more likely to pose difficulties when running on normalcomputers. The appearance of such difficulties depends on the size

of the analysed structure. In this study, since the dimensions of the

analysed samples are not too large and the analysis can be run

using a normal PC, 3-D modelling was chosen to simulate both

the quasi-static and dynamic analyses for both types of joints (with

1 and 3 CFRP layers per side). This is in order to obtain more accu-

rate results and to enable clear comparisons between the failure

modes for both quasi-static and dynamic loadings.

Three-dimensional models are developed in ABAQUS software

to numerically investigate the effect of increasing the test speed

on the bond between steel plate and CFRP patch using double-

strap joint samples. To clearly highlight this effect, non-linear

quasi-static and dynamic analyses have been carried out using

both ABAQUS implicit and explicit codes respectively. Due to

material and geometry symmetry conditions, only one eighth of

Joint

(a) Joints used for static tests of 3 CFRP layers and impact tests of 1 CFRP layer per side

25 mm

5 mm

5 mm

5 mm

210 mm 210 mm

75 mm75 mm L2 L1

Joint Steel tabs

CFRP sheet

(b) Joints used for impact tests of 3 CFRP layers per side

Adhesive layers

mm012mm012

L1L2Steel plate

Adhesive layers

5 mm

CFRP sheet

50mm

210 mm 210 mm

G1 G2 G3 G4 G5 G6

L1L2

15 mm

G1 G2 G3 G4 G5 G6 G7

(c) Specimen’s top face view

CFRP Steel plate

CFRP

50mm

Steel plate

L1L2

G8 G9

210 mm210 mm

(d) Specimen’s bottom face view

Fig. 1. A schematic view of the specimen’s geometry and instrumentation used in the experimental program (not to scale).

H. Al-Zubaidy et al./ Composite Structures 99 (2013) 48–61 49


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the continuum shell elements allow a fully three-dimensional

model while they are more computationally attractive than the

standard brick elements because they are able to capture

through-the-thickness shear stress without using one element

per layer [21,24,25]. Furthermore, their ability to capture three-

dimensional geometry leads to improved accuracy in resolving

contact problems. Despite their visual resemblance to ordinary

three-dimensional elements, these elements maintain constitutivebehaviour and formulation similar to conventional shell elements,

consequently allowing the usage of standard plan stress failure cri-

teria for the composite employed for damage modelling of CFRP

layers [23].

5. Material models

5.1. CFRP sheet

For adhesively-bonded composite materials, it is always ex-

pected that failure will occur within the composite materials. This

failure may take place either in the patching material or the bond-

ing material, or both. For more adequate and comparable numeri-

cal models, damage to composites must be numerically considered

in the analysis of fibre reinforced composite materials used to

strengthen and/or repair metal structures.

The general behaviour of the unidirectional normal modulus

carbon fibre reinforced polymer sheet (CFRP) is elastic-brittle

material, as clearly reported by the authors previous study [26].

Among the available material models in ABAQUS software is dam-

age and failure for fibre-reinforced composites. Consequently, uti-

lising such a material model facilitates the implementation of

damage initiation and propagation for elastic-brittle materials

with an isotropic behaviour such as the unidirectional normal

modulus fibre reinforced polymer CFRP sheet. Therefore, modelling

of the failure and damage of CFRP sheet has been achieved in this

study using this material model, which depends on continuum

damage mechanisms and employs Hashin’s failure criteria

[27,28]. By adopting this material model, the plasticity of CFRP

composite is always neglected and damage is detected and charac-

terised based on the material stiffness reduction. This material

degradation can be numerically achieved based on Hashin’s failure

criteria [27,28] which offer numerical simulation of composite

materials damage. Therefore, in this study, to provide a more accu-

rate validation of the numerical models with the experimental re-

sults, the CFRP composite damage has been considered during the

quasi-static and dynamic analyses of double-strap joints for both

joints with 1 CFRP layer and 3 CFRP layers per side.

5.2. Adhesive

For both quasi-static and dynamic analyses of double strap

joints, appropriate modelling of the adhesive layer is importantin order to enable correct modelling of the failure of joints. ABA-

QUS has a special type of element known as a ‘‘cohesive element’’

which is more suitable to model the adhesive response and is

applicable for both types of ABAQUS analyses (implicit and expli-

cit). It has been reported in ABAQUS [25] that the cohesive element

is more practical and suitable to model interfaces in composites

and any cases where the integrity and strength of interfaces may

be of interest as well as the behaviour of adhesively-bonded joints.

Furthermore, damage and delamination in composites can also be

successfully predicted using this type of element [22,29–31]. By

adopting this element type, it is possible to model damage or crack

initiation and damage evolution leading to eventual failure at the

interface. Therefore, in this study, the adhesive layer (cohesive

zone) is modelled as cohesive elements with fracture mechanism

constitutive definitions. It is worth noting that the cohesive zone

must be discretised with a single layer of cohesive elements

through the thickness as specified by the ABAQUS manual [25].

This requirement is based on the definition of cohesive element.

Otherwise, the utilisation of more than one cohesive element via

the adhesive thickness is not recommended because it may cause

unreliable results [32]. According to traction-separation law and

as mentioned in the ABAQUS manual [25], the separation is calcu-lated based on the relative displacement of the top and bottom sur-

face of the cohesive element. Thus the cohesive element thickness

(adhesive thickness) is assumed to be one, or can be calculated

from the nodal coordinates of the cohesive element.

However, generally, failure of adhesive includes crack initiation

and propagation and both can be simulated using the cohesive ele-

ment. Thus, damage initiation represents the onset of degradation

in the response of the adhesive material and this starts when the

stresses and/or strains fulfil the requirements of the adopted fail-

ure criterion. The built-in library of ABAQUS has four different fail-

ure criteria for damage initiation under the traction-separation

law. These are maximum nominal stress criterion, maximum nom-

inal strain criterion, quadratic nominal stress criterion and qua-

dratic nominal strain criterion. The first two criteria assume that

adhesive damage begins only when the maximum nominal stress

or strain reaches the capacity of the adhesive, whereas the last

two criteria consider the combination effect of stresses or strains

on the damage initiation in the adhesive layer. It has been reported

by da Silva et al. [33] that adhesively-bonded joints are subjected

to complex states of stress (shear and peeling stresses) and these

stresses contribute to the adhesive failure. Therefore, in this study,

the mixed mode failure criterion, the quadratic traction damage

initiation criterion (QUADSCRT), which considers both mode I

and mode II failures, is selected. For the QUADSCRT failure crite-

rion, adhesive damage is assumed to initiate when the following

equation is fulfilled:

ðt nÞ

t on

2

þ ðt sÞ

t os

2

þ ðt t Þ

t ot

2

¼ 1 ð1Þ

where t n, t s and t t denote the stresses in three directions of the

adhesive layer (normal, first and second shear direction). t on; t os and

t ot refer to the peak values of the nominal stresses of adhesive in

three directions layer (normal, first and second shear direction). n,

s and t represent the directions normal, first and second shear direc-

tion which are parallel to the interface between adhesive and

adherents.

5.3. Steel plate

For the technique of adhesively bonded joints, Hart-Smith [34]

has outlined that the theoretically-calculated effective bond length

of adhesively-bonded joints is significantly influenced by the ulti-

mate tensile strength of steel. Therefore, for both quasi-static anddynamic analyses, steel plate is modelled as elastic–plastic mate-

rial to accurately model double strap joints for joints with 1 CFRP

layer and 3 CFRP layers per side.

6. Material properties

Detailed information about the measured quasi-static and dy-

namic material properties of CFRP and adhesive and steel plate

can be found in Tables 1 and 2 respectively. The tensile properties,

which have been used in this study to define the material proper-

ties of finite element models, involve the tensile strength, modulus

of elasticity and failure strain of each material. The shear proper-

ties of the adhesive layer (cohesive element) are also tabulated in

Table 3. In the case of joints with 3 CFRP layers, experimentally,



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the CFRP patch is formed on each side of the double-strap joint by

adhesively bonding three CFRP layers using three adhesive layers.

Therefore, in the current FE simulations, the CFRP patch is assumed

to consist of three CFRP layers and two adhesive layers (the adhe-

sive layers between the CFRP layers). It is also assumed thatthe thickness of the two adhesive layers is identical, which is

equal to the thickness of the adhesive layer between the steel

plates and the CFRP patch. As has been mentioned in the experi-

mental study [20], the total joint thickness was measured using a

digital measuring tool (a Mitutoyo Absolute Digimatic Caliper

500-196-20) with accuracy of 0.002 mm. The total patch thickness

is determined by subtracting the steel plate thickness from this

measurement. Consequently, the thickness of the adhesive layer

can be determined using the formula below because the thickness

of the CFRP layer is already known:

t ðeqÞCFRPpatch ¼ ð3 t CFRP Þ þ ð2 t adÞ ð2Þ

where t eq,CFRPpatch, t CFRP and t ad denote to equivalent thickness of the

CFRP patch, thickness of the CFRP sheet and thickness of the adhe-sive layer respectively.

Thus, for simplicity, the material properties of the CFRP patch

are found using the macroscopic material properties technique

and such a method of calculation the material properties has been

also used in another study [1]. Based on this strategy, the material

properties of the CFRP patch are considered to be mainly depen-

dent on the properties of the CFRP sheet and adhesive because

the CFRP patch consists of CFRP sheet and adhesive only. Conse-

quently, the CFRP patch properties are calculated as equivalent

tensile strength, modulus of elasticity and strain. This can be

achieved following the formula:

rðeqÞCFRPpatcht ðeqÞCFRPpatch ¼ rCFRP t CFRP þ radt ad

rðeqÞCFRPpatch ¼rCFRP t CFRP þ radt ad

t ðeqÞCFRPpatch

ð3Þ

where r(eq)CFRPpatch, t (eq)CFRPpatch, rCFRP , t CFRP , rad and t ad, and repre-

sent the equivalent tensile strength of the CFRP patch, equivalent

thickness of the CFRP patch, tensile strength of the CFRP sheet,

thickness of the CFRP sheet, tensile stress of the adhesive and thick-

ness of the adhesive layer respectively.

The modulus of elasticity is also determined as below following

the same concept:

E ðeqÞCFRPpatcht ðeqÞCFRPpatch ¼ E CFRP t CFRP þ E adt ad

E ðeqÞCFRPpatch ¼E CFRP t CFRP þ E adt ad

t ðeqÞCFRPpatch

ð4Þ

where E (eq)CFRPpatch, t (eq)CFRPpatch, E CFRP , t CFRP , E ad and t ad and refer toequivalent modulus of elasticity of the CFRP patch, equivalent thick-

ness of the CFRP patch, modulus of elasticity of the CFRP, thickness

of the CFRP sheet, modulus of elasticity of the adhesive and thick-

ness of the adhesive layer respectively.

7. Comparison of results

7.1. Ultimate joint capacity

Tables 4–11 present a clear comparison of the experimentally-

measured ultimate joint capacities and those predicted from FEA

for double-strap joints with 1 and 3 CFRP layers per side. The data

compared are the quasi-static and three impact loadings at speeds

of 3.35 m/s, 4.43 m/s and 5 m/s and for various bond lengths rang-ing from 10 mm to 100 mm. For joints with 1 CFRP layer, it is evi-

dent in Tables 4–7 that the predicted ultimate joint capacities for

all test speeds and for the different bond lengths are consistent

with the ultimate tensile loads observed from the experimental

test program reported in [20]. The correlation of the tensile failure

loads of varying bond lengths and for the four loading speeds, as

predicted by the FEA and as measured experimentally, is illus-

trated in Fig. 3. It can be seen that the (P FE/Avg. P ult) ratios range

from 0.846 to 1.003, 0.876 to 1.035, 0.951 to 0.992 and 0.999 to

1.030 for the quasi-static and dynamic test speeds of 3.35 m/s,

4.43 m/s and 5 m/s respectively. Thus, it can be concluded that

each of the quasi-static and dynamic joint strengths for all the

bond lengths are predicted reasonably well.

Table 1

Quasi-static and dynamic material properties of the CFRP sheet and Araldite 420 adhesive.

Property CFRP sheet Araldite 420

Loading speed (m/s) Loading speed (m/s)

3.33 10-5 3.35 4.43 5 3.33 10-5 3.35 4.43 5

Tensile strength (MPa) 1935 2420 2767 3108 29.00 93.25 96.06 99.42

Tensile modulus (GPa) 206.6 244.2 250.7 261.89 1.455 2.848 2.998 3.102

Tensile failure strain (%) 0.91 0.99 1.13 1.20 9.32 4.66 4.29 4.11

Table 2

Quasi-static and dynamic tensile material properties steel plate.

Property Loading speed (m/s)

3.33 105 3.35 4.43 5

Yield stress (MPa) 371.04 570.30 628.22 673.07

Ultimate tensile strength (MPa) 526.27 691.70 743.54 780.60

Tensile modulus (GPa) 204.25 212.30 216.26 220.24

Ultimate strain (%) 19.30 19.06 18.97 18.89

Table 3

Quasi-static and dynamic shear properties of the adhesive layer (cohesive element).

Loading

speed (m/s)

Shear strength

(MPa)

Stiffness of the interface (N/mm)

Normal

direction

1st shear

direction

2nd shear

direction

3.33 105 24.78 2745 1017 1017

3.35 66.23 5373 1990 1990

4.43 69.49 5657 2095 2095

5 71.2 5853 2168 2168

Table 4

Comparison between the quasi-static experimental and finite element analysis results

for joints with 1 CFRP layer.

Specimen

label

L1 (mm) L2 (mm) Experiment Finite element analysis

Avg. P ult (kN) P FE (kN) P FE/Avg. P ult

CF-1-A 10 80 19.84 19.88 1.002

CF-1-A 20 80 37.87 32.04 0.846

CF-1-A 30 80 45.22 44.30 0.980

CF-1-A 40 80 44.06 44.18 1.003

CF-1-A 50 80 47.44 44.14 0.930

CF-1-A 60 80 46.17 44.15 0.956

CF-1-A 70 100 46.33 44.16 0.953

CF-1-A 80 100 48.18 44.40 0.922

CF-1-A 90 115 45.82 44.18 0.964

CF-1-A 100 115 46.73 44.19 0.946

52 H. Al-Zubaidy et al. / Composite Structures 99 (2013) 48–61


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With regard to CFRP/steel double strap joints with 3 CFRP layers

per side, Tables 8–11 show a clear comparison between the numer-

ically-predicted and experimentally-measured ultimate joint

capacities of various bond lengths and four different test speeds.

In general, it is evident that FE models predict the ultimate joint

capacities well for all test speeds and for the different bond lengths

included in the experimental test program. This close consistency

is more obvious in Fig. 4, which depicts the correlation of the ten-

sile joint capacities for various bond lengths and for all the four dif-

ferent loading velocities as calculated by the FEA and as

experimentally-measured. It shows that the ratio of P FE/Avg. P ultranges from 0.865 to 1.083, 0.939 to 1.045, 1.01 to 1.068 and

1.018 to 1.080 for the quasi-static and the three loading speeds

of 3.35 m/s, 4.43 m/s and 5 m/s respectively. Compared to the ob-

served correlation ratios from joints with 1 CFRP layers, it is clear

that these ratios are slightly higher than those obtained from joints

with 1 CFRP layer. The reason for this slight difference is mainly

attributed to the slight change in the predicted failure modes com-

pared to those realised experimentally. The CFRP delamination is

not detected by FE models for all loading speeds (quasi-static

and dynamic), whereas this failure is clearly recognised under

experimental conditions. This will be discussed further in Sec-

tion 7.3. Finally, even though there is little change in the predicted

failure mode, it can be concluded that all quasi-static and dynamic

joint strengths are predicted reasonably well.

Table 5

Comparison between the dynamic experimental and finite element analysis results

for joints with 1 CFRP layer at loading speed of 3.35 m/s.

Specimen

label



CF-1-A 10 80 45.66 47.24 1.035

CF-1-A 20 80 63.49 55.62 0.876

CF-1-A 30 80 57.77 55.12 0.954

CF-1-A 40 80 57.37 55.32 0.964

CF-1-A 50 80 56.21 55.00 0.978

CF-1-A 60 80 57.17 54.72 0.957

CF-1-A 70 100 56.37 54.84 0.973

CF-1-A 80 100 57.16 54.76 0.958

CF-1-A 90 115 56.65 54.4 0.960

CF-1-A 100 115 56.99 54.08 0.949

Table 6


for joints with 1 CFRP layer at loading speed of 4.43 m/s.

Specimen

label



CF-1-A 20 80 56.21 55.74 0.992

CF-1-A 30 80 58.73 56.26 0.958

CF-1-A 40 80 58.94 56.08 0.951

CF-1-A 50 80 57.26 56.12 0.980

CF-1-A 60 80 58.18 56.18 0.966

CF-1-A 70 100 58.09 56.06 0.965

Table 7


for joints with 1 CFRP layer at loading speed of 5 m/s.

Specimen

label



CF-1-A 20 80 57.04 58.76 1.030

CF-1-A 30 80 58.85 59.28 1.007CF-1-A 40 80 59.43 59.36 0.999

CF-1-A 50 80 57.67 59.22 1.027

CF-1-A 60 80 58.23 59.18 1.016

CF-1-A 70 100 57.66 59.24 1.027

Table 8

Comparison between the quasi-static experimental and finite element analysis results

for joints with 3 CFRP layers.

Specimen

label



CF-3-A 10 80 29.61 25.60 0.865

CF-3-A 20 80 54.20 52.32 0.965

CF-3-A 30 80 68.88 67.86 0.985CF-3-A 40 80 82.88 79.13 0.955

CF-3-A 50 80 96.83 102.88 1.062

CF-3-A 60 80 101.35 106.16 1.047

CF-3-A 70 100 103.24 106.48 1.031

CF-3-A 80 100 97.40 105.44 1.083

CF-3-A 90 115 97.38 105.40 1.082

CF-3-A 100 115 99.22 105.12 1.059

Table 9


for joints with 3 CFRP layers at loading speed of 3.35 m/s.

Specimen

label



CF-3-A 10 80 84.29 79.12 0.939

CF-3-A 20 80 110.03 107.72 0.979

CF-3-A 30 80 129.83 131.44 1.012

CF-3-A 40 80 136.21 142.36 1.045

CF-3-A 50 80 152.59 148.96 0.976

CF-3-A 60 80 143.26 148.53 1.037

CF-3-A 70 100 144.70 148.61 1.027

CF-3-A 80 100 145.18 149.46 1.029

CF-3-A 90 115 144.70 150.12 1.037

CF-3-A 100 115 146.41 149.24 1.019

Table 10


for joints with 3 CFRP layers at loading speed of 4.43 m/s.

Specimen

label



CF-3-A 20 80 114.08 115.48 1.012

CF-3-A 30 80 135.51 140.02 1.033

CF-3-A 40 80 145.15 154.96 1.068

CF-3-A 50 80 155.00 156.56 1.010

CF-3-A 60 80 148.15 156.01 1.053

CF-3-A 70 100 154.39 156.24 1.012

CF-3-A 90 115 149.50 156.60 1.047

Table 11


for joints with 3 CFRP layers at loading speed of 5 m/s.

Specimen

label

L1

(mm) L2

(mm) Experiment Finite element analysis


CF-3-A 20 80 124.10 126.28 1.018

CF-3-A 30 80 148.24 151.44 1.022

CF-3-A 40 80 154.04 164.60 1.069

CF-3-A 50 80 157.58 164.96 1.047

CF-3-A 60 80 152.95 165.20 1.080

CF-3-A 70 100 158.16 164.96 1.043

CF-3-A 90 115 157.02 164.76 1.049



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7.2. Effective bond length

The effect of increasing the test speed on the effective bond

length of CFRP/steel double-strap joints with 1 and 3 CFRP layers

per side using Araldite 420 adhesive has been experimentally

investigated and the results presented in [20]. In relation to joints

with 1 CFRP layer per side, this effect is shown again in Fig. 5 where

the predictions by the FEA are also included. It is evident that thereis a slight reduction in the effective bond length with increasing

the loading speed and this trend is well captured by FE models.

It is explicitly depicted by both the experimental results and the

FE models that the quasi-static bond length is 30 mm, whereas it

reduces insignificantly to 20 mm at dynamic loading speeds. It is

also found that it remains almost the same for all three different

loading speeds. This means that FE models capture such a phenom-

enon well, which indicates that increasing the loading speed be-

yond 3.35 m/s has not affected the effective bond length.

Concerning CFRP/steel double-strap joints with 3 CFRP layers

per side, the effect of testing speed on the effective bond length

has been numerically determined using FE models as exhibited

in Fig. 6. This graph shows a clear comparison between the

numerically-predicted and experimentally-observed effectivebond lengths for the quasi-static and loading speeds of 3.35 m/s,

4.43 m/s and 5 m/s. Again, similar to the double-strap joints with

1 CFRP layer, it is obvious that the developed FE models determine

the effective bond length for all loading speeds quite well, and the

results confirm the general trend, which is gradually decreasing

with increasing impact velocity, as experimentally observed.

This means that the numerical modelling is quite capable of

determining the effective bond lengths for all loading speeds. It

is believed that the fluctuations of the strength values determined

experimentally for bond lengths in excess of effective bond length

is attributed to the presence of CFRP delamination through the

CFRP layers. This type of failure is not detected by FE models

because the three CFRP layers are modelled as one patch of known

properties, and as a consequence, CFRP delamination failure cannotbe simulated.

As mentioned in the previous investigation [20] and clearly

illustrated in Fig. 6 by both the experimental results and the FE

models, the quasi-static effective bond length is 50 mm. However,

for the three dynamic tests, it can be seen that although it remains

50 mm at a test speed of 3.35 m/s like the quasi-static bond length,

it slightly reduces to 40 mm for loading speeds of 4.43 m/s and

5 m/s. Thus, this excellent agreement between FE models and

experimental results highlights the adequacy of the FEA analyses.

7.3. Failure pattern

In the case of CFRP/steel double-strap joints with 1 CFRP layer

per side, the FEA results of all the various bond lengths and differ-ent loading speeds have indicated almost similar failure modes to

Fig. 3. Correlation between the experimental and predicted ultimate loads form

FEA for joint with 1 CFRP layer at different loading speeds.

Fig. 4. Correlation between the experimental and predicted ultimate loads form

FEA for joint with 3 CFRP layers at different loading speeds.

Fig. 5. Effect of test speed on effective bond length for joints with 1 CFRP layer

(experiment and FEA).

Fig. 6. Effect of test speed on effective bond length for joints with 3 CFRP layers

(experiment and FEA).



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those observed in the experiments. As reported in the authors pre-

vious study [20], the prevalent failure pattern in the experiments is

CFRP failure (fibre breakage and some CFRP delamination). Fig. 7a–

d shows the failure modes predicted by FE models for the quasi-

static and three impact loading speeds. Inspection of these figures

clearly illustrates that FE models are able to detect CFRP breakage,

while the experimentally-observed slight CFRP delamination can-

not be clearly realised. It is believed that this is because the CFRPlayer is modelled as one layer of known properties, whereas in

reality it comprises many carbon fibre bundles and these bundles

are impregnated by epoxy during the manufacture of double strap

joints to form a CFRP patch with 1 CFRP layer. It is also important

to note that the type of failure determined in this study is based on

checking both the deformation of the failed samples at failure and

the satisfaction of the adopted failure criteria of both CFRP and

adhesive.

Concerning the failure mechanisms of CFRP/steel double-strap

joints with 3 CFRP layers per side, it has been shown in [20] that

the experimentally-observed quasi-static failure modes were deb-

onding (steel and adhesive interface failure) and CFRP delamina-

tion, whereas CFRP delamination was the prevailing dynamicfailure pattern for all dynamic tests. However, some differences ex-

ist between the predicted and experimentally-observed failure

modes. The quasi-static FE model indicates one failure mode sim-

ilar to those observed in the experiments. This is debonding failure,

as shown in Fig. 8a. The other failure mode, CFRP delamination, is

Fig. 7. Predicted failure patterns from FEA for joints with 1 CFRP layer per side (a) 3.34 105 m/s, (b) 3.35 m/s, (c) 4.43 m/s, (d) 5 m/s.



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not detected. This is attributed to the fact that the three CFRP lay-

ers per side are simulated as an equivalent laminate with known

properties, as calculated in Section 6. Thus, the FE models are un-

able to predict CFRP delamination which occurs experimentally

via the fibre bundles for joints with 1 CFRP layer and within subse-

quent layers for joints with 3 CFRP layers.

On the other hand, in relation to the dynamic failure patterns,

the numerically-predicted failure modes have also highlighted lit-

tle variance in comparison with those observed experimentally.

Fig. 8b–d illustrates that the failure mode commonly predicted

by the explicit FE models for all the impact loading speeds is CFRP

breakage instead of CFRP delamination, and these predictions are

similar to those modes predicted numerically for CFRP/steel

double-strap joints with 1 CFRP layers per side. Thus, CFRP

delamination disappears again for the reason mentioned above. It

is worth noting that although CFRP delamination is not predicted

numerically, the detection of CFRP breakage confirms the key

experimental finding of this study, which is that no debonding fail-

ure (steel and adhesive interface failure) occurs under any of the

dynamic loading speeds. This is attributed to the shear strength

enhancement of the epoxy between the CFRP patch and the steel

plate under dynamic loading, as explained in [20].

Overall, although there is some difference between the numer-

ically-predicted and experimentally-observed failure patterns, the

Fig. 7. (continued)



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failure mode predictions of FE models are still considered reason-

ably high, especially when compared with the predictions of other

parameters (ultimate joint strength, effective bond length and

strain distributions along the CFRP bond length).

7.4. Strain distribution along the bond length

The experimentally-measured and numerically-predicted strain

distributions along the bond length of CFRP/steel double strap

joints with 1 and 3 CFRP layers per side at quasi-static and three

dynamic loading speeds of 3.35 m/s, 4.43 m/s and 5 m/s are com-pared in Figs. 9a–d and 10a–d respectively. The comparison is

made at three load levels. For comparison purposes, the load levels

of both experimental and numerical strain distributions are chosen

to be as close as possible to each other. As clearly depicted in the

authors previous investigation [20], strain values were experimen-

tally recorded using several foil strain gauges mounted at fixed dis-

tances (15 mm) starting from the mid-joint towards the end of the

CFRP patch. Thus, the strain monitoring points in the FE models are

selected as close as possible to the experimental locations where

the strain gauges were placed.

For CFRP/steel double-strap joints with 1 CFRP layer, in general,

it can be seen in Fig. 9a–d that the FE models simulate the straindistributions along the bond length for both the quasi-static and

Fig. 8. Predicted failure patterns from FEA for joints with 3 CFRP layers per side (a) 3.34 105 m/s, (b) 3.35 m/s, (c) 4.43 m/s, (d) 5 m/s.



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all the three dynamic speeds reasonably well. Very close matching

is realised between the measured and predicted strain values for

all load levels and this is the case for all four test speeds. This

can be attributed to the fact that the observed failure mode of both

the numerical analyses and experiments is very similar (fibre

breakage).

Careful inspection of Fig. 10a–d reveals that the predicted strain

values along the CFRP patch of CFRP/steel double-strap joints with

3 CFRP layers per side for all the quasi-static and dynamic speeds

are consistent with the experimental results, with the exception

of the strain reading at the mid-joint location. The measured strain

at this position represents the strain captured by strain gauge 1

(G1) as depicted in [20]. It is evident that there is a pronounced dif-

ference between the predicted and measured strain values at this

location, as the former is much higher than the latter. Thus, the ra-

tio of the predicted strain/measured strain is found to be approxi-

mately 1.18, 1.56, 1.57 and 1.51 for the quasi-static and for the

dynamic test speeds, 3.35 m/s, 4.43 m/s and 5 m/s respectively. It

Fig. 8. (continued)



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Fig. 9. Comparison of the predicted and measured strain distribution at quasi-static rate for joints with 1 CFRP layer (experiment and FE).

Fig. 10. Comparison of the predicted and measured strain distribution at quasi-static rate for joints with 3 CFRP layers (experiment and FE).



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is clear that the quasi-static ratio is much lower than the dynamic

ratios. This is because the occurrence of CFRP delamination accel-

erates with increasing test speed, as discussed in [20]. However,

it is believed that this marked difference between the predicted

and measured strain is related to the slight change between the

numerically-predicted and experimentally-observed failure mech-

anisms. While the experimentally-observed quasi-static failure

modes were debonding (steel and adhesive interface failure) andCFRP delamination, CFRP delamination was shown to be the dom-

inant dynamic failure for all dynamic speeds. Conversely, CFRP

breakage rather than CFRP-delamination is numerically predicted.

The reasons for this slight change in failure mode are explained in

Section 7.3.

Compared to the strain profiles of joints with 1 CFRP layer, a

clear difference between the predicted and measured strain value

appears specifically at the mid-joint of the joints with 3 CFRP lay-

ers although generally there is a very close matching between the

predicted and measured strain distribution at other locations along

the bond length. This is because the probability of occurrence of

CFRP delamination for joints with 1 CFRP layer is much lower than

that for joints with 3 CFRP layers. This is evident when the exper-

imentally-observed failure modes of both types of CFRP/steel dou-

ble-strap joints with 1 and 3 CFRP layers are compared.

8. Concluding remarks

In this paper, three-dimensional finite element method is uti-

lised in the numerical analysis of both CFRP/steel double-strap

joints with 1 and 3 CFRP layers per sides using ABAQUS program.

Steel plate has been modelled as elastic–plastic material and CFRP

and adhesive failures are taken into account in these simulations.

Continuum shell elements are utilised to simulate the CFRP patch

whereas the adhesive layer is modelled as a cohesive element.

The findings from this work are:

Overall, the developed FE models reasonably predicted thequasi-static and dynamic behaviour of both CFRP/steel dou-

ble-strap joints with 1 and 3 CFRP layer per side. This is proven

through the sufficient prediction of the peak load, effective

bond length, failure patterns and strain distribution along the

bond length of types of joints.

It is found that, generally, there is a good correlation between

the predicted and experimental ultimate joint strength of both

types of joints with 1 and 3 CFRP layers. However, the predicted

joint strength for joints with 3 CFRP layers is slightly higher

than the experimental one, specifically for bond lengths equal

to or greater than the effective bond length and at higher load-

ing speed (5 m/s). This is due to the inability of the FE model to

simulate CFRP-delamination through the layers which is the

experimentally common failure mode.

The numerical simulations predict well the effective bond

length for both joints with 1 and 3 CFRP layers and are in excel-

lent agreement with those determined experimentally. This

proved to be the case for all loading speeds.

Little difference between the experimentally observed and the

numerically predicted failure patterns is realised for both types

of joints especially for joints with 3 CFRP layers. Delamination

through CFRP layers is the dominant failure mode experimen-

tally, however, it does not realise numerically. This is attributed

to the fact that the three CFRP layers per side are simulated as

an equivalent laminate with macroscopic properties.

There is an excellent match between the predicted and the

experimentally measured strain profiles along the bond length

for all loading speeds and at all load levels particularly for joints

with 1 CFRP layer. However, compared to joints with 3 CFRP

layers, a clear difference between the measured and predicted

strain value is detected at the mid-joint whereas the other

strain values along the bond length are in good agreement.

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