The study focuses on using fracture mechanics to evaluate mixed-mode fracture properties of adhesively bonded aerospace material systems. As a part of experimental efforts, mixed-mode fracture tests were performed using modified Arcan specimens consisting of several combinations of adhesive, composite and metallic adherends using a special loading device. By varying the loading angle, alpha from 0 degrees to 90 degrees, mode I, mixed-mode and mode II fracture data were obtained experimentally. Experimental and theoretical studies of mixed-mode fracture behaviour of adhesively bonded aluminium, steel and CF/PEI composite joints were also performed using an adhesive in the aerospace industry. Finite element analyses were carried out on specimens with different adherends. Based on those analyses, mixed-mode fracture criterions for the adhesively bonded systems under consideration have been determined

Choupani, Naghdali

Mai, Yiu-Wing

Ye, Lin

University of Queensland eSpace

SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
 
Mixed-Mode Fracture Of Adhesively Bonded Joints 
Naghdali Choupani, Lin Ye and Yiu-Wing Mai 
Centre for Advanced Materials Technology, School of  Aerospace, Mechanical and Mechatronic Engineering 
J07, The University of Sydney, Sydney, NSW 2006, Australia 
 
 
 
ABSTRACT:    The study focuses on using fracture mechanics to evaluate mixed-mode fracture properties of 
adhesively bonded aerospace material systems. As a part of experimental efforts, mixed-mode fracture tests were 
performed using modified Arcan specimens consisting of several combinations of adhesive, composite and 
metallic adherends using a special loading device. By varying the loading angle,α from 0ο to 90ο, mode I, mixed-
mode and mode II fracture data were obtained experimentally. Experimental and theoretical studies of mixed-
mode fracture behaviour of adhesively bonded aluminium, steel and CF/PEI composite joints were also 
performed using an adhesive in the aerospace industry. Finite element analyses were carried out on specimens 
with different adherends. Based on those analyses, mixed-mode fracture criterions for the adhesively bonded 
systems under consideration have been determined.  
 
1 INTRODUCTION 
Adhesively bonded joints and bonded repairs made to cracked metallic structures have been 
continuously receiving attention in the aerospace industry for the purpose of enhancing the fatigue 
resistance and restoring the stiffness and strength of damaged/cracked structures. Although stress-
based approaches, which focuses on indicating both shear and normal (peel) stresses, have been the 
subject of a vast amount of research, fracture mechanics has also been proven to be a viable tool for 
adhesively bonded joint analysis. Fracture mechanics deals with the effects of flaws and fatigue in the 
presence of cracks [Kinloch, 1987]. A number of test methods have been proposed by many 
researchers to determine fracture toughness of adhesively bonded joints. The double cantilever beam 
(DCB) test is the most widely used method for measuring mode-I (opening) fracture toughness. The 
end-notched flexure (ENF) has emerged as one of the most convenient mode-II (shear) type cracking 
[Glyn et al, 1997]. Various attempts have been made to characterize fracture toughness under mixed-
mode loading conditions in adhesively bonded joints, but mostly beam type specimens were used. The 
crack lap shear (CLS) and the mixed-mode bending (MMB) test specimens have been proposed by 
combining the schemes used for DCB and ENF tests to study the mixed mode fracture of bonded joints 
[Ducept et al, 1999]. However, for these test methods there are problems to create a wide range of 
mixed-mode ratios which limit their usefulness. Also, different beam type specimens would be 
required in order to obtain reliable results for fracture toughness in pure mode-I, pure mode-II, and 
mixed- mixed-mode loading conditions [Rikards, 2000]. 
Previous work at CAMT in this area has centered on the double cantilever beam (DCB) and double-
lap and lap-strap joints [Yan et al, 2001]. However, deeper understanding of the fracture behavior of 
adhesively bonded joints, and particularly under mixed mode loading conditions, is needed in order to 
fully achieve the benefits of adhesive bonding [Pang, 1995]. In this work, a modified version of Arcan 
specimen is made for the mixed-mode fracture test of adhesively bonded joints, which allows mode-I, 
mode-II, and almost any combination of mode-I and mode-II loading to be tested with the same test 
specimen configuration [Arcan et al, 1978]. Therefore, the limitations presented in the previous mixed-
mode toughness test methods can be avoided.  
2 EXPERIMENTAL PROCEDURES 
2.1 Material 
This study examined a number of different substrates including aluminum, steel and CF/PEI 
composite. Although there are no such bonded structures on the aerospace applications, it was decided 
to investigate the mixed mode fracture of these bonded systems to better understand the behavior of the 
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
FM® 300-2 adhesive and to calculate the effect of adherends. FM® 300-2 is a high strength rubber 
modified film adhesive widely used for bonding composite structures in aerospace bonding 
applications. The adhesive were processed according to the manufacturer’s specification. A non-
adhering film was inserted in the middle of the adhesive layer in order to introduce a starter crack. The 
composite adherend was a woven plate consisting of 12 plies of CF/PEI prepergs, in order to obtain a 
plate thickness of approximately 3mm. The prepergs were laid up by hand to the required number of 
plies and were produced using hot press. The specimens were cut with a diamond wheel and machined 
to the dimensions of 30x10x3 mm. The elastic constants of adherends and adhesive used in FEM 
analyses are summarized in Table 1. The CF/PEI composite is similar to the material investigated 
previously [Choupani et al, 2004], where 1 is the direction parallel to the fiber and 2 and 3 are the 
directions transverse to the fibers, while the direction of the crack coincides with the fiber direction 
(Figure 1). 
 
Table I Elastic Properties of adhesive and adherends.  
Material 
E1 
[GPa] 
E2 
[GPa] 
E3 
[GPa] 
G12 
[GPa] 
G13 
[GPa] 
G23 
[GPa] υ12 υ13 υ23 
FM® 300-2 2.3 2.3 2.3 0.8 0.8 0.8 0.4 0.4 0.4 
Aluminum 72 72 72 27 27 27 0.3 0.3 0.3 
Steel 207 207 207 79.6 79.6 79.6 0.3 0.3 0.3 
CF/PEI 57.6 57.6 8.7 3.1 2.8 2.8 0.03 0.4 0.4 
 
2.2 Test method and setup 
The loading device and modified version of Arcan specimen are shown In Figure 1. The composite 
strip was attached into aluminum plates using adhesive. Bonding was carried out using a special jig to 
ensure alignment of the specimen halves. Steel substrates were polished prior to bonding using sand 
paper and degreased by an alkaline solution. For surface preparation of aluminum plates, FPL-Etch 
method was applied [ASTM, 1995]. Composite surface preparation method involved degreasing with 
methyl ethyl ketone (MEK), rinse and check for water break, hand abrasion with 320 grit aluminum 
oxide abrasive papers and clean for bonding [Daghyani et al, 1995]. The specimens were pinned into 
the loading device in order to transmit the applied loads. With the application of load P and by varying 
the loading angle,α from 0ο to 90ο , pure mode-I, pure mode-II, and all mixed- mode loading 
conditions can be created and tested. Fracture tests were conducted by controlling the constant 
displacement rate of 0.5 mm/min and the fracture loads and displacements were recorded. All tests 
were carried out using an Instron 5567 testing machine. Tests were repeated at least 3 times for each 
loading angle. The load-displacement curves generated by the test machine were used to determine 
maximum loads and displacement (Figure2). After testing, optical microscopy was used to examine the 
appearance of the fracture surface. 
 
                                                (a)                                          (b)                                           (c) 
Figure 1 Overview of test rig and set up: (a) Mode-I test; (b) Mode-II test; (c) Geometry of the test fixture 
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
3 ANALYSIS OF MIXED-MODE FRACTURE 
The energy release rates for isotropic material can be calculated from the following relationships: 
0
1000
2000
3000
4000
5000
6000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Displacement [mm]
Lo
ad
 [N
]
α=90°
α=75°
α=45°
α=60°
α=0°
α=30°
α=15°
 
FIGURE 2 typical load-displacement relationships for adhesive with aluminum adherends 
 
EKGEKG IIIIII
22 , ==                                                   (1)    
where EE =  for plane stress, )1/( 2ν−= EE  for plane strain conditions, IK  and IIK  are mode-I and 
mode-II stress intensity factors, respectively. 
The stress intensity factors ahead of the crack tip for a modified version of Arcan specimen were 
calculated by using the following equations: 
)/(sin),/(cos 21 wafwt
aP
Kwaf
wt
aP
K cIIcI απαπ ==                             (2)    
where cP  is critical load at fracture, α is loading angle, w is specimen length, t is specimen thickness 
and a  is crack length. In turn IK  and IIK  are obtained using geometrical factors )/(1 waf  
and )/(2 waf , respectively, which are obtained through finite element analysis of Arcan test specimen. 
In the context of quasi-static analysis the J-integral in two dimensions is defined as: 
Γ⋅⎟⎠
⎞⎜⎝
⎛
∂
∂⋅−⋅= ∫Γ→Γ dWJ qxuσIn0lim                                                    (3) 
where Γ is an arbitrary contour, W is the elastic strain energy for elastic material, q is a unit vector in 
the virtual crack extension direction, n is the outward normal to Γ, σ is the stress tensor and u is the 
displacement vector, as shown in Figure 3. The method used to calculate the stress intensity factor was 
an interaction integral method performed in ABAQUS, and is required to separate the components of 
the stress intensity factors in conjunction of finite element analysis. In the interaction integral method 
[Habbit et al, 2001; Sukumar, 2004], the two-dimensional auxiliary fields are introduced and 
superposed on the actual fields. By judicious choice of the auxiliary fields, the interaction integral can 
be directly related to the stress intensity factors int4 JBK ⋅= π  where TIIIIII JJJ ],,[ intintintint =J . Based on 
the definition of the J-integral, the interaction integrals αintJ  can be expressed as: 
Γ⋅⎟⎟⎠
⎞
⎜⎜⎝
⎛
∂
∂⋅−⎟⎠
⎞⎜⎝
⎛
∂
∂⋅−⋅= ∫Γ→Γ dJ aux
aux
aux qx
u
x
uσIn α
α
αα σεσ :lim
0int
                                  (4)    
The subscript aux represents three auxiliary pure Mode I, Mode II, and Mode III crack-tip fields for 
α=I, II, III, respectively. The domain form of the interaction integral is: ( ) dAquuJ jA iauxijauxiijjauxikik ,1,1,1int ∫ −−−= σσδεσα                                            (5) 
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
Figure 3 shows example of the mesh pattern of the specimen, which were performed with ABAQUS. 
The entire specimen with the initial crack a  was modeled using eight node collapsed quadrilateral 
element and the mesh was refined around crack tip, so that the smallest element size found in the crack 
tip elements was 
approximately 0.05mm. A linear 
elastic finite element 
analysis was performed under
 
  
 
 
 
 
 
 
 
 
 
 
 
 
Figure 3 Finite element mesh pattern of the entire specimen and around the crack tip 
 
a plane strain condition using r/1  stress field singularity. To obtain a r/1  singularity term of the 
crack tip stress field, the elements around the crack tip were focused on the crack tip and the mid side 
nodes were moved to a quarter point of each element side (as in Figure 3). If nodes a, b, and c are 
constrained to move together by specifying the same node number in the list of nodes forming the 
element, the strains and stresses are square root singular (suitable for linear elasticity). 
 
4 RESULTS AND DISCUSSION 
In order to assess stress intensity factors at fracture, IK  and IIK  using Equations (2), geometrical 
factors )/(1 waf and )/(2 waf  for both loading modes were determined. The wa /  ratio was varied 
between 0.3 and 0.7 at 0.1 intervals and a fourth order polynomial was fitted through finite element 
analysis as (for aluminum substrate): 
6447.2)/(617.20)/(834.65)/(463.90)/(822.45)/(
7013.3)/(767.33)/(632.99)/(6.122)/(629.46)/(
234
2
234
1
+−+−=
−+−+−=
wawawawawaf
wawawawawaf
                 (6)  
It is of interest to compare the non-dimensional stress intensity factors for different substrates under 
different loading angles. In Figure 4, it can be seen for all adherends that for loading angles α≤60o, the 
mode-I fracture becomes dominant. As mode-II loading contribution increases, 1f decreases and 2f  
increases. For α≥75o mode-II fracture becomes dominant. Adherends with different properties were 
found to have significant effects on the stress intensity factors that decrease as the adherend modulus 
increases. The difference between the modes-I stress intensity factors decreases as load application 
angle, α  increases, while mode-II stress intensity factors exhibits the opposite trend. 
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
0
0.2
0.4
0.6
0.8
1
1.2
0 15 30 45 60 75 90
Loading angle [degree]
G
eo
m
et
ric
al
  f
ac
to
rs
f1(CF/PEI)
f2(CF/PEI)
f1(Aluminum)
f2(Aluminum)
f1(Steel)
f2(Steel)
 
Figure 4 Geometrical factors vs. loading angle,α for different adherends 
The energy release rates were calculated using conventional Equations (1) and the calculated 
mixed-mode ratios of energy release rates for aluminum substrates are shown in Table 2. The 
relationship between the mixed-mode ratios of energy release rates and the loading angles α is 
presented in Figure 5. For loading angles close to pure mode-I loading, very high ratios of mode-I to 
mode-II is dominant. The ratios of strain energy release rates close to pure mode-II loading exhibits the 
opposite trend. It confirms that by varying the loading angle of Arcan specimen pure mode-I, pure 
mode-II and a wide range of mixed-mode loading conditions can be created and tested. 
 
Table II Mixed-mode ratios of energy release rates for aluminum adherends 
α 0° 3° 6° 9° 12° 15° 30° 45° 60° 75° 78° 81° 84° 87° 90° 
GII/GI 0 0.0007 0.003 0.007 0.01 0.02 0.09 0.3 0.8 3.7 5.9 10.6 24.4 101.1 ∞ 
-3.5
-2.5
-1.5
-0.5
0.5
1.5
2.5
0 15 30 45 60 75 90
Loading angle (degree)
M
ix
ed
 m
od
e 
ra
tio
lo
g(
G
II/
G
I)
 
Figure 5 The ratio of mode-II to mode-I, GII/GI (in logarithmic scale), vs. loading angle,α for aluminum adherends 
 
Figure 6 shows GIC, GIIC and GTC =GIC+GIIC, obtained by experiments for different adherends under 
various loading conditions. Mode-I and Mode-II fracture toughness of aluminum substrate specimens 
were approximately 210 J/m2 and 550 J/m2, respectively. The fracture path was generally cohesive in 
this system for all loading conditions, suggesting that surface preparation of the adherends were 
adequate. Joints with steel and composite adherends showed lower fracture toughness under all modes 
of loading. Mode-I and Mode-II fracture toughness of the steel and composite systems were 80 J/m2, 
279 J/m2 and 153 J/m2, 235 J/m2, respectively. Crack growth in the steel specimens was almost 
cohesive, but the crack meandered from one interface to the other with no distinct pattern. In composite 
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
adherends, the crack often departed from the adhesive layer and appeared to occur in the matrix layer 
of the composite strap within the plies nearest the bond line and a small number of fibers embedded in 
the adhesive remaining on the adherend (Figure 7). 
0
100
200
300
400
500
600
0 15 30 45 60 75 90
Loading angle [degree]
Cr
iti
ca
l e
ne
rg
y 
re
le
as
e 
ra
te
s 
(J
/m
2 )
GIC(CF/PEI)
GIIC(CF/PEI)
GTC(CF/PEI)
GIC(Aluminum)
GIIC(Aluminum)
GTC(Aluminum)
GIC(Steel)
GIIC(Steel)
GTC(Steel)
 
 Figure 6 Experimental results of GIC, GIIC, GTC=GIC+GIIC vs. loading angle,α for different adherends 
 
 
                                 (a)                                             (b)                                          (c) 
Figure 7 Fracture surfaces: (a) Aluminum adherends; (b) Steel adherends; (c) CF/PEI adherends 
 
5 CONCLUSION 
In this paper the mixed-mode fracture behavior for adhesively bonded joints constructed of several 
combinations of adhesive, composite and metallic adherends was investigated based on experimental 
and numerical analyses. A modified version of Arcan specimen was employed to conduct mixed-mode 
test using the special test loading device. The full range of mixed-mode loading conditions including 
pure mode-I and pure mode-II loading can be created and tested. It is a simple test procedure, 
clamping/unclamping the specimens is easy to achieve and only one type of specimen is required to 
generate all loading conditions. Results of joints with steel and composite adherends showed lower 
fracture toughness under all modes of loading. 
SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
 
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Daghyani, H. R., L. Ye, and Y.-W. Mai. “Mixed-mode Fracture of Adhesively Bonded CF/Epoxy Composite 
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83, 1995. 
Rikards, R “Interlaminar Fracture Behaviour of Laminated Composites,”Comp. and  Structures, 76:11-18, 2000. 
Sukumar, Z. Y. Huang, J.-H. Prevost and Z. Suo, ‘Partition of Unity Enrichment for Bimaterial Interface cracks’,  
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Yan, C., Y.-W. Mai, Q. Yuan, L. Ye, J. Sun. “Effects of Substrate Materials on Fracture Toughness 
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SIF2004 Structural Integrity and Fracture. http://eprint.uq.edu.au/archive/00000836 
 


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Mixed-Mode Fracture Of Adhesively Bonded Joints

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