INTRODUCTION
The technique of repairing cracked metallic aircraft structures was first done
by the Aeronautical and Maritime Research Laboratories (AMRL), in 1970s (Prosser
et al., 1995). Baker et al. (1988) performed
a mathematical approach based on an analogy with a onedimensional lapjoint
analysis has previously been used to estimate adhesive and plate stresses for
simple repairs. Belason et al. (1994) conducted
two and threedimensional linear elastic FEA as well as a series of laboratory
tests to evaluate the performance of bonded boron/epoxy doublers for 7075T6
aluminum aircraft sheets. They investigated stresses in adhesive, boron/epoxy
patch and aluminum plate for three different and two structural boundary conditions.
They observed that the shear and peel stresses in the adhesive due to the thermal
loads are of about the same value, but act in the opposite direction of applied
of tensile load. Sun et al. (1996) presented
a simple analysis method to analyze cracked aluminum plates repaired with composite
patch using Mindlin plate theory. The adhesive layer was modeled using of springs
attached to the patch and aluminum plate. A threedimensional finite element
analysis was performed using a commercial code ABAQUS and a comparison was made
between crack opening displacements obtained from both cases.
Chue et al. (1996) investigated the effect of
composite patch size, patch length and stacking sequence on the performance
of bonded repair of cracked hole in 2024T3 aluminum plate. They used a threedimensional
finite element method, linear elastic fracture energy and strain energy density
theory. They observed that the more increase in the composite patch size results
the less strain energy level of the crack tip. They also demonstrated that the
layer sequence of the laminate had a little effect on the strain energy distribution
in the vicinity of the crack.
Schubbe and Mall (1999) successfully modeled a cracked
thick metallic structure with bonded composite patch repair using a threelayer
technique. The finite element model of the composite repair consisted of three
layers of twodimensional 4noded Mindlin plate elements used to model the patch,
plate and adhesive separately. The significant feature of this study was modeling
of the adhesive layer. They modeled the adhesive as an elastic continuum medium
between the plate and the patch. The displacements through the thickness were
assumed linear and the constraints on the plateadhesive interface and the adhesivepatch
interface were based on the Mindlin plate theory. Only a quarter elements were
modeled due to symmetry.
HosseiniToudeshky et al. (2005) used finite
element fatigue crack growth method to see the effects of using asymmetric repaired
panels to predict the actual crack front shape and crack growth life of the
repaired panels with various patch and panel thicknesses. Lee
and Lee (2004) performed numerical and experimental crack growth analyses
of centrally cracked aluminum panels repaired with graphite/epoxy composite
material. They showed that there is a good agreement between the crack front
shapes obtained from finite element analysis and those obtained from experiments
for various repaired panels.
Bouiadjra et al. (2007) and Fekirini
et al. (2008) demonstrated that the quality of the adhesives is a
very important factor affecting the stress intensity factor at repaired crack
tips. The patch technique with two adhesive bands consists in used of two adhesive
bands with different mechanical properties: the band of adhesive with higher
shear modulus is used on the crack region for repair and the second band with
lower shear modulus is used beyond the crack region to avoid the adhesive failure
between the aluminium plate and the composite patch.
In this study, the tensile behavior of the cracked aluminum plates repaired
with FML composite patches, were studied by obtaining crack opening displacement
and J integral for test specimens. To this purpose three factors are changed,
i.e., crack length, crack angle and the layup of FML layers. Each factor contains
three levels. The results in tow state LEFM and EPFM were presented. The results
were discussed and the effects of mentioned factors were surveyed.
MODELING OF THE STRUCTURE
The structure contains three parts, (1) Aluminum panel (2) Adhesive layer and
(3) FML patch. Here, the adhesive layer was not modeled and the patch has been
attached to the specimen using Tie technique. The Aluminum panel were made of
AL AA1035 having dimensions of 179x76x1.5 mm. The crack angle with respect to
the width axis of specimen have three angle states, as 0, 30 and 45° and
by ratio a/w = 0.3, 0.4 and 0.5 of specimen width were modeled on center of
specimens (a = crack length and w = specimen width).
The FML composite patch was fabricated with two woven glassfabric (T(90°)/M200E10)
layer ass the fiber layers (GFRP) and one thin Aluminum sheet (AA1035, 0.3 mm)
as the metal layer that having dimensions of 80x50x0.7 mm . The layup of the
FML patch vary in different make up so that the metal layer can be near or far
from the repair surface. In specimens the layup of the patch was FFAL in
bottomup direction, in second repaired specimens the layup was FALF and
finally in patches the layup was ALFF. The direction of warp and fill fibers
in the patch layup are equally along 0 and 90° in all patches. The mechanical
properties of Aluminum plate and GFRP layer were given in Table
1.
FINITE ELEMENT ANALYSIS
The behavior of the cracked aluminum specimen under the tensile load is ductile.
As a result, as soon as, the growth of the crack starts, a huge area of the
crack front enters the plastic area, therefore, EPFM (ElasticPlastic Fracture
Mechanic) should be used to model the crack. But due to two reasons, it is better
to use LEFM (Linear Elastic Fracture Mechanic) instead of PEFM. (a) the main
purpose of numerical modeling is to compare the influence of using different
patches in different crack angles and lengths. So, it is not necessary to obtain
exact experimental results in the process of modeling; it is just enough to
see which patch in what crack length and what crack angle has a better function.
(b) The time for running LEFM is much less than PEFM. Therefore, in this study
LEFM method was used.
To observe the behavior of specimens, integral J and crack opening displacement
have been chosen from different parameters of fracture mechanic. The patch has
been attached to the specimen using Tie technique. All the freedom degrees of
one side of the specimens have been restrained and the other side, because of
load application, is free. In order to model the elements of crack front singular
elements have been used. Elements around the crack front are quadratic wedge
elements, type C3D15, and the technique of meshing in this area is Sweep. All
the other elements used in the other area of the Aluminum specimen and FML patch
are quadratic brick elements, type C3D20R (Fig. 1, 2).
Table 1: 
Properties of plate and patch material 


Fig. 1(ab): 
(a) Meshed Patched and (b) unpatched specimen 

Fig. 2: 
Elements around the crack front 
Figure 1 shows a schematic view of the meshed patched and
unpatched specimen and Fig. 2 shows the used elements around
the crack front.
RESULTS AND DISCUSSION
Comparing of J integral in nods of crack front: As shown in Fig.
3 and 4, for the specimens without repair, the highest
J integral is related to the middle node of the crack front and for the repaired
specimens this integral is related to the furthest node from the repaired surface.
Accordingly, when presenting the results, the results related to these nodes
will be discussed. It is observed that the amount of J integral for the node
that places on the repaired surface is incorrect.
Crack opening displacement (COD): Here, the nodes displacement of crack
mouth were studied. As Fig. 5 shows U_{1} displacement
of nodes were calculated and compared. U_{2} and U_{3} displacements
for all of nodes are nearly zero.
Effect of crack length on the COD: In the unpatched specimens that
having same crack angle but different crack length, can valuated the effect
of crack length on the COD. In Fig. 6, the amounts of COD
were shown. It is found with increasing crack length the COD was increased.
Effect of crack angle on the COD: In the unpatched specimens that having
same crack length but different crack angle, can valuated the effect of crack
length on the COD. Figure 7 shows that with increasing crack
angle the COD was decreased.
Effect of FML patch on the COD: Figure 8 indicates
the comparison of COD of specimen with a/w = 0.5 and θ = 0° that by
three type of patches had repaired. It is found that COD of patched specimens
as compared to unpatched specimens is less. Maximum loss occurs in the side
that repaired. Gradually with moving toward another side, the displacement increase.
Almost three layup of patch has the same effect on COD. One sees that FFAL
patches have more effect on decreasing of COD.

Fig. 3(ab): 
J integrals in nodes of crack front of unpatched specimen 

Fig. 4(ab): 
J integrals in nodes of crack front of patched specimen 
J integral: Here, In order to understand the results better, at first
the results related to different angles of the crack will be discussed separately.

Fig. 5: 
Nodes of crack mouth and direction of displacement measurement 

Fig. 6: 
The effect of crack length on the COD 

Fig. 7: 
The effect of crack angle on the COD 

Fig. 8: 
The effect of patch layup on the COD 
Then, will compare them together.
J integral for specimens with θ = 0°: Figure
911 compare the results of specimens with θ = 0°.
Scrutinize the obtained amounts in each figure separately, it is found that
the patch type FFAL has the most effect and the patch type FALF has the
least effect on the increase of J integral.
Also comparing figures of specimens with different crack length, it is observed
that the effect of using patches in longer crack lengths is greater. In order
to understand this issue better, must be calculated the proportion of the J
integral of the repaired specimen, with one type of patch, to the J integral
of that specimen but without repair. Now must be obtained the abovementioned
proportion for specimens with different crack lengths and compare them together.
The less this amount, the more the effect of patch in the related crack length
will be. For instance, this proportion for specimen with crack angle θ
= 0° and crack length a/w = 0.3 (repaired with the FFAL patch) will be
0.66 and for specimen with same crack angle and patch but crack length a/w =
0.5 will be 0.55. As a result, the effect of using patches in the crack length
a/w = 0.5 is more than a/w = 0.3.
J integral for specimens with θ=30°: Figure
1214 compare the results of specimens with θ =
30°. The results of scrutinize the obtained amounts in these figures is
similar to obtained results in previous section. However, it is found that changing
the patch layup, make partly little change in the J integral (relation to specimens
with θ = 0°).

Fig. 9: 
Comparison of J integral for specimens with a/w = 0.3 (θ
= 0°) 

Fig. 10: 
Comparison of J integral for specimens with a/w = 0.4 (θ
= 0°) 

Fig. 11: 
Comparison of J integral for specimens with a/w=0.5 (θ
= 0°) 

Fig. 12: 
Comparison of J integral for specimens with a/w=0.3 (θ
= 30°) 

Fig. 13: 
Comparison of J integral for specimens with a/w=0.4 (θ
= 30°) 

Fig. 14: 
Comparison of J integral for specimens with a/w=0.5 (θ
= 30°) 

Fig. 15: 
Comparison of J integral for specimens with a/w=0.3 (θ
= 45°) 

Fig. 16: 
Comparison of J integral for specimens with a/w = 0.4 (θ
=45°) 
J integral for specimens with θ = 45°: Figure
1517 compare the results of specimens with θ =
45°. With comparing these figures with previous figures, found that increasing
the angle of the crack, the effect of changing the patch layup on the J integral
will be less. For example, in the specimen with crack length a/w = 0.3 and crack
angle θ = 0°, with changing the patch from type of FALF to FFAL,
the amount of J integral increase nearly 7%. While this value for crack with
angle θ = 45°, is 2%. This criterion for specimens with crack length
a/w = 0.4 and 0.5 is truthful too.
Finally, in order to compare the effect of patches with different angles, the
proportion of the J integral of the repaired specimen with one type of patch
and those specimens having no patches must be calculated. The abovementioned
proportion has obtained for specimens with different crack angles and then compare
together. The less this amount, the more the effect of patch in the related
crack angle will be.

Fig. 17: 
Comparison of J integral for specimens with a/w=0.5 (θ
= 45°) 
For instance, this proportion for specimen with crack angle θ = 0°
and crack length a/w = 0.3 (repaired with the FFAL patch) will be 0.66 and
for specimen with same crack angle and patch but crack angle θ = 45°
will be 0.35. As a result, the effect of using patches in the crack angle θ
= 45° is more than θ = 0°. Therefore, in the greater crack angle
the effect of using patch is more.
CONCLUSIONS
From the study, the following conclusion has been drawn:
• 
In the unpatched specimens, the highest J integral is related
to the middle point of the crack front while this amount for patched specimens
is related to the furthest node from the repaired surface 
• 
With increasing crack length and decreasing the crack angle the crack
opening displacement was increased 
• 
All of the patches have the same effect on the crack opening displacement 
• 
When the Al layer of the patch structure is located far from the repair
surface of AL plate, amount of J integral will be more and when the AL layer
is in the middle of other layers the J integral has the lowest amount 
• 
Comparison of J integral of repaired specimens and J integral of same
specimens but without repair, indicates the more effect of using patches,
in more crack length and more crack angle 
• 
The effect of changing the patch layup on the increment of J integral,
with increasing the crack angle, is less 