International Journal of Adhesion & Adhesives 105 (2021) 102781

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International Journal of Adhesion and Adhesives

journal homepage: http://www.elsevier.com/locate/ijadhadh

Fatigue crack growth in aluminum panels repaired with different shapes of

single-sided composite patches
Sohail M.A. Khan Mohammed a, b, Rachid Mhamdia c, Abdulmohsen Albedah a, **,
Bel Abbes Bachir Bouiadjra a, c, *, Bachir Bachir Bouiadjra c, Faycal Benyahia a
a
Mechanical Engineering Department, College of Engineering, King Saud University, Riyadh, Saudi Arabia
b
Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, M5B 2K3, Ontario, Canada
c
LMPM, Department of Mechanical Engineering, University of Sidi Bel Abbes, BP 89, Cité Ben M’hidi, Sidi Bel Abbes, 22000, Algeria

A R T I C L E I N F O A B S T R A C T

Keywords: In this study, the effects of patch shape on the performance of bonded composite repairs on aircraft structures are
Bonded composite repair investigated using experimental and numerical approaches. Fatigue tests under constant amplitude loading, with
Patch shape a positive stress ratio, are performed on V-notch cracked specimens using two aluminum alloys, 2024-T3 and
Aluminum alloys
7075-T6 that are repaired with bonded carbon/epoxy patches. Three composite patch shapes are used: rectan­
Fatigue life
gular, trapezoidal, and triangular. Left- and right-oriented triangular patch shapes are used to analyze the effects
Stress intensity factor
Adhesive stresses of the patch orientation on the repair efficiency. Numerical models are built with these patch shapes and ori­
entations. The stress intensity factors and adhesive stresses are computed to numerically evaluate the repair
performances obtained with the different patch shapes and orientations. The experimental results demonstrate
that rectangular patches provide the most efficient repair, whereas the triangular shape with a left-orientation
may lead to catastrophic results, particularly with the 2024-T3 aluminum alloy. The numerical results concur
with the experimental observations.

1. Introduction life by ~4 times compared to an unrepaired structure, while Jian-Bin

et al. [5] found an improvement on the order of 31 times. This
Adhesively-bonded joints that are under mechanical or thermal discrepancy is due to the differences between the mechanical and
loading transfer stress from the softest to the stiffest adherend geometrical properties of the components involved in these studies, as
throughout the adhesive layer. This property is used in repairing well as the type of fatigue loading used in each study. The loading
damaged aircraft structures with bonded composite patches. Patch- condition is the most influential parameter on the effectiveness of a
bonding allows for the reduction of stress around the crack tip, which composite patch repair. Khan et al. [6] have shown that a positive stress
improves the residual fatigue life, as shown by Katlan et al. [1], Okafor ratio leads to a better repair performance. Albedah et al. . [7] concluded
et al. [2], and Baker et al. [3]. The main advantage of the bonded that an load history plays a vital role on fatigue performance, while
composite repair (BCR) technique is the uniformity of the stress transfer Albedah et al. [8] affirmed that the patch size directly affects the fatigue
through the bonded area and thus increasing fatigue life of repaired crack growth rate (FCGR) of the repaired panels.
structure. Stress concentrations are thus avoided, contrary to fastened Several authors have shown that BCR design is very difficult because
doublers, for which stress zone concentrations are inevitable. All re­ of the interactions between the effects resulting from several parame­
searchers who have worked in this field have observed a net improve­ ters, including the mechanical properties of the different materials
ment in the residual fatigue life after the application of a BCR. However, involved (e.g., aluminum panels, composites, and adhesives), the
there is no agreement on the rate of this improvement. For example, geometrical properties of the composite patch and aluminum panel, as
Schubbe et al. [4] showed that a composite patch improves the fatigue well as the loading conditions. The design of single-sided composite

* Corresponding author. Tel.: +213559222651; fax: +21348544100. LMPMDepartment of Mechanical Engineering, University of Sidi Bel Abbes, BP 89, Cité Ben
M’hidi, Sidi Bel Abbes, 22000, Algeria.
** Corresponding author.
E-mail addresses: albedah@ksu.edu.sa (A. Albedah), bachirbou@yahoo.fr, belabbes.bachirbouiadjra@univ-sba.dz (B.A. Bachir Bouiadjra).

https://doi.org/10.1016/j.ijadhadh.2020.102781

Available online 24 November 2020

0143-7496/© 2020 Elsevier Ltd. All rights reserved.
S.M.A. Khan Mohammed et al. International Journal of Adhesion and Adhesives 105 (2021) 102781

patches is more complex than double-symmetric patches. In single-sided better fatigue resistance to tensile loads, whereas Al 7075-T6 is more
patches, a bending moment is generated by the shift of the neutral axis of resistant to compressive loads. The specimen thickness was ~2 mm, and
the aluminum panel. This moment increases the stress in the cracked the other dimensions of this system are shown in Fig. 1. Fatigue tests
region and reduces the repair effectiveness. The minimization of this were performed on single edge-notched tension specimens using an
moment must be considered when optimizing the stiffness ratio between Instron machine with a capacity of 100 kN, as was utilized in our pre­
the composite patch and the aluminum panel. The stiffness ratio is vious work [7] (see Fig. 2). Carbon fiber/epoxy was used for bonding the
defined as: cracked plate. The composite plates were fabricated using
pre-impregnated carbon fibers with a 60% fiber volume. Eight plies were
Et tr
S= (1) used a in unidirectional manner to achieve a thickness of ~1.5 mm,
Ep tp
which corresponds to a stiffness ratio of 1.48, as calculated using Eq. (1).
where Er is the longitudinal elastic modulus of the composite, Ep is the The recommended stiffness ratio to avoid any kind of asymmetry and
elastic modulus of the aluminum alloy, tr is the thickness of the com­ buckling lies between 1.2 and 1.5 [12]. The patches were cut using
posite patch, and tp is the thickness of the aluminum panel. abrasive jet machining into the specified dimensions and shapes, as
It has been shown by Ahn et al. [9] that the minimization of the shown in Fig. 3: rectangular, triangular and trapezoidal patch shapes
bending moment requires a stiffness ratio between 1.2 and 1.5. How­ were used. For the triangular shape we have changed the orientation of
ever, the optimization of the stiffness ratio alone is insufficient to predict the patch (left oriented and right oriented) in order to analyze the effect
the fatigue life of a structure repaired with a composite patch. It is of this orientation on the repair performances.
therefore important to control the effects of several parameters, such as The patches and aluminum plate were bonded with the Araldite
the effects of the patch shape, as recommended by Genest et al. [10], 2015 epoxy adhesive that is used in aerospace industries. This structural
Denney and Mall [11], Fekih et al. [12], and Rose et al. [13]. It has been adhesive is bonded at room temperature, without heating, thereby
established that the repair efficiency is directly related to the patch eliminating thermal residual stresses. No pre-treatment was performed
shape. Mhamdia et al. [14] investigated numerically (with no experi­ on the aluminum sheets before bonding with the patch; however, the
mental validation) the effects of the patch shape on the BCR perfor­ surface was cleaned using acetone followed by cleaning with ethanol to
mance. The double arrow shape was used in the analysis on a substrate remove the presence of any debris or grease on the sheets. If the struc­
with an edge crack as can be found at. The authors confirmed that a tural adhesive is used to assemble two pieces, other surface treatments
patch shaped in the form of an arrow provides low values of the stress are required.
intensity factor (SIF) at the crack tip. Consequently, the fatigue life of the To perform the fatigue tests, a cyclic load was applied using constant
repaired structure is improved. Mhamdia et al. [14] also showed that a amplitude loading. The maximum stress was σmax = 70 MPa and the
double arrow shape leads to minimal adhesive stresses, which results in stress ratio was R = 0.1. The maximum stress represents 1/5 of the yield
better repair durability. However, their results have not yet been vali­ stress of the 2024-T3 Al alloy and 1/7 of that of Al 7075-T6. We choose
dated experimentally. Brighenti et al. [15] tried to optimize the patch an amplitude of 70 MPa as the maximum fatigue stress to ensure that the
shape by minimizing the SIF at the crack tip. They provided an exact
optimal shape; however, they found that complex shapes are impractical
for bonding with aircraft structures. Albedah et al. [16] showed that a
circular patch shape provides significant efficiency when double sym­
metric patching is used; however, their study was limited to numerical
analyses. Bouiadjra et al. [17] showed numerically, without experi­
mental validation, that a trapezoidal patch shape leads to the improved
efficiency and durability of a BCR. Benyahia et al. [18] compared the
performances of semicircular and semielliptical patch shapes for
reducing thermal residual stresses due to adhesive curing. We postulate
that the analysis of the effects of the patch shape has been insufficient in
some cases (e.g., for rectangular, trapezoidal, and triangular shapes).
The effects of patch orientation must also be analyzed. The mechanical
properties of the different materials involved in BCR (i.e., aluminum,
composites, and adhesives) have very significant effects on the repair
performances, as described by Equation (1). The high rigidity of the
repaired metal reduces load transfer, whereas stiffer composites and
adhesives allows for greater stress transfer from the aluminum plate,
thereby increasing the repair efficiency.
Most researchers who have addressed the effects of patch shape used
numerical models in their studies. In this paper, we opt for an experi­
mental approach to estimate the effects of the patch shape on the repair
efficiency. Fatigue tests are carried out to determine the fatigue life for
cracked aluminum panels repaired with different shapes of bonded
composite patches. The effects of other parameters, representing the
origin of this study, are investigated to address the effects of patch
orientation on the repair efficiency. Triangular-shaped patches are used
to highlight this effect. Numerical computations are also performed for
comparison with the experimental results.

2. Experimental setup

Two aerospace-grade aluminum alloys, Al 2024-T3 and Al 7075-T6,

were used in the present study. It is well known that Al 2024-T3 presents Fig. 1. Schematic of the specimens repaired with a square patch (all di­
mensions are in mm).

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S.M.A. Khan Mohammed et al. International Journal of Adhesion and Adhesives 105 (2021) 102781

chosen for the proceeding numerical analysis.

3. Finite element model

To perform the numerical analysis of the system shown in Figs. 1 and

3, we used a finite element (FE) code (Abaqus) to build a model of the V-
notch unrepaired and repaired plates. The SIF was used to evaluate the
repair efficiency and is calculated using a 3D FE analysis of the repaired
plate. The displacement correlation technique was selected to perform
this calculation. The displacement correlation method (DCM) was
initially used for calculating the SIF at the tip of 2D crack with quarter-
point finite elements. The expressions of the SIF are calculated using the
nodal displacement in the vicinity of the crack tip. Gupta et al. [19]
generalized this method for 3D crack. The formulation of the SIF pre­
sented by these authors use the nodal displacements around the crack
front. The computed displacements are not necessarily at the nodal
points.
The model of the aluminum plate and composite patch was meshed
using 20-node brick elements. Eight-node cohesive elements imple­
Fig. 2. Photo taken during fatigue testing. mented in the Abaqus code were applied to model the adhesive layer.
The technique of block elements was used to model the crack front.
crack will propagate in an elastic strain field. This allows us to apply the These elements represent crack blocks. These blocks were modeled using
concepts of linear fracture mechanics. Crack monitoring was performed brick elements that were mapped onto the original elements in space.
using a digital camera. From the fatigue tests, the variations of the crack The mesh model of the repaired structures is shown in Fig. 4. Table 1
length as a function of the cycle number (i.e., the fatigue life curves) presents the mechanical properties of the different materials and Table 2
were plotted for the different patch shapes and orientations. From these presents the cohesive properties of the Araldite 2015 epoxy adhesive.
curves, the fatigue crack growth (FCG) rate curves, da/dN = f(a), were The maximum (Kmax) and minimum (Kmin) SIF values were calculated
extracted. At least two samples were tested for each case to evaluate the using the maximum and minimum loads of 70 MPa and 0.7 MPa,
reproducibility of the results. Scanning electron microscope (SEM) ob­ respectively. The SIF values for repaired cases were calculated numeri­
servations were performed on the fractured surface of a failed specimen cally. The maximum applied stress was 70 MPa, which represents 20%
to analyze the nature of the fractures (e.g., brittle or ductile). These of the yield stress of Al 2024-T3 and 12% of that of Al 7075-T6. This
observations were used to justify the fracture mechanics that were level of stress ensures the initiation of the cracks in an elastic field, as

Fig. 3. Sizes of the different patch shapes (in mm): (a) rectangular, (b) left-oriented triangular, (c) right-oriented triangular, and (d) trapezoidal.

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S.M.A. Khan Mohammed et al. International Journal of Adhesion and Adhesives 105 (2021) 102781

a maximum stress of 70 MPa and a stress ratio of 0.1 were performed on

the V-notch specimens composed of either 2024-T3 or 7075-T6
aluminum alloy. These specimens were repaired using different patch
shapes (i.e., rectangular, trapezoidal, left-oriented triangular, and right-
oriented triangular). We carried out two fatigue tests for each the results
are pretty close and the difference did not exceed 5%. This is mainly due
to regulated fatigue loading (constant amplitude loading). Fig. 5 pre­
sents the fatigue life curves for the repaired and unrepaired specimens
composed of aluminum alloy 2024-T3. The BCRs are all shown to
improve the fatigue life of the cracked plates except for the left-oriented
triangular-shaped patch. This improvement is due to the load transfer
between the aluminum plate and the composite patch throughout the
adhesive layer. The number of cycles to failure is about 126,700 cycles
for the unrepaired specimen. This increases dramatically to 371,800
cycles with the use of the rectangular patch and 360,980 cycles with the
trapezoidal patch. Therefore, the improvement in the fatigue life using
rectangular and trapezoidal patches was about 4 times compared to the
unrepaired specimen. It must be noted that all the samples failed in the
Fig. 4. Typical mesh model of the repaired plate. adhesive and no delamination of the composite patch was observed.
Fig. 6a and b confirm these observations, these figures present photos of
failed specimens for triangular and square patch, respectively. it can be
Table 1 seen that the in the case of triangular patch shape, the crack has prop­
Mechanical properties of the different materials (the Al alloy and adhesive agated according to a quasi pure mode 1 but in the case of the rectan­
properties were provided by the suppliers and the composite properties were gular patch, there a slight inclination of the crack during its propagation,
taken from a previous study [14]). which means that the speed of the crack propagation for the triangular
Properties Material patch was higher. This behavior is mainly due to a more significant
Al Al Carbon/ Adhesive
adhesive disbond around the crack front in the case of a triangular patch
7075- 2024- Epoxy (Araldite 2015) shape. The rectangular and the trapezoidal patch shapes provided
T6 T3 approximately identical repair efficiencies, this was not the case for the
Longitudinal Young’s 71.7 72.4 130 2.52 triangular shapes, wherein the triangle base is bonded to the notched
Modulus (GPa) edge of the aluminum specimen (for the right-oriented triangular
Transversal Young’s 71.7 72.4 9 2.52 shape). The fatigue life of the repaired specimen with a right-oriented
Modulus (GPa)
triangular patch was about 222,600 cycles. This is two times greater
Longitudinal Poisson 0.33 0.33 0.33 0.36
Ratio
than the fatigue life recorded for the unrepaired specimen. This means
Transversal Poisson 0.33 0.33 0.03 0.36 that the patch shape with right-orientation provides a less significant
Ratio repair efficiency than the rectangular and trapezoidal patches. It must be
Hardness, HV 39.1 29.5 – – noted that the triangular shape use in the present analysis is different
Elongation at break (%) 10 18
from the one used by Mhamdia et al. [14] where they used double arrow
– –
Shear Modulus (GPa) 28 26.9 0.954
Yield Strength (MPa) 503 370 and reported a significantly higher bonding efficiency compared to
square patch. This lower performance of the triangular patch shape may
be explained by two main factors. The first is that the lowest
bonded-area of the left-oriented triangular shape is near the crack tip,
Table 2
Cohesive properties of the Araldite epoxy adhesive [20].
while the second is the presence of the sharp corner at the top of the
triangular shape, which can lead to higher concentrations of adhesive
Cohesive properties Toughness (N/mm) Cohesive Strength (MPa)
stresses. Under cyclic loading, these stresses can provoke adhesive fail­
Mode I 0.43 21.63 ure. Additionally, in Fig. 5 it is shown that the fatigue life provided by
Mode II 4.70 17.9 the left-oriented triangular patch is lower than that of the unrepaired
Mode III 4.70 17.9

well as that the crack propagation is elastic, particularly for Al 7075-T6.

The numerical studies are therefore more valid for the 7075-T6
aluminum alloy.

4. Results and discussion

The current study was carried out to experimentally and numerically

analyze the effects of the patch shape and orientation on the perfor­
mance of the BCR of metallic structures. To highlight the effects of the
patch orientation, two configurations of the triangular patch shape were
bonded to the cracked aluminum plate. Triangular shapes with left- and
right-orientations were used.

4.1. Experimental results

Load-controlled fatigue tests under constant amplitude loading with Fig. 5. Fatigue lives of the repaired and unrepaired specimens with Al 2024-T3.

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S.M.A. Khan Mohammed et al. International Journal of Adhesion and Adhesives 105 (2021) 102781

unrepaired and repaired cracks is also not large. When the crack length
increases, greater load transfer occurs from the cracked plate to the
composite patch. The stress intensity around the repaired crack is very
low compared to the unrepaired crack, which leads to crack retardation.
All of these phenomena can be quantified by plotting the crack growth
rate, da/dN, as a function of the SIF range, ΔK. However, in the case of
the repaired cracks, this procedure is difficult because the SIF exhibits an
asymptotic behavior when the crack length increases [8,18]. This means
that the increase in the SIF range is very small, such that a clear variation
of da/dN cannot be easily demonstrated as a function of ΔK. Establishing
a relationship between da/dN and ΔK is therefore very difficult.
Fig. 7 shows SEM observations of the fractured surface of the 2024-
T3 specimens repaired with rectangular and triangular patches after
failure. Fatigue striations are observed, confirming that the brittle fail­
ure mode is dominant. This is expected because the applied stress, 70
MPa, represents one fifth of the yield stress of the aluminum alloy 2024-
T3, which leads to a confined plastic zone around the crack tip. The
brittle mode of fracture allows us to use the concepts of linear fracture
mechanics in the numerical portion of this study.
Fig. 8 presents the FCG curves, da/dN = f(a), for the specimens
composed of aluminum alloy 2024-T3 that were repaired using different
composite patch shapes. For comparison, the FCG curve of the unre­
paired specimen composed of this alloy is also shown in Fig. 8. From this
Fig. 6. Failure in (a) triangular patch (b) Square patch.
diagram, we note that the triangular patch with a left-orientation pro­
vides higher values of the crack growth rate, da/dN, confirming that this
specimen. This means that the patch bonding accelerates the crack patch orientation is indeed very dangerous, and it may lead to inverse
growth instead of retarding it, and the BCR therefore has a negative stress transfer from the patch to the aluminum plate. The trapezoidal
effect in this case. patch shape provides the exact same crack growth velocity as the
It is very difficult to provide an exact explanation for the afore­
mentioned behavior of the left-oriented triangular patch, but it is likely
due to the auxiliary bending moment caused by the shift of the neutral
axis that occurs after applying a single-sided patch. For a left-oriented
triangular patch, this moment is more significant because the over­
lapping areas of the zones of crack initiation and stable crack propaga­
tion are smaller compared to the zones of final failure. Therefore, we
reaffirm that the choice of the patch shape and orientation is critical to
the success of the repair of aircraft structures using bonded composite
patches [21]. Alternatively, we can see in Fig. 5 that the crack initially
grows rapidly at the beginning of the fatigue cycling. This growth then
essentially stops for a long period when patch bonding is used. This
behavior is more apparent in the case of the rectangular and triangular
patches. We may therefore confirm that crack growth retardation occurs
due to patching. This behavior can be explained by the fact that, at the
beginning of the fatigue loading, the crack length is small. The stress
intensity, as will be shown in the numerical analysis, around this crack is
therefore insufficient to generate a sensible load transfer between the
aluminum plate and the composite patch. The difference in the stress
intensities between the unrepaired and repaired cracks, in this case, is Fig. 8. FCGRs for the Al 2024-T3 specimens repaired using different
insignificant. The difference in the crack growth rate between the patch shapes.

Fig. 7. Fracture surface observations of specimens repaired with (a) rectangular and (b) triangular patches after failure.

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S.M.A. Khan Mohammed et al. International Journal of Adhesion and Adhesives 105 (2021) 102781

rectangular patch until the crack length reaches a value of 9 mm. Before
this length, the crack under the trapezoidal patch propagates faster than
that under the rectangular-shaped patch. Whatever the orientation, the
triangular shape leads to higher crack growth rates compared to the
rectangular and trapezoidal shapes.
By analyzing the results shown in Figs. 5 and 8, we determined that it
would be useful to perform these fatigue tests involving different patch
shapes on a second aeronautical aluminum alloy. We choose the 7075-
T6 aluminum alloy, which is more resistant and less ductile than the
2024-T3 alloy. Fig. 8 presents the fatigue life curves of the V-notched
specimens in the 7075-T6 Al alloy repaired with different patch shapes.
The fatigue life curve of the unrepaired specimen is presented as refer­
ence. We first note that the fatigue lives of the Al 7075-T6 specimens
change less drastically than those of the 2024-T3 aluminum alloy. For
example, the unrepaired 7075-T6 specimen has a fatigue life of about
46,400 cycles, which is about 2.7 times lower than that measured for the
unrepaired 2024-T3 specimen. For the rectangular patch shape, the fa­ Fig. 10. FCGRs for the Al 7075-T6 specimens repaired with different
tigue life is about 185,480 cycles for the repaired 7075-T6 specimens, patch shapes.
which is about half that of the fatigue cycle value measured for the 2024-
T3 Al alloy repaired with a rectangular patch. This result can be with the same area of 1250 m2 were used. These composite patches were
explained by the fact that the 2024-T3 aluminum alloy is more resistant bonded onto cracked specimens composed of the aluminum alloy 2024-
to tension-tension cyclic loading. Fig. 9 confirms that the composite T3. As in the previous experiments, triangular patches with left- and
patches also improve the fatigue life of the aluminum alloy 7075-T6. The right-orientations were used. Fatigue tests were performed on the
rate of improvement of the fatigue life for this alloy is almost identical to repaired specimens, and the results are presented in Fig. 11. From this
that observed for the 2024-T3 aluminum alloy. The trapezoidal patch figure, the rectangular and the right-oriented triangular patches provide
shape provides approximately the same number of failure cycles as the approximately the same fatigue life values, although the cycle failure
rectangular shape. The triangular patch shape with a right-orientation number of the rectangular patch is slightly higher. This indicates that the
provides a failure cycle value of 88,420 cycles. This is 2.2 times patch size has a very significant effect on the repair efficiency. Alter­
greater than that measured for the unrepaired specimen. However, the natively, the left-oriented triangular patch leads to a slightly higher fa­
triangular patch with a left-orientation provides a fatigue life very close tigue life than was obtained with the unrepaired specimen. Despite the
to that of the unrepaired specimen. We may therefore conclude that the fact that this composite patch has the same bonding area as the rect­
triangular patch with a left-orientation has no effect on the repaired angular shape, it does not significantly improve the fatigue life. The left-
7075-T6 specimen, whereas it is catastrophic for the 2024-T3 oriented triangular patch therefore does not beneficially effect the fa­
specimens. tigue life significantly, even when its size is increased. These results
Fig. 10 presents the FCG curves, da/dN = f(a), for the Al 7075-T6 confirm that patch orientation highly affects the repair performance.
specimens repaired using different patch shapes. The rectangular and
trapezoidal patch shapes lead to slower crack growth compared to the
other patch shapes. The crack propagation velocity for the left-oriented 4.2. Numerical results
triangular shape is similar to that of unrepaired specimens. These results
confirm those observed for the 2024-T3 aluminum alloy. To confirm the experimental results, we numerically computed the
In obtaining these results, patches with different shapes were used, SIF at the crack tip for the different patch shapes with the same bonding
and these shapes differed in their sizes. The rectangular patches are areas. Fig. 12 presents the variation of the mode I SIF range, ΔK, as a
larger in size compared to the trapezoidal and triangular patches, function of the crack length, a. The rectangular patch provides low SIF
thereby providing a larger bonded area for the rectangular patches. The values compared to the left- and right-oriented triangular patches.
stress transfer is therefore more significant for this patch shape, and the Additionally, the SIF values of the right-oriented triangular patch are
repair provided by this shape is more efficient. To eliminate the effects of much lower than those of the left-oriented triangular patch. These
the bonding sizes, rectangular and triangular composite patch shapes

Fig. 11. Fatigue life of the 2024-T3 aluminum alloy specimens repaired with
Fig. 9. Fatigue life of the repaired and unrepaired Al 7075-T6 specimens. different patch shapes that possess the same areas.

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S.M.A. Khan Mohammed et al. International Journal of Adhesion and Adhesives 105 (2021) 102781

levels in Fig. 13 are much greater than the yield stress of the material.
But the stress levels exceeding 450 MPa do not appear clearly in the
figure because there are very confined around the crack tip, we have
thus a case of confined plasticity and the LEFM concept can be applied.
On the other hand, our numerical study is qualitative, the objective is to
explain the experimental fatigue live curves. But we agree that the use of
elastic-plastic model make more sense. The effect of the out-of-plane
bending moment is clearly shown in these figures. The shift of the
neutral axis due to the single patch generates a bending moment that
increases the stress intensity at the crack tip. This moment reduces the
repair efficiency. The non-symmetrical triangular shape leads to an
additional shift of the neutral axis, which can increase the bending
moment. For the triangular geometry, the SIF at the crack tip is
increased by this increase of the bending moment. This confirms both
the lower values of the SIF and the higher values of the fatigue life for the
rectangular patch that were previously obtained. In Fig. 13, it can also
be observed that the stress levels are lower for the rectangular patch.
Fig. 12. SIF range versus the crack length for the different patch shapes.
This is because of the more significant load transfer and the relatively
less significant effect of the bending moment that are obtained by using
results confirm the experimental observations, showing that the rect­ this shape.
angular patch provides a better repair efficiency, while the left-oriented Fig. 14(a) presents the distribution of the peel stresses in the adhesive
triangular patch is inconvenient for repairing fatigue cracks. The rela­ layer for the rectangular patch configuration. In this configuration, the
tive difference in the SIF values between the rectangular and right- maximum peel stresses in the adhesive layer are located in the crack
oriented triangular patches is about 11%, and about 35% between the front region. Thus, the stress transfer occurs principally in the crack
rectangular and the left-oriented triangular patches. front region, which is beneficial for increasing the repair efficiency. This
The SIF range was calculated on the repaired side of the crack front. also confirms that the rectangular patch is more appropriate for
Because of the load transfer, the SIF on this side of the crack front is repairing cracked plates.
lower than that of the unrepaired plate regardless of the patch shape. Fig. 14(b) shows the distribution of the peel stresses for the right-
However, on the unrepaired side of the crack front, the SIF range is more oriented triangular patch. The maximum stresses are also located over
significant as in this case there is no load transfer and the auxiliary the crack region, but two zones of maximum peel stresses are shown.
bending moment increases the stress intensity at the crack front. For the The first has a red color, indicating positive stress values, while the
left-oriented triangular patch, the auxiliary bending moment can greatly second has a blue color, indicating negative stress values. The presence
increase the SIF until it exceeds that of the unrepaired plate. of these two zones attenuates the globally transferred stresses and re­
To better understand the effects of the patch shape and orientation duces the repair efficiency. In Fig. 14(c), we present the distribution of
on the repair efficiency, we determined the stress distribution of both the adhesive peel stresses for the left-oriented triangular patch. The
the normal stresses on the aluminum plate and the peel stresses on the maximum stresses are located at the free edge of the adhesive layer. In
adhesive layer for the differently shaped patches. Fig. 13 presents the this case, the stress transfer does not principally act over the cracked
distribution of the normal stresses, σyy, in the aluminum plate for the region, thereby confirming that the left-oriented triangular shape is
three patch shapes (i.e., rectangular, left-oriented triangular, and right- inconvenient for repairing cracks.
oriented triangular) at an applied stress of 70 MPa. The maximum stress

Fig. 13. Distribution of the normal stresses in the Al plate according to the applied load direction (y-direction) at an applied stress of 70 MPa for the (a) rectangular,
(b) right-oriented triangular, and (c) left-oriented triangular patches.

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S.M.A. Khan Mohammed et al. International Journal of Adhesion and Adhesives 105 (2021) 102781

Fig. 14. Distribution of the adhesive peel stresses for the (a) rectangular patch (b) right-oriented triangular patch (c) left-oriented triangular patch.

5. Conclusion [2] Okafor AC, Singh N, Enemuoh UE, Rao SV. Design, analysis and performance of
adhesively bonded composite patch repair of cracked aluminum aircraft panels.
Compos Struct 2005;71(2):258–70.
It was shown in this study that the patch shape has a significant effect [3] Baker AA, Rose LF, Jones R, editors. Advances in the bonded composite repair of
on the performances of BCRs in aircraft structures. The numerical and metallic aircraft structure. Elsevier; 2003.
experimental results both confirmed that the use of patch shapes [4] Schubbe JJ, Mall S. Investigation of a cracked thick aluminum panel repaired with
a bonded composite patch. Eng Fract Mech 1999;63(3):305–23.
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