Mixed-mode fatigue crack growth of thin aluminium panels with single-side repair using experimental and numerical methods

10.1111/j.1460-2695.2007.01142.x

Mixed-mode fatigue crack growth of thin aluminium panels withsingle-side repair using experimental and numerical methods

H. HOSSEINI-TOUDESHKY, B. MOHAMMADI and S. BAKHSHANDEHAerospace Engineering Department and Centre of Excellence in Computational Aerospace Engineering, Amirkabir University of Technology, 424 HefezAve., Tehran, Iran

Received in final form 17 March 2007

A B S T R A C T In this paper, experimental and numerical fatigue crack growth of thin aluminium panelscontaining a central inclined crack of 45◦ with single-side glass/epoxy composite patchare performed. Effects of patch lay-up configuration on the restarting crack growth (crackre-initiation) life and crack growth rate of the repaired panels are investigated. Theobtained experimental results are compared with those predicted using finite elementanalysis based on both mid-plane and unpatched surface fracture parameters. In the finiteelements analyses, it is assumed that the crack-front remains perpendicular to the panel’ssurfaces during its propagation. It is shown that the finite element crack re-initiation andpropagation lives predictions using the unpatched surface results are too conservative.However, the finite element mid-plane results lead to a non-conservative life prediction.It is experimentally shown that, the most effective patch lay-up configurations to retardthe crack growth of the repaired panels is [−45/+45]2; however, the most life extensionincluding the crack propagation cycles belongs to the patch lay-up of [904]. It is alsoshown that using the asymmetric patch lay-up configuration similar to [902/02] with aproper bonding process may lead to a very slow crack growth rate, even slower than thepatch lay-up of [904].

Keywords: aluminium alloy; bonded repair; fatigue crack propagation; glass/epoxy com-posite patch; mixed-mode.

I N T R O D U C T I O N

To enhance the life of an ageing aircraft structure,the application of adhesively bonded composite patchesbecomes an important issue in the aerospace and ship in-dustries as well as in other lightweight engineering con-structions. Ease of application, no damage to the parentstructure, high stiffness to weight ratio and forming to thevarious complex shapes are some advantages of bondedrepair using laminated composite patches. A double-sidesrepair increases considerably the fatigue life of a crackedplate, although, owing to manufacturing difficulties, asingle-side repair is normally preferred. A single-siderepair produces unrestrained bending due to neutral axisoffset. This type of bending is usually a severe situation asmost (aircraft) structures are stiffened or supported by ahoneycomb core. But, in most practical cases, both sides ofthe cracked panels are not available to perform a symmet-rical repair. Repair of aluminium structures was initiatedby Baker in the early 1970s.1 Following that researchers

Correspondence: H. Hosseini-Toudeshky. E-mail: [email protected]

proposed different numerical techniques for stress analy-sis and subsequent derivation of stress intensity factor ofthe repaired panels. For instance, Sun et al.1 developed afinite element model for analysing the stress distributionand stress intensity factor of cracked plates repaired witha single sided patch. Jones et al.3,4 studied the theoreti-cal and design aspects of the repaired panels. They useda finite element method (FEM) based on the displace-ment field and assumed a shear stress through thicknessprofile adopted in the development of a patch element.Baker5 also studied the fatigue crack propagation of edgecracked aluminium panels repaired with Boron/Epoxycomposites.

The stress variations over the thickness of a cracked platein a single-side repair present a great challenge in mod-elling due to the existence of out-of-plane bending. Fur-thermore, in many studies the stress and strain fields ofthe mid-plane have been used to calculate the fracture pa-rameters6–9; however, the maximum stresses and strainsoccur on the unpatched surface of the repaired panels.10

The stress variations through the thickness of the crackedpanels in single-side repairs produces non-uniform crack

c© 2007 The Authors. Journal compilation c© 2007 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 30, 629–639 629

630 H. HOSSE IN I -TOUDESHKY et al.

propagation along the panel’s thickness leading to a curvi-linear crack-front shape and various crack propagationpaths at patched and unpatched surfaces of the repairedpanels.11–13

The majority of the previous investigations on frac-ture analysis of repaired aluminium panels using com-posite patches were focused on the safety evaluation andlife prediction of components under uniaxial loading inmode-I condition. However, in real applications, compo-nents are subjected to various loading conditions and crackgrowth and failure occur due to the conjoiner of such load-ings. In practical applications, cracks under mixed modeconditions can be encountered frequently. These flawsmay experience mixed mode loading due to mainly threefactors: (1) mixed remote loading, i.e. normal and shearremote loads acting on a component having perpendicularcrack to the normal loading direction, (2) deflected or in-clined crack under normal/uniaxial remote loading beforeits propagation or considerable growth and (3) mechani-cal and/or thermal loads combined with arbitrary restraintconditions.

Experiments on fatigue crack growth in repaired platesusing composite material under mixed-mode conditionshas not been actively carried out. There are only afew publications on repaired panels in mixed-mode con-ditions14,15. These works investigate the fatigue crackgrowth life and crack propagation direction of the repairedpanels using experimental method. Chung and Young15

performed fatigue crack growth tests for repaired thickpanels containing edge cracks with various inclined an-gles. They used Al 6061-T6 alloy for the base materialand HT145/RS1222 for the composite single-side patch.They used only one lay-up configuration and patch thick-ness for various inclined crack angles. The fatigue crackgrowth rate and the crack propagation direction of theinclined cracks were investigated in their study. Theyshowed that, the crack growth was non-uniform throughthe thickness and the difference between the crack lengthson the patched and unpatched surfaces was measured onthe order of the plate thickness. They did not investi-gate the effect of patch layers orientation and thickness oncrack growth rate and crack propagation direction. Exper-iments on fatigue crack-growth of plates with a central in-clined crack repaired with a glass/epoxy composite patchhave not been carried out to the authors’ knowledge. Itis obvious that the glass/epoxy composite material is notas stiff as boron/epoxy and graphite/epoxy composites,but it is more accessible and much cheaper than them.In addition, a disadvantage of composite patches such asboron/epoxy and graphite/epoxy results from their rela-tively low coefficient of thermal expansion compared tothe parent material which results in residual tensile stressesin repaired components.16,17 The thermal expansion co-

efficient of the glass/epoxy material is much higher thanthe thermal expansion coefficient of graphite/epoxy andslightly higher than boron/epoxy material. Moreover, us-ing a low curing temperature (60 ◦C) for glass/epoxy ma-terial reduces the residual stresses significantly. Crooks18

performed experimental studies on the residual thermalstresses of single side repaired aluminium panels usinggraphite/epoxy patches. He showed that reduction of cur-ing temperature from 120 ◦C (250 ◦F) to 93 ◦C (200 ◦F) re-sults in a residual stress reduction of 20%. He also showedthat using the graphite/epoxy as a patching material with acuring temperature of 120 ◦C in aluminium repaired pan-els may lead to the maximum residual stress of 6.8 MPa(1000 psi).

Hosseini-Toudeshky et al.11,13 performed three-dim-ensional finite element analysis to study the effects ofpatch thickness and patch lay-up configurations on fa-tigue crack growth life and crack trajectory of repairedpanels containing various central inclined cracks of 30◦,45◦ and 60◦. In these analyses, it was assumed that thecrack-front line through the thickness remains perpendic-ular to the panel’s surfaces during its propagation (uniformcrack growth). They showed that the patch thickness hasnot a considerable effect on the crack propagation path.They indicated that, there are about 10% differences be-tween the crack propagation paths predicted based onthe obtained fracture parameters at unpatched surfacewith those obtained based on the mid-plane parameters.The obtained crack propagation life for a repaired panelwith an inclined crack of 45◦ using mid-plane fractureparameters showed that the patch fibre orientation ofθ = 90o (in loading direction) is an optimum fibre anglewhich leads to a longer fatigue crack growth life. How-ever, the optimum patch layers angle is θ = 105◦ to extendthe crack re-initiation life (restarting the crack growth) ofthe repaired panels.

In this paper, effects of various patch lay-up configu-rations on fatigue crack growth life and restarting crackgrowth life for thin aluminium panels containing a centralinclined crack of 45◦ with single-side glass/epoxy compos-ite patch are studied using both experimental and FEMs.The analyses are only carried out for the panels with thetypical inclined crack of 45◦ in mixed-mode conditionsdue to the expenses of the experimental investigations andthe existence of maximum interaction between fracturemodes before crack propagation. The patch lay-up con-figurations are selected based on the results of numericalinvestigations of the repaired panels containing an ini-tial inclined crack, which were already performed by theauthors.10,11,13 The obtained experimental results arecompared with those predicted using the finite elementanalysis results. These comparisons would give an esti-mation on the approximation degree to use with the FEM

c© 2007 The Authors. Journal compilation c© 2007 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 30, 629–639

MIXED-MODE FATIGUE CRACK GROWTH 631

Fig. 1 Typical geometry and loading of single-side repaired panels.

results of the repaired panels performed for other inclinedcrack angles in mixed-mode conditions.

FAT I G U E A N D F R A C T U R E A N A LY S I S

Figure 1 shows a typical geometry and loading of thesingle-side repaired panels containing an inclined crack.The problem needs to be studied as a mixed-mode crackproblem. Having the stress and strain fields around thecrack tip, fracture parameters for mixed-mode problemsare calculated to predict the crack propagation path andfatigue life of the repaired panels. For this purpose, we mayuse the fracture parameters such as K I, K II and J-integral.The main assumptions in the crack growth analysis are: (1)linear elastic fracture mechanics behaviour, (2) the crackfront line through the thickness remains perpendicularto the plate surfaces during crack propagation and (3) node-bonding occurs between the panel surface and patchduring crack propagation.

J-integral definition considers a balance of mechanicalenergy for a translation in front of the crack along thelocal crack-tip x-axis, which is a path independent contourintegral defined as 19:

J =∮

C

[Wn1 − σi j n j

∂ui

∂x

]ds , (1)

where, W is strain energy density, σi j stress components,ui the displacements corresponding to the local i-axis, sthe arc length of the contour, nj the jth component of theunit vector outward normal to the contour C, which is anypath of vanishing radius surrounding the crack-tip. Usingthe assumption of linear elastic fracture mechanics and thefollowing equation, K I and K II parameters are decoupledfrom the obtained J values.20

J = K 2I /E ′ + K 2

II/E ′, (2)

where E ′is modulus of elasticity,E ′ = E for plane stresscondition and E ′ = E/(1 − ν2) for plane strain conditionproblems. To solve the problem for K I and K II the ratio ofK I over K II is also obtained from the ratio of the normaldisplacement to the horizontal displacement (at the localcrack-tip coordinate system) of the two closest nodes tothe crack-tip which have been coincided before loadingon the crack-free surfaces.

Having the fracture parameters, a criterion is neededto predict the crack growth direction in a mixed-modeproblem. Several criteria have already been proposed forthis purpose. Previous research21,23 shows that there areno significant differences between the obtained cracktrajectories based on various crack propagation criteria.Using stress as a parameter, the maximum tangential stress(MTS) criterion was presented by Erdogan and Sih.22

This criterion states that a crack propagates in a direc-tion corresponding to the direction of maximum tangen-tial stress along a constant radius around the crack-tip.Using the Westergaurd stress field in polar co-ordinatesand applying the MTS-criterion, the following equationis obtained to predict the crack propagation direction ineach incremental step23:

tan2(

α

2

)− µ

2tan

(α

2

)− 1

2= 0, (3)

where µ is defined as the ratio of K I over K II (µ = K I/K II)and α is the incremental crack propagation angle. Tofind the maximum root value of Eq. (3), the conditionof ∂2σα/∂α2 < 0 should be satisfied.

Having the fracture parameters and crack propagationdirection from the above formulation, fatigue life of eachcrack growth increment can be calculated. A number ofcrack growth laws have been developed relating crackgrowth rate to stress intensity factors. The well-knownParis equation has been used in this paper which is givenas follows24:

dad N

= C �K m (4)

where �K = Kmax − Kmin is the stress intensity factorrange in fatigue loading, N is the number of load cycles,da is the crack growth increment, and C and m are em-pirical material constants. In mixed-mode problems, theeffective stress intensity factor range, �K eff, can be usedinstead of �K and it can be calculated as follows25:

�Keff =√

(KI + |KIII|)2 + 2K 2II. (5)

Having the effective stress intensity factor and mate-rial data, Eq. (4) can be used to calculate the fatiguecrack growth lives of the cracked panels in mixed-modeconditions.



E X P E R I M E N T S

Typical geometry and loading of the aluminium panels,adhesive layer and composite patch are shown in Fig. 1.The specimens were made of 2024-T3 aluminium alloywith thickness of 2.29 mm containing an inclined sharpflaw of 2a = 10 mm length and 0.2 mm wide with aninclined angle of β = 45◦. It is noted that pre-cracking us-ing the fatigue cycles cannot be performed for the currentspecimens’ configurations and normal jigs due to the exis-tence of mixed-mode conditions. Therefore, the producedinitial sharp flaws were considered as the initial cracks.The specimens’ dimensions followed the ASTM E-647standard.

The surface of each specimen was prepared with a P2etching process26. In this method the surface of the panelis degreased with acetone and abraded with emery cloth,and then alkaline cleaning is applied. The part is immersedfor 10–12 min at 65–70 ◦C P2 etch mixture of 15% byweight FeSo4, 37% H2So4 and 48% water, then washedwith clean cold running water, followed by clean hot water,and dried with hot air. The temperature of the hot waterand air must not be greater than 65 ◦C.

After that the specimens are bonded with four layers ofglass/epoxy unidirectional composites with various lay-upconfigurations of [90]4, [105]4, [−45]4, [−45/+45]2 and[902/02]. The lay-up angles are based on the defined θ inFig. 1. The lay-up configurations were defined based onthe results of our previous finite element investigations onthe variation of the fracture parameters due to the vari-ation of the unidirectional lay-ups angle (θ ) of repairedpanels.11,13 The boron/epoxy composite patch was used inthese panels. The analyses showed that the patch lay-up of[1054] is the best lay-up configuration among the consid-ered lay-ups in terms of crack re-initiation life (restartingthe crack growth after bonding). The asymmetric patchlay-up of [902/02] produces secondary bending against theout of plane bending based on classical laminate plate the-ory (CLPT). It was also shown that the patch lay-up of[902/02] is the best lay-up configuration among the con-sidered lay-ups in terms of crack propagation life usingthe mid-plane fracture parameters.13

Two specimens of each repaired panel with the samepanel and patch configuration were prepared to repeatthe tests. The patches were made using the hand lay-uptechnique and commercial L20 epoxy was used for thisprocessing. The adhesive thickness was about 0.1 mm andit was co-cured with the composite patch. Each specimenremained in room temperature for 2 h to pass the gel timewithout any pressure. They were then kept under pressureusing a screw manual fixture for 18 h at room temperature.In the next step specimens were cured for 16 h under pres-sure and at a temperature of 60 ◦C in an autoclave. Therewas no precuring process for the patches. It is noted that

Fig. 2 Typical un-repaired (a) and repaired (b) specimens.

no considerable warping and bending was seen after cur-ing of the specimens. Typical repaired and un-repairedspecimens are shown in Fig. 2.

Finally, cyclic loads were applied to both repaired andun-repaired specimens with a frequency of 10 Hz, a loadratio of R = 0.05 and a maximum applied remote stress of116 MPa at ambient temperature using a servo-hydraulicDARTEC 9600 machine. Crack-tip at the unpatched sur-face of the repaired panels was detected and marked dur-ing the crack propagation. The x-coordinate of the initialcrack-tip was 3.52 mm. It was very difficult to recognisethe starting crack growth from this initial crack-tip posi-tion. Therefore, the life cycles after a small crack growthvalue of 1.0 mm (x = 4.52 mm) at the unpatched surfaceof the repaired panels were recorded as crack re-initiationlife values. The differences between these values and thatobtained for the un-repaired panel are considered as theindication for the effect of various patch lay-up configura-tions on crack re-initiation life. When the x-coordinate ofthe crack length at the unpatched surface of the panelreached the value of X ctip = 16.5 mm, the tests werestopped and the number of cycles recorded. Then, a statictensile load was applied to each specimen until failureoccurred. Therefore, the crack-front shape due to the fa-tigue crack growth can be detected on the broken surfaceof the repaired panels.

Two un-repaired specimens with an initial crack angle ofβ = 0◦ were also prepared. Fatigue crack growth of thesespecimens was performed to obtain the material constantsin the Paris equation using the ASTM E-647 method. Thecalculated material constants are: m = 3.7927 and C =2.29e-14 in the metric system.

F I N I T E E L E M E N T S A N A LY S I S

Finite element methods are widely employed for the solu-tion of mixed-mode crack problems. Three-dimensionalelastic analyses were performed to obtain the stress and



strain fields of the repaired panels using the ANSYS finiteelement program. Typical geometry and loading config-uration of a repaired plate are shown in Fig. 1. Materialproperties of the aluminium cracked panel, adhesive, andcomposite patch are given in Tables 1 and 2. In these

Table 1 Material properties of Aluminium alloy 2024-T3 andadhesive [10]

Parameters Aluminium alloy Adhesive FM 73

E (GPa) 71.02 1.83υ 0.3 0.33Thickness (mm) 2.29 0.1

Table 2 Material properties of composite patch Glass/Epoxy [17]

Elasticity modulus (GPa) Shear modulus (GPa) Poisson’s ratio

E11 27.82 G12 2.56 ν12 0.31E22 5.83 G13 2.56 ν13 0.31E33 5.83 G23 2.24 ν23 0.41

Fig. 3 Typical 3D finite element mesh of the repaired panels, (a) Hole patched area, (b) Initial deformed crack-tip area, (c) Crack-tip areaafter a few steps growth.

analyses, an isotropic 8-node-solid element with extrashape function was used to model the aluminium paneland adhesive layer. Furthermore, a layered 8-node-solidelement was used to model the laminated composite patch.A typical mesh of the component is shown in Fig. 3.Our investigations show that different J-integral contoursand various refined meshes on the surfaces and throughthe thickness of the repaired panels (variation of 2–10 elements along the thickness) result in about 2% differ-ences in the obtained fracture parameters. Therefore, twoelements in the thickness of each part, plate, adhesive andpatch were used and a very fine mesh was generated forthe region close to the crack-tip. Each model containeda total number of 12 744 elements and the plane area of(0.1 × 0.1 mm) close to the crack-tip contained about900 elements as shown in Fig. 3.

A macro-program was developed using ANSYS Para-metric Design Language (APDL) to handle the crackgrowth modelling procedure as well as to find the cracktrajectory analysis of each repaired panel. In these analy-ses, it was assumed that the crack front line remains per-pendicular to the plate surfaces (uniform crack growthalong the thickness) and there is no de-bonding between



the plate and patch during the crack propagation. In thisprocedure a dynamic mesh generation was designed togenerate automatic mesh of the repaired panels at eachcrack growth step. The J-integral value for the presentedcrack configuration was computed in each step, and thenusing Eq. (2) and the explained decoupling procedure inSection 2, the values of K I and K II were calculated. Us-ing the obtained values of K I and K II and Eq. (3), thecrack growth direction, α, was determined. The equationswere numerically solved in each step and then the geome-try was updated with the new crack length configuration.The above procedure was performed for the new con-figuration and repeated for several steps to find the cracktrajectory in each repaired panel. The full explanation andflowchart of the developed APDL program is available inreference.11

R E S U LT S A N D D I S C U S S I O N S

Figure 4 shows the comparison between experimentaland finite element crack growth rates in the X-directionfor un-repaired specimens. The good agreement betweenthe experimental and numerical results verifies the de-veloped finite element crack growth procedure and thematerial constants used in the Paris law.

Table 3 shows the crack re-initiation (restarting crackgrowth) life after repair of the panels with various patchlay-up configurations using both experimental and FEMs.In these studies, it was assumed that crack re-initiation oc-curs when the crack-tip reaches the first crack propagationobservation point (X ctip = 4.52 mm) or crack propagationof 1 mm at the unpatched surface of the panels is ob-served. The experimental results in this table show thatusing various four layer patch lay-up configurations, thecrack re-initiation life of the repaired panels may increase

0

2

4

6

8

10

12

14

16

18

0 5000 10000 15000 20000

Cra

ck L

engt

h (

mm

)

FEM

Experiment

Un-repaired Specimen

β=450

N (Cycles)

Fig. 4 Comparison between experimental and finite element crackgrowth rates (X-direction) for un-repaired specimens.

Table 3 Experimental and FEM fatigue crack re-initiation life ofthe repaired and un-repaired panels

Crack re-initiation life up to Xctip = 4.52 mm

Patch lay-up Mid-plane Unpatched Exp. A Exp. BFEM Surface

FEM

[−45/+45]2 20 046 9176 22 000 24 000[−454] 21 759 8737 20 000 20 600[904] 23 190 8392 17 400 16 000[1054] 24 488 8353 13 000 12 800[902/02] 21 759 9752 15 100 13 800Un-repaired 5192 5192 6500 7000

5400 6000

by the order of 200–400%. The most crack re-initiationlife extension of the repaired panels belongs to the onewith the patch lay-up of [−45/+45]2. The loading andgeometry of the crack at (β = 45◦) produce almost equalnormal and shear stresses at the initial crack-front. Thepatch layers with the angle of −45◦ resist directly againstthe normal stresses and the layers with +45◦ resist directlyagainst the shear stresses. This lay-up configuration wouldbe the best before crack propagation. The finite elementresults show that the crack growth direction is turned tothe direction perpendicular to the principal stress.

The patch lay-up of [−45]4 reduces the normal stressesperfectly, but it is weak against the shear stresses. The layerorientations in the other patch lay-up configurations arenot exactly in the directions of normal and shear stressesat the crack-front. Therefore, based on experimental re-sults, the most effective patch lay-up configuration forcrack arresting of the panels with the inclined crack ofβ = 45◦ is [−45/+45]2. Finite element analyses resultspresented in Table 3 show that, the crack arresting livesobtained using the unpatched surface results are too con-servative and the lives obtained from mid-plane resultslead to non-conservative life predictions. The mid-planelives obtained from the finite element analyses show thatthe patch lay-up of [1054] is the best lay-up configurationin terms of the restarting crack growth life. The differ-ences between the experimental and finite element resultsmay occur due to the assumption of uniform crack-frontduring the initial 1 mm crack propagation. The lives werealso calculated using the mid-plane stress intensity factorsassuming uniform crack growth which is different to thereal crack-front shape.

Table 4 shows the crack propagation life of the repairedpanels with various patch lay-up configurations using bothexperimental and FEMs. The crack growth lives were ob-tained for crack growth of between the initial crack-tipvalues of 3.52 mm in the X-direction to the crack-tip



Table 4 Experimental fatigue crack propagation life of therepaired and un-repaired panels

Fatigue life up to Xctip = 16.52 mm

Patch lay-up Mid-plane Unpatched Exp. A Exp. BFEM Surface

FEM

[−45/+45]2 45 575 18 824 36 312 36 000[−454] 46 078 18 233 37 800 38 000[904] 55 507 17 503 50 400 49 800[1054] 56 546 17 173 48 100 49 000[902/02] 53 729 20 478 48 000 49 284Un-repaired 16 348 16 348 16 646 16 670

16 383 16 172

Fig. 5 Typical crack propagation path of the repaired andun-repaired panels.

X-value of 16.5 mm. It is noted that both experimental andnumerical results show that the major component of thecrack growth is in the X-direction, see Fig. 5. In this figure,the typical experimental and finite element crack propa-gation path of the repaired panel with the patch lay-up of[−454] are compared with the crack propagation path ofthe un-repaired panel. The crack growth path turned ap-proximately to the X-direction from its initial value afterless than 1 mm growth for all repaired panels. The crackpropagation paths of the other repaired panels are not pre-sented to avoid crowding in the results. It is indicated that,there is about 10% difference between crack propagationpaths obtained for various repaired panels with differentpatch lay-ups at both patched and unpatched surfaces ofthe panels.

The experimental results in Table 4 shows that usingvarious four layers patch lay-up configurations, the crackpropagation life of the cracked panels may increase by theorder of 220–310%. The greatest life extension of the re-

paired panels including both restarting the crack growthand crack propagation lives belongs to the one with thepatch lay-up of [904]. The loading and geometry of thecrack produce almost equal normal and shear stresses atthe initial crack-front, but after a few steps of the crackpropagation and due to the crack growth direction, thecomponent of the stress intensity factor in mode I (K I)becomes dominant. Therefore, the patch layers with anangle of 90◦ resist directly against the remote loading andlocal normal stresses along the crack growth. The lay-ers orientation in the other patch lay-up configurationsis not exactly or completely in the directions of normalstresses at the crack-front. Therefore, based on the exper-imental results, the most effective patch lay-up configura-tion for crack growth life extension of the repaired panelsis [904].

The finite element analyses results presented in Table 4show that, the crack propagation lives obtained using theunpatched surface results are too conservative and the livesobtained from the mid-plane results may lead to 50% non-conservative life predictions. The obtained finite elementanalysis lives using the mid-plane results presented in thistable show that the patch lay-up of [1054] is the best lay-upconfiguration among the considered patch lay-ups. Thelife of the repaired panel with the lay-up of [1054] is onlyabout 2% larger than that for the lay-up of [904]. Assum-ing uniform crack propagation along the panel thicknessmay lead to the differences between the experimental andnumerical results. Three-dimensional crack propagationanalyses considering mode I, II and III at the crack-frontand assuming a non-uniform crack growth along the panelthickness are required to verify the finite element resultswith the experiments. This cumbersome task is currentlybeing investigated by the authors.

Figures 6–10 show the experimental and finiteelement crack growth rates in the X-direction for un-repaired and repaired panels with various patch lay-upconfigurations. The depicted finite element crack growthresults are based on both unpatched surface and mid-plane results. For comparison the experimental crackgrowth rate of the un-repaired panels are also depictedin these figures. These figures show that the finite el-ement crack growth behaviour of the repaired panelsobtained based on the unpatched surface results are farfrom the experimental results in both crack re-initiationand among the crack propagation for all patch lay-upconfigurations and therefore they are too conservative.These figures also show that, the crack growth obtainedbased on the mid-plane results is slower than those ob-tained from the experiments for all patch lay-up config-urations except for the early crack growth stages in thecase of [−45/+45]2 (Fig. 6) and therefore lead to the non-conservative crack growth predictions. Figure 6 showsthat the patch lay-up of [−45/+45]2 behaves well in crack



0

2

4

6

8

10

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14

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0 10000 20000 30000 40000 50000

Cra

ck L

engt

h (

mm

)

Un-patched surface (FEM)

Mid-plane (FEM)

Experiment

Un-repaired Exp.

Patch lay-up[-45/+45]2

N (Cycles)

Fig. 6 Experimental and finite elementcrack growth rates in the X-direction forun-repaired and repaired panels with patchlay-up of [−45/+45]2.

0

2

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0 10000 20000 30000 40000 50000

Cra

ck L

engt

h (

mm

)


Mid-plane (FEM)

Experiment

Un-repaired Exp.

Patch lay-up[-454]

N (Cycles)

Fig. 7 Experimental and finite elementcrack growth rates in the X-direction forun-repaired and repaired panels with patchlay-up of [−454].

arresting but it is weak in crack propagation life exten-sion of the repaired panels. The predicted crack growthbehaviour of the repaired panel with the patch lay-upof [902/02] (Fig. 10) is closer to the experimental resultsespecially at the early stages compared with the other lay-up configurations. It should be noted that using differ-ent patch layers angles can induce various elasticity inthe loading direction of the cracked panels. Effects ofpatch layers on fracture parameters vary with their dis-tance from the bonded surface of the cracked panels. Theasymmetric conditions in the lay-up of [902/02] produce asecondary bending against the existing out-of-plane bend-

ing due to the single-side repair of the structure. In thiscase, de-bonding of the patch was observed after a fewsteps crack growth at the edges of the patch during theexperiments that may occur due to the above mentionedasymmetric patch lay-up bending. The opposite bendingin this specimen causes tension or peeling at the bondedsurface of the repaired panels and therefore may lead tothe debounding of the patch from the panel during fatigueloading. Small crack growth slope of the specimens up to4–5 mm after the restarting crack growth is due to the ex-isting bending moment of the asymmetric [902/02] lay-up,but increase in the crack growth rate after that can be due



0

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0 10000 20000 30000 40000 50000 60000

Cra

ck L

engt

h (

mm

)Un-patched surface (FEM)

Mid-plane (FEM)

ExperimentUn-repaired Exp.

Patch lay-up[904]

N (Cycles)

Fig. 8 Experimental and finite elementcrack growth rates in the X-direction forun-repaired and repaired panels with patchlay-up of [904].

N (Cycles)

0

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0 10000 20000 30000 40000 50000 60000

Cra

ck L

engt

h (

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Un-patched surface (FEM)Mid-plane (FEM)ExperimentUn-repaired Exp.

Patch lay-up[1054]

Fig. 9 Experimental and finite elementcrack growth rates in the X-direction forun-repaired and repaired panels with patchlay-up of [1054].

to the de-bonding phenomena occurring in this specimen.If the bonding can be reinforced by improving the surfacepreparation method and using stronger fatigue resistanceadhesive in this case, the crack growth life extension ofbetter than the lay-up of the [904] may be obtained. Moreinvestigations are required in this regard. The fatigue lifepresented in Tables 3 and 4 using the finite element re-sults at the unpatched surface of the specimens also showthat the lives obtained for the panel with the patch lay-upof [902/02] are greater than the other patch lay-up con-figurations. It shows that the produced bending momentagainst the secondary bending due to the single-side repair

of the structure has a greater affect on the unpatched sur-face of the panel. Comparison between the crack growthrates at the unpatched surface of the repaired panels andun-repaired panels in Figs. 6–10 also show that the crackgrowth behaviour at unpatched surfaces of the repairedpanels is similar to the un-repaired crack growth.

Figure 11 shows the variation of crack length in theX-direction versus the number of load cycles obtainedfrom the experiments for various repaired panels. Thisfigure shows that the crack growth rate of the specimenwith [902/02] patch lay-up at the early stages (up to 5 mmfrom the initial crack-tip, Xctip = 8.5 mm) is smaller than



0

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Cra

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Experiment

Un-repaired Exp.

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N (Cycles)

Fig. 10 Experimental and finite elementcrack growth rates in the X-direction forun-repaired and repaired panels with patchlay-up of [902/02].

0

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[-45/+45]2

[-454][904]

[902/02]

[1054]

[-454][904][1054]

[902/02]

[-45/+45]2

N (Cycles)

Fig. 11 Comparison between variousexperimental crack propagations in theX-direction of repaired and un-repairedpanels.

the crack growth rates of all other lay-up configurations.As mentioned before, the de-bonding of patch from thepanel occurred after 5 mm crack growth. These exper-imental results show that if the problem of de-bondinghad not happened the patch lay-up of [902/02] could bethe best lay-up configuration. It can experimentally be ob-served from the crack-front shape that the crack growthdifference between the patched and unpatched surface ofthe repaired panels with [902/02] lay-up is smaller thanthe [904] and [1054] lay-ups. More explanation in this re-gard will be presented in a future publication. Figure 11also shows that the slope of the crack growth curves of the

repaired panels with the patch lay-up of [−45/45]2 and[−454] are similar to the un-repaired panel curve. There-fore it may be concluded that the major effects of thesetwo lay-up configurations are on the crack re-initiationlife of the repaired panels and they have minor effects onthe crack growth part of the fatigue life.

C O N C L U S I O N

In this paper, experimental and numerical fatigue crackgrowth of thin aluminium panels containing a central in-clined crack of 45◦ with single-side glass/epoxy composite



patch were performed. Effects of patch lay-up configura-tion on the restarting crack growth life and crack growthrate of the repaired panels were studied. It was shownthat finite element crack re-initiation and propagationlives prediction based on the unpatched surface results aretoo conservative. However, the finite element mid-planeresults may lead to an up to 50% non-conservative life pre-diction. The experimental results showed that using vari-ous four layer patch configurations, the crack re-initiationlife of the cracked panels may increase by the order of200–400% and the crack propagation life of them may in-crease by the order of 220–310%. It was experimentallyshown that, the most effective patch lay-up configurationfor crack arresting of the panels is [−45/+45]2 however,the most life extension including the crack propagationcycles belongs to the patch lay-up of [904]. It was alsoshown that using an asymmetric patch lay-up configura-tion similar to [902/02] with an improved bonding process,which produces a bending against the single-side repairout of plane bending of the panels, may leads to a veryslow crack growth rate even slower than the patch lay-up of [904]. Further investigations considering the surfacepreparation method, bonding and curing processes are re-quired in this regard.

R E F E R E N C E S

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2 Sun, C. T., Klug, J. and Arendt, C. (1996) Analysis of crackedaluminium plates repaired with bonded composite patches.AIAA Journal, 34(2), 369–374

3 Jones, R. and Callinan, J. (1979) Finite element analysis ofpatched cracks. J. Struct. Mech. 7, 107–130.

4 Jones, R., Callinan, J. and Aggarwal, K. C. (1983) Analysis ofbonded repair to damaged fiber composite structures.Eng. Fracture Mech. 17, 37–46.

5 Baker, A. A. (1991) Fatigue crack propagation studies onaluminium panels patched with boron/epoxy composite. In: Int.Conf. on Aircraft Damage Assessment and Repair, (Edited by R.Jones and N. J. Miller), Melborn, Australia, pp. 209–215.

6 Ratwani, M. M. (1979) Analysis of cracked adhesively bondedlaminated structures. AIAA J. 17(4), 988–994.

7 Rose, L. R. F. (1982) A cracked plate repaired by bondedreinforcements. Int. J. Fract. 18(2), 135–144.

8 Lu, J., Hu, Y. and Ju, D. (1991) An assessing method of fatiguelife on central-through cracked plate with adhesive bondedreinforcement. Fatigue, Fracture, and Risk, ASME 215,135–140.

9 Daghyani, H. R., Sayadi, A. and Hosseini-Toudeshky, H.(2003) Fatigue crack propagation of aluminium panels repairedwith adhesively bonded composite laminates. Proc. Instn Mech.Engrs. 217, 291–293.

10 Hosseini-Toudeshky, H., Mohammadi, B. and Daghyani, H. R.(2003) Effects of patch lay-up configuration on fractureparameters and fatigue life of single-sided repaired panels inmixed-mode conditions, 4th Iranian Aerospace Society Conference,Tehran, Iran.

11 Hosseini–Toudeshky, H., Mohammadi, B. and Daghyani, H.R. (2006) Mixed–mode fracture analysis of repaired aluminiumpanels using composite patches. Comp. Sci. Tech. 66, 188–198.

12 Hosseini-Toudeshky, H., Mohammadi, B. and Bakhshandeh, S.(2005) Mixed-Mode Experimental Fatigue Crack GrowthAnalyses of Thin Aluminum Panels Repaired with CompositePatches, DFC-8 & ETDCM-7 Conference, Sheffield, UK.

13 Hosseini–Toudeshky, H., Mohammadi, B. and Daghyani, H.(2004) Analysis of Mixed–Mode Cracked Panels Repaired withSingle-Sided Composite Patches. Proceedings of the FourthInternational Conference on Thin-Walled Structures, pp. 475–482,Loughborough, UK.

14 Bouiadjra, B. B., Belhouari, M. and Serier, B. (2002)Computation of the stress intensity factors for repaired crackswith bonded composite patch in mode I and mixed mode.Composite Structures 56, 401–406.

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18 Crooks, H. R. (2003) Reduction of Thermal Residual Strains inAdhesively Bonded Composite Repairs. MSc Thesis, USAF, AirForce Institute of Technology, USA.

19 Rice, J. (1968) A path independent integral and theapproximate analysis of strain concentration by cracks andnotches. J. Appl. Mech. (Trans. ASME), Series E, 379–386.

20 Farahmand, B., Bockrath, G. and Glassco, J. (1997) Fatigue andFracture Mechanics of High Risk Parts: application of LEFM andFMDM theory. International Thomson Publishing.

21 Hosseini-Toudeshky, H., Mohammadi, B. and Daghyani, H. R.(2003) Mixed-Mode Crack Propagation Based on VariousPropagation Angle Criteria. 11th Annual Conference(International) of Mechanical Engineering, Mashad, Iran.

22 Erdogan, F. and Sih, G. C. (1963) On the crack extension inplates under plane loading and transverse shear. J. of Basic Eng.85, 519–527.

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25 Mi, Yaoming (1996) Three-Dimensional Analysis of CrackGrowth. Computational Mechanics Publications, SouthamptonUK, Boston MA.

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Mixed-mode fatigue crack growth of thin aluminium panels with single-side repair using experimental and numerical methods

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