Failure Load Prediction of Single Lap Bonded Joint_Online First_Hung

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Failure Load Prediction by Damage ZoneMethod for Single-lap Bonded Joints of

Carbon Composite and Aluminum

KHANH-HUNG NGUYEN, JIN-HWE KWEON* AND JIN-HO CHOI

School of Mechanical and Aerospace engineering, Research Center for Aircraft Parts

Technology, Gyeongsang National University, Jinju, Gyeongnam 660-701, Korea

ABSTRACT: A damage zone method based on 3D finite element analysis wasproposed to predict the failure loads of single-lap bonded joints with dissimilarcomposite-aluminum materials. To simulate delamination failure, interply resinlayers between any two adjacent orthotropic laminas of composite adherend wereassumed with a thickness of one-tenth of a composite lamina. Geometrically non-linear effects due to the large rotation of the single-lap joint were included in theanalysis. Analysis also considered the material nonlinearity of the aluminum adher-end due to the stress exceeding yield level. Based on the experimental observationthat the failure modes of the specimens were dominated by delamination anddebonding, the Ye-criterion was applied to account for the out-of-plane failure of composite adherend and the Von Mises strain criterion was applied for the adhesive

layer. The failure indices were multiplied to the predicted damage zone as a weightfactor and the calculated damage zones were divided by an area or volume consid-ering the joint geometry. Predicted failure loads show deviation within 18% fromexperimental results for nine different bonding lengths or adherend thicknesses.

KEY WORDS: dissimilar materials, single-lap, bonded joint, damage zone.

INTRODUCTION

AN AIRCRAFT STRUCTURE is the assembly of many parts such as skins, stiffeners,frames and spars, etc. These parts must be connected through joints: mechanical or

bonded. Mechanical joints with fasteners such as bolts, screws, or rivets are simple and

widely used when disassembly for maintenance is necessary. However, the fasteners them-

selves are an important source of weight increase and the fastener holes induce stress

concentrations and consequently reduce the strength of joints.

*Author to whom correspondence should be addressed. E-mail: [email protected] 48, 10, 11 and 13 appear in color online: http://jcm.sagepub.com

Journal of COMPOSITE MATERIALS, Vol. 0, No. 00/2009 1

0021-9983/09/00 000126 $10.00/0 DOI: 10.1177/0021998309345295 The Author(s), 2009. Reprints and permissions:http://www.sagepub.co.uk/journalsPermissions.nav

Journal of Composite Materials OnlineFirst, published on August 17, 2009 as doi:10.1177/0021998309345295


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Adhesive bonding is another joining method that has been increasingly used. In adhe-

sively bonded joints, there is no fastener at all and, therefore, no stress concentration due

to fastener holes. The typical failure modes of bonded joints are cohesive failure, which is

failure within the adhesive, interfacial failure (failure along the interface between adherend

and adhesive), or adherend failure. Cohesive failure and interfacial failure are sometimes

referred to as bond line failure. Bond line failure is the typical failure mode of metallic

bonded joints. Adherend failure is mainly found in joints using composite laminate as the

adherend. The adherend failure modes in joints with composite adherend are very com-

plicated, and include such failures as matrix failure, fiber failure, and interlaminar and

intralaminar failures.

The research on bonded joints has a long history and has been conducted experimentally

and/or numerically. Researchers have targeted stress analysis, failure mode and strength

prediction, strength improvement, and the effects of various parameters such as material,

geometry and bonding method, etc. One difficulty for failure load prediction in a bonded

joint comes from the presence of the singularity at the ends of overlapped area. Harris and

Adams [1] conducted finite element analysis to predict the failure mode of metallic single-lap bonded joints. They took into account the geometrical and material nonlinearity of

single-lap joints. Their failure prediction method was based on material strength. The

failure was assumed to occur when the maximum principal strain or maximum principal

stress at one Gauss point close to the singular position inside the adhesive layer attained

the ultimate stress or strain of the adhesive material. The method, therefore, is dependent

on mesh refinement near the singularity point. The authors first applied this method to

predict the failure mode and failure load of metal-to-metal single-lap joints [1] and then

extended their work to lap joints with composite adherends [2]. The point-based method

proposed by Harris and Adams was shown by Kairouz and Matthews [3] to be useful in

predicting the failure mode and strength of bonded single-lap joints made of cross-plylaminated adherends.

To overcome the singularity problem, singularity parameter approaches [4,5] were also

used. A generalized stress intensity factor and a parameter called strength of the singu-

larity were defined and used successfully in the method for the prediction of fractures. In

addition, the approach was used for the prediction of fatigue crack initiation in adhesive

bonds [6,7]. Ishii et al. [8] considered the concentrated multiaxial stress state in the adhe-

sive layer in their analysis and proposed a method based on two-singularity parameters to

estimate the fatigue strengths of adhesively bonded joints made of carbon fiber reinforced

polymer and aluminum alloy. However, the singularity parameter approach did not con-

sider the nonlinearity of the adhesive layer and therefore the obtained generalized stress

intensity factor may not be correct when the adhesive layer shows highly nonlinear beha-

vior. The method also requires additional tests to define the fracture criteria using stress

singularity parameters.

Crocombe [9] proposed another method to predict the bond line failure of single-lap

bonded joints. Failure was assumed to occur as whole adhesive layers become plastic.

It was shown that this method can make a good estimation of joint strength for a

wide class of joints. In some cases, however, this approach can be incorrect because

local failure can occur before global yielding. However, the method contributed to estab-

lishing the concept of the damage zone method, in which a joint failure occurs after

adhesion in some area fails rather than after adhesion fails at a certain point. Clark and

McGregor [10] not only applied the point-based method but also proposed an approachbased on ultimate stress over a zone to predict the failure load and failure mode of

2 K.-H. NGUYEN ET AL.


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single-lap bonded joints. They showed that while the point-based method predicted lower

failure loads and failure initiation near the singularity, in contrast to observed experi-

ments, the damage zone-based method gave good predictions of failure loads of different

joint geometries.

As bonded joints with composite adherend are used, interlaminar failure (delamination)

is usually found over the failure surfaces. Interlaminar failure is caused by weakness of

composite adherends in the through-the-thickness direction. Assuming that both cohesive

and out-of-plane adherend crack initiation of adhesively bonded joints will occur after a

damage zone develops, Sheppard et al. [11] proposed a damage zone model to predict the

joint failure loads of different geometries. Using their developed method, the authors

showed that failure load predictions of aluminum joints and composite joints were

within the experimental scatter range.

Based on the fact that the intra/interlaminar failures occur in the layer close to the

adhesive, Tong [12] conducted a 2D analysis and tried six stress-based criteria to predict

the failure loads of double-lap bonded joints. The stress was taken at the center of one ply

element or one adhesive element at the free end where stresses were highly concentrated.The method is a point-based method and can be dependent on meshing near the singu-

larity. In addition, 3D effects such as the free edge effect, the anticlastic effect, and the

bending-twisting coupling effect can play important roles in the failure initiation and

failure load [13]. To overcome the problem of singularity, Kim et al. [14] used a charac-

teristic length method, which is widely used in failure prediction of mechanical joints.

2D analysis considering geometrical and material nonlinearity was conducted with the

use of a global yielding criterion for the adhesive layer and a quadratic delamination

criterion, which was proposed by Brewer and Palage [15], for the composite adherend.

Interfacial stresses in the specimens were calculated under the test failure loads. The char-

acteristic length was determined as the distance from the overlapped end along the inter-face to a location of the finite element model in which the quadratic delamination criterion

was satisfied. The optimal joint strength was found and a new joint strength improvement

technique was also suggested.

Shin and Lee [16] performed a 3D analysis considering the thermal load of co-cured

single-lap and double-lap joints without any additional adhesive. They predicted failure

load of the joints considering two criteria: the Ye-delamination failure criterion and the 3D

TsaiWu failure criterion. In the case of single-lap co-cured joints, failure loads predicted

by the Ye-criterion were in good agreement with the experimental results. Otherwise, using

the TsaiWu criterion was better for failure load prediction for double-lap bonded joints.

Other research [1720] has utilized fracture mechanics to predict the failure loads of

bonded joints. An initial crack is usually assumed to exist in the adhesive, at the interface

of the adherend/adhesive, or in the composite adherend. The crack propagates as the

strain energy release rate exceeds a critical value. The strain energy release rate can be

computed by the virtual crack closure technique in conjunction with finite element ana-

lysis. However, this energy-based approach relies on the existence of a crack in the inter-

face, and on the assumption of small-scale bridging and linear elasticity. If any of these

conditions are violated, an alternative approach such as cohesive zone modeling is

required [20]. The cohesive zone model, however, has some limitations such as mesh

sensitivity, lack of convergence, computing inefficiency, and so on. An improvement of

the cohesive zone model was done with the implementation of the discrete cohesive zone

model by Xie and Waas [21]. The authors showed that this model is not sensitive to themesh size and the load increment. Computation time was also reduced.

Failure Load Prediction by Damage Zone Method 3


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The former was used to manufacture the thin specimens and the latter to make the thick

specimens. The aluminum adherend was made with anodized aluminum 2024-T3 and

bonded to a composite adherend using adhesive FM73m by Cytec. The mechanical prop-

erties of the composite unidirectional prepreg (USN125 by SK Chemicals), adhesive layer,

and aluminum adherend are given in Table 1. The thicknesses of the anodized aluminum

2024-T3 adherend are 1.58 mm and 3.01 mm. The stressstrain curve for the tension test of

the adhesive experimentally obtained is shown in Figure 2(a), and that of the aluminum is

shown in Figure 2(b) [24].

Detailed dimensions of the specimens are given in Table 2 and experimental failure loadsare shown in Figure 3. The experimental result shows that higher overlap length yields

Table 1. Material properties of USN125 prepreg, adhesive, and aluminum 2024-T3.

USN125 AL2024-T3 FM73m

Tensile modulus E 11 (GPa) 162 73 2.8

E 22 (GPa) 9.6

E 33 (GPa) 9.6Shear modulus G12 (GPa) 6.1

G13 (GPa) 6.1

G23 (GPa) 3.5

Poisson’s ratio m12 0.298 0.33 0.38

m13 0.298

m23 0.47

Tensile strength X T (MPa) 2552

Y T (MPa) 43

Z T (MPa) 43

Shear strength S12 (MPa) 94

S13 (MPa) 94

S23 (MPa) 40

S t r e s s ( M P a )

500

400

300

200

100

00.00 0.01 0.02 0.03

Strain

0.04 0.05 0.06

Figure 2. Tensile stress

strain curve of (a) FM73m adhesive, and (b) aluminum 2024-T3.



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a higher failure load. Increase of the specimen thickness also affects the failure load of

single-lap bonded joints. However, failure loads increase only 1232% as the thicknesses

of the specimens nearly double.

In a metal-to-metal joint, a bond line failure is the typical failure mode. However, the

weakness of the composite material in the out-of-plane direction leads to a different failure

mode. Typical failure surfaces of specimens are shown in Figure 4. The failure surface of

the specimens is dominated by the delamination of composite adherend, and intralaminar

failures are locally observed. In addition to out-of-plane failure of the composite adherend,partial bond line failure is also found.

F a i l u

r e l o a d ( k N )

25

20

15

10.7

12.8

14.7

14.2 16.4 16.5

18.2

21.6

11.9

10

5

0

FM15 FM20 FM25 FM30 FM35 FM40 FM15D FM25D FM35D

Figure 3. Failure loads of specimens.

Table 2. Dimensions of composite-to-aluminum single-lap bonded joint.

Thickness (mm)

ID b (mm) Al Composite FM73m Total No. of specimens

FM15 15 1.58 1.68 0.112 3.372 5FM20 20 1.58 1.68 0.123 3.383 5

FM25 25 1.58 1.68 0.143 3.403 5

FM30 30 1.58 1.68 0.132 3.392 5

FM35 35 1.58 1.68 0.137 3.397 5

FM40 40 1.58 1.68 0.199 3.459 6

FM15D 15 3.01 3.38 0.168 6.558 6

FM25D 25 3.01 3.38 0.187 6.577 6

FM35D 35 3.01 3.38 0.193 6.583 6



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Finite Element Analysis

MODELING STRATEGY

Three-dimensional finite element analysis of single-lap joints was conducted by

MSC.Marc. A typical finite element model for joint FM15 is shown in Figure 5. A 3D

isometric element, Element 7 [25], was used to model the adherend and adhesive. The spew

fillet shape was modeled approximately as a right triangle with 0.4 mm long legs, as shown

in the right side of the figure. The mesh was created more finely at both ends and side

edges of the overlap area. Twenty elements were created along the width of the joints. The

smallest width (along the Y -direction) of the element at the free side edges was 0.0475 mm.

The effects of the mesh density of the model are discussed later in this article. Geometrical

nonlinearity from the large displacement and rotation caused by the eccentricity of

applied loads in single-lap joints were taken into account. Material nonlinearity was

also considered in the analysis, as the adhesive layer and aluminum adherend show

nonlinear stressstrain curves before failure. The Von Mises yield criterion was used to

model the stressstrain behavior of both the aluminum adherend and adhesive layer,

which are isotropic. The boundary conditions are shown in Figure 6.

Interlaminar stresses are the source of delamination in composite laminate.

Delamination failure can be defined as the failure of the interply resin-rich layers thatare made during the manufacturing process of composite laminate. Interlaminar stresses

FM25 FM25D

Figure 4. Typical failure surface of the joint FM25 (left) and FM25D (right).

z

Y

X

0.4 mm

0.4 mm

Figure 5. Finite element model of bonded joint specimens.



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can be considered as stresses on the interface between two adjacent plies or as stresses

inside these thin resin layers. Fenske and Vizzini [26], when investigating the delamination

of a plate subjected to an axial strain, found that the onset of delamination can be pre-dicted by considering the failure of interply resin layers.

In this article, the composite adherend is modeled as a combination of orthotropic plies

and isotropic interply resin layers. An interply resin layer is modeled to exist between any

two adjacent orthotropic plies. Consequently, delamination is considered as the failure of

these interply layers. Moduli of the interply resin layer are assumed to be the same as the

matrix properties of an orthotropic lamina. A schematic cross section at the overlapped

area of the joint is shown in Figure 7. As in the work of Fenske and Vizzini, all interply

resin layers are assumed to have a constant thickness that is equal to 10% of one ortho-

tropic ply thickness.

DAMAGE ZONE METHOD

In this article, four slightly different approaches based on the damage zone method are

applied to predict the failure load of single-lap bonded joints. The first approach is the

damage area method [11]. This approach assumes that the specimen fails as the damage

area inside it exceeds a critical value. In other words, the specimen fails as follows:

DA ¼ CDA ð1Þwhere DA and CDA are the total damage area inside a specimen and a critical damage

area, respectively.The second approach is the weighted damage area method proposed by Choi and Chun

[27] to predict the failure load of mechanical joints. This method considers not only the

damage area but also the magnitude of the failure index by using a given failure criterion

and the geometrical effects. The joint is assumed to fail as the weighted damage area ratio

equals a critical value:

DARn ¼P

FI n DAAG

¼ CDARn ð2Þ

where DAR n, FI , DA, AG, n, and CDARn are the damage area ratio, the failure index by a

failure criterion, the damage area, the area that is responsible for the geometrical effects,the weighting power factor, and the critical damage area ratio, respectively.

X

X

Distributeuniformly

F i x e d

b

Z

W

Y

Figure 6. Boundary conditions for the finite element analysis.



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In the above two approaches, the damage area is the main concern. As a 3D analysis is

conducted in this article, the damage volume approach can be obtained by expanding the

damage area concept. Simply put, damage volume can be used instead of damage area.

Equation (1) can be rewritten as follows:

DV ¼ CDV ð3Þ

where DV and CDV are the total damage volume inside a specimen and a critical damagevolume, respectively.

A weighted damage volume approach is given in Equation (4):

DVRn ¼P

FI n DV V G

¼ CDVRn ð4Þ

where DVRn, FI , DV , V G, n, and CDVRn are the damage volume ratio, the failure index

by a failure criterion, the damage volume, the volume the relates to geometrical effects,

the weighting power factor, and the critical damage volume ratio, respectively.

It is noted that the damage area is the in-plane damage area in the adhesive, interply

resin layers, and orthotropic plies. The area AG and the volume V G should account for thedifferences in geometry of the joints such as bonded length, thickness, and width. The

details of AG and V G are given in the next chapter. The weighting power factor n is an

integer such as 0, 1, or 2. When n equals 0, the failure index has no effect on the damage

volume ratio (DVR).

The general procedure to predict failure load of the joints was reported in Sheppard

et al. [11] and is rewritten here with a difference in the damage zone size, which may be the

size of the damage area, the damage volume, the damage area ratio, or the damage volume

ratio:

(1) Test one or more bonded joint(s) to record the failure load(s) and mode(s).

(2) Analyze the joint(s) under the experimental failure load(s) using an appropriate ana-lysis tool.

Z

Y

Interplyresin layers

Aluminum adherend

Adhesive layer

45°

–45°

90°

0°

45°

Figure 7. Cross section of the single-lap joint at the bonding area.



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(3) Use appropriate failure criterion and the relevant material allowable(s) to calculate the

damage zone size(s) in the joint and choose a value to be the critical value.

(4) Use the critical damage zone size calculated in the previous step to predict the critical

load of bonded joints with similar adherends, adhesives, and load paths.

FAILURE CRITERIA

Failure criteria selection depends on the failure mode of the specimens. The failure

mechanism of the bonded single-lap joint was out-of-plane failure and partial bond-line

failure. Based on the experimental failure modes, the Ye-delamination criterion [28] was

applied to the interply resin layers to take into account the interlaminar failure, and was

also applied to the orthotropic plies to account for the intralaminar transverse failure.

The Ye-delamination criterion is as follows:

233

Z 2 þ

213

S 213 þ

223

S 223 ¼1 ð

33

0Þ

213

S 213þ

223

S 223¼ 1 ð 335 0Þ

8>>><>>>:

ð5Þ

where 33, 13, 23, Z , S 13, and S 23 are the peel stress in interply layer or orthotropic ply,

out-of-plane shear stresses in interply layer or orthotropic ply, interlaminar normal

strength, and transverse shear strengths, respectively.

The adhesive used in this article shows a nonlinear stressstrain curve. Consequently,

the Von Mises strain criterion is applied to the adhesive layer:

"VM ¼ ffiffiffi2

p

3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið"1 "2Þ2 þ ð"2 "3Þ2 þ ð"3 "1Þ2q ð6Þ

where e1, e2, and e3 are the principal strains.

RESULTS AND DISCUSSION

Damage Area in Adhesive

Figure 8 shows the Von Mises stress distribution in the mid-plane of the adhesive

layer (Z ¼ 0) of joint FM15 subjected to its experimental failure load (10.67 kN), assum-ing a linear elastic adhesive. The same load was applied to obtain the results given

in Figures 914. The Von Mises stress distribution is uniform along the width direction

(Y -direction) of the joint, with the exception of the bonding area corners. The stress is very

high at the ends of the overlapped area (along the X -direction) where geometry (thickness)

changes discontinuously. The stress at the left end of the overlapped area (aluminum end)

is higher than that at the right end (composite end). This suggests that the left end of the

overlapped area is more in danger of debonding than is the other bonded area. This

analysis result concurs with the experimental observation [22], in which bond line failures

are mainly found at the end of aluminum parts. The material linear analysis is used to

easily show only this observation. The other results that follow come from the analysiswith both geometrical and material nonlinearities.



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V o n m i s e s s t r e s s ( M P a )

200

180

160

140

120

100

80

60

40

20

0–1.0

–0.5

–1.0

–0.5

1.0

020

406080100120140160180200

0.50.0

2 Y / W

0.02 X / b

0.51.0

Figure 8. Von Mises stress distribution in the adhesive of the joint FM15 without considering material

nonlinearity.

–1.0

0

20

40

60

80

100

V o n m i s e s s t r e s s ( M P a )

120

140

Nonlinear adhesiveLinear elastic adhesive160

180

0.5 1.00.0–5.0

2 X / b

Figure 9. Von Mises stress distribution along the center of the adhesive of joint FM15 with and without

considering material nonlinearity (Y ¼ Z ¼0).



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The Von Mises stress distribution along the centerline in the X -direction of the adhesive

(Y ¼Z ¼ 0) on the overlapped area (2X /b is from 1 to 1) considering the material non-linearity is compared with the results of the linear elastic adhesive model in Figure 9. While

the stress in the elastic adhesive model shows peaks at the ends of the bonding area on

both overlap free ends, the stress of the nonlinear adhesive model is nearly constant in the

end areas. Consequently, the inner overlapped area (far from ends) carries a larger load

and then shows higher stress compared with the results of the elastic adhesive model.Figure 10 shows the failure areas considering the material nonlinearity of the adhesive,

based on the Von Mises strain criterion. As expected, the failure of the adhesive is focused

over the end areas of the overlapped area where stresses are highly concentrated. The

failure area is slightly larger in the aluminum end area than in the composite end area.

Damage Area in Interply Resin Layers

Figure 11(a) shows the delamination failure index distribution by the Ye-criterion in

the interply layer between the first 45 and the first 45 layers of joint FM15 from theadhesive layer. Obviously, along the ends of the overlap area and free side edges of the

composite adherend, the stress is highly concentrated. Consequently, a high failure index

and large damage area are predicted over the regions. Pagano [29] reported that the high

stress along the free side edges area can be attributed to the stress singularity along the

edges. Figure 12 shows the failure index in the same layer at various positions of X - along

the Y -axis. The figure obviously shows that the failure index is high at the overlapped area

ends (2X /b¼1.0) and shows a peak value at the very limited free side edges.The delamination failure index of the second (between first 45 and 90 layers) and

the third interply layers (between the first 90 and 0 layers) of joint FM15 are shown inFigure 11(b) and (c), respectively. Similarly, the damage area and high failure index

are found near the ends of the bonded area and free side edges. It is interesting that

failure indices are very high along the free side edges of the non-overlapped region of the composite adherend. However, delamination was not visually observed over these

b

X

Y

Figure 10. Damage area in the adhesive of joint FM15 according to Von Mises strain criterion.



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areas in the experiment. As noted by Pagano [29], it is guessed that there is a singularity

along the free side edges between two plies. Therefore, a high-density mesh was created at

the free side edges. Consequently, high stresses were obtained at these singular positions.

However, the delamination should be predicted by the stress at some distance from the

singularity rather than at the singularity point itself because the singularity occurs in a very

limited area. Therefore, even though the failure index obtained is higher than unity at both

free edges far away from the bonding area, this does not mean that delamination occurs

there experimentally.

The peak failure index in Figure 11(a) is smaller than that in Figure 11(b) and (c). Thiscan be explained in terms of the compressive interlaminar peel stress at the free side edges

–2.0–1.5

–0.5

–0.5

0.0

0.0

0.5

0.5

1.0

1.0

–1.0

–1.0

0

2

68

4

02

4

6

8

(a)

(b)

Y e f a i l u r e i n d e x

–2.0–1.5

–0.5

–0.5

0.0

0.0

0.5

0.5

1.0

1.0

–1.0

–1.0

0

2

68

4

0

2

4

6

8

Y e f a i l u r

e i n d e x

2 Y / W

2 Y / W

2 X / b

2 X / b

Figure 11. Ye failure index in interply layers (a) between the first 45 and 45 layers, (b) between the first

45

and 90

layers, and (c) between the first 90

and 0

layers.



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of the interface between the 45 and 45 layers. As shown by Yang and He [30], the freeside edges between the 45 and 45 layers of a composite plate of [ 45]S subjected to anaxial strain experience compressive interlaminar peel stresses. Consequently, this compres-

sive stress reduces the delamination possibility and failure index.

The next interply between 45 and 45 layers is further from the adhesive layer thanthe first interply. Therefore, the failure index and the total damage area in this interply

layer were found to be smaller than those in the interply layer between the first 45 and the

first 45 layer. Similar phenomena were observed in the case of the interply layer between45 and 90 layers and also in that between 90 and 0 layers.

–2.0–1.5

–0.5

–0.5

0.0

0.0

0.5

0.5

1.0

1.0

–1.0

–1.0

0

2

68

4

0

2

4

6

8


2 Y / W

2 X / b

(c)

Figure 11. Continued.

2 Y / W

F a i l u r e i n d e x

1.4

1.2

1.0

0.8

0.6

0.4

0.2

X = –1.0b

X = –0.75b

X = –0.5b

0.0

–1.0 –0.5 0.0 0.5 1.0

–1.0b –1.5b

–0.75b b

X

Y

Figure 12. Ye failure indices in the interply layer between the first 45 and 45 layers.



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From the analysis, the failure area in the interply layers of the composite adherend,

which indicates interlaminar failure, is concentrated at both ends of the bonding area and

also at both edges of the composite adherend.

Damage Area in Orthotropic Plies

The Ye-criterion was also applied to the orthotropic plies to predict the intralaminar

transverse failure of joints. As shown in Figure 13, the peaks of the failure index

distribute at the ends of the bonding area (2X /b¼ 1.0 and 1.0) and the free side edges(2Y /W ¼ 1.0 and 1.0) of joint FM15. Maximum peaks are mainly found at the free sideedges, particularly, slightly outside the aluminum edge (where 2X /b is around

1.1 to

1.2). However, the region of high failure index at the free side edges is very limitedcompared with the failure region over the end area of the joint. The failure index in the

–2.0–1.5

–0.5

–0.5

0.0

0.0

0.5

0.5

1.0

1.0

–1.0–1.0

0

2

68

4

0

2

4

6

8

(a)

(b)


–2.0–1.5

–0.5

–0.5

0.0

0.0

0.5

0.5

1.0

1.0

–1.0

–1.0

0

2

6

8

4

0

2

4

6

8


2 Y / W

2 Y / W

2 X / b

2X / b

Figure 13. Ye failure index in the first (a) 45 layer, (b) 45 layer, (c) 90 layer, and (d) 0 layer of the joint FM15.



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90 orthotropic layer shown in Figure 14 is an example. The failure index and damage areain the first 45 orthotropic layer are larger than those in the second 45 layers in the samelaminate, which are further from the adhesive layer. The other layers with the same fiber

angle show the same trend as that of the 45 layers. These phenomena are also found in theother joints with different overlap lengths or joint thicknesses.

The summation of the damage area in the composite laminate and adhesive layer is

given in Table 3. For thin adherend joints (FM15FM40), interply failure contributes to

the total sum of the failure area more than does intralaminar failure of the orthotropic

plies. For thick joints (FM15DFM35D), however, intralaminar failure affects the most

joints, and is followed by adhesive and interplay failures. Considering these results, it can

be deduced that none of the three kinds of failures can be neglected when calculating the

failure zone. In joint FM30, the experimental failure load slightly deviated from the trend,as shown in Figure 3. Because of the smaller failure load compared with those of the

–2.0–1.5

–0.5

–0.5

0.0

0.0

0.5

0.5

1.0

1.0

–1.0–1.0

0

2

68

4

0

2

4

6

8

(c)

(d)


–2.0–1.5

–0.5

–0.5

0.0

0.0

0.5

0.5

1.0

1.0

–1.0

–1.0

0

2

6

8

4

0

2

4

6

8

Y e

f a i l u r e i n d e x

2 Y / W

2 Y / W

2 X / b

2X / b

Figure 13. Continued.



17/26

adjacent joints FM25 and FM35, a smaller damage zone is predicted for FM25 than for

those other joints.

Failure Load Prediction

From the analysis results, the damage area in the interply layers, orthotropic plies, and

adhesive of each joint are obtained. As observed in the experiment, the failure modes are

mostly delamination and adhesive debonding. Although aluminum adherend experiences

plastic deformation, aluminum failure (cracking) was not found. Consequently, the

damage area affecting the bonded joint failure is assumed to be the sum of the transverse

damage area in the interply resin layers, orthotropic plies, and adhesive layers.

A critical step in predicting the failure load of bonded joints by the damage zone method

is to choose a critical damage area, which is the damage area corresponding to structuralfailure. Figure 15 shows results of the failure load prediction when the critical damage

2 Y / W

F a i l u r e i n d e x

8

6

4

2

X = –1.0b

X = –0.75

b

X = –0.5b

0

–1.0 –0.5 0.0 0.5 1.0

–1.0b –1.5b

–0.75b b

X

Y

Figure 14. Ye failure index in the first 90 layer of the joint FM15.

Table 3. Damage area in composite adherend and adhesive layer.

Damage area (mm2)

ID Interply layer Orthotropic ply Adhesive layer Sum

FM15 57.4 89.4 117.5 264.3

FM20 55.8 80.9 160.0 296.7FM25 65.8 63.8 178.0 307.6

FM30 54.9 39.8 133.0 227.7

FM35 85.4 49.6 187.0 322.0

FM40 80.8 45.4 166.3 292.5

FM15D 90.4 141.6 106.2 338.2

FM25D 216.9 328.5 235.5 780.9

FM35D 208.2 280.3 256.9 745.4



18/26

areas of 307.6 and 780.9 mm2 are used, which are the damage areas at the failure loads of

joints FM25 and FM25D, respectively. Predicted failure loads when a critical damage area

(CDA) of 307.6 mm

2

is used are closer to the experimental results, except for jointsFM25D and FM35D. On the other hand, when CDA is set at 780.9 mm2, better results

are found in joints FM25D and FM35D. This means that when a thicker specimen’s data

(FM25D) is used, big deviations are found in the thinner joint and vice versa.

Consequently, it can be deduced that the damage zone approach is not robust without

considering the adherend thickness effect.

In the discussion of the damage areas given in Table 3, it was noted that the total

damage area of joint FM30 was out of trend and that the reason for this was the lower

experimental failure load. In the predicted failure load data shown in Figure 15 as well, the

same phenomenon is found for joint FM30. Moreover, it is found that the predicted

failure load of joint FM15D is out of trend compared with that of other thick adherend

joints (FM25D and FM35D). This is also attributed to the lower experimental failure load

of the joint. Observation of the two joints FM30 and FM15D suggests the possibility that

the failure loads of the joints were underestimated in the experiment.

As mentioned above, Figure 15 shows that adherend thickness should be considered as a

parameter affecting failure loads. Failure loads are also much different depending on the

critical damage area (CDA). To consider the magnitude of the failure index and the joint

geometry, Equation (2) was proposed as a failure criterion. In the equation, the failure

index is included as a weight factor for the damage area and the area AG, which is defined

in Equation (7):

AG ¼ tC ffiffiffiffiffiffibwp if b wtC w if b4w

ð7Þ

F a i l u r e l o a d ( N )

30,000

CDA = 307.6 mm2 (FM25)

CDA = 780.9 mm2 (FM25D)

Experiment failure load

25,000

20,000

15,000

10,000

5000

0

FM15 FM20 FM25 FM30 FM35

Joint

FM40 FM15D FM25D FM35D

Figure 15. Predicted failure loads using damage area approach with two different CDA values.



19/26

where tC , b, and w are the thickness of composite adherend, overlap length, and joint’s

width, respectively.

Figure 16 shows the failure loads predicted using the weighted damage area method inEquation (2) when the critical damage area ratio CDAR1 was set at 10.58 and 12.63, which

are the experimental failure load values corresponding to joints FM25 and FM25D,

respectively. Although the results using a CDAR1 of 10.58 show better agreement with

the experimental results than do the results obtained using the other value, except for the

thicker joints FM25D and FM35D, the results in both cases show quite good agreement

with the experimental failure loads. The relatively larger deviation between the predicted

and experimental failure loads is also found here for joints FM30 and FM15D.

Early in this investigation, the authors tried another definition of AG, which is shown in

Equation (8). However, the predicted failure loads show larger deviation from the test

results than when AG in Equation (7) was used:

AG ¼ w ffiffiffiffiffiffiffiffiffiffiffi

tC bp

if b ww ffiffiffiffiffiffiffiffiffiffiffitC wp if b4w

ð8Þ

where tC , b, and w are the thickness of the composite adherend, the overlap length, and the

joint’s width, respectively.

The weighted damage area ratios DARn and the weighted damage volume ratios by

Equation (4) DVRn of the joints with various weighting power factors n are summarized in

Table 4. In all the methods, the results of joints FM30 and FM15D are out of trend. The

differences between the experimental failure loads and those predicted by the weighted

damage area method are summarized in Table 5 when the weight power is n ¼ 1. As shownin the table, predicted failure loads are always within 15.6% of experimental result


30,000

CDAR 1 = 10.58 (FM25)

CDAR 1 = 12.63 (FM25D)


25,000

20,000

15,000

10,000

5000

0


Joint


Figure 16. Predicted failure loads using weighted damage area approach with two different CDAR1 values.



20/26

regardless of the CDAR1 value. When the two joints FM30 and FM15D are not consid-

ered, the maximum deviation decreases to 6.6%.

The accuracies of the predicted failure loads using the weighted damage area method

with the other weighting power factors are shown in Tables 6 and 7. As n is set at 0, the

maximum deviation between the predicted and experimental results is slightly larger than

that when n is 1. On the contrary, the results for n ¼ 2 show slightly better agreement withthe experiment, where the maximum deviation is 15%. It should be also noted that the

maximum deviations are always related to joints FM30 and FM15D. When the two

joints FM30 and FM15D are not considered with n¼ 2, the maximum deviation decreasesto 3.7%.

From the 3D finite element model, damage volume can be obtained and used instead of

damage area to predict the failure load. Basically, damage volume must be proportional to

the damage area. However, these factors are not linearly proportional because the interply,adhesive, and orthotropic laminas have different thicknesses.

Table 4. Damage area, weighted damage area ratios, damage volume, and weighteddamage area ratios of the joints subjected to experimental failure loads.

Failure DamageDARn

DamageDVRn

ID load (N) area (mm2) nV0 nV1 nV2 volume (mm3) nV0 nV1 nV2

FM15 10,676 264.3 8.22 11.27 16.85 22.2 0.036 0.051 0.080

FM20 12,874 296.7 7.99 10.99 16.56 27.9 0.034 0.048 0.075

FM25 14,737 307.6 7.41 10.58 16.86 32.1 0.031 0.046 0.078

FM30 14,202 227.7 5.49 7.63 11.64 21.9 0.021 0.030 0.048

FM35 16,380 322.0 7.76 11.69 19.81 31.1 0.030 0.048 0.086

FM40 16,513 292.5 7.05 10.43 17.46 29.0 0.028 0.043 0.077

FM15D 11,926 338.2 5.26 6.87 9.36 32.5 0.026 0.035 0.051

FM25D 18,185 780.9 9.41 12.63 18.27 78.0 0.038 0.053 0.082

FM35D 21,591 745.4 8.98 12.01 17.46 78.8 0.038 0.054 0.085

Table 5. Difference (%) between the predicted and experiment failure loads by theweighted damage area method with nV1.

CDAR111.27

(FM15)

10.99

(FM20)

10.58

(FM25)

7.63

(FM30)

11.69

(FM35)

10.43

(FM40)

6.87

(FM15D)

12.63

(FM25D)

12.01

(FM35D)

FM15 0.0 1.3 2.4 11.8 0.4 2.8 14.8 2.7 1.2FM20 0.8 0.0 1.1 10.4 1.8 1.4 13.4 4.0 2.6FM25 1.4 0.7 0.0 8.2 2.3 0.5 10.9 4.2 2.9FM30 10.4 9.8 8.8 0.0 11.3 8.5 2.0 13.2 12.0FM35

1.0

1.6

2.4

9.6 0.0

2.7

11.9 1.5 0.4

FM40 1.7 1.3 0.6 5.5 2.4 0.0 7.5 3.9 2.9FM15D 12.0 10.0 9.0 0.7 9.5 7.2 0.0 11.1 10.1

FM25D 4.5 5.2 6.2 13.6 3.5 6.6 15.6 0.0 2.6FM35D 1.8 2.6 3.7 11.8 0.7 4.1 14.0 1.9 0.0Max 12.0 10.0 9.0 0.7 11.3 8.5 0.0 13.2 12.0

Min 4.5 5.2 6.2 13.6 3.5 6.6 15.6 0.0 2.6



21/26

Similar to the area AG, the volume V G, relating to geometrical effects, in Equation (4)

was defined in Equation (9).

V G ¼ tC b w if b wtC w w if b4w

ð9Þ

where tC , b, and w are the composite adherend, the overlap length, and the width of

specimens, respectively.

Originally, the authors tried to find damage volume ratios with the volume V G of

thicknesswidth overlap length regardless of the ratio of the overlap length to width.However, it was impossible to find meaningful damage volume ratios with such a defined

volume V G. This means that the damage volume or area is not proportional to the overlap

length in this analysis method where the progressive stiffness degradation and damagezone propagation are not considered.

Table 6. Difference (%) between the predicted and experiment failure loads by theweighted damage area method with nV0.

CDAR08.22

(FM15)

7.99

(FM20)

7.41

(FM25)

5.49

(FM30)

7.76

(FM35)

7.05

(FM40)

5.26

(FM15D)

9.41

(FM25D)

8.98

(FM35D)

FM15 0.0 1.5 3.8 13.3 2.4 5.4 14.6 6.0 5.0FM20 1.3 0.0 2.2 12.2 0.6 3.9 13.6 5.8 4.2FM25 2.9 2.0 0.0 9.2 1.2 1.7 10.5 6.9 5.5FM30 13.6 12.8 10.5 0.0 11.8 8.9 0.0 17.7 16.3

FM35 1.4 0.6 1.5 10.1 0.0 3.0 11.3 5.2 3.9FM40 4.0 3.3 1.6 5.1 2.7 0.0 6.0 7.0 5.9FM15D 11.6 10.8 8.6 0.0 10.0 7.2 0.0 17.5 16.0

FM25D 4.3 5.1 7.2 14.0 6.0 8.5 14.8 0.0 1.6FM35D 2.3 3.2 5.5 12.9 4.1 6.9 13.8 2.3 0.0Max 13.6 12.8 10.5 0.0 11.8 8.9 0.0 17.7 16.3

Min 4.3 5.1 7.2 14.0 6.0 8.5 14.8 0.0 1.6

Table 7. Difference (%) between the predicted and experiment failure loads by theweighted damage area method with nV 2.

CDAR212.85

(FM15)

16.56

(FM20)

16.86

(FM25)

11.64

(FM30)

19.64

(FM35)

17.46

(FM40)

9.36

(FM15D)

18.27

(FM25D)

17.46

(FM35D)

FM15 0.0 0.6 0.2 9.4 3.8 0.7 14.8 1.8 0.7FM20 0.1 0.0 0.1 8.4 3.9 0.9 13.5 2.0 0.9FM25 0.2 0.5 0.0 7.3 3.0 0.5 11.5 1.4 0.5FM30 7.4 7.1 7.5 0.0 10.6 8.1 3.9 9.0 8.1

FM35 3.0 3.3 3.0 9.1 0.0 2.4 12.6 1.7 2.4FM40 0.2 0.5 0.2 5.7 2.2 0.0 8.9 1.0 0.3FM15D 11.0 7.1 7.3 1.9 12.0 7.9 0.0 11.6 10.5

FM25D 3.3 3.7 3.3 11.4 1.3 2.3 15.0 0.0 2.3FM35D 1.5 2.0 1.5 10.5 3.7 0.4 14.4 1.0 0.0Max 11.0 7.1 7.5 1.9 12.0 8.1 0.0 11.6 10.5

Min 3.3 3.7 3.3 11.4 0.0 2.4 15.0 1.7 2.4



22/26

Figure 17 shows the failure loads predicted using the damage volume method when the

critical damage volume is set at 32.1 and 78 mm3, which are the damage volumes of the

FM25 and FM25D joints, respectively. The predicted failure loads are much differentfrom the experimental result when CDV equals 78 mm3. Similar to the damage area

approach, the damage volume approach is not robust and the thickness difference

should be considered while predicting the failure load of bonded joints.

Figure 18 shows the predicted failure loads when CDVR1 equals 0.046 and 0.053, which

are the weighted damage volume ratios at the experimental failure loads of the FM25 and

FM25D joints, respectively. It is shown that when the thickness effect is considered, the

predicted failure loads show good agreement with the experimental values. The maximum

deviation between them is about 13%, as shown in the figure.

The predicted failure loads based on the weighted damage volume ratios are given in

Tables 8–10 with n

¼0, 1, and 2, respectively. As shown in the tables, the maximum

deviations are 17.8%, 16.6%, and 12.9%, respectively. The method with n ¼ 2 predictsthe failure loads the best. Once more, the maximum deviations are found when the damage

volume of joint FM30 is used as the critical value for failure evaluation.

Summarizing the finite element results, the damage volume ratio method gives the best

prediction of the failure loads. Among a total of nine joint specimens, the experimental

failure loads of joints FM30 and FM15D were out of trend and therefore resulted in large

deviations of failure load prediction. Without these two joints, the maximum deviation

was reduced to 4.1%, as shown in Table 10. It should also be noted that both the weighted

damage area and volume ratio methods are based on the 3D finite element analysis results.

To predict out-of-plane failure, 3D analysis is essential.

To investigate the effect of the mesh density of the model on the failure load prediction,refined mesh models were created. The interlaminar stresses obtained at the free side


30,000

CDV = 32.1 mm3 (FM25)

CDV = 78.0 mm3 (FM25D)


25,000

20,000

15,000

10,000

5000

0


Joint


Figure 17. Predicted failure loads using damage volume approach with two different CDV values.



23/26

edges can be affected by the mesh density there. Therefore, the number of elements along

the width of the joints increased (from 20 to 30 elements) and the smallest width (along Y -

direction) of a single element was reduced to 0.024 mm. The procedure of failure load

prediction using damage volume ratio was done again to predict the failure load of joint

FM25, which experimentally fails at 14,737 N. The results are given in Table 11. As shownin the table, the critical damage volume ratios can be slightly changed but the predicted


30,000

CDVR 1 = 0.046 (FM25)

CDVR 1 = 0.053 (FM25D)


25,000

20,000

15,000

10,000

5000

0


Joint


Figure 18. Predicted failure loads using weighted damage volume approach with two different CDVR1

values.

Table 8. Difference (%) between the predicted and experiment failure loads by theweighted damage volume method with nV0.

CDVR00.036

(FM15)

0.034

(FM20)

0.031

(FM25)

0.021

(FM30)

0.030

(FM35)

0.028

(FM40)

0.026

(FM15D)

0.038

(FM25D)

0.038

(FM35D)

FM15 0.0 3.3 5.8 17.6 6.7 8.9 11.1 0.2 0.5FM20 1.8 0.0 2.7 12.2 3.6 5.5 7.4 3.7 4.0FM25 4.3 2.7 0.0 10.5 0.5 2.5 4.5 5.8 6.1FM30 16.0 14.4 12.1 0.0 11.2 9.2 7.2 17.5 17.8

FM35 4.6 3.0 0.7 9.9 0.0 2.1 4.0 6.0 6.3FM40 6.1 4.4 2.3 5.8 1.5 0.0 1.7 7.7 8.0FM15D 4.8 3.5 1.7 6.8 1.0 0.6 0.0 5.9 6.2FM25D 1.3 3.0 5.3 13.9 6.1 7.9 9.6 0.0 0.7FM35D 1.3 3.1 5.4 14.1 6.2 8.0 9.7 0.4 0.0Max 16.0 14.4 12.1 0.0 11.2 9.2 7.2 17.5 17.8

Min 1.3 3.3 5.8 17.6 6.7 8.9 11.1 0.0 0.0



24/26

Table 9. Difference (%) between the predicted and experiment failure loads by theweighted damage volume method with nV1.

CDVR10.051

(FM15)

0.048

(FM20)

0.046

(FM25)

0.030

(FM30)

0.048

(FM35)

0.043

(FM40)

0.035

(FM15D)

0.053

(FM25D)

0.054

(FM35D)

FM15 0.0 3.7 4.6 16.6 3.8 6.7 12.5 0.3 0.3FM20 2.2 0.0 0.4 11.7 0.4 2.2 7.5 3.2 3.7FM25 2.4 0.9 0.0 9.4 0.9 1.3 5.8 3.3 3.8FM30 12.6 11.1 10.5 0.0 11.1 8.9 4.4 13.5 14.0

FM35 1.3 0.1 0.7 9.4 0.0 2.0 6.1 2.1 2.5FM40 0.6 1.8 2.3 9.5 1.8 0.0 6.8 0.1 0.4FM15D 3.8 2.8 2.3 4.3 2.8 1.3 0.0 4.4 4.7FM25D 2.1 4.0 4.8 13.9 4.0 6.5 11.0 0.0 0.4FM35D 1.7 3.6 4.4 13.8 3.6 6.2 10.7 0.5 0.0Max 12.6 11.1 10.5 0.0 11.1 8.9 4.4 13.5 14.0

Min 2.1 4.0 4.8 16.6 4.0 6.7 12.5 0.5 0.4

Table 10. Difference (%) between the predicted and experiment failure loads by theweighted damage volume method with nV 2.

CDVR20.080

(FM15)

0.075

(FM20)

0.078

(FM25)

0.048

(FM30)

0.086

(FM35)

0.077

(FM40)

0.051

(FM15D)

0.082

(FM25D)

0.085

(FM35D)

FM15 0.0 1.8 0.8 12.0 1.4 1.2 10.9 0.5 1.3FM20 1.3 0.0 0.8 9.5 2.8 0.4 8.5 1.9 2.7FM25 0.6 0.5 0.0 8.3 1.9 0.1 7.4 1.1 1.8FM30 9.7 8.5 9.3 0.0 11.0 8.9 1.4 10.2 10.9

FM35

1.4

2.4

1.7

8.9 0.0

2.0

8.2

0.9

0.4

FM40 1.2 0.3 0.9 5.5 2.1 0.0 4.8 1.6 2.0FM15D 3.8 3.0 3.5 2.1 4.6 3.3 0.0 4.1 4.5FM25D 2.1 3.7 2.7 12.1 0.3 3.2 11.3 0.0 0.4FM35D 2.4 4.1 3.1 12.9 0.5 3.6 12.0 1.7 0.0Max 9.7 8.5 9.3 0.0 11.0 8.9 1.4 10.2 10.9

Min 2.4 4.1 3.1 12.9 0.5 3.6 12.0 1.7 0.4

Table 11. Predicted failure load of the joint FM25 obtained by weighted damage volumemethod with two different meshes.

Original mesh Refined meshDifferent of predicted

CDVR1Predicted

failure load (N) CDVR1Predicted

failure load (N)

failure loads from

different meshes (%)

0.051 (FM15) 15,095 0.050 (FM15) 15,051 0.3

0.048 (FM35) 14,867 0.046 (FM35) 14,875 0.05

0.035 (FM15D) 13,882 0.036 (FM15D) 13,822 0.4

0.053 (FM25D) 15,228 0.054 (FM25D) 15,311 0.5

0.054 (FM35D) 15,290 0.054 (FM35D) 15,291 0



25/26

failure loads of joint FM25 obtained using two meshes are very close, showing only 0.5%

of the maximum difference. Consequently, the original mesh density is believed to be

suitable to predict the failure loads of the joints.

CONCLUSION

A weighted damage area method and volume ratio method were proposed to predict the

failure loads of single-lap bonded joints with dissimilar composite-aluminum materials. In

the 3D finite element analysis, interply resin layers were assumed to simulate the delami-

nation. Geometric and material nonlinear effects were included in the analysis. The Ye-

criterion and Von Mises strain failure criterion were applied for the composite adherend

and adhesive, respectively. Analysis results were compared with the experimental data for

nine different bonding lengths or adherend thicknesses. The damage zone method based

on the simply calculated damage area or volume did not predict the failure load accurately.

When the intensity of the failure index and geometrical effects were considered with the

weighting power factor n ¼ 2, however, the damage volume ratio method predicted failureloads within a deviation of 13% from experimental values. When a damage zone method is

used, it is very important to set the critical damage zone for failure evaluation. The more

accurate the experimental data that are obtained, the more accurate the critical damage

zone definition; as a result, failure load prediction is possible.

ACKNOWLEDGMENTS

This work was supported by a Korea Research Foundation Grant funded by theKorean Government (KRF-2008-J01001) and second BK21 project at Gyeongsang

National University.

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Failure Load Prediction of Single Lap Bonded Joint_Online First_Hung

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