Influence of adherend’s delamination on the response of single lap and socket tubular adhesively bonded joints subjected to torsion

Composite Structures 93 (2011) 1765–1774

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Composite Structures

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Influence of adherend’s delamination on the response of single lap and sockettubular adhesively bonded joints subjected to torsion

Ramadan A. Esmaeel 1, Farid Taheri ⇑Department of Civil and Resource Engineering, Dalhousie University, 1360 Barrington Street, Halifax, NS, Canada B3J 1Z1

a r t i c l e i n f o

Article history:Available online 18 January 2011

Keywords:Adhesive jointsSingle lap jointSocket jointComposite adherendsDelaminationFinite Element analysis (FEA)

0263-8223/$ - see front matter � 2011 Elsevier Ltd Adoi:10.1016/j.compstruct.2010.12.009

⇑ Corresponding author. Tel.: +1 902 494 3935; faxE-mail address: [email protected] (F. Taheri).

1 Visiting Assistant Professor, Fayoum University, Fa

a b s t r a c t

Tubular adhesively bonded joints are widely used in many industries such as the oil-and-gas, aerospaceand automotive. Such joints are often used to mate dissimilar materials. Composite materials, because oftheir superior specific strength and stiffness and high resistance to corrosion, have also been widely usedto form tubular components. When composites are mated to other materials (such as metals) by adhe-sives, the stress concentration in the adhesive layer becomes even more exasperated due to the mismatchin the mechanical properties of the mating adherends, thus posing further challenges. Moreover, thepresence of a delamination in the composite adherend can significantly influence the stress distributionwithin the adhesive layer; therefore, the assessment of the adhesive layer stresses in the presence of adelamination is of importance, thus forms the main objective of the present work.

A comprehensive parametric study, using the commercial finite element code ABAQUS, was conductedto investigate the performance of single lap and socket adhesively bonded joints made of composite adh-erends hosting a delamination. The influence of several parameters on the stress distribution within theadhesive in joints mating composite to composite and composite to aluminum adherends were investi-gated. The parameters considered included the location and length of the delamination, composite mate-rial’s mechanical properties and fiber orientation of the composite adherend.

Results show that the existence of a through-the-thickness delamination affects the structural responseof both the single lap and socket adhesively bonded joints by various degrees, depending on the localityof the delamination. Moreover, interestingly, the presence of a delamination resulted in a significantdecrease in the adhesive peel and shear stresses in both joint configurations.

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1. Introduction

Adhesively bonded joints are commonly used to mate variousstructural components in aerospace and oil-and-gas industriesdue to their ease of construction and superior mechanical perfor-mance. Composite materials are nowadays widely used in variousindustries due to their high strength to weight ratio and their flex-ibility to be tailored to various complex shapes. However, compos-ite materials sometimes suffer from defects that are inadvertentlyincepted during their manufacturing in the form of interlayerseparation that is commonly known as delaminations. Delamina-tions can also exist in a composite laminate due to several reasonsbesides the manufacturing related anomalies; these could be dueto a sudden impact by an external object, improper laminationdesign and due to drilling of holes to accommodate bolts andrivets. The existence of delaminations in a composite structure

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can significantly affect the mechanical performance of thestructure and prevent the full utilizations of its strength.

Adhesively bonded joints were extensively studied during thepast two decades using analytical and computational models. Acomprehensive literature survey that summarized the analyticalmodels used for characterization of the behavior of adhesivelybonded joints was done by da Silva et al. [1]. They mentioned mostof the notable analytical works done to assess the behavior ofadhesively bonded joints composed of both metallic and compositeconstituents with linear and nonlinear adhesive layer propertiesformed by flat and tubular adherends.

Tubular lap joints mating steel and composite pipe adherendsand subjected to torsion were studied by Hipol [2] using a compu-tational procedure. He proposed an optimization scheme to mini-mize the peak stresses induced in the adhesive layer. He alsomade some interesting observations in that the maximum stressconcentration in the adhesive layer existed in the end that wasconnected to the less stiffness adherend. Moreover, he mentionedthat the maximum shear stress is a function of the adherend stiff-ness imbalance and can be reduced by controlling this factor.

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1766 R.A. Esmaeel, F. Taheri / Composite Structures 93 (2011) 1765–1774

Zou and Taheri [3] performed a comprehensive investigation onthe shear stress distribution in the adhesive layer of bonded sand-wich pipe joints subjected to torsional moments. They performed

ta

Y Z

Lo

z y

l1 l2t1

L1

L

BA

h (2)outR(1)

outR

Rz

y

t1

ZY

A

L1

l2l1

tsLs

h

ta B

outR

(a)

(b)

Τ

Τ

Fig. 1. Basic dimensions of both joint configurations: (a) sing

(b) (Fig. 2. (a) ASJ’ FEM mesh, and the through the thickness. Locations of th

Table 1Material properties of the joints constituents.

Aluminum pipe Glass–epoxy pipe

Linear elasticE = 70.0 GPa, t = 0.30

E1 = 50.0 GPa, E2 = 15.2 GPa, E3 = 15.2 GPat23 = 0.428, t13 = 0.254, t12 = 0.254G23 = 3.28 GPa, G13 = 4.70 GPa, G12 = 4.70 GPa

E or Ei: elastic modulus in direction i, tij: Poisson’s ratio, Gij: shear modulus.

their analysis both analytically and computationally using theFinite Element method (FEM). They considered both single lapand socket joint configurations with different adherend materials.

2

t2φ

in

L2

t2 φ

le lap joint configuration, (b) socket joint configuration.

(a)

c) (d)e delamination: (b) h/t1 = 0.0625, (c) h/t1 = 0.1250 (d) h/t1 = 0.1875.

Graphite–epoxy pipe Adhesive layer

E1 = 155.0 GPa, E2 = 12.1 GPa, E3 = 12.1 GPa E = 2.8 GPa, t = 0.40t23 = 0.458, t13 = 0.248, t12 = 0.248G23 = 3.20 GPa, G13 = 4.40 GPa, G12 = 4.40 GPa

Fig. 3. Finite Element models of the two delaminated adhesive joints.

Table 2Material properties of the metallic adherends used in Zou and Taheri [3] models.

Aluminumadherend

Steel adherend Adhesive layer

Young’s modulus E 68.9 GPa 206.0 GPa 3.33 GPaPoisson’s ratio t 0.30 0.33 0.34

R.A. Esmaeel, F. Taheri / Composite Structures 93 (2011) 1765–1774 1767

Their analytical model agreed well with their computational modeland hence they provided analytical justification for Hipol’s [2]observations. In their model, the adhesive layer was modeled asan isotropic material and the study was mainly dedicated to inves-tigate the out-of-plane shear stress induced in the adhesive layer.

An analytical model for tubular adhesive joints based on thevariational principle applied to the potential energy of deformationoccurring in the adhesive layer was accomplished by Nemes et al.[4]. Their model was capable of detecting the intensity and distri-butions of stresses in the adhesive layer of a joint composed of iso-tropic adherends subjected to tensile loading.

Hosseinzadeh and Taheri [5] performed a coupled experimental– Finite Element investigation for assessing the effect of the over-lap length on the torsional capacity of tubular adhesively bondedjoints. They concluded that the static torsional capacity of the com-posite–aluminum tubular adhesive joint can be increased byincreasing the bonding length, but only up to a certain limit (i.e.the effective length), after which there would be no noticeable in-crease in the joint torsional capacity with the increase of the over-lap length. This observation gave valuable information aboutdesigning an optimum joint that could offer the maximum tor-sional capacity with a minimum bonding length.

A Finite Difference solution for the stress analysis of tubularadhesively bonded joints subjected to torsional loading was intro-duced by Wei and Guoqiang [6]. They provided a comprehensiveevaluation of the peel and the two out-of-plane shear stresses in-duced in the adhesive layer. They also concluded that there wasa significant stress variation along the thickness of the adhesivelayer and that the peel stress cannot be neglected for a generallaminated adherends due to the in-plane shear-normal coupling.

Recently Das and Pradhan [7] introduced a Finite Element mod-el to study the adhesion failure damage propagation in single lapadhesively bonded tubular joints. They calculated the Strain En-ergy Release Rate (SERR) based on the Virtual Crack Closure Tech-nique (VCCT) and a failure index was proposed based on thecohesion failure criterion. The damage was introduced as an inter-facial disbond between the adhesive layer and the adherends. Theyalso drew valuable conclusions, emphasizing the importance ofusing 3D models instead of 2D models for accurately modelingsuch problems, since the free edges of the adhesive–adherendoverlap region undergo a 3D state of stresses. Moreover, they ob-served that the resulting peel stress was significantly high com-pared to the shear stress in the critical zones along the overlaplength.

The effect of the existence of a through-the-thickness delamina-tion in tubular structures has also been extensively studied; how-

ever, the effect of the existence of such a delamination on theintegrity of adhesively bonded joints assembled with compositeadherends has not been given sufficient attention. One of the fewnotable studies in this topic is the work of Qin and Dzenis [8]who effectively analyzed a single lap adhesive joint with flat com-posite adherends that hosted a delamination. Their analytical mod-el was dedicated to measuring the strain energy release rate at thedelamination tips. They concluded that the strain energy releaserate decreased as the crack length increased. Moreover, theirexperimental observations confirmed their analytical results.Panigrahi and Pradhan [9] also studied the effect of the existenceof an across-the-width delamination on the stability of an adhe-sively bonded joint with plate-like composite adherends. Theirwork concluded that the existence of a delamination near the sur-face adjacent to the adhesive layer could significantly decrease themaximum value of the shear stress induced in the adhesive layer.

Esmaeel and Taheri [10] also studied the effect of an embeddeddelamination in the composite adherends of a single lap adhesivelybonded tubular joint subjected to torsional loading. Their compu-tational model (using the Finite Element method) considered theadhesive layer as a nonlinear continuum. Also they performed aparametric study to assess the effect of the delamination geometricparameters and the composite material properties on the adhesivelayer peel and shear stresses.

The main objectives of this work is to systematically character-ize the stresses induced in the adhesive layer of tubular single lapand socket joints with a delaminated composite adherend. The fullstate of stresses induced in the adhesive layer, for both joint con-figurations, is studied with attention to the peel and shear stresses,as they are the most significant stress components in such systems.

2. Finite Element model

The basic geometrical parameters of the FE model are illus-trated in Fig. 1 for both adhesive single lap joint (ASLJ) and adhe-sive socket joint (ASJ) configurations. For the single lap joint theinner pipe (Adherend 1) is made of composite, while the outer pipe

Table 3Geometry and material properties of composite adherends used in Zou and Taheri [3] models.

Sandwich composite Young’s modulus Poisson’s ratio Thickness (mm)

Top face sheet E1 = 15 GPa, E2 = 7.2 GPa t12 = 0.24, t21 = 0.12 0.5Core E = 8.5 GPa t = 0.14 0.5Bottom face sheet E1 = 15 GPa, E2 = 7.2 GPa t12 = 0.24, t21 = 0.12 0.5

Normalized overlap length

Adhe

sive

she

ar s

tress

(N/m

m2 )

-1000

-800

-600

-400

-200

0

Steel-to-steel Zou and Taheri [3]Steel-to-steel presentAluminum-to-aluminum Zou and Taheri [3]Aluminum-to-aluminum presentComposite-to-composite Zou and Taheri [3]Composite-to-composite present

Normalized overlap length1.00.0 0.2 0.4 0.6 0.8

Adhe

sive

she

ar s

tress

(N/m

m2 )

-2000

-1500

-1000

-500

0

500

1000

1500

Steel-to-steel Zou and Taheri [3]Steel-to-steel presentAluminum-to-aluminum Zou and Taheri [3]Aluminum-to-aluminum presentComposite-to-composite Zou and Taheri [3]Composite-to-composite present

1.00.0 0.2 0.4 0.6 0.8

(a) (b)

Fig. 4. Comparison of the stress distributions within the adhesive layer obtained from the FEA and analytical solution of Zou and Taheri for (a) intact single lap joints and (b)intact socket joints formed with various adherends.

Normalized overlap length

-1000

-800

-600

-400

-200

0

3 elements in thickness1 element in thickness

Normalized overlap length0.0 0.2 0.4 0.6 0.8 1.0

Adhe

sive

she

ar s

tress

(N/m

m2 )

-1500

-1000

-500

0

500

1000

1500

3 elements through thickness1 element through thickness

0.0 0.2 0.4 0.6 0.8 1.0

Adhe

sive

she

ar s

tress

(N/m

m2 )

(a) (b)

Fig. 5. Influence of using extra element layers in modeling the stress distribution within the adhesive layer of the intact (a) single lap and (b) socket joints.

Table 4Geometric parameters of adhesively bonded joints.

Adhesive single lap joint Adhesive socket joint

t1 = t2 = 2.00 mm t1 = t2 = ts = 2.00 mmta = 0.15 mm ta = 0.15 mmLo = 25.00 mm Ls = 25.00 mmL1 = L2 = 102.50 mm L1 = L2 = 90.00 mm

Rð1Þout = 14.40 mm Rin = 12.40 mm

Rð2Þout = 16.55 mm Rout = 16.55 mm

/ = 45� / = 45�


(Adherend 2) is made of composite or aluminum. The two adher-ends of the socket joint are identical; both the adherends and thesocket are made of composite materials. The overlap length andthe thickness of the adhesive layer were kept constant throughthe analysis for all models. The material properties of the compos-ite and aluminum pipes as well as the adhesive layer are listed inTable 1. It should be noted that in this study the adhesive layerwas modeled as a linear elastic medium; hence, any material non-linearity experienced by the adhesive layer was not taken into con-sideration. The thicknesses of all adherends and the socket are keptfixed at 2 mm, while the adhesive layer thickness is 0.15 mm, in allcases. The composite tubes are formed by stacking 16 plies, each of0.125 mm thick.

The existence of a delamination in a composite componentwould cause degradation of its mechanical properties. Moreover,the location of the delamination is considered as one of the mostcritical factors affecting the damage progression. According to a

previous study done by Panigrahi and Pradhan [9] on single lapjoints with delaminated composite plate adherends, the criticallocation of the delamination that caused the most critical effectwas identified as that when the delamination center was alignedwith the edge of the bonding length (see Fig. 1). This observation


was also confirmed by Esmaeel and Taheri [10] for tubular singlelap joints. For this reason, the location of the delamination waschosen to be aligned with the left edge of the bonding length, adja-cent to the adhesive layer in both joint configurations. The circum-ferential width of the delamination was defined using the angle /(see Fig. 1) and was kept fixed through the study so that / = 45�.The location of the delamination through the thickness is shownin Fig. 2; this figure represents three different cases, in which thedelamination is placed between the first and second plies, betweenthe second and third plies, and between the third and fourth plies.Theses through-the-thickness locations (see Fig. 2) of the delami-nation therefore create three different thicknesses for the upperdelaminated region; that is: h = 0.125 mm, h = 0.250 mm, andh = 0.375 mm, respectively.

The gap between the two adherends in the socket joint config-uration was eliminated and a surface-to-surface contact with tan-gential coefficient of friction of 0.30 was defined between theadjacent surfaces of the adherends. A hard surface-to-surface con-tact was also used to prevent the penetration between the upperand lower sublaminates. Tie multipoint constraint was used to as-sure a full bond between the adjacent surfaces of the adherendsand the adhesive layer. The nodes located at the far right edge ofboth joint type assemblies were fully constrained, while the far leftedge nodes were allowed to rotate around the Z-axis, but wereconstrained against translational degrees of freedom.

0.0 0.2 0.4 0.6 0.8 1.0

σ 11,σ

22,σ

33,τ

12,τ

23 (M

Pa)

-5

-4

-3

-2

-1

0

1

2

τ 23 (M

Pa)

0

5

10

15

20

25

30

35

σ11

σ22

σ33

τ12

τ13

τ23

Normalized overlap length z/Lo

Fig. 6. State of stresses induced within the adhesive layer of the intact single lapjoint with glass/epoxy–aluminum adherends (T = 100 N m).

Fig. 7. Influence of the delamination length on the stress states induced within the adheT = 100 N m).

The FE mesh was carefully descritized through this study suchthat consistent pairs of nodes were available for all adjacent sur-faces that were in contact or fully bonded. Fig. 3 shows the FE meshfor both ASLJ and ASJ configurations and the local coordinate sys-tem used to define the fiber orientations and the stacking se-quence. The delaminated zone (confined by the angle /, seeFig. 1) was modeled using 16 rows of elements in the circumferen-tial direction and the rest of the circumference was modeled using32 rows of elements. In this study we took the advantage of thelayered composite element provided by ABAQUS software [11] tomodel the laminate composite. To measure the accuracy and theadmissibility of using only a single layer of elements in the thick-ness direction to model the laminate, for the case of the intactjoint, the analysis was repeated using four layers of elements inthe thickness direction and it was found that the difference be-tween the maximum value of stresses at the edges of the adhesivelayer between the two models was less than 2%. The decision wastherefore made to model the intact joint with only single layer ofelements through the thickness (each element modeling the 16plies), and to model the delaminated regions with two layers ofelements in the thickness direction (one layer of elements repre-senting the upper delaminated zone (having 1, 2 or 3 plies,depending on the location of the delamination) and one layer ofelements for the lower delaminated zone (i.e. modeling 15, 14, or13 plies, respectively and accordingly). By this procedure the mod-els would be computationally relatively inexpensive without com-promising the accuracy.

3. Results and discussion

3.1. Model verification and definition of the parameters

In order to verify the modeling procedure described in the pre-vious section, several preliminary models were created and the re-sults were compared with those obtained through the analyticalsolution developed by Zou and Taheri [3]. The analytical solutionwas developed based on intact adhesively bonded joints formedwith adherends made of three different materials. In that study,one of the adherends was made of sandwich core material (a coresandwiched between two glass–epoxy layers), the other two adh-erends were made of steel or aluminum. The dimensions andmaterial properties of the joints constituents considered by Zouand Taheri [3] are listed in Tables 2 and 3.

Fig. 4a shows the comparison between the shear stress distribu-tion in the single lap joints (at the mid-plane of the adhesive layer)

sive layer of a single lap joint with glass/epoxy–aluminum adherends (h/t1 = 0.0625,


obtained by the analytical solution and the present model for jointswith steel–steel, aluminum–aluminum, and composite–compositeadherends, respectively. The excellent correlations between the re-sults are clearly noted for the intact joints.

Moreover, to further assess the integrity of the layered elementof the ABAQUS, the analysis was repeated using two different meshdensities along the wall thickness of both the adherends and thesocket. In the first scenario, one layer of element was used toimplicitly represent the three layers of the materials (plies) usedin forming the wall thickness of the adherends, while in the secondscenario three layers of elements were used to model the constit-uents through the thickness (i.e., each layer of element modeled asingle ply). It should be noted that for the last part of the analysis(i.e. the effect of number of layers of elements through the thick-ness) the core layer was accounted for by providing its materialproperties. The results shown in Fig. 5a clearly shows the excellentagreement between the shear stress distributions simulated by thetwo models, thereby validating the integrity of the layered elementof the ABAQUS.

The same verification procedure was repeated for the adhe-sively bonded socket joint configuration, with the comparative re-sults shown in Figs. 4b and 5b. Again, very good agreementbetween the results of our FEA and the analytical solutions isachieved.

0

5

10

15

20

25

30Intactl2/Lo= 0.08l2/Lo= 0.16l2/Lo=0.24

0.0 0.2 0.4 0.6 0.8 1.0

(a) (b

Shea

r stre

ss τ

23 (M

Pa)


Fig. 9. Influence of the delamination length on the stress states induced within th(h/t1 = 0.0625).


σ 11,σ

22,σ

33,τ

12,τ

13 (M

Pa)

-6

-4

-2

0

2

τ 23 (M

Pa)

0

5

10

15

20

25

30

σ11σ22σ33τ12τ13τ23

0.0 0.2 0.4 0.6 0.8 1.0

Fig. 8. State of stresses induced within the adhesive layer of single lap joint withglass/epoxy–glass/epoxy adherends (T = 100 N m).

With the aim of making the comparison of the results moreclear, some dimensionless parameters are introduced. For instance,the distance along the overlap length (in the z-direction), as well asthe distance of the delamination within the overlap length (l2) wasnormalized with respect to the total overlap length (Lo) for the sin-gle lap joint and with respect to the socket length (Ls) for the socketjoint, hence providing the parameters z/Lo, z/Ls, l2/Lo, and l2/Ls. Also,the dimensionless parameter h/t1 represents the location of thedelamination within the wall thickness (h), normalized with re-spect to the total thickness of Adherend 1 (t1). Unless otherwiseindicated, all the models had adherends with stacking sequenceof [+45/�45]8. A parametric study was conducted for both jointconfigurations and the results will be presented in the next subsec-tions. The main geometric parameters for both joint configurationsare shown in Table 4.

3.2. Adhesively bonded single lap joint

The state of stresses induced in the adhesive layer is presentedalong a path taken at the mid-plane of the adhesive layer at theupper most part of the joint (i.e. from edge A (z = 0) to edge B(z = Lo), see Fig. 1). Fig. 6 shows the full state of stresses inducedin the adhesive layer under 100 N m torsional moment for an SLJwhose Adherend 1 is made of glass–epoxy composite while Adher-end 2 is made of aluminum. The most dominant stress componentwas the out-of-plane shear s23 which showed its maximum valuesat the edges of the overlap length. As seen, the shear stress distri-bution along the overlap length is not symmetric because of thedifferential rigidity of the composite and aluminum adherends. Itshould be noted from Fig. 6 that all the stress components were al-most zero along the overlap length except s12 which experienced aconstant nonzero value along the whole bonding length.

3.2.1. Effect of delamination length (l2/Lo)Delamination length is one of the most important parameters

that affects the behavior and integrity of such joints. Fig. 7a andb shows, respectively, the distribution of adhesive shear and peelstresses along the overlap length for normalized delaminationlengths (l2/Lo) ranging from 0.08 to 0.24, for the case where thedelamination location through-the-depth is fixed at h/t1 = 0.0625.A considerable decrease in the maximum shear stress s23 is ob-served at the left end of the bonding length for all delaminatedmodels compared to the intact model. It should be also noted thatthe maximum decrease in the edge shear stress was observed forthe shortest delamination length. A secondary peak was observed

-12

-10

-8

-6

-4

-2

0

2

4

Intactl2/Lo = 0.08l2/Lo = 0.16l2/Lo = 0.24

)

Peel

stre

ss σ

33 (M

Pa)

0.0 0.2 0.4 0.6 0.8 1.0


e adhesive layer of a single lap joint with glass/epoxy–glass/epoxy adherends


at the right delamination tip for all models; the amplitude of thesesecondary peaks is decreased with the increase in the delaminationlength. Additionally, it should be noted that this specific location ofthe delamination does not induce any effect on the maximumstresses at the right edge of the bonding length.

The stresses induced in the adhesive layer for an SLJ assembledfrom composite–composite glass–epoxy adherends are shown inFig. 8. Generally the adhesive layer stresses decreased by changingthe aluminum adherend by a composite one except for the shearstress s23 which shows a considerable increase in its value at theright end of the overlap, as expected. Fig. 9a and b shows the effectof increasing the normalized delamination length in the compos-

Long

itudi

nal s

tress

σ11

(MPa

)

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6(a) (b

Normalized overlap length z/Ls

Peel

stre

ss σ

33 (M

Pa)

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6(c) (d

Shea

r stre

ss τ

13 (M

Pa)

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0(e)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(f

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0



Fig. 10. State of stresses induced within the adhesive layer of the intact ASJ under 100 N m(e) shear stress s13 (f) shear stress s23.

ite–composite SLJ on the shear and peel stresses. It should be notedthat for l2/Lo = 0.08, the decrease in the maximum shear stress inthe composite–aluminum joint was almost one and a half timesthat of the composite–composite case (see Figs. 7a and 9a).

3.3. Adhesively bonded socket joint

The state of stresses induced in the adhesive layer for the socketjoint case showed a different trend from that observed in the ASLJ.This is believed to be due to the discontinuity in the adherends. Inthis study, there was no gap between the two adherends, and onlya discontinuity existed in between the two adherends. Fig. 10

Hoo

p st

ress

σ22

(MPa

)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5)

Shea

r stre

ss τ

12 (M

Pa)

-50

-40

-30

-20

-10

0

)

Shea

r stre

ss τ

23 (M

Pa)

-30

-20

-10

0

10

20

30)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0




: (a) longitudinal stress r11 (b) hoop stress r22 (c) peel stress r33 (d) shear stress s12


shows the state of stresses in the adhesive layer of an ASJcomposed of composite glass–epoxy adherends and socket. It isobserved that the maximum stress concentration due to thediscontinuity of the adherends exists within the distribution of

-30

-20

-10

0

10

20

30Glass-epoxy Graphite-epoxy

Shea

r stre

ss τ

23 (M

Pa)

(a) (b

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Fig. 11. State of the stresses induced within the adhesive layer of the

-30

-20

-10

0

10

20

30intactl2/Ls = 0.08l2/Ls = 0.16l2/Ls = 0.24

Shea

r stre

ss τ

23 (M

Pa)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Fig. 12. Effect of delamination length on the stress distributions within the

-20

-15

-10

-5

0

5

10

15

20Intactl2/Ls = 0.08l2/Ls = 0.16l2/Ls = 0.24

(a) (

Shea

r stre

ss τ

23 (M

Pa)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Fig. 13. Effect of delamination length on distribution of stresses within the ad

the in-plane shear stress (s12). Moreover, another dominant stressconcentration is seen in the distribution of the through-the-thickness shear stress (s23), along with large fluctuations occurringat both ends of the overlap region, as well as at its mid-length,

-0.5

0.0

0.5

1.0

1.5

2.0Glass-epoxy Graphite-epoxy

Peel

stre

ss σ

33 (M

Pa)

)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Normalized overlap length z/Ls

intact socket joint with glass/epoxy–graphite/epoxy adherends.


-10

-8

-6

-4

-2

0

2

4

Intactl2/Ls = 0.08 l2/Ls = 0.16 l2/Ls = 0.24

Peel

stre

ss σ

33 (M

Pa)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

adhesive layer of glass/epoxy–glass/epoxy socket joints (h/t1 = 0.0625).


-14

-12

-10

-8

-6

-4

-2

0

2

4

6

Intactl2/Ls = 0.08l2/Ls = 0.16l2/Ls = 0.24

b)

Peel

stre

ss σ

33 (M

Pa)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

hesive layer of graphite/epoxy–graphite/epoxy socket joint (h/t1 = 0.0625).


where the adherends discontinuity exists. Fig. 11a and b shows,respectively, the comparison between the shear and peel stressesinduced in the adhesive layer along the overlap length for jointsmade of glass–epoxy and graphite–epoxy adherends/socket.

3.3.1. Effect of delamination length (l2/Ls)To study the effect of the normalized delamination length l2/Ls

on the adhesive layer stresses, the distribution of the shear andpeel stresses were plotted along the overlap length AB for glass–epoxy adherends/socket as shown in Fig. 12a and b and for graph-ite–epoxy adherends/socket as illustrated in Fig. 13a and b. Fromthese figures, one can see the presence of the secondary peaks inboth peel and shear stresses, similar to those previously observedin the ASLJ. Increasing the normalized delamination length causesan increase in the stresses at the ends of the overlap lengthtowards the values observed in the intact joint. It is also realizedthat the presence of a delamination at the left edge of the overlaplength has no effect on the maximum stresses occurring at theright edge of the adhesive layer.

3.3.2. Effect of delamination location through the thickness (h/t1)Fig. 14a and b shows the distribution of the shear and peel

stresses within the adhesive layer by changing the normalizedthrough-the-thickness location of the delamination (i.e. h/t1 =

Shea

r stre

ss τ

23 (M

Pa)

0.0-40

-30

-20

-10

0

10

20

30

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Intact= = =

0.9

0.06250.12500.1875

1.0


(a)h/t1h/t1h/t1

Fig. 14. Effect of the through-the-depth location of the delamination on the stress disadherends (l2/Ls = 0.08).

Shea

r stre

ss τ

23 (M

Pa)

-60

-40

-20

0

20

40

[0]16[90]16[45]16[0/90]8[+45/-45]8

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(a) (


Fig. 15. Influence of ply fiber orientation of the stress distribution within the adhesivh/t1 = 0.0625).

0.0625, 0.125, and 0.1875) for a glass epoxy ASJ with normalizeddelamination length of l2/Ls = 0.08 subjected to 100 N m torsionalmoment. The noted through-the-thickness delamination locationscorrespond to a delamination located between the first and second,second and third, and third and fourth plies, respectively. A consid-erable decrease in the peak stresses could be realized when thedelamination is located between the first and second plies (i.e. h/t1 = 0.0625) and adjacent to the adhesive layer. When the delami-nation is moved deeper through the thickness (away from theadhesive layer), the peak stresses tended to approach thoseobserved in the intact joint and the secondary peak as mentionedearlier, tends to disappear. From these observations, one may con-clude that the most effective location of the delamination is whenthe delamination is located nearest the outermost ply.

3.3.3. Effect of fiber orientationsFor all the results represented thus far in this study, fiber orien-

tation of [+45/�45]8 was used. In this part of the investigation theinfluence of the stacking sequence is considered. The stress distri-butions for various fiber orientations are shown in Fig. 15a and b,respectively. As seen, the largest peak shear stress at the left edgeof the overlap length occurs in the [90]16 stacking sequence (theangles are measured with respect to the longitudinal axis), andthe lowest peak occurs in [+45]16 stacking sequence. Moreover,

Peel

stre

ss σ

33 (M

Pa)

-6

-4

-2

0

2

4


h/t1h/t1h/t1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(b)

= = =

Intact0.06250.12500.1875

tributions within the adhesive layer of socket joint with glass/epoxy–glass/epoxy


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Peel

stre

ss σ

33 (M

Pa)

-20

-15

-10

-5

0

[0]16[90]16[45]16[0/90]8[+45/-45]8

b)

e layer of a socket joint with glass/epoxy–glass/epoxy adherends (l2/Ls = 0.08 and


no considerable change in the peel stress with different fiber orien-tations, with the exception of the [+45]16 stacking sequence thatexhibited totally different distribution trend in comparison to allthe others. As seen, therefore, the fiber orientation has a consider-able effect on the shear and peel stresses within the adhesive.

4. Conclusions

In this study, a pre-existing delamination was assumed to existwithin the composite adherend of an adhesively bonded jointmade up of composite–aluminum or composite–compositeadherends having both a single lap and socket configurations. Aparametric study was carried out to account for the effect of thepre-existing delamination on the state of stresses developed withinthe adhesive layer, focusing mainly on the adhesive layer shear andpeel stresses. The findings of this study can be summarized asfollows:

� For both joint configurations, all components of the stressesdeveloped within the adhesive layer tended to assume largevalues at or near both ends of the overlap length, but becomealmost zero along the rest of the overlap length, except for s12

component, which as expected, showed a constant nonzerovalue along the overlap length away from the edges.� While a marked decrease in the maximum value of the shear

stress was observed in the adhesive layer when the locationof the through-the-thickness delamination was aligned withoverlap’s edge; nevertheless, the stresses induced in the com-posite adherend, in the vicinity of the delamination location,did not markedly change as a result of the presence of such adefect.� The values of the maximum shear and peel stresses tended to

reach their values observed in the intact counterpart joint as

the delamination’s length increased. Also a secondary peak inboth the shear and peel stresses was noticed exactly at theend of the delaminated zone.� In the socket joint configuration, not only did the stress concen-

trations developed at the edges of the overlap length, but also atthe location of discontinuities between the adherends (wherethe adherends faced each other), causing a considerable discon-tinuity in the state of stresses of such joints.� The secondary peak realized in the shear and peel stresses in the

single lap joint was also observed in the adhesive socket jointconfiguration.� In both joint configurations, when the through-the-thickness

location of the delamination was moved deeper into the thick-ness, the secondary peak amplitude was decreased noticeably,and the edge maximum stresses approached their values inthe intact joint.� Finally the fiber orientations had no considerable effect on peel

stress in the socket joint configuration, except for the joint with[45]16 layup. Moreover, the maximum decrease in the peakshear stress was noticed for the [+45/�45]8 layup.

References

[1] da Silva Lucas FM, das Neves Paulo JC, Adams RD, Spelt JK. Int J Adhes Adhes2009;29:319–30.

[2] Hipol Philip J. J Compos Mater 1984;18:298–311.[3] Zou GP, Taheri F. Int J Solids Struct 2006;43:5953–68.[4] Nemes O, Lachaud F, Mojtabi A. Int J Adhes Adhes 2006;26:474–80.[5] Hosseinzadeh R, Taheri F. Compos Struct 2009;91:186–95.[6] Wei Xu, Guoqiang Li. Int J Adhes Adhes 2010;30:191–9.[7] Das RR, Pradhan B. Int J Adhes Adhes 2010;30:425–38.[8] Qin M, Dzenis YA. Composites 2003;34B:167–73.[9] Panigrahi SK, Pradhan B. Int J Adhes Adhes 2009;29:114–24.

[10] Esmaeel RA, Taheri F. J Adhes Sci Technol 2009;23:1827–44.[11] ABAQUS Version 6.9EF User Manual, ABAQUS Inc., 2010. <http://

www.abaqus.com>.

http://www.abaqus.com

http://www.abaqus.com

Documents

Influence of adherend’s delamination on the response of single lap and socket tubular adhesively bonded joints subjected to torsion