Proceedings of PACAM XICopyright c© 2009 by ABCM

11th Pan-American Congress of Applied Mechanics - PACAM XIJanuary 04-08, 2010, Foz do Iguaçu, PR, Brazil

DEVELOPMENT OF A COMPUTATIONAL TOOL FOR BONDEDJOINT ANALYSIS

Marcelo Leite Ribeiro, malribei@usp.brRicardo Afonso Angélico, ricardoangelico@gmail.comVolnei Tita, voltita@sc.usp.brDepartment of Materials, Aeronautical and Automobilist - São Carlos School of Engineering - University of São Paulo

Abstract. The use of bonded joints is one of the most efficient ways of transmitting loads between the parts ofa structure. Showing some different advantages when compared to fastener joints, it also allows the bonding ofdissimilar materials, as metals and composites. For structural design these joints, it is necessary to know the forces,moments, displacements and stress acting in the joint after load application. In order to help the design process ofbonded joints, a computer program which is capable to evaluate single and double lap bonded joint is proposed. Theset of differential equations for each part (adherents and adhesive) of the problem geometry are obtained from theconstitutive and equilibrium equations. To solve the set of equations of this boundary value problem, a computationaltool in MatlabTMprogram is used. Two commercial programs are used to validate the program por computationaltool implemented. One is the finite element program ABAQUSTM, and the other one is ESACompTM. The comparisonbetween these programs showed a good curve fit for joint displacement field and adhesive stresses for compositejoints, as well as for hybrid joints (metal-composite).

Keywords: bonded joints, hybrid joints, composite materials, boundary value problem, analytical methods

1. INTRODUCTION

In the last years, the use of composite materials as a primary structural element have been increased. Some new aircraftdesign, for example: Airbus A380 and Boeing 787 use composite materials even in primary structural elements such aswing spars and fuselage skins, achieving lighter structures without loss of airworthiness. One way to assembly, thesestructures consists on using bonded joints which shows some advantages like a better fatigue endurance, joining dissimilarmaterials, better insulation, smooth surface and lighter weight. Nevertheless, there is no possibility to disassembly thejoints, peeling stress should be minimized and the preparation of the surfaces that will be bonded must be done carefully(Mortensen, 1998).

Many researches have been carried out about bonded joints, trying to predict the behavior, failure, and the strengthof bonded joints using finite element models, analytical models or experimental tests. Thomsen (1992) showed that anincrease in the overlap lenght reduces the stress in the adhesive layer and application of adhesive layer with lower elasticshear and tensile moduli decreases the adhesive stress that is better use identical or nearly identical adherents in bondedjoints. Mortensen (1998), in his PhD thesis, presented a development of a computational tool for analysis of bonded jointsshowing the equations and hypothesis for various type of bonded joints, as well as, the solving process of differentialequations using the multi-segment method of integration. Ganesh and Choo (2002) showed the effect of spatial gradingof adherent elastic modulus on the peak stress and stress distribution in the single lap joint, which lead to decreasing inthe stress peak and a more uniform shear stress distribution.

Belhouari, Bouiadjra, and Kaddouri (2004) showed a comparison between single and double lap joint using a finiteelement model. In that study, the researchers showed the advantages of using symmetric composite patch for repairingcrack, also, that double patch has lower stress when compared with single patch repair. Myeong et. al. (2008) showed thatan increase of bonding pressure leads to higher strength bonded joints, an increase in the overlap lenght also leads to higherstrength bonded joints and the major failure mode for single lap hybrid composite/aluminum joints is the delamination ofthe composite adherent. Agnieszka (2009) showed a numerical method, regarding the sensitivity for hydrostatic stress, forprediction of the delamination initiation, which allows to simulate the failure of the joint (overlap region) and compositeadherent.

In order to help the design process of bonded joints, it was developed a software called SAJ (System of Analysisfor joints), which is capable of analyze a bonded joint behavior in detail, not only for single lap joint, but also, fordouble lap joint. These joints could be made of composite/composite materials or dissimilar materials i.e. hybrid joints(metal/composite). The software developed can calculate the joints stresses, loads and displacements. Two commercialsoftware were used to perform SAJ validation, a finite element software, ABAQUSTM, and specific composite analysissoftware, ESACompTM.

Proceedings of PACAM XICopyright c© 2009 by ABCM

11th Pan-American Congress of Applied Mechanics - PACAM XIJanuary 04-08, 2010, Foz do Iguaçu, PR, Brazil

2. COMPUTATIONAL TOOL

In order to help the assessment of bonded joints was developed a computational tool that are able to calculate the jointloads, displacements, stress and adhesive/adherents stresses. Only linear elastic results are showed in this paper.

A computational tool was developed in order to help the analysis of single and double lap bonded joints. This softwarewas programmed in MatlabTMlanguage. In the case of composite adherents, this software is also capable to obtain thestress and strain for each layer. SAJ is also capable to solve composite/composite and metal/composite bonded joints.

SAJ reads an input file within data of adherents, adhesive and joint characteristics. These file contains informationsuch as lay up and layer thickness in case of composite adherents, mechanical properties for adherents and adhesives, jointdimensions of adhesive and adherents, as well as, loads and boundary conditions. For results, SAJ shows the graphics offorces, displacements and adhesive stresses, also these results are given in tabular form.

2.1 Mathematical formulation

SAJ solves a set of differential equations of the multi-domain boundary value problem using MatlabTM. In orderto obtain the set of differential equations, first a subdivision of the joint in three regions were made, one part with onlyadherents, other part with the bonded region and the last part again only with adherents. These subdivisions are showed forsingle lap joint in Fig. 1(a) and for double lap joint in Fig. 1(b). In these figures are also showed the boundary conditions,loads and coordinate system.

(a) Single lap joint (b) Double lap joint

Figure 1. (a)Single lap joint boundary conditions, loads and coordinate system, (b) Double lap joint boundary conditions,loads and coordinate system.

For each region, using the equilibrium equations of an infinitesimal element are obtained the set of differential equa-tions as showed in Fig. 2 for single and double lap joint. With Classical Laminate Theory, and assuming the hypothesisthat all derivatives in y direction are equal zero, plane stress state, Kirchhofft’s kinematic relations and the equilibriumequations leads to the complete set of differential equations.

For the regions with only adhrents (subdivisions 1 and 3 of Fig. 1(a) and (b)), the set of differential equations areshowed in Fig. 3(a). Figure 3(b) shows the equations for adherent 1 (subdivision 2 of Fig. 1(b))for a double lap caseinside the overlap region, and Fig. 3(c) shows the equations for adherents 1 and 2 for single lap case and for adherents 2and 3 for double lap case inside the overlap region (subdivision 2 of Fig. 1(a) and (b)).

Where ti is the thickness of the i adherent; ta is the adhesive thickness; κx is the rotation of the x axis; u0 is themidplane displacement in u direction; v0 is the midplane displacement in v direction.

The adhesive is simulated as tension/compression and shear springs (Mortensen, 1998), Eq. (1) to Eq. (3) shows theequations for the adhesive model.

τax =Ga

ta(ui0 −

ti(x)

2κix − uj0 −

tj(x)

2κjx) (1)

τay =Ga

ta(νi0 − νj0) (2)

σax =Ea

ta(wi − wj) (3)

These differential equations system for each subdivision are solved using MatlabTM, which can deal with multi-domainboundary values problem.

Proceedings of PACAM XICopyright c© 2009 by ABCM

11th Pan-American Congress of Applied Mechanics - PACAM XIJanuary 04-08, 2010, Foz do Iguaçu, PR, Brazil

xx=0mm

x=100mm

x=-80mm

Adherent 1

Adhesive

Adherent 2

Subdivision 1 Only adherents

Subdivision 2Adherents and adhesives Subdivision 3

Only adherents

x

X=-80mm

x=100mm

x=0mm

Adherent 1

Adherent 2 and 3

Adhesive

Subdivision 1 Only adherents

Subdivision 2Adherents andadhesives Subdivision 3

Only adherents

M yyi ∂M yy

i /∂ ydyM xy

i ∂M xyi /∂ ydy

Q yi∂Q y

i /∂ y dy

N xyi ∂N xy

i /∂ ydyN yyi ∂N yy

i /∂ ydy

M yyi

M xyi

Q yiN yy

i

N xyi

M xxi

M xyi

Qxi

N xxi

N xyi

M xyi ∂M xy

i /∂ xdx

M xxi ∂M xx

i /∂ xdx N xxi ∂N xx

i /∂ xdxN xyi ∂N xy

i /∂ xdx

Qxi∂Qx

i /∂ ydy

x

yz

M yy1 ∂M yy

1 /∂ ydy

M xy1 ∂M xy

1 /∂ xdx

sa1dxdy

sa1dxdytay1dxdy

tax1dxdy

tax1dxdytay1dxdy

sa2dxdytay2dxdy

tax2dxdy

sa2dxdy

tax2dxdytay2dxdy

M yy1

M xx1

M xy1

M xx1 ∂M xx

1 /∂ xdx

M xy1 ∂M xy

1 /∂ ydy

M xy1

Q y1N yy

1

N xy1

Qx1

N xx1

N xy1

Q y1∂Q y

1 /∂ y dy

N xy1 ∂N xy

1 /∂ ydyN yy1 ∂N yy

1 /∂ ydy

N xx1 ∂N xx

1 /∂ xdxN xy1 ∂N xy

1 /∂ xdx

Qx1∂Qx

1 /∂ ydy

M yy2 ∂M yy

2 /∂ ydy M xy2 ∂M xy

2 /∂ ydy

Q y2∂Q y

2 /∂ y dy

N xy2 ∂N xy

2 /∂ ydyN yy2 ∂N yy

2 /∂ ydy

M yy3 ∂M yy

3 /∂ ydyM xy

3 ∂M xy3 /∂ ydy

Q y3∂Q y

3 /∂ y dy

N xy3 ∂N xy

3 /∂ ydyN yy3 ∂N yy

3 /∂ ydy

M yy3

M xy3

Q y3N yy

3

N xy3

M yy2

M xy2

Q y2N yy

2

N xy2

M xx3

M xy3

Qx3

N xx3

N xy3

M xx2

M xy2

Qx2

N xx2

N xy2

M xy3 ∂M xy

3 /∂ xdx

M xx3 ∂M xx

3 /∂ xdx N xx3 ∂N xx

3 /∂ xdxN xy3 ∂N xy

3 /∂ xdx

Qx3∂Qx

3 /∂ ydy

M xy2 ∂M xy

2 /∂ xdx

M xx2 ∂M xx

2 /∂ xdx N xx2 ∂N xx

2 /∂ xdxN xy2 ∂N xy

2 /∂ xdx

Qx2∂Q x

2/∂ ydy

x

yz

M yy1 ∂M yy

1 /∂ y dy

M xy1 ∂M xy

1 /∂ xdx

sa1dxdy

sa1dxdytay1dxdy

tax1dxdy

tax1dxdytay1dxdy

M yy1

M xx1

M xy1

M xx1 ∂M xx

1 /∂ xdx

M xy1 ∂M xy

1 /∂ ydy

M xy1

Q y1N yy

1

N xy1

Qx1

N xx1

N xy1

Q y1∂Q y

1 /∂ y dy

N xy1 ∂N xy

1 /∂ ydyN yy1 ∂N yy

1 /∂ ydy

N xx1 ∂N xx

1 /∂ xdx

N xy1 ∂N xy

1 /∂ xdx

Qx1∂Q x

1 /∂ ydy

M yy2 ∂M yy

2 /∂ y dy M xy2 ∂M xy

2 /∂ ydy

Q y2∂Q y

2 /∂ y dy

N xy2 ∂N xy

2 /∂ ydy

N yy2 ∂N yy

2 /∂ ydy

M yy2

M xy2

Q y2N yy

2

N xy2

M xx2

M xy2

Qx2

N xx2

N xy2

M xy2 ∂M xy

2 /∂ xdx

M xx2 ∂M xx

2 /∂ xdx N xx2 ∂N xx

2 /∂ xdxN xy2 ∂N xy

2 /∂ xdx

Qx2∂Qx

2/∂ ydy

Figure 2. Free body equilibrium forces for each subdivision part.

u0, xi −a11

i N xxi −a13

i N xyi −b11

i M xxi =0

w , xi x

i=0K xi , x−b11

i N xxi −b13

i N xyi −d 11

i M xxi =0

0, xi −a21

i N xxi −a23

i N xyi −b21

i M xxi =0

N xx , xi =0

N xy , xi =0

M xx , xi −Q x

i=0Q x , xi =0

(a)

u0, x1 −a11

1 N xx1 −a13

1 N xy1 −b11

1 M xx1 =0

w , x1 x

1=0K x1 , x−b11

1 N xx1 −b13

1 N xy1 −d 11

1 M xx1 =0

0, x1 −a21

1 N xx1 −a23

1 N xy1 −b21

1 M xx1 =0

N xx , x1 ax

1 −ax2 =0

N xy , x1 ay

1 −ay2 =0

M xx , x1 −Q x

1ax1 t1t a1

2−ax

2 t 1t a22

=0

Q x , x1 −a

1a2=0

(b)

u0, xi −a11

i N xxi −a13

i N xyi −b11

i M xxi =0

w , xi x

i=0K xi , x−b11

i N xxi −b13

i N xy1 −d 11

i M xxi =0

0, xi −a21

i N xxi −a23

i N xyi −b21

i M xxi =0

N xx , xi ax

i =0N xy , xi ay

i =0

M xx , xi −Q x

iaxi t1ta1

2=0

Q x , xi −a

i=0

(c)

Figure 3. (a)Set of differential equations for bonded joint out of overlap zone for i=1,2,3.; (b) Set of differential equationsfor double lap joint adherent 1; (c)Set of differential equations for adherents in the overlap joint. For single lap, i=1,2 and

for double lap, i=2,3.

Proceedings of PACAM XICopyright c© 2009 by ABCM

11th Pan-American Congress of Applied Mechanics - PACAM XIJanuary 04-08, 2010, Foz do Iguaçu, PR, Brazil

2.2 Computational Implementation

The analysis starts reading input data from a file that prescribe the joint type (single or double), adherents and adhe-sives mechanical properties, ply thickness and orientation (in case of composite materials), adhesive thickness and thedimensions, as well as, loads and boundary conditions. With all necessary data, first SAJ, using the classical laminatetheory, perform the calculus of the stiffiness and the compliance matrix.

After calculus of compliance matrix and knowing the joint type and the boundary conditions, the next step consists onto, solve the boundary value problem using bvp4c MatlabTMfunction. Figure 4 presents the SAJ block diagram.

Figure 4. SAJ block diagram.

2.3 Finite element model

A finite element model for single and double lap joint using a commercial software ABAQUSTMwere simulated tocompare to the SAJ computational results. The finite element model use a second order element with 20 nodes (C3D20)for adherents and adhesives even for single and double lap joint C3D20 is used also for modeling composite adherents.Figure 5(a) shows the finite element model for single lap bonded joint and Fig. 5(b) shows the finite element model fordouble lap bonded joint. Notice that these models are simulating the boundaries conditions and loads for each joint asshowed in Fig. 1(a) for single lap and Fig. 1(b) for double lap joint.

xz

y

(a) Single lap joint

xz

y

(b) Double lap joint

Figure 5. (a)Single lap joint finite element model, (b) Double lap joint finite element model.

ABAQUSTMconstraint function "tie" is used to join the adhesive and adherents in the overlap region. The constraintfunction tie transfer all degrees of freedom between adherents and adhesive.

2.4 Results

For a first case study a composite/composite joints, using symmetric laminate, were used and the adherents andadhesives mechanical properties, as well as, the characteristics given in Tab.1 (Hexcel T3T-190-F155). The boundaryconditions in Fig. 1(a) for single lap joint and Fig. 1(b) for double lap joint. The adherents were carbon fiber reinforcedplastics and the adhesive was epoxy (Tab.1). A normal load of 0.015kN/mm were used for single and double lap joint toproceed with this comparison. It is important to notice that this load is small enough do not cause any plasticity even inadherents or in adhesive.

Table 1. Hexcel T3T-190-F155 carbon fiber reinforced plastic, Hysol EA 9321 epoxy adhesive and aluminum 2024-T3mechanical properties and characteristics.

E1[kN/mm2] E2[kN/mm

2] G12[kN/mm2] ν Thickness[mm] Orientation

Hexcel T3T-190-F155 126.0 7.1 4.0 0.30 0.8(0.2mm per ply) [0/45]sEpoxy adhesive 1.485 - - 0.35 0.5 -

2024-T3 72.0 - - 0.33 0.8 -

Proceedings of PACAM XICopyright c© 2009 by ABCM

11th Pan-American Congress of Applied Mechanics - PACAM XIJanuary 04-08, 2010, Foz do Iguaçu, PR, Brazil

- 8 0 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 8 0 1 0 0

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

o v e r a l l l e n g t h ( m m )

w (mm

)

E S A C o m p S A J A B A Q U S

(a) Single lap joint

w (mm

)

- 8 0 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 8 0 1 0 0- 0 . 0 0 1 5

- 0 . 0 0 1 0

- 0 . 0 0 0 5

0 . 0 0 0 0

0 . 0 0 0 5

0 . 0 0 1 0

0 . 0 0 1 5

o v e r a l l l e n g t h ( m m )

E S A C o m p S A J A B A Q U S

(b) Double lap joint

E S A C o m p σz , E S A C o m p τz x S A J σz , S A J τz x A B A Q U S σz , A B A Q U S τz x

0 5 1 0 1 5 2 0- 0 . 0 0 10 . 0 0 00 . 0 0 10 . 0 0 20 . 0 0 30 . 0 0 40 . 0 0 50 . 0 0 6

σ z, τ zx [MPa

]

" o v e r l a p " ( m m )

(c) Single lap joint

E S A C o m p σz , E S A C o m p τz x S A J σz , S A J τz x A B A Q U S σz , A B A Q U S τz x

0 5 1 0 1 5 2 0- 0 . 0 0 1 2- 0 . 0 0 1 0- 0 . 0 0 0 8- 0 . 0 0 0 6- 0 . 0 0 0 4- 0 . 0 0 0 20 . 0 0 0 00 . 0 0 0 20 . 0 0 0 40 . 0 0 0 60 . 0 0 0 80 . 0 0 1 00 . 0 0 1 20 . 0 0 1 40 . 0 0 1 6

σ z, τ zx [MPa

]

" o v e r l a p " ( m m )

(d) Double lap joint

Figure 6. (a) Single lap joint displacement in w direction; (b) Double lap joint displacement in w direction; (c) Single lapjoint σz ans τzx; (d) Double lap joint σz and τzx.

The results in Fig. 6(a) shows the displacement field for single lap joint and in Fig. 6(b) shows the displacement fieldfor double lap joint. Figure. 6(c) shows σz and τzx for single lap bonded joint, Fig. 6(d) shows σz and τzx for double lapjoint.

- 8 0 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 8 0 1 0 0- 1 . 0- 0 . 50 . 00 . 51 . 01 . 52 . 02 . 53 . 03 . 5

C o m p o s i t e

w (mm

)

o v e r a l l l e n g t h ( m m )

E S A C o m p S A J A B A Q U S

A l u m i n u m

(a) Single lap joint

- 8 0 - 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0 8 0 1 0 0- 0 . 0 0 1 6- 0 . 0 0 1 4- 0 . 0 0 1 2- 0 . 0 0 1 0- 0 . 0 0 0 8- 0 . 0 0 0 6- 0 . 0 0 0 4- 0 . 0 0 0 20 . 0 0 0 00 . 0 0 0 20 . 0 0 0 40 . 0 0 0 60 . 0 0 0 80 . 0 0 1 00 . 0 0 1 20 . 0 0 1 40 . 0 0 1 6

o v e r a l l l e n g t h ( m m )C o m p o s i t e

w (mm

)

E S A C o m p S A J A B A Q U S

A l u m i n u m

(b) Double lap joint

E S A C o m p σz , E S A C o m p τz x S A J σz , S A J τz x A B A Q U S σz , A B A Q U S τz x

0 5 1 0 1 5 2 0- 0 . 0 0 2

0 . 0 0 0

0 . 0 0 2

0 . 0 0 4

0 . 0 0 6

0 . 0 0 8

0 . 0 1 0

σ z, τ zx [MPa

]

" o v e r l a p " ( m m )

(c) Single lap joint

E S A C o m p σz , E S A C o m p τz x S A J σz , S A J τz x A B A Q U S σz , A B A Q U S τz x

0 5 1 0 1 5 2 0- 0 . 0 0 1 2- 0 . 0 0 1 0- 0 . 0 0 0 8- 0 . 0 0 0 6- 0 . 0 0 0 4- 0 . 0 0 0 20 . 0 0 0 00 . 0 0 0 20 . 0 0 0 40 . 0 0 0 60 . 0 0 0 80 . 0 0 1 00 . 0 0 1 20 . 0 0 1 40 . 0 0 1 60 . 0 0 1 8

σ z, τ zx [MPa

]

" o v e r l a p " ( m m )

(d) Double lap joint

Figure 7. (a) Single lap hybrid joint displacement in w direction; (b) Double lap hybrid joint displacement in w direction;(c) Single lap joint σz and τzx; (d) Double lap joint σz and τzx.

Proceedings of PACAM XICopyright c© 2009 by ABCM

11th Pan-American Congress of Applied Mechanics - PACAM XIJanuary 04-08, 2010, Foz do Iguaçu, PR, Brazil

For a second case study, a double and a single lap hybrid bonded joint (metal-composite) was investigated. Aluminumwas used for adherent 1 and laminate for adherent 2 (see Fig. 1(a)) for single lap, and for double lap hybrid bonded joint,aluminum was used for adherent 1 and laminate for adherents 2 and 3 (see Fig. 1(b)). The materials properties wereshowed in Tab. 1.

The results in Fig.7(a) shows the displacement field for single lap hybrid joint, in this figure ESACompTMmodelshows to be more flexible in the composite side and more stiff in the aluminum side, SAJ presents results betweenESACompTMand FEM model, these differences happens due to differences in computational method applied to solvethe problem, as well as, little differences between load and boundary conditions applications. Figure7(b) shows thedisplacement field for double lap hybrid joint, also some difference, mostly between ESACompTMand other modelsoccurs, althought these differences, when compared with joint dimmensions are small. Figure. 7(c) shows σz and τzxfor single lap hybrid bonded joint, Fig.7(d) shows σz and τzx for double lap hybrid bonded joint.

Due to σz and τzx possess a more significant role in the failure analysis, the results for τzy were suppressed. Otherimportant parameter, results for displacement, are also shown in this work, more details about SAJ validation in Ribeiro(2009) and Tita, Angelico and Ribeiro (2008).

3. CONCLUSIONS

The proposed program, SAJ, had showed to be adequate to perform composite/composite and metal/composite bondedjoint analysis for single and double lap joint types.

4. ACKNOWLEDGEMENTS

The authors are grateful for the financial support from FAPESP and CAPES.The authors, also would like to thank Prof. Reginaldo Teixeira Coelho for the ABAQUSTMlicense, which allow SAJ

validation.

5. REFERENCES

Anderson, T.L., 1995, "Fracture Mechanics - Fundamentals and Applications", Ed. CRC Press.Belhouari, M., Bouiadjra, B. B. and Kaddouri, K., 2004, "Comparison of Double and Single Bonded Repairs to Symmetric

Composite Structures: A Numerical Analysis", Composite Structures, Vol.65, pp. 47-53.Gagnieszka, D., 2009, "Prediction of the Failure Metal-Composite Bonded Joints", Computational Materials Science,

Vol.45, pp.735-738.Ganesh, V. K., Choo, T. S., 2002,"Modulus Graded Composite Adherents for Single Lap Bonded Joints", Journal of

Composite Materials, Vol.36, pp.1757-1767.Mortensen, F., 1998, "Development of Tools for Engineering Analysis and Design of High-Performance FRP-Composite

Structural Elements", PhD Thesis, Institute of Mechanical Engineering, Aalborg University, Aalborg.Myeong-Su, S., et al, 2008, "A Parametric Study on the Failure of Bonded Single-Lap Joints of Carbon Composite and

Aluminum", Composite structures, Vol.86, pp.135-145.Qian, H., Sun, C. T., 2008, "Effect of Bondline Thickness on Model I Fracture in Adhesive Joints", Proceedings of

the 49rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Schaumburg,Illinois.

Ribeiro M. L., 2009, "Programa para Análise de Juntas Coladas: Compósito/Compósito e Metal/Compósito.", Masterthesis, Escola de Engenharia de São Carlos, Universidade de São Paulo, São Carlos (in Portuguese).

San Román, J. C., 2005,"Eperiments on Epoxy, Polyurethane and ADP Adhesives", Composite Structure Laboratory,Technical Report, no CCLab2000.1b/1.

Thomsen,O. T., 1992, "‘Elasto-Static and Elasto-Plastic Stress Analysis of Adhesive Bonded Tubular Lap Joints", Com-posite Structures, Vol. 21, pp. 249-259.

Tita, V. ; Angelico, R. A. ; Ribeiro, M. L., 2008, "Failure Mechanisms Modeling of Hybrid Joints (Metal-Composite)."In: Brazil AFOSR Workshop on Advanced Structural Mechanics and Computational Mathematics, Campinas.

6. RESPONSIBILITY NOTICE

The authors are the only responsible for the printed material included in this paper.