Makine Teknolojileri Elektronik DergisiCilt: 6, No: 4, 2009 (55-64)

Electronic Journal of Machine TechnologiesVol: 6, No: 4, 2009 (55-64)

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How to cite this articleAldaş K., Palancıoğlu H., Şen F. “Thermal stresses in adhesively bonded double lap joints by FEM” Electronic Journal of Machine Technologies, 2009, (6) 55-64

Bu makaleye atıf yapmak içinAldaş K., Palancıoğlu H., Şen F. “Yapıştırıcı ile Birleştirilmiş Çift Bindirme Bağlantılarında Isıl Gerilmeler” Makine Teknolojileri Elektronik Dergisi 2009, (6) 55-64

Article(Makale)

Thermal stresses in adhesively bonded double lap joints by FEM

Kemal Aldaş, Hakan Palancıoğlu, Faruk Sen*

Aksaray University Department of Mechanical Engineering, 68100, Aksaray, Turkeyfaruk.sen@deu.edu.tr

Abstract

In this paper, thermal stresses were calculated in adhesively bonded double lap joints. The finite element method (FEM) was preferred to obtain the thermal stress distributions based on uniform temperature loadings. The thermal stress analyses were carried out using ANSYS 10.0 code. Thermal stresses were computed for the dissimilar sheet materials, i.e. steel and aluminum. The influences of different uniform thermal loadings on thermal stresses were also examined in terms of the FEM results. According to obtained results, the magnitudes and distributions of the improved thermal stresses were significantly affected from bonded material properties, boundary conditions and rising values of uniform thermal loads. Keywords: Thermal stress analysis, double lap joint, epoxy adhesive, stress analysis

Yapıştırıcı ile Birleştirilmiş Çift Bindirme Bağlantılarında Isıl Gerilmeler

ÖzetBu çalışmada, yapıştırıcı ile birleştirilmiş çift bindirme bağlantılarındaki ısıl gerilmeler hesaplanmıştır. Uniform sıcaklık uygulanmasından dolayı oluşan, ısıl gerilme dağılımlarının elde edilmesi için sonlu elemanlar metodu tercih edilmiştir. Isıl gerilme analizleri ANSYS 10.0 programı kullanılarak yapılmıştır. Isıl gerilmeler, birbirinden farklı özelliklere sahip alüminyum ve çelik gibi ince metal levhalar için hesaplanmıştır. Isıl gerilmelerin üzerine farklı ısıl yüklemelerin etkileri incelenmiştir. Elde edilen sonuçlara göre, oluşan ısıl gerilmelerin değerleri ve dağılımları, yapıştırılan malzemelerin özellikleri, sınır şartları ve uniform sıcaklık miktarındaki artıştan önemli ölçüde etkilenmektedir.Anahtar Kelimeler: Isıl gerilme analizi, çift bindirme bağlantısı, epoksi yapıştırıcı, gerilme analizi

1.INTRODUCTION

Today, adhesive bonding method is frequently used in almost all the industries of the world and this is mainly due to its high strength-weight ratio, low cost and high efficiency [1]. Nonetheless, the construction of safe and cost effective bonded joints is a major challenge. It forces on the designer to have a good understanding of the effect of material and geometric parameters on the joint’s strength [2]. Indeed, the adhesive joints experience not only mechanical loads but also thermal loads. Since, the adhesive joints consist of materials with different mechanical and thermal properties, the thermal strains in the joint members may cause important stresses [3]. For instance, adhesive joints used in supersonic aircraft need to withstand low and high-temperatures, typically from -55 oC (depending on altitude) to as much as 200 oC or more. As an instance, if a supersonic aircraft flies at Mach 2.7, the air friction at this speed would produce a surface temperature of about 232 oC. It might eventually be possible to build up an adhesive which will operate successfully from -55 oC to more than 200 oC, but this is unlikely in the near future [4]. Meanwhile, in the last almost four decades FEM has become the widespread technique used

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for analyzing physical phenomena in the research area of structural, solid, and fluid mechanics as well asfor the solution of field problems [5].

A quantity of preceding studies considering thermal loads in adhesive joints are offered: Gustafson et al. [6] developed two thermomechanical analytical models for orthotropic double lap joints with a examination to identifying key dimensionless parameters that defined the behavior of the joint under combined thermal-mechanical loads. The solutions, based on the principle of virtual work, vary in the complexity of the assumed stress area. Apalak et al. [7] performed a transient thermal analysis of an adhesively bonded and laser-spot welded joint based on a thermal model developed for the laser-spot welding of multi-layered sheets using a pulsed Nd:YAG laser. The material non-linear properties of adhesive and sheets were considered using the non-linear finite element method during the thermal stress analysis. The keyhole development and temperature distributions in the region of the keyhole were investigated for the different sheet materials, i.e. aluminum, steel and titanium. Rastogi et al. [8] investigated thermal stresses in aluminum-to-composite, symmetric, double-lap joints via FEM. The joint arrangement considered aluminum adherent in combination with four different unidirectional laminated composite adherents subjected to uniform temperature loading. Morais et al. [9] studied the strength of stainless-steel joints bonded with two epoxy adhesives. The experimental process included tests on single-lap and butt joints, as well as thick-adherent and napkin ring shear tests. Nevertheless, FEM raised doubts on the true adhesive strengths, due to the complex stress position in joint tests and pressure-dependent adhesive behavior. In spite of some worries, FEM illustrated that damage could be fairly well predicted by a maximum shear strain criterion. Nakano et al. [10] carried out a thermal stress analysis of an adhesive butt joint which contained circular holes and rigid fillers in an adhesive and was under a non-uniform temperature loading. The adherents were assumed to be rigid and the adhesive was replaced with a finite strip having holes and rigid fillers in it and the thermal stress distribution in the adhesive was investigated using a two-dimensional theory of elasticity. Lucas and Adams [11] examined a mixed adhesive joint. Experiments were performed for titanium/titanium and titanium/composite double lap joints. It was shown that, for a joint with dissimilar adherents, the combination of two adhesives gave a better performance over the temperature range than a high temperature adhesive alone.

In this work, a thermal stress analysis was carried out for adhesively bonded double lap joints. During the analyses, the problem was modeled for different metal sheets bonded epoxy adhesive such as aluminum and steel by FEM. The different uniform thermal loadings were applied on the developed FEM models and then thermal stress distributions were determined, numerically.

1. MATERIALS AND METHODS

1.1 Problem Characterization

Thermal and mechanical properties of aluminum, steel adherents and epoxy adhesive are given in Table 1 [7]. During the solution, it is assumed that material properties were not changed related to increasing values of applied uniform temperatures, because the analyses were not applied at higher temperatures. Geometry and dimensions of an adhesively bonded double lap joint are illustrated in Figure 1-a. The thickness of metal sheet was modeled as 2 mm, while the thickness of epoxy adhesive was 0.2 mm. Nevertheless, the lengths of each sheets and adhesive were 20 mm and 6 mm, respectively. Two dissimilar joint systems were considered in terms of bonded materials. Firs of all, the double bonded metal sheets were assumed as aluminum (AlEpAl). Then, all of them were considered as steel (StEpSt). However, the adhesive material was selected as epoxy resin for all of the modeled structures. Since, it is known that epoxies have excellent combination of mechanical properties, corrosion resistance, dimensionally stable, good adhesion, relatively inexpensive and good electrical properties [12]. Boundary conditions are shown in Figure 1-b. As seen from this figure, boundary condition was selected as the simply supported for free-end of the model, while other edge was fixed. However, the half part of the

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double bonded structure was modeled because of the symmetry. For this reason, the numbers of both nodes and elements were reduced; therefore the solution time was decreased.

Table 1 Thermal and mechanical properties of aluminum, steel and epoxy

Property Aluminum Steel Epoxy

Density, (kg/m3) 2707 7780 1264

Specific heat, cp (J/kgK) 896 460 1046

Thermal conductivity, k (W/mK) 204 80.3 0.179

Elasticity modulus, E (GPa) 66 207 3.3

Poisson’s ratio, 0.33 0.29 0.30

Thermal expansion coefficient, (m/moC) 23.6 12.6 43.3

a) Geometry and dimensions (mm)

b) Boundary condition and path definition

Figure 1 The adhesively bonded double lap joint

The FEM was used to compute thermal stresses. For this purpose, powerful FEM program for both scientific researches and industrial applications called as ANSYS was chosen. For the duration of the mesh generation procedure, PLANE42, 2-D solid element type [13] was used. The geometry, node locations, and the coordinate system for this element are illustrated in Figure 2.

Figure 2 PLANE42 element type [13]

2

20

20

0.2 Metal sheet

Adhesive

2

Metal sheet

Metal sheet

2

6

0.2

y

x Symmetry line

y

xB

A C

D

E

F

G

H

Symmetry line

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PLANE42 is used for 2-D modeling of solid structures. The element can be used either as a plane element (plane stress or plane strain) or as an axisymmetric element. The element is expressed by four nodes having two degrees of freedom at each node, translations in the nodal x and y directions. The FEM pattern of the adhesively bonded double lap joint is shown in Figure 3 with detail. This figure indicates that the fine mesh arrangement was formed on the bonded model. In addition, the refine mesh was prepared on the adhesive area and close areas of metal sheets due to the providing a high-quality FEM solution. Following the mesh process, the half model of the bonded joint was divided into 623 elements and 705 nodes. As mentioned previously, the uniform temperature loadings were applied on the model as 40, 50 and 60 oC. Furthermore, the reference temperature was assumed as 25 oC.

Figure 3 Mesh pattern of an adhesively bonded single-lap joint with detail

1.2 Calculation of Thermal Stresses

In many real applications, the adhesively bonded joints can practice complex thermal loads. The main reason of this, both adhesive and adherents have dissimilar thermal and mechanical properties as seen from Table 1. The thermal expansion coefficients of these materials may cause high thermal stresses on the bonded joint, especially. In this investigation, it was assumed that the joint were subjected to uniform thermal loads. For calculation of thermal stresses, cartesian coordinates (x, y) are used. The notations for stress components are x, y and xy. By using the FEM, strain displacement can be written as [13, 14],

eB (1)

where [B] is the strain-displacement interpolation matrix and { }e is the displacement vector for element (e). The stress-strain displacement relation for a two dimensional element is expressed as follows,

C (2)

where [C] is the elasticity matrix. Thermal stresses are calculated by using the principle of virtual work. In this method, one considers infinitesimal small node displacements, {}e imposed onto the body. This causes external total virtual work (this external virtual work is equal to the internal virtual work which is defined by stresses {} and strains {}e). Using integration over the volume of element,

dVRTe

V

eTe (3)

By using equations (1) and (2),

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dVBCBR T

V

e (4)

Here,

dVBCBK T

V

e (5)

is the stiffness matrix of element “e”. By assembling the stiffness matrix of all elements, the total stiffness matrix [K] is calculated. Analogous to the equation (3) it can be written as,

KR (6)

The load vector {R} includes only thermal forces. By using the mean thermal expansion coefficient m

and temperature gradient {T} one can calculate,

dVTBCBR mT

V

T (7)

The thermal force is integrated as,

T1 RK (8)

Finally, thermal stresses can be calculated according to the next equation

TCBC m (9)

2. RESULTS and DISCUSSION

The four paths are defined on the FEM model to evaluate for thermal stress analyses results. These paths are shown in Figure 1-b. As seen from this figure, the paths are positioned on fixed edge of the metal sheet (Path A-B), free end of the metal sheet (Path G-H) and free-ends of the epoxy adhesive with metal sheets (Path D-C and Path E-F). Since, these parts of the joint are very important because of intensity of the thermal stresses. The changing of thermal stresses related to uniform temperature loadings on Paths A-B, C-D, E-F and G-H are shown in Figures 4-7, respectively. First of all, thermal stresses on Paths A-B and G-H are higher than Paths C-D and E-F. Since the applied boundary conditions cause the intensity of the stresses on Paths A-B and G-H. However, the highest values of thermal stresses are calculated on Paths A-B and G-H for y-direction. Therefore, the compressive stresses for y-direction must be concerned for these investigated structures since it may cause some unexpected problems on the joints such as thermal fatigue, cracking etc. Figures 5 and 6 point out, the magnitudes of thermal stresses are changed on the adhesive and close areas of metal sheets. Besides, the forms of thermal stresses on the Paths D-D and E-F are become different from tensile to compressive or compressive to tensile. Since the material properties of metal sheets and epoxy adhesive are very differ from each other as expressed in Table 1. For example, thermal expansion coefficient of epoxy is very differing from aluminum and steel, especially.

Thermal stresses computed for bonded steel sheets are higher than bonded aluminum sheets. The reason of this result is also based on different physical properties of the materials. Consequently, it is said that thermal compatibility of aluminum sheets with epoxy is seen well than steel sheets. According to obtained results, thermal stresses are increased by increasing of uniform thermal loadings, so the highest values of thermal normal and shear stresses are calculated at 60 oC thermal loads both aluminum and steel bonded systems.

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a) x b) y

c) xy

Figure 4 Thermal stresses on Path A-B

Thermal stresses observed on the adhesive area are very significant due to providing a safety double bonded joint. Therefore, their distributions on adhesive part under 60 oC are shown in Figure 8 as an example of all study. These contours are plotted for both left and right free edges of the adhesive for a good comparison. As seen from this figure, thermal stresses on the adhesive for StEpSt system are higher than AlEpAl system. In addition, their values for x-direction are upper than y-direction. The uppermost value of thermal stresses on the adhesive is calculated as 3,704 MPA compressive form for StEpSt system at 60 oC. An important result from Figure 8, the forms of thermal stresses are observed as compressive, especially. The occurrence of compressive stresses on the adhesive is seen as appropriate, since thermal expansion coefficient of epoxy higher than sheet metals both steel and aluminum. After the application of thermal loadings, the epoxy adhesive desires to expand far too much according to adherents, but they block the adhesive. Thus, compressive stresses occur on the adhesive, generally.

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a) x b) y

c) xy

Figure 5 Thermal stresses on Path C-D

a) x b) y

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c) xy

Figure 6 Thermal stresses on Path E-F

a) x b) y

c) xy

Figure 7 Thermal stresses on Path G-H

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a) x, AlEpAl

b) x, StEpSt

c) y, AlEpAl

d) y, StEpSt

e) xy, AlEpAl

f) xy, StEpStFigure 8 Thermal stress distributions on the left and right edges of epoxy adhesive at 60 oC (MPa)

4. CONCLUSIONS

In this study, a thermal stress analysis was performed for adhesively bonded double lap joint utilizing FEM. Thermal stress fields were obtained for using different adherent materials and applied various uniform temperature loads. According to obtained results, some significant remarks can be concluded as; both thermal and mechanical mismatches of the metal sheets and epoxy adhesive caused high stress concentrations on the adhesive regions close to adherent-adhesive interfaces around the adhesive free ends. The thermal stresses were raised by raising values of uniform thermal loadings. Moreover, the

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magnitudes of thermal stresses were calculated as higher, if the differences of physical properties between adhesive and metal sheets are upper than each other. Consequently, a designer who studied adhesively bonded joint must select the appropriate adherent materials and adhesive for providing low thermal stresses on the adhesively bonded double lap joint. Since thermal stresses may cause some unexpected problems such as thermal fatigue, cracking etc.

REFERENCES

1. You, M., Yan, Z.M., Zheng, X.L., Yu, H.Z. and Li, Z. 2007, A numerical and experimental study of gap length on adhesively bonded aluminum double-lap joint, Int. Journal of Adhesion and Adhesives, 27, 696-702.

2. Derewonko, A., Godzimirski, J., Kosiuczenko, K., Niezgoda, T. and Kiczko, A. 2008, Strength assessment of adhesive-bonded joints, Computational Materials Science, 43, 157-164.

3. Apalak, M.K., Gunes, R. 2002, On non-linear thermal stresses in an adhesively bonded single lap joint, Computers and Structures, 80, 85-98.

4. Silva, L.F.M., Adams, R.D. 2007, Joint strength predictions for adhesive joints to be used over a widetemperature range, International Journal of Adhesion and Adhesives, 27, 362-379.

5. Mackerle, J. 1997, Finite element analysis and simulation of adhesive bonding, soldering and brazing: A bibliography (1976-1996), Modeling and Simulation in Materials Science and Engineering, 5, 159-185.

6. Gustafson, P.A., Bizard, A., Waas, A.M. 2007, Dimensionless parameters in symmetric double lap joints: An orthotropic solution for thermomechanical loading, Int. Journal of Solids and Structures, 44, 5774-5795.

7. Apalak, M.K., Aldas, K., and Sen, F., 2003, Thermal non-linear stresses in an adhesively bonded and laser-spot welded single-lap joint during laser-metal interaction, Journal of Materials Processing Technology, 142, 1-19.

8. Rastogi, N., Soni, S.R. and Nagar, A. 1998, Thermal stresses in aluminum-to-composite double-lap bonded joints, Advances in Engineering Software, 29, 273-281.

9. Morais, A.B., Pereira, A.B., Teixeira, J.P. and Cavaleiro, N.C. 2007, Strength of epoxy adhesive-bondedstainless-steel joints, International Journal of Adhesion and Adhesives, 27, 679-686.

10. Nakano, Y., Katsuo, M. et al. 1998, Two-dimensional thermal stress analysis in adhesive butt joints containing hole defects and rigid fillers in adhesive under non-uniform temperature field, Adhesion, 65, 57-80.

11. Silva, L.F.M. and Adams, R.D. 2007, Adhesive joints at high and low temperatures using similar and dissimilar adherents and dual adhesives, International Journal of Adhesion and Adhesives, 27, 216-226.

12. Callister, W.D. 2003, Materials Science and Engineering and Introduction, John Wiley & Sons, Inc. USA,

13. ANSYS, Release 10.0 Documentation, Swanson Analysis System Inc. Houston, PA, USA.

14. Huebner, K.H. and Thornton, E.A. 1982, Finite Element for Engineers, Wiley, New York.

15. Sen, F., Sayman, O. Toparli, M., Celik, E. 2006, Stress analysis of high temperature ZrO2 insulation coatings on Ag using finite element method, Journal of Materials Processing Technology, 180: 239-245.