- Email: [email protected]
Three dimensional finite element analysis of bi-adhesively bonded double lap joint
International Journal of Adhesion & Adhesives 37 (2012) 50–55
Contents lists available at SciVerse ScienceDirect
International Journal of Adhesion & Adhesives journal homepage: www.elsevier.com/locate/ijadhadh
Three dimensional finite element analysis of bi-adhesively bonded double lap joint ¨ zer a,n, O ¨ zkan O ¨zb Halil O a b
Mechanical Engineering Department, Faculty of Mechanical Engineering, Yıldız Technical University, Barbaros Bulvarı, 34349 Yıldız, Istanbul, Turkey Machine Education Division, Faculty of Technical Education, Karabuk University, Balıklarkayası mevkii, 78050 Karabuk, Turkey
a r t i c l e i n f o
a b s t r a c t
Available online 21 January 2012
Hybrid-adhesive joints are an alternative stress reduction technique for adhesively bonded joints. The joints have two types of adhesives in the overlap region. The stiff adhesive should be located in the middle and flexible adhesive at the ends. In this study, the effect of the hybrid-adhesive bondline on the shear and peeling stresses of a double lap joint were investigated using a three-dimensional finite element model. We developed a three dimensional model of the double lap joint based on solid and contact elements. Contact problem is considered to model the interface as two surfaces belonging to adherend and adhesive. Finite element analyses were performed for four different bond-length ratios (0.2,0.4,0.7 and 1.3). The results show that the stress components can be optimized using appropriate bond-length ratios. To validate the finite element analysis results, comparisons were made with available closed-form solutions. The numerical results were found in good agreement with the analytical solutions. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Finite element stress analysis Stress distribution Joint design
1. Introduction Structural adhesives have been used extensively in the space, aviation, automotive, and naval industries. Techniques reducing peeling and shear stress concentration are tapering the adherend, forming an adhesive fillet, changing the lap joint geometry, etc. However, these techniques can have some disadvantages. For example, tapering the adherend damages fiber structure of the fiber reinforced composites and forming an adhesive fillet is quite difficult when using low viscosity adhesives. An alternative technique is to use a combination of stiff and flexible adhesives along the bondline. The stiff adhesive should be located in the middle and flexible adhesive at the ends. High stress concentrations at the ends can be reduced using this technique. Hybrid-adhesive joints have been studied in a limited number of papers in the literature. Pires et al. [1] investigated a hybridadhesive joint with aluminum adherends using both experimental and numerical (finite element) techniques. They proved that joint strength can be optimized by choosing appropriate joint geometry and material. Fitton and Broughton [2] used a linear elastic 2D finite element method to compare hybrid and mono-adhesive bondlines. They showed that significant strength improvement can be obtained if joint failure stresses are considerably less than the shear strength
n
Corresponding author. Tel.: þ90 212 3832776; fax: þ90 212 2616659. ¨ zer). E-mail address: [email protected] (H. O
0143-7496/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijadhadh.2012.01.016
of the adhesive. Three dimensional finite element analyses of hybridadhesive joints under cleavage and tensile loading were carried out by Kong et al. [3]. They showed that maximum stresses along the bondline can be decreased using appropriate bond-length ratios. Also, they emphasized that it is necessary to take into account the change of loading modes when optimizing the hybrid-adhesive joint. Kumar [4] investigated the effect of functionally graded bondlines on the stress components in tubular joints. He suggested spatially controlling the modulus of the adhesive for optimization of the peeling and shear strengths. Variable flexibility and strength along the overlap length were described as an ideal adhesive joint by da Silva and Lopes [5]. They concluded that if the ductile adhesive has a joint strength lower than that of the brittle adhesive, a mixedadhesive joint with both adhesives gives a joint strength higher than the joint strength of the adhesives used individually. This synergetic effect can be explained by the shear stress distribution of the adhesive at failure. The effect of the hybrid-adhesive on the stress distribution of weld-bonded joints was studied by You et al. [6]. They showed that the load bearing capacity of the weld-bonded joints may be increased by transferring some parts of stress from the adhesive layer to the weld nugget. Da Silva and Adams [7] studied titanium/titanium and titanium/composite double lap joints formed using a hybrid-adhesive bondline. They showed that the suitable combination of two adhesives gives a better performance over a wide temperature range ( 55 1C–200 1C) than a high temperature adhesive alone for a joint with dissimilar adherends. Temiz [8] studied the effect of a hybrid-adhesive bondline on the strength of
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
double strap joints subjected to external bending moments. He concluded that stress concentration at the overlap ends decreases by applying the flexible adhesive towards the edges of the overlap in bonded joints. Using the flexible adhesive in bi-adhesively-bonded joints, the strains do not increase significantly when compared with increase in predicted failure load. This indicates that the adjacent stiffer adhesive has the constraining effect on the strain in the flexible adhesive. Das Neves et al. [9] developed an analytical model for hybrid-adhesive single and double lap joints subjected to low and high temperatures. They compared the solutions of the analytical model with a finite element analysis and observed only small differences close to the overlap ends where the maximum adhesive shear and peel stresses occurred. Even for a simple adhesive joint such as the single-lap joint, stresses are of three dimensional nature. This was investigated by Gonc- alves et al. [10] who performed threedimensional linear elastic finite element analysis of a single-lap joint. They showed that stress distributions in the overlap, near the free surface are quite different from those occurring in the interior. In this paper, the effect of a hybrid-adhesive bondline on the peeling stress (transverse normal stress) and shear stress distributions of the double lap joint was investigated using a three dimensional finite element model. The aim of the work is to develop a model of three-dimensional finite element analysis of double lap joint based on solid and contact elements, and demonstrate the three-dimensional nature of the stresses. Aluminum was used as adherend bonded with stiff and flexible adhesives. The stiff adhesive was located in the middle and the flexible adhesive was located at the ends. Finite element analyses were performed for four different bond-length ratios (0.2,0.4,0.7 and 1.3). The numerical analyses were performed using the Ansys finite element code. To validate the finite element analysis results, comparisons were made with available closed-form solutions. This study is part of a research project. The next step of this study is to perform an experimental work and validate the results with the experimental testing. The same geometry, material, and loading were used in this study as stated in the research project offer.
2. Finite element model Aluminum alloy 7075 was used as inner and outer adherends, and Hysol EA 9313 and Terokal 5045 epoxy adhesives, produced by Henkel, were used as stiff and flexible adhesives, respectively. Material properties of adherend and adhesives are given in Table 1 [10–13]. Geometry, dimensions and boundary conditions of the hybridadhesive double lap joint are shown in Fig. 1. The thickness of the adherends and adhesives are 1.5 mm and 0.25 mm, respectively. The total overlap length lt, 2l1 þl2, was taken as 12.5 mm. The bond-length ratios of the adhesive layer were varied as l1/l2 ¼0.2, 0.4, 0.7, 1.3, where l1 is the length of the flexible adhesive bondline and l2 is the length of the stiff adhesive bondline. Therefore, four different bondline configurations were investigated. Gonc- alves et al.
Table 1 Material properties of adherend and adhesives.
Modulus of elasticity (MPa) Shear strength (MPa) Poisson’s ratio Elongation at break (%)
Adherend (aluminum alloy 7075)
Flexible adhesive (Terokal 5045)
Stiff adhesive (Hysol EA 9313)
71700 152 0.33 10
437.4 20 0.38 11.3
2274 27.6 0.36 8
51
Fig. 1. Hybrid-adhesive double lap joint: (a) geometry and dimensions and (b) boundary conditions.
Fig. 2. Finite element model of the joint.
[10] analyzed a single-lap joint using the three-dimensional linear elastic finite element. They used a static force of 1.8 kN. A static force of 3.6 kN (two times 1.8 kN) was applied to the left side of the inner adherend. Half-symmetry boundary condition was used in order to reduce the solution time. This type of symmetry boundary conditions have been employed for the double lap joints in the literature [14–16]. The three-dimensional finite element analysis was performed using ANSYS. The finite element model of the joint is shown in Fig. 2. Adherends and adhesives were meshed with twenty-node solid elements (solid95). A refined mesh was used in the contacting surfaces in order to achieve the convergence and get more contact detection points. Five different meshing schemes were investigated to optimize number and size of the elements. The sizes of the elements were graded for the finer mesh in the critical regions. Finally, the element size near the stress concentration was set to 0.06 mm, which is fine enough to describe the severe stress variation near the critical regions. All elements in the bondlines of the adhesives were of equal size. This was important in order to prevent any problems as the graduation point of the bond-length ratios in the hybrid-adhesive bondlines varied. Four elements were used through the thickness of the adherends. The bondline was divided by three layers of elements. The mesh consisted of 119,880 elements and 347,165 nodes. Contact modeling of the overlap surfaces summarized below. The overlap surfaces of the adherends and the adhesives were modeled using surface to surface contact elements. Surface to surface contact elements use gauss integration points as a default,
52
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
which generally provide more accurate results than the nodal detection scheme, which uses the nodes themselves as the integration points. This type of contact transmits contact pressure between gauss points, and not forces between nodes. Contact pairs were created using contact element ‘‘CONTA174’’ and target element ‘‘TARGE170’’ between the adherends and adhesive overlap surfaces (see Fig. 3). CONTA174 elements were generated on the bottom and upper surfaces of adhesive. CONTA174 is a 3-D, 8-node, higher order quadrilateral element. TARGE170 elements were used on the overlap surfaces of the adherends. TARGE170 is used to represent various 3-D ‘‘target’’ surfaces for the associated contact element. Contact surfaces are in contact with the target surfaces. The difference between target surface and contact surface was that the contact surface is more deformable. The Penalty method was selected as the contact algorithm. Penalty function is a displacement-based solution and manages surface contact by adding springs to model each element gauss points. It deals with contact stiffness and penetration. When contact is involved, convergence is directly linked to the amount of penetration. To obtain a converged solution, penetration must be as small as possible. This can be obtained by increasing contact stiffness as much as possible. In ANSYS, contact stiffness is increased by the normal penalty stiffness factor (FKN), a default value of 1. Finite element analysis must be repeated to obtain the optimal convergence rate and acceptable penetration by changing FKN. In this study, the finite element model of mono-adhesive joints were used to determine the effect of FKN on the optimal convergence rate and acceptable penetration, where the mono-adhesive means that one-type adhesive was used in the overlap region. Analyses were repeated by increasing the value of FKN. According to the results from repeated analyses, FKN was set to 107. Contact surface behavior was chosen as ‘‘Bonded always’’. Bonded always contact brings first the target and contact surfaces together to eliminate the gap, and then permanently holds the surfaces together. Sliding is not permitted [17,18]. Debonding of two surfaces was not considered in this study. This study dealt with a comparative study of the shear and peeling stress distributions along the mono and hybrid-adhesive bondlines, and also the stress distributions along the midplane and the bottom plane of the adhesive thickness, bottom plane in the rest of the paper. However, the stresses at the upper plane of the adhesive thickness were also studied to confirm the critical plane of the adhesive thickness. All the stress components were plotted along the upper plane and compared with the same stress components of the bottom plane. The results showed that the peak values of the stress components at the bottom plane are much higher than the peak values of the stress components at the upper plane. According to these results, the bottom plane is more critical from the upper plane. Therefore, the distributions of the stress components at the bottom plane are showed in this study. Schematic representation of the adhesive layer is seen in Fig. 4. The values of the stress components change with the z coordinate. Table 2 shows different fixed z values in the transverse
Fig. 4. Schematic representation of the adhesive layer.
Table 2 Z-coordinate values corresponding to stress peaks (all dimensions in mm). Peeling stress
Shear stress
Midplane Flexible adhesive Stiff adhesive
3.5, 21.5 2.5, 22.5
0, 25 0, 25
Bottom plane Flexible adhesive Stiff adhesive
1.5, 23.5 1.5, 23.5
1.5, 23.5 1.5, 23.5
coordinate (z), where the peeling and shear stresses reach their maximum values. All the stresses data were obtained from the midplane and the bottom plane. Using these z values (z¼constant), the distributions of the stress components were plotted along the bondline. The distributions of the stress components for the hybrid and mono-adhesive joints along the bondline are given in the same figures. All the stress components were normalized with respect to average shear stress (tavg). In the figures, stiff and flexible adhesive correspond to the mono-adhesives. As seen in Table 2, the maximum peeling stress of the stiff adhesive midplane occurs at the longitudinal line of z¼2.5 mm (line ST in Fig. 4) and z¼22.5 mm, however the maximum peeling stress of the flexible adhesive midplane occurs at the longitudinal line of z¼3.5 mm and z¼ 21.5 mm. In addition, the maximum shear stress of the stiff and flexible adhesive midplanes occur at the longitudinal line of z¼0 (line FG in Fig. 4) and z¼25 mm(line EH in Fig. 4). In the bottom plane, both maximum peeling and shear stresses occur at the same longitudinal line of z¼1.5 mm (line PR in Fig. 4) and z¼23.5 mm for the stiff and flexible adhesives (see also Fig. 5). Although the peeling stress peaks at z¼ 3.5 mm for the flexible adhesive midplane and at z¼2.5 mm for the stiff adhesive midplane, the difference between the peak values of the peeling stress at z¼2.5 mm and z¼3.5 mm for the flexible adhesive midplane is very small (1.38%). Therefore, for the comparative study of the stress values along the mono and hybrid adhesive bondlines, the peeling stress distributions at z ¼3.5 mm were not considered. The peeling stress distributions were plotted at z ¼2.5 mm for the flexible adhesive midplane.
3. Results and discussion
Fig. 3. Modeling scheme of the overlap surfaces.
In this section, the peeling and shear stress components are firstly plotted at the adhesive midplane in Figs. 6 and 7. Secondly,
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
Fig. 5. Shear and peeling stress distributions across the adhesive in the stiff and flexible adhesive bondlines: (a) midplane and (b) bottom plane.
Fig. 6. Normalized stress distributions at the adhesive midplane along the longitudinal line of z ¼0: (a) shear stress and (b) peeling stress.
53
Fig. 7. Normalized stress distributions at the adhesive midplane along the longitudinal line of z ¼2.5 mm: (a) shear stress and (b) peeling stress.
these stress components were also plotted at the bottom plane along the bondline in Fig. 8. Finally, the results from the finite element analysis were compared and discussed with those of Volkersen and Tsai, Oplinger and Morton (hereafter referred to as TOM) [19] closed-form solutions (Fig. 9). Figs. 6 and 7 show the distributions of the stress components at the adhesive midplane (y¼ 0.125 mm) along the bondline, where z¼0 for Fig. 6 (line FG in Fig. 4) and z¼ 2.5 mm for Fig. 7 (line ST in Fig. 4). The distributions of the stress components for the hybrid and mono-adhesive joints along the bondline are given in the same figures. The stress distributions for the flexible adhesive are more uniform than those for the stiff adhesive and asymmetrical at the adhesive midplane. In the mono-adhesive bondline, the maximum shear and peeling stresses occur close to the left side of the overlap region. However, in the hybridadhesive bondline, these stress components peak between the adhesives. The maximum stress components are higher near the side of the applied load, as seen in Figs. 6 and 7. As seen in Figs. 6(a) and 7(a), the shear stress in the stiff adhesive part of the hybrid-adhesive bondline is higher than that in the stiff mono-adhesive bondline. However, values of the shear stress are lower than those in the flexible mono-adhesive bondline. Peak values of shear stress increase for all four bond-length ratios. Also, it is seen that the position of the maximum shear stress in the mono adhesive bondline moves from the ends of the overlap to a new position between adhesives in the hybrid adhesive bondlines. Figs. 6(b) and 7(b) show the distributions of the peeling stress along the bondline. Peeling stress in the stiff and flexible adhesive parts of hybrid-adhesive bondline are lower than that in the stiff and flexible mono-adhesive bondlines. Peak values of peeling stress decrease for the ratios l1/l2 ¼0.2,0.4 and 0.7, but increase for the ratio l1/l2 ¼1.3.
54
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
Fig. 8. Normalized stress distributions at the bottom plane along the longitudinal line of z ¼ 1.5 mm: (a) shear stress and (b) peeling stress.
Secondly, at the bottom plane the effects of the hybrid adhesive bondline on the peel and shear stresses are studied in Fig. 8. These stress components were plotted at the longitudinal line of z¼1.5 mm (line PR in Fig. 4) along the bondline. It is seen in Fig. 8 that maximum values of the stress components occur at the left end of overlap for the mono-adhesive bondline. However, in the hybridadhesive bondlines, the peak values of stress components occur between the adhesives. It is noted that stress components in the stiff and flexible adhesive parts of the hybrid-adhesive bondline are lower than those in the stiff and flexible mono-adhesive bondlines. As seen in Fig. 8(a), the peak value of the shear stress decreases for the ratios l1/l2 ¼0.2,0.4 and 0.7, but increases for the ratio l1/l2 ¼1.3. The peak value of the peeling stress decreases for all four bondlength ratios (see Fig. 8(b)). It is also observed that the peak stresses at the bottom plane are much higher than those at the midplane. Finally, in order to compare and validate the results of this study, a comparison was made between the shear stress results in mono adhesive bondlines and the analytical solutions of Volkersen and TOM (see Fig. 9). The shear stresses values of the stiff and flexible adhesive were taken from the adhesive midplane at the longitudinal line of z ¼0 (line FG in Fig. 4) and z¼12.5 mm (line VY in Fig. 4). As seen in Fig. 9(a), close to the ends of the stiff adhesive bondline, the shear stress value of Volkersen shear lag model is higher than that of the TOM model. However, both the shear stress distributions coincide for the flexible adhesive bondline (see Fig. 9(b)). Compared with the classical solutions, shear stress at path2 is predicted to be higher by the finite element analysis. This shows the high stress gradients near the ends of the overlap and highlights the three-dimensional nature of the stresses. Therefore, predictions based on the classical solutions underestimate shear stress concentrations near the ends of the overlap and do not satisfy the free surface shear stress condition.
4. Conclusions This paper described the preliminary stage of a research project. A three dimensional model of a double lap joint based on solid and contact elements was presented. Finite element analyses were performed for four different bond-length ratios (0.2, 0.4, 0.7 and 1.3). The effect of the bondline configuration in the hybrid joint model on the stress distributions was discussed and compared. The results show measurable decrease in the stress components of the hybrid adhesive joints compared with those in which single adhesives were used over the full length of the bondline. The results from the numerical analysis highlight the three-dimensional nature of the stresses and show that the stress components can be optimized using appropriate bond-length ratios. It is seen that the position of the maximum shear stress in mono adhesive bondline moves to a new position between adhesives in hybrid adhesive bondline. As expected, the maximum stress components give higher values near the side of the applied load. In order to test the presented modeling technique and the results from the finite element analysis, the shear stress values in mono adhesive bondlines were compared with closed-form solutions. The results were in good agreement with those obtained from the Volkersen and TOM models. Further research will be focused on performing an experimental work and validate these numerical results.
Acknowledgments
Fig. 9. Comparisons between the finite element results and the analytical solutions of Volkersen and TOM: (a) stiff adhesive and (b) flexible adhesive.
The authors are grateful to reviewers for their valuable comments on this article. This work was funded by Yıldız Technical University under research project no. 2011-06-01-DOP04.
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
References [1] Pires I, Quintino L, Durodola JF, Beevers A. Performance of bi-adhesive bonded aluminium lap joints. Int J Adhes Adhes 2003;23:215–23. [2] Fitton MD, Broughton JG. Variable modulus adhesives: an approach to optimized joint performance. Int J Adhes Adhes 2005;25:329–36. [3] Kong F, You M, Zheng X. Three-dimensional finite element analysis of the stress distribution in bi-adhesive bonded joints. J Adhes 2008;84:105–24. [4] Kumar S. Analysis of tubular adhesive joints with a functionally modulus graded bondline subjected to axial loads. Int J Adhes Adhes 2009;29:785–95. [5] da Silva LFM, Lopes MCQ. Joint strength optimization by the mixed-adhesive technique. Int J Adhes Adhes 2009;29:509–14. [6] You M, Yan J, Zheng X, Zhu D, Li J, Hu J. The numerical analysis on the weldbonded joints with bi-adhesive. In: Proceedings of seco nd international conference on computer modeling and simulation. Sanya, China; 22–24 January 2010. [7] da Silva LFM, Adams RD. Adhesive joints at high and low temperatures using similar and dissimilar adherends and dual adhesives. Int J Adhes Adhes 2007;27:216–26. [8] Temiz S- . Application of bi-adhesive in double-strap joints subjected to bending moment. J Adhesion Sci Technol 2006;20:1547–60. [9] das Neves PJC, da Silva LFM, Adams RD. Analysis of mixed adhesive bonded Joints Part I: theoretical formulation. J Adhes Sci Technol 2009;23:1–34.
55
[10] Gonc- alves JPM, de Moura MFSF, de Castro PMST. A three-dimensional finite element model for stress analysis of adhesive joints. Int J Adhes Adhes 2002;22:357–65. [11] Gonc- alves JPM, de Moura MFSF, Magalhaes AG, de Castro PMST. Application of interface finite elements to three-dimensional progressive failure analysis of adhesive joints. Fatigue Fract Eng Mater Struc 2003;26:479–86. [12] /www.matweb.comS. (January 2011). [13] /www.henkelna.comS. (January 2011). [14] de Castro J, Keller T. Ductile double-lap joints from brittle GFRP laminates and ductile adhesives, Part II: numerical investigation and joint strength prediction. Compost Part B 2008;39:282–91. [15] Campilho RDSG, Banea MD, Pinto AMG, da Silva LFM, de Jesus AMP. Strength prediction of single- and double-lap joints by standard and extended finite element modelling. Int J Adhes Adhes 2011;31:363–72. [16] Adams RD, Peppiatt NA. Stress analysis of adhesive-bonded lap joints. J Strain Anal Eng Des 1974;9:185–96. [17] Contact technology guide. Release 12.0, SAS IP, U.S.A.; 2009. [18] Lanoue F, Vadean A, Sanschagrin B. Finite element analysis and contact modeling considerations of interference fits for fretting fatigue strength calculations. Simulation Model Pract Theory 2009;17:1587–602. [19] Zhu Y, Kedward K. Methods of analysis and failure predictions for adhesively bonded joints of uniform and variable bondline thickness, Repot no., DOT/ FAA/AR-05/12. Department of Mechanical & Environmental Engineering. University of California. Santa Barbara; 2005.
Contents lists available at SciVerse ScienceDirect
International Journal of Adhesion & Adhesives journal homepage: www.elsevier.com/locate/ijadhadh
Three dimensional finite element analysis of bi-adhesively bonded double lap joint ¨ zer a,n, O ¨ zkan O ¨zb Halil O a b
Mechanical Engineering Department, Faculty of Mechanical Engineering, Yıldız Technical University, Barbaros Bulvarı, 34349 Yıldız, Istanbul, Turkey Machine Education Division, Faculty of Technical Education, Karabuk University, Balıklarkayası mevkii, 78050 Karabuk, Turkey
a r t i c l e i n f o
a b s t r a c t
Available online 21 January 2012
Hybrid-adhesive joints are an alternative stress reduction technique for adhesively bonded joints. The joints have two types of adhesives in the overlap region. The stiff adhesive should be located in the middle and flexible adhesive at the ends. In this study, the effect of the hybrid-adhesive bondline on the shear and peeling stresses of a double lap joint were investigated using a three-dimensional finite element model. We developed a three dimensional model of the double lap joint based on solid and contact elements. Contact problem is considered to model the interface as two surfaces belonging to adherend and adhesive. Finite element analyses were performed for four different bond-length ratios (0.2,0.4,0.7 and 1.3). The results show that the stress components can be optimized using appropriate bond-length ratios. To validate the finite element analysis results, comparisons were made with available closed-form solutions. The numerical results were found in good agreement with the analytical solutions. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Finite element stress analysis Stress distribution Joint design
1. Introduction Structural adhesives have been used extensively in the space, aviation, automotive, and naval industries. Techniques reducing peeling and shear stress concentration are tapering the adherend, forming an adhesive fillet, changing the lap joint geometry, etc. However, these techniques can have some disadvantages. For example, tapering the adherend damages fiber structure of the fiber reinforced composites and forming an adhesive fillet is quite difficult when using low viscosity adhesives. An alternative technique is to use a combination of stiff and flexible adhesives along the bondline. The stiff adhesive should be located in the middle and flexible adhesive at the ends. High stress concentrations at the ends can be reduced using this technique. Hybrid-adhesive joints have been studied in a limited number of papers in the literature. Pires et al. [1] investigated a hybridadhesive joint with aluminum adherends using both experimental and numerical (finite element) techniques. They proved that joint strength can be optimized by choosing appropriate joint geometry and material. Fitton and Broughton [2] used a linear elastic 2D finite element method to compare hybrid and mono-adhesive bondlines. They showed that significant strength improvement can be obtained if joint failure stresses are considerably less than the shear strength
n
Corresponding author. Tel.: þ90 212 3832776; fax: þ90 212 2616659. ¨ zer). E-mail address: [email protected] (H. O
0143-7496/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijadhadh.2012.01.016
of the adhesive. Three dimensional finite element analyses of hybridadhesive joints under cleavage and tensile loading were carried out by Kong et al. [3]. They showed that maximum stresses along the bondline can be decreased using appropriate bond-length ratios. Also, they emphasized that it is necessary to take into account the change of loading modes when optimizing the hybrid-adhesive joint. Kumar [4] investigated the effect of functionally graded bondlines on the stress components in tubular joints. He suggested spatially controlling the modulus of the adhesive for optimization of the peeling and shear strengths. Variable flexibility and strength along the overlap length were described as an ideal adhesive joint by da Silva and Lopes [5]. They concluded that if the ductile adhesive has a joint strength lower than that of the brittle adhesive, a mixedadhesive joint with both adhesives gives a joint strength higher than the joint strength of the adhesives used individually. This synergetic effect can be explained by the shear stress distribution of the adhesive at failure. The effect of the hybrid-adhesive on the stress distribution of weld-bonded joints was studied by You et al. [6]. They showed that the load bearing capacity of the weld-bonded joints may be increased by transferring some parts of stress from the adhesive layer to the weld nugget. Da Silva and Adams [7] studied titanium/titanium and titanium/composite double lap joints formed using a hybrid-adhesive bondline. They showed that the suitable combination of two adhesives gives a better performance over a wide temperature range ( 55 1C–200 1C) than a high temperature adhesive alone for a joint with dissimilar adherends. Temiz [8] studied the effect of a hybrid-adhesive bondline on the strength of
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
double strap joints subjected to external bending moments. He concluded that stress concentration at the overlap ends decreases by applying the flexible adhesive towards the edges of the overlap in bonded joints. Using the flexible adhesive in bi-adhesively-bonded joints, the strains do not increase significantly when compared with increase in predicted failure load. This indicates that the adjacent stiffer adhesive has the constraining effect on the strain in the flexible adhesive. Das Neves et al. [9] developed an analytical model for hybrid-adhesive single and double lap joints subjected to low and high temperatures. They compared the solutions of the analytical model with a finite element analysis and observed only small differences close to the overlap ends where the maximum adhesive shear and peel stresses occurred. Even for a simple adhesive joint such as the single-lap joint, stresses are of three dimensional nature. This was investigated by Gonc- alves et al. [10] who performed threedimensional linear elastic finite element analysis of a single-lap joint. They showed that stress distributions in the overlap, near the free surface are quite different from those occurring in the interior. In this paper, the effect of a hybrid-adhesive bondline on the peeling stress (transverse normal stress) and shear stress distributions of the double lap joint was investigated using a three dimensional finite element model. The aim of the work is to develop a model of three-dimensional finite element analysis of double lap joint based on solid and contact elements, and demonstrate the three-dimensional nature of the stresses. Aluminum was used as adherend bonded with stiff and flexible adhesives. The stiff adhesive was located in the middle and the flexible adhesive was located at the ends. Finite element analyses were performed for four different bond-length ratios (0.2,0.4,0.7 and 1.3). The numerical analyses were performed using the Ansys finite element code. To validate the finite element analysis results, comparisons were made with available closed-form solutions. This study is part of a research project. The next step of this study is to perform an experimental work and validate the results with the experimental testing. The same geometry, material, and loading were used in this study as stated in the research project offer.
2. Finite element model Aluminum alloy 7075 was used as inner and outer adherends, and Hysol EA 9313 and Terokal 5045 epoxy adhesives, produced by Henkel, were used as stiff and flexible adhesives, respectively. Material properties of adherend and adhesives are given in Table 1 [10–13]. Geometry, dimensions and boundary conditions of the hybridadhesive double lap joint are shown in Fig. 1. The thickness of the adherends and adhesives are 1.5 mm and 0.25 mm, respectively. The total overlap length lt, 2l1 þl2, was taken as 12.5 mm. The bond-length ratios of the adhesive layer were varied as l1/l2 ¼0.2, 0.4, 0.7, 1.3, where l1 is the length of the flexible adhesive bondline and l2 is the length of the stiff adhesive bondline. Therefore, four different bondline configurations were investigated. Gonc- alves et al.
Table 1 Material properties of adherend and adhesives.
Modulus of elasticity (MPa) Shear strength (MPa) Poisson’s ratio Elongation at break (%)
Adherend (aluminum alloy 7075)
Flexible adhesive (Terokal 5045)
Stiff adhesive (Hysol EA 9313)
71700 152 0.33 10
437.4 20 0.38 11.3
2274 27.6 0.36 8
51
Fig. 1. Hybrid-adhesive double lap joint: (a) geometry and dimensions and (b) boundary conditions.
Fig. 2. Finite element model of the joint.
[10] analyzed a single-lap joint using the three-dimensional linear elastic finite element. They used a static force of 1.8 kN. A static force of 3.6 kN (two times 1.8 kN) was applied to the left side of the inner adherend. Half-symmetry boundary condition was used in order to reduce the solution time. This type of symmetry boundary conditions have been employed for the double lap joints in the literature [14–16]. The three-dimensional finite element analysis was performed using ANSYS. The finite element model of the joint is shown in Fig. 2. Adherends and adhesives were meshed with twenty-node solid elements (solid95). A refined mesh was used in the contacting surfaces in order to achieve the convergence and get more contact detection points. Five different meshing schemes were investigated to optimize number and size of the elements. The sizes of the elements were graded for the finer mesh in the critical regions. Finally, the element size near the stress concentration was set to 0.06 mm, which is fine enough to describe the severe stress variation near the critical regions. All elements in the bondlines of the adhesives were of equal size. This was important in order to prevent any problems as the graduation point of the bond-length ratios in the hybrid-adhesive bondlines varied. Four elements were used through the thickness of the adherends. The bondline was divided by three layers of elements. The mesh consisted of 119,880 elements and 347,165 nodes. Contact modeling of the overlap surfaces summarized below. The overlap surfaces of the adherends and the adhesives were modeled using surface to surface contact elements. Surface to surface contact elements use gauss integration points as a default,
52
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
which generally provide more accurate results than the nodal detection scheme, which uses the nodes themselves as the integration points. This type of contact transmits contact pressure between gauss points, and not forces between nodes. Contact pairs were created using contact element ‘‘CONTA174’’ and target element ‘‘TARGE170’’ between the adherends and adhesive overlap surfaces (see Fig. 3). CONTA174 elements were generated on the bottom and upper surfaces of adhesive. CONTA174 is a 3-D, 8-node, higher order quadrilateral element. TARGE170 elements were used on the overlap surfaces of the adherends. TARGE170 is used to represent various 3-D ‘‘target’’ surfaces for the associated contact element. Contact surfaces are in contact with the target surfaces. The difference between target surface and contact surface was that the contact surface is more deformable. The Penalty method was selected as the contact algorithm. Penalty function is a displacement-based solution and manages surface contact by adding springs to model each element gauss points. It deals with contact stiffness and penetration. When contact is involved, convergence is directly linked to the amount of penetration. To obtain a converged solution, penetration must be as small as possible. This can be obtained by increasing contact stiffness as much as possible. In ANSYS, contact stiffness is increased by the normal penalty stiffness factor (FKN), a default value of 1. Finite element analysis must be repeated to obtain the optimal convergence rate and acceptable penetration by changing FKN. In this study, the finite element model of mono-adhesive joints were used to determine the effect of FKN on the optimal convergence rate and acceptable penetration, where the mono-adhesive means that one-type adhesive was used in the overlap region. Analyses were repeated by increasing the value of FKN. According to the results from repeated analyses, FKN was set to 107. Contact surface behavior was chosen as ‘‘Bonded always’’. Bonded always contact brings first the target and contact surfaces together to eliminate the gap, and then permanently holds the surfaces together. Sliding is not permitted [17,18]. Debonding of two surfaces was not considered in this study. This study dealt with a comparative study of the shear and peeling stress distributions along the mono and hybrid-adhesive bondlines, and also the stress distributions along the midplane and the bottom plane of the adhesive thickness, bottom plane in the rest of the paper. However, the stresses at the upper plane of the adhesive thickness were also studied to confirm the critical plane of the adhesive thickness. All the stress components were plotted along the upper plane and compared with the same stress components of the bottom plane. The results showed that the peak values of the stress components at the bottom plane are much higher than the peak values of the stress components at the upper plane. According to these results, the bottom plane is more critical from the upper plane. Therefore, the distributions of the stress components at the bottom plane are showed in this study. Schematic representation of the adhesive layer is seen in Fig. 4. The values of the stress components change with the z coordinate. Table 2 shows different fixed z values in the transverse
Fig. 4. Schematic representation of the adhesive layer.
Table 2 Z-coordinate values corresponding to stress peaks (all dimensions in mm). Peeling stress
Shear stress
Midplane Flexible adhesive Stiff adhesive
3.5, 21.5 2.5, 22.5
0, 25 0, 25
Bottom plane Flexible adhesive Stiff adhesive
1.5, 23.5 1.5, 23.5
1.5, 23.5 1.5, 23.5
coordinate (z), where the peeling and shear stresses reach their maximum values. All the stresses data were obtained from the midplane and the bottom plane. Using these z values (z¼constant), the distributions of the stress components were plotted along the bondline. The distributions of the stress components for the hybrid and mono-adhesive joints along the bondline are given in the same figures. All the stress components were normalized with respect to average shear stress (tavg). In the figures, stiff and flexible adhesive correspond to the mono-adhesives. As seen in Table 2, the maximum peeling stress of the stiff adhesive midplane occurs at the longitudinal line of z¼2.5 mm (line ST in Fig. 4) and z¼22.5 mm, however the maximum peeling stress of the flexible adhesive midplane occurs at the longitudinal line of z¼3.5 mm and z¼ 21.5 mm. In addition, the maximum shear stress of the stiff and flexible adhesive midplanes occur at the longitudinal line of z¼0 (line FG in Fig. 4) and z¼25 mm(line EH in Fig. 4). In the bottom plane, both maximum peeling and shear stresses occur at the same longitudinal line of z¼1.5 mm (line PR in Fig. 4) and z¼23.5 mm for the stiff and flexible adhesives (see also Fig. 5). Although the peeling stress peaks at z¼ 3.5 mm for the flexible adhesive midplane and at z¼2.5 mm for the stiff adhesive midplane, the difference between the peak values of the peeling stress at z¼2.5 mm and z¼3.5 mm for the flexible adhesive midplane is very small (1.38%). Therefore, for the comparative study of the stress values along the mono and hybrid adhesive bondlines, the peeling stress distributions at z ¼3.5 mm were not considered. The peeling stress distributions were plotted at z ¼2.5 mm for the flexible adhesive midplane.
3. Results and discussion
Fig. 3. Modeling scheme of the overlap surfaces.
In this section, the peeling and shear stress components are firstly plotted at the adhesive midplane in Figs. 6 and 7. Secondly,
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
Fig. 5. Shear and peeling stress distributions across the adhesive in the stiff and flexible adhesive bondlines: (a) midplane and (b) bottom plane.
Fig. 6. Normalized stress distributions at the adhesive midplane along the longitudinal line of z ¼0: (a) shear stress and (b) peeling stress.
53
Fig. 7. Normalized stress distributions at the adhesive midplane along the longitudinal line of z ¼2.5 mm: (a) shear stress and (b) peeling stress.
these stress components were also plotted at the bottom plane along the bondline in Fig. 8. Finally, the results from the finite element analysis were compared and discussed with those of Volkersen and Tsai, Oplinger and Morton (hereafter referred to as TOM) [19] closed-form solutions (Fig. 9). Figs. 6 and 7 show the distributions of the stress components at the adhesive midplane (y¼ 0.125 mm) along the bondline, where z¼0 for Fig. 6 (line FG in Fig. 4) and z¼ 2.5 mm for Fig. 7 (line ST in Fig. 4). The distributions of the stress components for the hybrid and mono-adhesive joints along the bondline are given in the same figures. The stress distributions for the flexible adhesive are more uniform than those for the stiff adhesive and asymmetrical at the adhesive midplane. In the mono-adhesive bondline, the maximum shear and peeling stresses occur close to the left side of the overlap region. However, in the hybridadhesive bondline, these stress components peak between the adhesives. The maximum stress components are higher near the side of the applied load, as seen in Figs. 6 and 7. As seen in Figs. 6(a) and 7(a), the shear stress in the stiff adhesive part of the hybrid-adhesive bondline is higher than that in the stiff mono-adhesive bondline. However, values of the shear stress are lower than those in the flexible mono-adhesive bondline. Peak values of shear stress increase for all four bond-length ratios. Also, it is seen that the position of the maximum shear stress in the mono adhesive bondline moves from the ends of the overlap to a new position between adhesives in the hybrid adhesive bondlines. Figs. 6(b) and 7(b) show the distributions of the peeling stress along the bondline. Peeling stress in the stiff and flexible adhesive parts of hybrid-adhesive bondline are lower than that in the stiff and flexible mono-adhesive bondlines. Peak values of peeling stress decrease for the ratios l1/l2 ¼0.2,0.4 and 0.7, but increase for the ratio l1/l2 ¼1.3.
54
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
Fig. 8. Normalized stress distributions at the bottom plane along the longitudinal line of z ¼ 1.5 mm: (a) shear stress and (b) peeling stress.
Secondly, at the bottom plane the effects of the hybrid adhesive bondline on the peel and shear stresses are studied in Fig. 8. These stress components were plotted at the longitudinal line of z¼1.5 mm (line PR in Fig. 4) along the bondline. It is seen in Fig. 8 that maximum values of the stress components occur at the left end of overlap for the mono-adhesive bondline. However, in the hybridadhesive bondlines, the peak values of stress components occur between the adhesives. It is noted that stress components in the stiff and flexible adhesive parts of the hybrid-adhesive bondline are lower than those in the stiff and flexible mono-adhesive bondlines. As seen in Fig. 8(a), the peak value of the shear stress decreases for the ratios l1/l2 ¼0.2,0.4 and 0.7, but increases for the ratio l1/l2 ¼1.3. The peak value of the peeling stress decreases for all four bondlength ratios (see Fig. 8(b)). It is also observed that the peak stresses at the bottom plane are much higher than those at the midplane. Finally, in order to compare and validate the results of this study, a comparison was made between the shear stress results in mono adhesive bondlines and the analytical solutions of Volkersen and TOM (see Fig. 9). The shear stresses values of the stiff and flexible adhesive were taken from the adhesive midplane at the longitudinal line of z ¼0 (line FG in Fig. 4) and z¼12.5 mm (line VY in Fig. 4). As seen in Fig. 9(a), close to the ends of the stiff adhesive bondline, the shear stress value of Volkersen shear lag model is higher than that of the TOM model. However, both the shear stress distributions coincide for the flexible adhesive bondline (see Fig. 9(b)). Compared with the classical solutions, shear stress at path2 is predicted to be higher by the finite element analysis. This shows the high stress gradients near the ends of the overlap and highlights the three-dimensional nature of the stresses. Therefore, predictions based on the classical solutions underestimate shear stress concentrations near the ends of the overlap and do not satisfy the free surface shear stress condition.
4. Conclusions This paper described the preliminary stage of a research project. A three dimensional model of a double lap joint based on solid and contact elements was presented. Finite element analyses were performed for four different bond-length ratios (0.2, 0.4, 0.7 and 1.3). The effect of the bondline configuration in the hybrid joint model on the stress distributions was discussed and compared. The results show measurable decrease in the stress components of the hybrid adhesive joints compared with those in which single adhesives were used over the full length of the bondline. The results from the numerical analysis highlight the three-dimensional nature of the stresses and show that the stress components can be optimized using appropriate bond-length ratios. It is seen that the position of the maximum shear stress in mono adhesive bondline moves to a new position between adhesives in hybrid adhesive bondline. As expected, the maximum stress components give higher values near the side of the applied load. In order to test the presented modeling technique and the results from the finite element analysis, the shear stress values in mono adhesive bondlines were compared with closed-form solutions. The results were in good agreement with those obtained from the Volkersen and TOM models. Further research will be focused on performing an experimental work and validate these numerical results.
Acknowledgments
Fig. 9. Comparisons between the finite element results and the analytical solutions of Volkersen and TOM: (a) stiff adhesive and (b) flexible adhesive.
The authors are grateful to reviewers for their valuable comments on this article. This work was funded by Yıldız Technical University under research project no. 2011-06-01-DOP04.
¨ zer, O ¨. O ¨ z / International Journal of Adhesion & Adhesives 37 (2012) 50–55 H. O
References [1] Pires I, Quintino L, Durodola JF, Beevers A. Performance of bi-adhesive bonded aluminium lap joints. Int J Adhes Adhes 2003;23:215–23. [2] Fitton MD, Broughton JG. Variable modulus adhesives: an approach to optimized joint performance. Int J Adhes Adhes 2005;25:329–36. [3] Kong F, You M, Zheng X. Three-dimensional finite element analysis of the stress distribution in bi-adhesive bonded joints. J Adhes 2008;84:105–24. [4] Kumar S. Analysis of tubular adhesive joints with a functionally modulus graded bondline subjected to axial loads. Int J Adhes Adhes 2009;29:785–95. [5] da Silva LFM, Lopes MCQ. Joint strength optimization by the mixed-adhesive technique. Int J Adhes Adhes 2009;29:509–14. [6] You M, Yan J, Zheng X, Zhu D, Li J, Hu J. The numerical analysis on the weldbonded joints with bi-adhesive. In: Proceedings of seco nd international conference on computer modeling and simulation. Sanya, China; 22–24 January 2010. [7] da Silva LFM, Adams RD. Adhesive joints at high and low temperatures using similar and dissimilar adherends and dual adhesives. Int J Adhes Adhes 2007;27:216–26. [8] Temiz S- . Application of bi-adhesive in double-strap joints subjected to bending moment. J Adhesion Sci Technol 2006;20:1547–60. [9] das Neves PJC, da Silva LFM, Adams RD. Analysis of mixed adhesive bonded Joints Part I: theoretical formulation. J Adhes Sci Technol 2009;23:1–34.
55
[10] Gonc- alves JPM, de Moura MFSF, de Castro PMST. A three-dimensional finite element model for stress analysis of adhesive joints. Int J Adhes Adhes 2002;22:357–65. [11] Gonc- alves JPM, de Moura MFSF, Magalhaes AG, de Castro PMST. Application of interface finite elements to three-dimensional progressive failure analysis of adhesive joints. Fatigue Fract Eng Mater Struc 2003;26:479–86. [12] /www.matweb.comS. (January 2011). [13] /www.henkelna.comS. (January 2011). [14] de Castro J, Keller T. Ductile double-lap joints from brittle GFRP laminates and ductile adhesives, Part II: numerical investigation and joint strength prediction. Compost Part B 2008;39:282–91. [15] Campilho RDSG, Banea MD, Pinto AMG, da Silva LFM, de Jesus AMP. Strength prediction of single- and double-lap joints by standard and extended finite element modelling. Int J Adhes Adhes 2011;31:363–72. [16] Adams RD, Peppiatt NA. Stress analysis of adhesive-bonded lap joints. J Strain Anal Eng Des 1974;9:185–96. [17] Contact technology guide. Release 12.0, SAS IP, U.S.A.; 2009. [18] Lanoue F, Vadean A, Sanschagrin B. Finite element analysis and contact modeling considerations of interference fits for fretting fatigue strength calculations. Simulation Model Pract Theory 2009;17:1587–602. [19] Zhu Y, Kedward K. Methods of analysis and failure predictions for adhesively bonded joints of uniform and variable bondline thickness, Repot no., DOT/ FAA/AR-05/12. Department of Mechanical & Environmental Engineering. University of California. Santa Barbara; 2005.