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A numerical and experimental study of gap length on adhesively bonded aluminum double-lap joint
ARTICLE IN PRESS
International Journal of Adhesion & Adhesives 27 (2007) 696–702 www.elsevier.com/locate/ijadhadh
A numerical and experimental study of gap length on adhesively bonded aluminum double-lap joint Min You, Zhan-Mou Yan, Xiao-Ling Zheng, Hai-Zhou Yu, Zhi Li College of Mechanical and Material Engineering, China Three Gorges University, Yichang 443002, China Accepted 17 February 2007 Available online 2 March 2007
Abstract The elastic finite element analysis (FEA) and the experimental method were used to investigate the effect of the gap, as well as its length, on the stress distribution in both the mid-bondline and the adherend near the interface along the lap zone of adhesively bonded aluminum double-lap joint. The values of the peak stresses distributed in the mid-bondline were increased a little when an 8 mm length gap was arranged symmetrically around the center of the lap zone. Both peak stresses and stress at the point close to the edge of the gap in the mid-bondline were increased when the gap length was increased, but the increment of the peak stresses was small when the lap length was not greater than 16 mm. The results from the FEA simulation showed that the effect of the gap length on the ultimate load of the joint was small as the gap length was increased. It is supported with the results from the experiments that the ultimate load of the aluminum double-lap joint decreased a little when the gap length was less than 12 mm. r 2007 Elsevier Ltd. All rights reserved. Keywords: Epoxy; Aluminum and alloy; Finite element analysis; Gap length
1. Introduction Adhesive bonding technology is widely used today in almost all the industries fields of the world and this is mainly due to its high strength–weight ratio, low cost and high efficiency [1]. In recent years, the studies related to the effect of gap (recessing) in the bondline on the mechanical properties of adhesively bonded joint was mainly from viewpoint of treating the gap as a defect in the joint and they mainly focused on the single-lap joint [2–4]. Olia and Rossetos [2] reported that the effect of the gap on peak stresses of the peel stress and the shear stress in single-lap joint under bending was small, unless it was sufficiently close to the end of the lap zone. Lang and Mallick [3] discussed that the effect of the gap on peak stress of the joint under tensile load was negligible compared with the result from the finite element method. The results of de Moura et al. [4] from experiments and numerical simulation showed that the influence of the gap length and width on nominal strength of the joint was less. In our earlier work [5], the intermittent Corresponding author. Tel.: +86 717 639 2004; fax: +86 717 639 5410.
E-mail address: [email protected] (M. You). 0143-7496/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijadhadh.2007.02.005
(or gapped) bonding technology is introduced. It demonstrated that the joint bonded by a reasonable intermittent adhesive layer may increase the actual strength (the ultimate load over the real area of the adhesive layer) markedly and for this, it used experiments and the finite element analysis (FEA). It is known that the double-lap joint is widely used today in aeronautical and other industries [6,7] for avoiding the great eccentricity of stress that occurred in the single-lap joint. In practice, a hole or gap in the adhesive is often discovered by the non-destructive test (NDT) and the loadcarrying capacity of the joint is significantly affected by these, hole and gap. It is necessary to study the mechanical behavior of the double-lap joint with a gap and see how significant it is. The aim of this work is to investigate the effect of the gap as well as its length on the stress distribution in the adhesively bonded aluminum double-lap joint through elastic FEA and verify the analysis with the results from the experiments.
1.1. The finite element model and the mesh The schematic diagram of the whole joint and the gaps arranged in the adhesive of the overlap zone are shown in
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Fig. 1. Schematic diagram of the (a) joint and (b) overlap zone (unit: mm).
Fig. 2. Finite element model: (a) boundary condition, (b) mesh for over lap zone and (c) detail mesh.
Fig. 1. The sum length of the overlap is 25 mm and the length and location of the recessing in adhesive layer is shown in Fig. 1(b). The model and the mesh were built using ANSYS finite element software as shown in Fig. 2. The properties of the materials are shown in Table 1. The aluminum specimen was prepared in accordance with the Chinese standard GB7124 (equivalent to ISO 4587) and bonded with a 0.2-mm-thick epoxy adhesive XH-11 as listed in Table 1. Because the element PLANE183 is an 8node element and has quadratic displacement behavior and is well suited for modeling irregular meshes and may be used as a plane element (plane stress, plane strain and generalized plane strain), it was used as both adherend and adhesive. The bondline was divided into four layers through the thickness, and the element length of the neighboring adherend was set as 0.05 mm. The load applied was 4.5 kN. Boundary conditions of the model, mesh and detail of the fillet are shown in Fig. 2. All the stresses data are obtained from the mid-bondline (y ¼ 1.1 mm) and the adherend near the interface (y ¼ 1.25 mm). 2. Finite element analysis 2.1. Effect of the gap in the adhesive The stress distribution in the mid-bondline (y ¼ 1.1 mm) and the aluminum adherend near the interface (y ¼ 1.25 mm)
Table 1 Material property Material
Elastic modulus (E/GPa)
Poisson’s ratio (g)
Aluminum alloy Epoxy adhesive XH-11
71 2.88
0.32 0.42
is shown in Fig. 3. The symbol is used to represent stress distribution in the joint when an 8 mm length gap (as shown in Fig. 1b, L1: L2: L3 ¼ 8.5:8:8.5 mm) was arranged in the adhesive symmetrically at the point x ¼ 12.5 mm and the symbol is used to present the stress distribution in the normal joint (without a gap). From Fig. 3(a)–(e) it can be seen that the effect of the gap in the adhesive is obviously on the stress distribution along the mid-bondline as well as the values of the peak stress near the left edge of the lap zone. Where there was no adhesive, there was no stress component in the midbondline. The peak values of the stresses in the double-lap joint appear at the ends of the lap zone, and the maximum stress occurred near the left end and hence the effect of gap is not negligible. Especially for the longitudinal stress Sx in Fig. 3(a), the peak stress was increased about 55% (from 3.97 to 6.15 MPa) and the stress near the right end of the lap zone was increased a little. In the face of the upper adherend (y ¼ 1.25 mm) parallel to the interface, the stress distribution are shown in Fig. 3(f)–(j). The distribution tendency of the peel stress Sy and the shear stress Sxy in the joint with an
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8 mm length gap is almost similar to that of the continuous layer along the lap zone except that the stress is changed at several points (shown in Fig. 3g and h). However, the effect of an 8 mm length gap on the peak value of the peel stress Sy in the adherends near the interface is large. The stress distributions of the other three kinds of components, the longitudinal
stress Sx, the first principal stress S1 and the von Mises equivalent stress Seqv, are similar as shown in Fig. 3(f), (i) and (j) respectively. When there exists a gap, the stress is less than that joint bonded with the continuous adhesive layer, but it is higher than the later one in the range corresponding to the gap. Relatively higher peak stresses (over 45 MPa) appear at
Normal
4
Peel stress Sy (MPa)
Longitudinal stress Sx (MPa)
12 6 Recessed
2
0
8
Normal
Recessed
4
0
-4 -2 0
6
12
18
24
0
18
24
Distance from the edge (mm)
16
24
12
Normal
1st principal stress S1 (MPa)
Shear stress Sxy (MPa)
12
6
Distance from the edge (mm)
Recessed
8
4
0 0
6
12
18
Normal
Recessed
16
8
0 0
24
12
6
18
24
Distance from the edge (mm)
Distance from the edge (mm)
Recessed
Normal
24
Longitudinal stress Sx (MPa)
von Mises equivalent stress Seqv (MPa)
50 Normal
18
12
6
Recessed
40 30 20 10 0
0 -10 0
6
12
18
Distance from the edge (mm)
24
0
6
12
18
24
Distance from the edge (mm)
Fig. 3. Effect of an 8 mm length gap centered at x ¼ 12.5 mm on the stresses distribution in double-lap joint: the longitudinal stress Sx in the (a) midbondline and (f) adherend; the peel stress Sy in the (b) mid-bondline and (g) adherend; the shear stress Sxy in the (c) mid-bondline and (h) adherend; the first principal stress S1 in the (d) mid-bondline and (i) adherend and the von Mises equivalent stress Seqv in the (e) mid-bondline and (j) adherend.
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15 Shear stress Sxy (MPa)
Peel stress Sy (MPa)
10
0 Normal
-10
Recessed
-20
10
Normal
Recessed
5
0 -30 0
12
6
18
0
24
50
Normal
40 Normal
40
18
24
Distance from the edge (mm)
von Mises equivalent stress Seqv (MPa)
1st principal stress S1 (MPa)
12
6
Distance from the edge (mm)
Recessed
30 20 10
Recessed
30
20
10
0 0
6
12
18
0
24
6
12
18
24
Distance from the edge (mm)
Distance from the edge (mm)
Fig. 3. (Continued)
point x ¼ 25 mm in Fig. 3(f), (i) and (j). The longitudinal stress Sx at the point of x ¼ 9 mm is about 57.8% higher than that in continuous adhesive joint as shown in Fig. 3(f). From Fig. 3, it can be imagined that the load-carrying capacity of the double-lap joint is nearly not affected by an 8 mm length gap arranged symmetrically at the point x ¼ 12.5 mm. 2.2. Effect of the gap length In Fig. 4(a)–(e) the effect of the gap length on stress distribution in the mid-bondline of the double-lap joint is presented. The length of the gaps were taken as 4 mm (L1:L2:L3 ¼ 15:4: 6 mm), 8 mm (L1:L2:L3 ¼ 13:8:4) and 12 mm (L1:L2:L3 ¼ 11:12:2 mm) and they were all centered at the point x ¼ 17 mm. To understand the effect of longer gaps, two other gaps were also introduced. One of them was a 16 mm length gap (L1:L2:L3 ¼ 6:16:3 mm, centered at x ¼ 14 mm) and the other was a 19 mm length gap (L1:L2:L3 ¼ 6:19:0 mm, centered at x ¼ 15.5 mm, referring to Fig 1b). The peak values and the distribution of all the stresses both in the mid-bondline and in the adherend are
nearly the same when the gap lengths are 8 and 12 mm. But the peak stresses are increased at the point close to the left end of the lap zone and the edge of the gap (for the shear stress Sxy and the von Mises equivalent stress Seqv) when the gap length is 19 mm. In Fig. 4(e) peak values of the von Mises equivalent stresses at the point x ¼ 0.5 mm are all about 26 MPa when the gap length is not greater than 12 mm (e.g. 25.9 MPa for a 4 mm length gap, 26.0 MPa for an 8 mm length gap or 26.3 MPa for a 12 mm length gap) but increased from 28.7 (16 mm) to 34.8 MPa (gap length 19 mm) at the same point as the gap length is increased. At the point near the left edge of the gap (x ¼ 5.5 mm), the peak value of the von Mises equivalent stress Seqv with a 19 mm length gap is 27.4 MPa and almost twice the value from the joint with a 16 mm length gap (14.1 MPa). This implies that the ultimate load of the double-lap joint may be decreased slightly when the gap length was increased till 12 mm. In other words, while the ultimate load decreases a little the actual strength of the joint may be increased as the length of the adhesive in the overlap zone is reduecd. In Figs. 4(f)–(j) tendencies of the stress distributions in the adherend along the lap zone are similar and a relatively
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higher value of peak stress (over 44 MPa) appears in the curves representing the stress distribution of the longitudinal stress Sx, the first principal stress S1 and the von Mises equivalent stress Seqv. When the gap length is increased from 16 (L1:L2:L3 ¼ 6:16:3 mm) to 19 mm (L1:L2:L3 ¼ 6: 19:0 mm), the peak stresses are increased because there was no adhesive at all from the point
x ¼ 6 mm to the right end of the lap zone, which corresponds to the lap length reduction in the joint. 3. Experimental results In order to understand the effect of the gap length on stress distribution in adhesively bonded aluminum
L=4
L=12 L=8 L=19 L=16
Peel stress Sy (MPa)
Longitudinal stress Sx (MPa)
20 8
4
0
L=8 L=4 L=16
10
L=12 L=19
0
-10
-4
0
6
12
18
24
0
Distance from the edge (mm)
L=4
1st principal stress S1 (MPa)
Shear stress Sxy (MPa)
12
18
24
32
18 L=12 L=8 L=19 L=16
12
6
L=4
24
L=12 L=8 L=19 L=16
16
8
0
0 0
6
12
18
24
0
6
12
18
24
Distance from the edge (mm)
Distance from the edge (mm)
60 Longitudinal stress Sx (MPa)
von Mises equivalent stress Seqv (MPa)
6
Distance from the edge (mm)
32 L=4
L=12 L=8 L=19 L=16
24 16 8
45
30
15 L=4
L=12 L=8 L=19 L=16
0
0 0
6
12
18
Distance from the edge (mm)
24
0
6
12
18
24
Distance from the edge (mm)
Fig. 4. Effect of gap length on the stress distribution in adhesively bonded double-lap joint: longitudinal stress Sx in the (a) mid-bondline and (f) adherend; the peel stress Sy in the (b) mid-bondline and (g) adherend; the shear stress Sxy in the (c) mid-bondline and (h) adherend; the first principal stress S1 in the (d) mid-bondline and (i) adherend and the von Mises equivalent stress Seqv in the (e) mid-bondline and (j) adherend (unit: mm).
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20 18
L=12 L=8 L=19 L=16
Shear stress Sxy (MPa)
Peel stress Sy (MPa)
L=4 10
0
-10
L=4 12
6
0
-20 0
6
12
18
24
0
Distance from the edge (mm) von Mises equivalent stress Seqv (MPa)
45
30
15 L=4 0 0
6
L=12 L=8 L=19 L=16
12
18
6
12
18
24
Distance from the edge (mm)
60 1st principal stress S1 (MPa)
L=12 L=8 L=19 L=16
50
40
30
20 L=4
L=12 L=8 L=19 L=16
10 0
24
6
12
18
24
Distance from the edge (mm)
Distance from the edge (mm)
Fig. 4. (Continued)
double-lap joint better, the experiment partly satisfied the condition of the finite element simulation had been carried out. The gaps length were taken as 4 (L1:L2:L3 ¼ 15:4: 6 mm), 8 (L1:L2:L3 ¼ 13 :8:4 mm) and 12 mm (L1:L2: L3 ¼ 11:12:2 mm), while the gaps were all centered at the point x ¼ 17 mm. The specimens were prepared according to Chinese Standard GB 7124 (equivalent to ISO 4587) and the thickness of adhesive layer was about 0.2 mm obtained by means of controlling deposited volume of the adhesive, open assembly time and curing fixture. Three aluminum alloy plates 2 mm thick were used as adherends of the tensile shear double-lap joints. Plates were first polished using emery paper, then degreased using acetone and dried. Finally, they were bonded with an epoxy adhesive listed in Table 1 and thus the specimens are prepared. A special technology has been developed to prepare the joints with desired gaps lengths, 4, 8 or 12 mm. After curing the specimen in the oven for 2 h at 50 1C, they were moved out and continuously cured for 24 h at room temperature (about 20 1C). The shear strength tests were performed at a speed of 5 mm/min for crosshead to determine the ultimate loads. For each group, it had at least four specimens to
obtain the average ultimate load. The failure mode of the joints was mainly adhesion failure. The effect of the gap length on the failure load and the actual shear strength of the single-lap joints made of aluminum adherends and an epoxy adhesive are shown in Fig. 5, where the symbol ‘‘.’’ presents the highest ultimate load or the actual shear strength, and the symbol ‘‘m’’ presents the lowest ultimate load or the actual shear strength from several specimens in same group. From Fig. 5, it can be seen that the ultimate load of the joint decreased a little as the length of the gap increased and the effect on the actual shear strength is increased. The average ultimate load of the joint was decreased from 7.6 to 6.2 kN (i.e. decreased about 18.4%) and the average shear strength increases from about 12.2 to 19.1 MPa (increased about 56.6%) as the gap length increased from 0 (continuous adhesive) to 12 mm (L1:L2:L3 ¼ 11:12:2 mm). It is clear that the effect of the existence of shorter gaps in the adhesive is not important to the ultimate load of the double-lap joint. The results obtained from the experiments are in compliance with the ones obtained from the finite element simulation.
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20 Shear strength (MPa)
Failure load (kN)
8 6 4 2 0
15 10 5 0
0
4 8 Gap length (mm)
12
0
4 8 Gap length (mm)
12
Fig. 5. Effects of gap length on failure load and actual strength of adhesively bonded aluminum double-lap joints.
4. Conclusion Based on the results from elastic finite element simulation, it is shown that the effect of a centered 8 mm length gap in the mid-bondline on the peak stresses of double-lap joint is considerable for longitudinal stress Sx, shear stress Sxy, the first principal stress S1 and the von Mises equivalent stress Seqv. But the effect of the gap on the stress distribution in the bondline out of the zone corresponding to the gap is negligible. On the other hand, the effect of an 8 mm length gap on the peak value of peel stress Sy in the adherends near the interface is large but for the effect on the stress distributed along the middle part of the overlap zone is negligible. It is clear that the loadcarrying capacity of the double-lap joint may not be markedly affected by an 8 mm length gap arranged symmetric at the point x ¼ 12.5 mm. Both peak stress and stress at the point near the edge of gap in the mid-bondline are increased when gap length is increased from 8 to 16 mm, but the increment of the peak stress is very small. In other words, if a gap with 8 to 16 mm length is arranged in the bondline, the influence on the ultimate load might not be important. When the gap length is larger than 16 mm, the increment of the peak stress is significant. The results from the experiment also showed that the ultimate load of the double-lap joint decreases a little to the joint bonded with continuous adhesive layer when the gap length is not greater than 12 mm. They are in
accordance with the results from the simulation of the elastic FEA. Acknowledgments The authors would like to acknowledge the financial support by the Major Research Programs of Hubei Provincial Department of Education (2003Z001), China. References [1] Hart-smith LJ. Aerospace. In: Adams RD, editor. Adhesive bonding. Cambridge England: Woodhead Publishing Ltd.; 2005. p. 489–94. [2] Olia M, Rossetos JN. Analysis of adhesively bonded joints with gaps subjected to bending. Int J Solids Struct 1996;33(18):2681–93. [3] Lang TP, Mallick PK. The effect of gaping on the stresses in adhesively bonded single-lap joints. Int J Adhes Adhes 1999;19:257–71. [4] de Moura MFSF, Daniaud R, Magalhaes AG. Simulation of mechanical behaviour of composite bonded joints containing strip defects. Int J Adhes Adhes 2006;26(6):464–73. [5] Zheng X-L, You M, Zheng Y, et al. The effect of off-center gaping on the strength of adhesively bonded single-lap joint. In: Proceedings of seventh international conference on structural adhesives in engineering (SAE VII, 13-15 July 2004, Bristol, UK), IOM Communications Ltd. London, 2004. p. 171–74. [6] Keller T, Vallee T. Adhesively bonded lap joints from pultruded GFRP profiles. Part I: Stress–Strain Analysis and Failure Modes. Composites: Part B 2005;36:331–40. [7] 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.
International Journal of Adhesion & Adhesives 27 (2007) 696–702 www.elsevier.com/locate/ijadhadh
A numerical and experimental study of gap length on adhesively bonded aluminum double-lap joint Min You, Zhan-Mou Yan, Xiao-Ling Zheng, Hai-Zhou Yu, Zhi Li College of Mechanical and Material Engineering, China Three Gorges University, Yichang 443002, China Accepted 17 February 2007 Available online 2 March 2007
Abstract The elastic finite element analysis (FEA) and the experimental method were used to investigate the effect of the gap, as well as its length, on the stress distribution in both the mid-bondline and the adherend near the interface along the lap zone of adhesively bonded aluminum double-lap joint. The values of the peak stresses distributed in the mid-bondline were increased a little when an 8 mm length gap was arranged symmetrically around the center of the lap zone. Both peak stresses and stress at the point close to the edge of the gap in the mid-bondline were increased when the gap length was increased, but the increment of the peak stresses was small when the lap length was not greater than 16 mm. The results from the FEA simulation showed that the effect of the gap length on the ultimate load of the joint was small as the gap length was increased. It is supported with the results from the experiments that the ultimate load of the aluminum double-lap joint decreased a little when the gap length was less than 12 mm. r 2007 Elsevier Ltd. All rights reserved. Keywords: Epoxy; Aluminum and alloy; Finite element analysis; Gap length
1. Introduction Adhesive bonding technology is widely used today in almost all the industries fields of the world and this is mainly due to its high strength–weight ratio, low cost and high efficiency [1]. In recent years, the studies related to the effect of gap (recessing) in the bondline on the mechanical properties of adhesively bonded joint was mainly from viewpoint of treating the gap as a defect in the joint and they mainly focused on the single-lap joint [2–4]. Olia and Rossetos [2] reported that the effect of the gap on peak stresses of the peel stress and the shear stress in single-lap joint under bending was small, unless it was sufficiently close to the end of the lap zone. Lang and Mallick [3] discussed that the effect of the gap on peak stress of the joint under tensile load was negligible compared with the result from the finite element method. The results of de Moura et al. [4] from experiments and numerical simulation showed that the influence of the gap length and width on nominal strength of the joint was less. In our earlier work [5], the intermittent Corresponding author. Tel.: +86 717 639 2004; fax: +86 717 639 5410.
E-mail address: [email protected] (M. You). 0143-7496/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijadhadh.2007.02.005
(or gapped) bonding technology is introduced. It demonstrated that the joint bonded by a reasonable intermittent adhesive layer may increase the actual strength (the ultimate load over the real area of the adhesive layer) markedly and for this, it used experiments and the finite element analysis (FEA). It is known that the double-lap joint is widely used today in aeronautical and other industries [6,7] for avoiding the great eccentricity of stress that occurred in the single-lap joint. In practice, a hole or gap in the adhesive is often discovered by the non-destructive test (NDT) and the loadcarrying capacity of the joint is significantly affected by these, hole and gap. It is necessary to study the mechanical behavior of the double-lap joint with a gap and see how significant it is. The aim of this work is to investigate the effect of the gap as well as its length on the stress distribution in the adhesively bonded aluminum double-lap joint through elastic FEA and verify the analysis with the results from the experiments.
1.1. The finite element model and the mesh The schematic diagram of the whole joint and the gaps arranged in the adhesive of the overlap zone are shown in
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Fig. 1. Schematic diagram of the (a) joint and (b) overlap zone (unit: mm).
Fig. 2. Finite element model: (a) boundary condition, (b) mesh for over lap zone and (c) detail mesh.
Fig. 1. The sum length of the overlap is 25 mm and the length and location of the recessing in adhesive layer is shown in Fig. 1(b). The model and the mesh were built using ANSYS finite element software as shown in Fig. 2. The properties of the materials are shown in Table 1. The aluminum specimen was prepared in accordance with the Chinese standard GB7124 (equivalent to ISO 4587) and bonded with a 0.2-mm-thick epoxy adhesive XH-11 as listed in Table 1. Because the element PLANE183 is an 8node element and has quadratic displacement behavior and is well suited for modeling irregular meshes and may be used as a plane element (plane stress, plane strain and generalized plane strain), it was used as both adherend and adhesive. The bondline was divided into four layers through the thickness, and the element length of the neighboring adherend was set as 0.05 mm. The load applied was 4.5 kN. Boundary conditions of the model, mesh and detail of the fillet are shown in Fig. 2. All the stresses data are obtained from the mid-bondline (y ¼ 1.1 mm) and the adherend near the interface (y ¼ 1.25 mm). 2. Finite element analysis 2.1. Effect of the gap in the adhesive The stress distribution in the mid-bondline (y ¼ 1.1 mm) and the aluminum adherend near the interface (y ¼ 1.25 mm)
Table 1 Material property Material
Elastic modulus (E/GPa)
Poisson’s ratio (g)
Aluminum alloy Epoxy adhesive XH-11
71 2.88
0.32 0.42
is shown in Fig. 3. The symbol is used to represent stress distribution in the joint when an 8 mm length gap (as shown in Fig. 1b, L1: L2: L3 ¼ 8.5:8:8.5 mm) was arranged in the adhesive symmetrically at the point x ¼ 12.5 mm and the symbol is used to present the stress distribution in the normal joint (without a gap). From Fig. 3(a)–(e) it can be seen that the effect of the gap in the adhesive is obviously on the stress distribution along the mid-bondline as well as the values of the peak stress near the left edge of the lap zone. Where there was no adhesive, there was no stress component in the midbondline. The peak values of the stresses in the double-lap joint appear at the ends of the lap zone, and the maximum stress occurred near the left end and hence the effect of gap is not negligible. Especially for the longitudinal stress Sx in Fig. 3(a), the peak stress was increased about 55% (from 3.97 to 6.15 MPa) and the stress near the right end of the lap zone was increased a little. In the face of the upper adherend (y ¼ 1.25 mm) parallel to the interface, the stress distribution are shown in Fig. 3(f)–(j). The distribution tendency of the peel stress Sy and the shear stress Sxy in the joint with an
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8 mm length gap is almost similar to that of the continuous layer along the lap zone except that the stress is changed at several points (shown in Fig. 3g and h). However, the effect of an 8 mm length gap on the peak value of the peel stress Sy in the adherends near the interface is large. The stress distributions of the other three kinds of components, the longitudinal
stress Sx, the first principal stress S1 and the von Mises equivalent stress Seqv, are similar as shown in Fig. 3(f), (i) and (j) respectively. When there exists a gap, the stress is less than that joint bonded with the continuous adhesive layer, but it is higher than the later one in the range corresponding to the gap. Relatively higher peak stresses (over 45 MPa) appear at
Normal
4
Peel stress Sy (MPa)
Longitudinal stress Sx (MPa)
12 6 Recessed
2
0
8
Normal
Recessed
4
0
-4 -2 0
6
12
18
24
0
18
24
Distance from the edge (mm)
16
24
12
Normal
1st principal stress S1 (MPa)
Shear stress Sxy (MPa)
12
6
Distance from the edge (mm)
Recessed
8
4
0 0
6
12
18
Normal
Recessed
16
8
0 0
24
12
6
18
24
Distance from the edge (mm)
Distance from the edge (mm)
Recessed
Normal
24
Longitudinal stress Sx (MPa)
von Mises equivalent stress Seqv (MPa)
50 Normal
18
12
6
Recessed
40 30 20 10 0
0 -10 0
6
12
18
Distance from the edge (mm)
24
0
6
12
18
24
Distance from the edge (mm)
Fig. 3. Effect of an 8 mm length gap centered at x ¼ 12.5 mm on the stresses distribution in double-lap joint: the longitudinal stress Sx in the (a) midbondline and (f) adherend; the peel stress Sy in the (b) mid-bondline and (g) adherend; the shear stress Sxy in the (c) mid-bondline and (h) adherend; the first principal stress S1 in the (d) mid-bondline and (i) adherend and the von Mises equivalent stress Seqv in the (e) mid-bondline and (j) adherend.
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15 Shear stress Sxy (MPa)
Peel stress Sy (MPa)
10
0 Normal
-10
Recessed
-20
10
Normal
Recessed
5
0 -30 0
12
6
18
0
24
50
Normal
40 Normal
40
18
24
Distance from the edge (mm)
von Mises equivalent stress Seqv (MPa)
1st principal stress S1 (MPa)
12
6
Distance from the edge (mm)
Recessed
30 20 10
Recessed
30
20
10
0 0
6
12
18
0
24
6
12
18
24
Distance from the edge (mm)
Distance from the edge (mm)
Fig. 3. (Continued)
point x ¼ 25 mm in Fig. 3(f), (i) and (j). The longitudinal stress Sx at the point of x ¼ 9 mm is about 57.8% higher than that in continuous adhesive joint as shown in Fig. 3(f). From Fig. 3, it can be imagined that the load-carrying capacity of the double-lap joint is nearly not affected by an 8 mm length gap arranged symmetrically at the point x ¼ 12.5 mm. 2.2. Effect of the gap length In Fig. 4(a)–(e) the effect of the gap length on stress distribution in the mid-bondline of the double-lap joint is presented. The length of the gaps were taken as 4 mm (L1:L2:L3 ¼ 15:4: 6 mm), 8 mm (L1:L2:L3 ¼ 13:8:4) and 12 mm (L1:L2:L3 ¼ 11:12:2 mm) and they were all centered at the point x ¼ 17 mm. To understand the effect of longer gaps, two other gaps were also introduced. One of them was a 16 mm length gap (L1:L2:L3 ¼ 6:16:3 mm, centered at x ¼ 14 mm) and the other was a 19 mm length gap (L1:L2:L3 ¼ 6:19:0 mm, centered at x ¼ 15.5 mm, referring to Fig 1b). The peak values and the distribution of all the stresses both in the mid-bondline and in the adherend are
nearly the same when the gap lengths are 8 and 12 mm. But the peak stresses are increased at the point close to the left end of the lap zone and the edge of the gap (for the shear stress Sxy and the von Mises equivalent stress Seqv) when the gap length is 19 mm. In Fig. 4(e) peak values of the von Mises equivalent stresses at the point x ¼ 0.5 mm are all about 26 MPa when the gap length is not greater than 12 mm (e.g. 25.9 MPa for a 4 mm length gap, 26.0 MPa for an 8 mm length gap or 26.3 MPa for a 12 mm length gap) but increased from 28.7 (16 mm) to 34.8 MPa (gap length 19 mm) at the same point as the gap length is increased. At the point near the left edge of the gap (x ¼ 5.5 mm), the peak value of the von Mises equivalent stress Seqv with a 19 mm length gap is 27.4 MPa and almost twice the value from the joint with a 16 mm length gap (14.1 MPa). This implies that the ultimate load of the double-lap joint may be decreased slightly when the gap length was increased till 12 mm. In other words, while the ultimate load decreases a little the actual strength of the joint may be increased as the length of the adhesive in the overlap zone is reduecd. In Figs. 4(f)–(j) tendencies of the stress distributions in the adherend along the lap zone are similar and a relatively
ARTICLE IN PRESS M. You et al. / International Journal of Adhesion & Adhesives 27 (2007) 696–702
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higher value of peak stress (over 44 MPa) appears in the curves representing the stress distribution of the longitudinal stress Sx, the first principal stress S1 and the von Mises equivalent stress Seqv. When the gap length is increased from 16 (L1:L2:L3 ¼ 6:16:3 mm) to 19 mm (L1:L2:L3 ¼ 6: 19:0 mm), the peak stresses are increased because there was no adhesive at all from the point
x ¼ 6 mm to the right end of the lap zone, which corresponds to the lap length reduction in the joint. 3. Experimental results In order to understand the effect of the gap length on stress distribution in adhesively bonded aluminum
L=4
L=12 L=8 L=19 L=16
Peel stress Sy (MPa)
Longitudinal stress Sx (MPa)
20 8
4
0
L=8 L=4 L=16
10
L=12 L=19
0
-10
-4
0
6
12
18
24
0
Distance from the edge (mm)
L=4
1st principal stress S1 (MPa)
Shear stress Sxy (MPa)
12
18
24
32
18 L=12 L=8 L=19 L=16
12
6
L=4
24
L=12 L=8 L=19 L=16
16
8
0
0 0
6
12
18
24
0
6
12
18
24
Distance from the edge (mm)
Distance from the edge (mm)
60 Longitudinal stress Sx (MPa)
von Mises equivalent stress Seqv (MPa)
6
Distance from the edge (mm)
32 L=4
L=12 L=8 L=19 L=16
24 16 8
45
30
15 L=4
L=12 L=8 L=19 L=16
0
0 0
6
12
18
Distance from the edge (mm)
24
0
6
12
18
24
Distance from the edge (mm)
Fig. 4. Effect of gap length on the stress distribution in adhesively bonded double-lap joint: longitudinal stress Sx in the (a) mid-bondline and (f) adherend; the peel stress Sy in the (b) mid-bondline and (g) adherend; the shear stress Sxy in the (c) mid-bondline and (h) adherend; the first principal stress S1 in the (d) mid-bondline and (i) adherend and the von Mises equivalent stress Seqv in the (e) mid-bondline and (j) adherend (unit: mm).
ARTICLE IN PRESS M. You et al. / International Journal of Adhesion & Adhesives 27 (2007) 696–702
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20 18
L=12 L=8 L=19 L=16
Shear stress Sxy (MPa)
Peel stress Sy (MPa)
L=4 10
0
-10
L=4 12
6
0
-20 0
6
12
18
24
0
Distance from the edge (mm) von Mises equivalent stress Seqv (MPa)
45
30
15 L=4 0 0
6
L=12 L=8 L=19 L=16
12
18
6
12
18
24
Distance from the edge (mm)
60 1st principal stress S1 (MPa)
L=12 L=8 L=19 L=16
50
40
30
20 L=4
L=12 L=8 L=19 L=16
10 0
24
6
12
18
24
Distance from the edge (mm)
Distance from the edge (mm)
Fig. 4. (Continued)
double-lap joint better, the experiment partly satisfied the condition of the finite element simulation had been carried out. The gaps length were taken as 4 (L1:L2:L3 ¼ 15:4: 6 mm), 8 (L1:L2:L3 ¼ 13 :8:4 mm) and 12 mm (L1:L2: L3 ¼ 11:12:2 mm), while the gaps were all centered at the point x ¼ 17 mm. The specimens were prepared according to Chinese Standard GB 7124 (equivalent to ISO 4587) and the thickness of adhesive layer was about 0.2 mm obtained by means of controlling deposited volume of the adhesive, open assembly time and curing fixture. Three aluminum alloy plates 2 mm thick were used as adherends of the tensile shear double-lap joints. Plates were first polished using emery paper, then degreased using acetone and dried. Finally, they were bonded with an epoxy adhesive listed in Table 1 and thus the specimens are prepared. A special technology has been developed to prepare the joints with desired gaps lengths, 4, 8 or 12 mm. After curing the specimen in the oven for 2 h at 50 1C, they were moved out and continuously cured for 24 h at room temperature (about 20 1C). The shear strength tests were performed at a speed of 5 mm/min for crosshead to determine the ultimate loads. For each group, it had at least four specimens to
obtain the average ultimate load. The failure mode of the joints was mainly adhesion failure. The effect of the gap length on the failure load and the actual shear strength of the single-lap joints made of aluminum adherends and an epoxy adhesive are shown in Fig. 5, where the symbol ‘‘.’’ presents the highest ultimate load or the actual shear strength, and the symbol ‘‘m’’ presents the lowest ultimate load or the actual shear strength from several specimens in same group. From Fig. 5, it can be seen that the ultimate load of the joint decreased a little as the length of the gap increased and the effect on the actual shear strength is increased. The average ultimate load of the joint was decreased from 7.6 to 6.2 kN (i.e. decreased about 18.4%) and the average shear strength increases from about 12.2 to 19.1 MPa (increased about 56.6%) as the gap length increased from 0 (continuous adhesive) to 12 mm (L1:L2:L3 ¼ 11:12:2 mm). It is clear that the effect of the existence of shorter gaps in the adhesive is not important to the ultimate load of the double-lap joint. The results obtained from the experiments are in compliance with the ones obtained from the finite element simulation.
ARTICLE IN PRESS M. You et al. / International Journal of Adhesion & Adhesives 27 (2007) 696–702
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20 Shear strength (MPa)
Failure load (kN)
8 6 4 2 0
15 10 5 0
0
4 8 Gap length (mm)
12
0
4 8 Gap length (mm)
12
Fig. 5. Effects of gap length on failure load and actual strength of adhesively bonded aluminum double-lap joints.
4. Conclusion Based on the results from elastic finite element simulation, it is shown that the effect of a centered 8 mm length gap in the mid-bondline on the peak stresses of double-lap joint is considerable for longitudinal stress Sx, shear stress Sxy, the first principal stress S1 and the von Mises equivalent stress Seqv. But the effect of the gap on the stress distribution in the bondline out of the zone corresponding to the gap is negligible. On the other hand, the effect of an 8 mm length gap on the peak value of peel stress Sy in the adherends near the interface is large but for the effect on the stress distributed along the middle part of the overlap zone is negligible. It is clear that the loadcarrying capacity of the double-lap joint may not be markedly affected by an 8 mm length gap arranged symmetric at the point x ¼ 12.5 mm. Both peak stress and stress at the point near the edge of gap in the mid-bondline are increased when gap length is increased from 8 to 16 mm, but the increment of the peak stress is very small. In other words, if a gap with 8 to 16 mm length is arranged in the bondline, the influence on the ultimate load might not be important. When the gap length is larger than 16 mm, the increment of the peak stress is significant. The results from the experiment also showed that the ultimate load of the double-lap joint decreases a little to the joint bonded with continuous adhesive layer when the gap length is not greater than 12 mm. They are in
accordance with the results from the simulation of the elastic FEA. Acknowledgments The authors would like to acknowledge the financial support by the Major Research Programs of Hubei Provincial Department of Education (2003Z001), China. References [1] Hart-smith LJ. Aerospace. In: Adams RD, editor. Adhesive bonding. Cambridge England: Woodhead Publishing Ltd.; 2005. p. 489–94. [2] Olia M, Rossetos JN. Analysis of adhesively bonded joints with gaps subjected to bending. Int J Solids Struct 1996;33(18):2681–93. [3] Lang TP, Mallick PK. The effect of gaping on the stresses in adhesively bonded single-lap joints. Int J Adhes Adhes 1999;19:257–71. [4] de Moura MFSF, Daniaud R, Magalhaes AG. Simulation of mechanical behaviour of composite bonded joints containing strip defects. Int J Adhes Adhes 2006;26(6):464–73. [5] Zheng X-L, You M, Zheng Y, et al. The effect of off-center gaping on the strength of adhesively bonded single-lap joint. In: Proceedings of seventh international conference on structural adhesives in engineering (SAE VII, 13-15 July 2004, Bristol, UK), IOM Communications Ltd. London, 2004. p. 171–74. [6] Keller T, Vallee T. Adhesively bonded lap joints from pultruded GFRP profiles. Part I: Stress–Strain Analysis and Failure Modes. Composites: Part B 2005;36:331–40. [7] 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.