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A numerical study of parallel slot in adherend on the stress distribution in adhesively bonded aluminum single lap joint
ARTICLE IN PRESS
International Journal of Adhesion & Adhesives 27 (2007) 687–695 www.elsevier.com/locate/ijadhadh
A numerical study of parallel slot in adherend on the stress distribution in adhesively bonded aluminum single lap joint Zhan-Mou Yana, Min Youa,, Xiao-Su Yib, Xiao-Ling Zhenga, Zhi Lia a
College of Mechanical and Material Engineering, China Three Gorges University, Yichang 443002, China National Key Laboratory of Advanced Composites, Beijing Institute of Aeronautical Materials, Beijing 100095, China
b
Accepted 17 February 2007 Available online 3 March 2007
Abstract The effect of the length and depth of a parallel slot as well as the elastic modulus of the adhesive on the stress distribution at the midbondline and in the adherend was investigated using the elastic finite element method. The results showed that the peak stress in midbondline decreased markedly when there were two of parallel slots located in the outside of the adherend, corresponding to the middle part of the lap zone and the original low stress in this zone of the joint increases. The peak stress decreased at first, and then increased again as the length of the parallel slot was increased. The stress distribution in the mid-bondline at the position corresponding to the parallel slot decreased significantly as the depth of the parallel slot was increased. The high peak stresses caused by the tensile load occurred close to the edge of the parallel slot in the adherend. Almost all the peak values of stresses at the mid-bondline increased when the elastic modulus of the adhesive was increased. The effect of the parallel slot on the peak stress at the mid-bondline with a low elastic modulus adhesive was negligible, but the peak stress decreased markedly for adhesives with a high elastic modulus. r 2007 Elsevier Ltd. All rights reserved. Keywords: Epoxy; Aluminum and alloy; Finite element analysis; Lap joint
1. Introduction Adhesively bonded joints are widely used in the aeronautics and astronautics industry as a result of their high strength–weight ratio and convenience in using the single lap joint is the most common one, although it is geometrically nonlinear due to the non-collinear load path. The eccentricity causes a significant stress concentration at the ends of the lap zone, where cracks may initiate, and this has a negative effect on the strength of joint [1]. In general, there are two kinds of method to reduce the stress concentration, using changes in the material or geometry. Material modifications are mainly optimizing the properties of both adhesive and adherend. Pires et al. [2] showed that the use of a bi-adhesive system was advantageous to the joint: the more flexible the adhesive, the more uniform the stress distribution in single lap joint and the smaller the stress concentration. Fitton and Broughton [3] studied the 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.2007.02.003
effect of variable modulus adhesive as an approach to optimize the performance of the joint. The results of Broughton [4] showed that the use of a rigid adherend made the stress distribution more uniform. Geometrical modifications mainly include fillet, pre-bending the adherend, tapering, chamfering and notching, etc. Lang and Mallick [5] concluded that the larger the fillet size and angle, the lower is the peak stress. The experimental and numerical simulation results from You et al. [6,7] showed that the existence of metal component in the fillets increases the strength of a single lap joint. Avila and Bueno [8] showed that the stress distribution was more uniform by using a wavy-lap bonded joint, giving a higher strength from their experiments and numerical simulation. The conclusions drawn by Sancaktar and Nirantar [9] were the smaller the taper angle of adherend at the ends of lap zone, the higher the strength of the joint. Oterkus et al. [10] investigated the effect of tapered edges on the performance of the joint. Belingardi et al. [11] discussed the results from the finite element analysis as the smaller the inner chamfering angle in the unloaded ends of the adherend,
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Z.-M. Yan et al. / International Journal of Adhesion & Adhesives 27 (2007) 687–695
the lower the peak stress in single lap joint. Sancaktar [12] also reported that a top and bottom notch at the ends of the lap zone increased the strength of the joint. Shokrieh and Lessard [13] verified the double-notch test method with the finite element technique, and found an optimal geometry for the specimen. Pettersson and Neumeister [14] reported they developed the inclined double notch shear (IDNS) test further and achieved accurate interlaminar shear strength values. Therefore, it can be seen that if we shift the top and bottom notch at the ends of lap zone (as in Ref. [12]) to the middle of the lap zone, the stress concentrations might be decreased. The object of this work is to study the parallel slot at the middle of the lap zone on the stress distribution of adhesively bonded single lap joints using the elastic finite element method. 2. Finite element model and mesh The model and mesh were built using the ANSYS finite element software as shown in Figs. 1 and 2. The load applied was taken as 3 kN and the constraint of the model is also shown in Fig. 1. The properties of the materials used in this study are listed in Table 1.The dimensions of the aluminum adherend is in accordance with the Chinese standard GB 7124 (equivalent to ISO 4587) with a length of 100 mm, width of 25 mm, and a thickness of 2 mm. In the outside of the joint there were two parallel slots in the middle of the lap zone. Because the element PLANE183 of ANSYS is a higher order 2-D, 8-node element and has quadratic displacement behavior and has a very good mixed formulation capability for quadrilateral elements and triangular elements (such as triangle for fillet and quadrilateral for adherend) and it may be used as a plane element (plane stress, plane strain and generalized plane
strain), it was used for both the adherend and the adhesive (0.2 mm thick). The bondline was divided into four layers through the thickness, and the smallest element length of fillets and the neighboring adherend is 0.05 mm. Fillets were divided into triangular elements, and the others were divided into quadrilateral element, as shown in Fig. 2. 3. Finite element analysis 3.1. Effect of parallel slot When the length and depth of the parallel slot was 7 and 1.5 mm and the adherends bonded with an epoxy adhesive XH-11, the effect of the parallel slot was investigated. The origin of coordinate y is at the bottom of the upper adherend and the origin of coordinate x is located at the left edge of the fillet or free end of lower adherend as shown in Fig. 1. In Fig. 3(a)–(e) the effect of parallel slot on the stress distribution of joint in the mid-bondline (y ¼ 0.1 mm) and in the adherend near the interface (y ¼ 0.25 mm) is presented. All the peak stresses in the mid-bondline decrease markedly for the adherend with a parallel slot, and the original low stress in the middle of the lap zone increases especially for the longitudinal stress Sx (Fig. 3(a)) and the peel stress
Table 1 Materials properties Material
Elastic modulus E (GPa) Poisson’s ratio g
Aluminium sheet LY12 71 Acrylate adhesive 0.05 Epoxy resin adhesive 1.89 Epoxy resin adhesive XH-11 2.88
Fig. 1. Finite element model.
Fig. 2. Mesh of (a) lap zone and (b) fillet.
0.32 0.45 0.33 0.42
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Sy (Fig. 3(b)) though the change of each stress at the edges of the fillets is smaller. The reason may be that the stiffness of the middle part of adherend was reduced after the adherend had been processed into a parallel slot so that the high level of the stress concentration occurred at the left and right ends was decreased and much stress transferred through the middle part, corresponding to a parallel slot in the mid-bondline. The stress distribution in the adherend near the interface also shows that tendency in Fig. 3(f)–(j). The distribution of the longitudinal stress Sx (Fig. 3(f)) and the 1st principal stress S1 (Fig. 3(i)) are similar to that of the von Mises equivalent stress Seqv (Fig. 3(j)). The stress increases greatly near the parallel slot, especially for Sy (Fig. 3(g) and Seqv (Fig. 3(j)). Similar to what happened in the mid-bondline, the original low stress in the middle part of the joint increase, so the middle of joint is subjected to high loads and the value of peak stress at the end of the overlap is decreased. It is the same as the result from that of biadhesive bonded single lap joint in Ref. [2]. There is almost no difference to the distribution of the von Mises equivalent stress Seqv in the lower adherend near the right end of the lap zone between the joint with or without a parallel slot (Fig. 3(j)).
3.2. Effect of parallel slot length When the parallel slot depth was kept constant at 1.5 mm, the parallel slot length L was set as 1, 7 and 12 mm, respectively, and the effect of the parallel slot length on the stress distribution in the mid-bondline (y ¼ 0.1 mm) and in the adherend near the interface (y ¼ 0.25 mm) are presented in Fig. 4. For the longitudinal stress Sx in the mid-bondline, the peak stress and the stress near the parallel slot decreases as the parallel slot length increases and the minimum value of the peak stress is achieved when the slot length is approximately equal to 7 mm (Fig. 4(a)). The distribution tendency of the shear stress Sxy (Fig. 4(c)), the 1st principal stress S1 (Fig. 4(d)) and the von Mises equivalent stress Seqv (Fig. 4(e)) was similar to that of the longitudinal stress Sx (Fig. 4(a)) as the parallel slot length was increased. When the length of the parallel slot increased to 12 mm close to the boundary of the adherend end and the fillet, the peak stress increases again (Fig. 4(a)). The reason is where the stress concentration occurred. However, for the peel stress Sy, the peak stress, and the stress near the parallel slot decrease as the parallel slot length was increased (Fig. 4(b)). The distribution of longitudinal stress Sx (Fig. 4(f)) and the 1st principal stress
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Fig. 3. Effect of the parallel slot on the stresses distribution in the joint: longitudinal stress Sx in (a) mid-bondline and (f) adherend; peel stress Sy in (b) mid-bondline and (g) adherend; shear stress Sxy in (c) mid-bondline and (h) adherend; 1st principal stress S1 in (d) mid-bondline and (i) adherend and von Mises equivalent stress Seqv in (e) mid-bondline and (j) adherend.
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Fig. 3. (Continued)
S1 (Fig. 4(i)) are also similar to that of the von Mises equivalent stress Seqv (Fig. 4(j)). For the peel stress Sy, the peak stress changed markedly from positive to negative at the left end of the lap zone (Fig. 4(g), which was beneficial and improved the load bearing ability of the joint [13]. The stress increases greatly near the parallel slot, especially for the peel stress Sy (Fig. 4(g)). 3.3. Effect of parallel slot depth The effect of the parallel slot depth on the stress distribution of the joint in the mid-bondline (y ¼ 0.1 mm) and the adherend near the interface (y ¼ 0.25 mm) along
the length of the lap zone is shown in Fig. 5 when the parallel slot length was kept constant at 7 mm and the parallel slot depth was taken as 1, 1.5 and 1.7 mm, respectively. As the parallel slot depth increased, the peak value of the longitudinal stress Sx in the mid-bondline near the free end of the adherend decreased and the stress level in the middle part corresponding to the parallel slot increased (Fig. 5(a)). The distribution of the 1st principal stress S1 (Fig. 5(d)) is also similar. For the peel stress Sy, the peak stress at the point corresponding to the edge of the parallel slot increases greatly as the depth of the slot increases, but the stresses in the middle zone are nearly the same (Fig. 5(b))
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and it is similar to what shows in Fig. 5(g) in the adherend near the interface. The stress distribution of the longitudinal stress Sx (Fig. 5(f)) and the 1st principal stress S1 (Fig. 5(i)) are also similar to that of the von Mises equivalent stress Seqv (Fig. 5(j)). On the whole, each peak stress near the end of the lap zone increases gradually as the slot depth increases while the peel stress Sy decreases a little. When the parallel slot depth was taken as 1.7 mm, all the peak stresses of Sx, S1 and Seqv in the adherend at the point corresponding to the edge of the slot reached a value over 170 MPa.
3.4. Effect of the elastic modulus of the adhesive When the parallel slot length and depth were kept at 7 and 1.5 mm, respectively, the effect of the elastic modulus of the adhesives on the stress distribution of joint in the mid-bondline was studied and the results from the FEM analysis are shown in Fig. 6 where the letter ‘‘N’’ means from the normal specimen (without a parallel slot). All the peak stresses increase as the elastic modulus of the adhesive increases for the joint with a parallel slot. The reason may be that the smaller the elastic modulus of the adhesive, the
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Fig. 4. Effect of the parallel slot length on the stresses distribution in the joint: longitudinal stress Sx in (a) mid-bondline and (f) adherend; peel stress Sy in (b) mid-bondline and (g) adherend; shear stress Sxy in (c) mid-bondline and (h) adherend; 1st principal stress S1 in (d) mid-bondline and (i) adherend and von Mises equivalent stress Seqv in (e) mid-bondline and (j) adherend.
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0 Shear stress Sxy (MPa)
Peel stress Sy (MPa)
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Fig. 4. (Continued)
smaller is the stiffness of the joint and the stress concentration at the end of lap zone is also decreased. The longitudinal stress Sx (Fig. 6(a)) and the peel stress Sy (Fig. 6(b)) corresponding to the parallel slot increase as the elastic modulus of the adhesive increases. When a low elastic modulus adhesive was used, the effect of the parallel slot on each peak stress and the stress distribution in the mid-bondline was negligible. The reason is that the stress distribution along the bondline of the joint with a low elastic modulus adhesive was very smooth, and the stress concentration at the end is lower [15]. When a high elastic modulus adhesive was used, both the peak stresses and the stress distribution varied markedly. For the aluminum joint bonded with an adhesive of high elastic modulus, the original low stresses as well as their peaks in the middle of joint increased and much load was carried by that part while the stress concentration and the peak stress at the end of the lap zone was seem to decrease. 4. Conclusion When two parallel slots were arranged in the adherend, the peak values of the longitudinal stress Sx, the shear stress Sxy, the 1st principal stress S1 and the von Mises equivalent stress Seqv in the mid-bondline decreased
markedly and the stress level in the middle part of the overlap zone also increased. In the adherend near the interface, the peak stresses of the longitudinal stress Sx, the shear stress Sxy, the 1st principal stress S1 and the von Mises equivalent stress Seqv of the joint are almost the same at the point near the two ends of the overlap zone whether there is or is not a slot. When the slot existed, the stress level in the middle part of the overlap zone is higher than that of the normal joint. For the peel stress Sy, the peak stress changed markedly from positive to negative at the left end of the lap zone and it is of benefit to restrict the harmful effect of the peel stress on the joint. The values of the peak stresses in the mid-bondline decrease when the parallel slot length is increased, except that the peak peel stress Sy decreases all the time. As the parallel slot depth was increased, the stress in the midbondline at the point near the end of the lap zone decreases gradually while the stress in the middle part of the lap zone corresponding to the parallel slot also increases. The stress in the adherend with the parallel slot increases gradually as the parallel slot depth increases. In the joint with a parallel slot, the peak stress increases as the elastic modulus of the adhesive increases. The effect of a parallel slot on the peak stress and the stress distribution at the mid-bondline is negligible when a low
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Fig. 5. Effect of the parallel slot depth on the stresses distribution in the joint: longitudinal stress Sx in (a) mid-bondline and (f) adherend; peel stress Sy in (b) mid-bondline and (g) adherend; shear stress Sxy in (c) mid-bondline and (h) adherend; 1st principal stress S1 in (d) mid-bondline and (i) adherend and von Mises equivalent stress Seqv in (e) mid-bondline and (j) adherend.
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694
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Fig. 6. Effect of the elastic modulus of the adhesive on the stress distribution in the joint with a parallel slot at the mid-bondline (unit: GPa): (a) longitudinal stress Sx; (b) peel stress Sy; (c) shear stress Sxy; (d) 1st principal stress S1 and (e) von Mises equivalent stress Seqv.
elastic modulus adhesive was used. When a high elastic modulus adhesive was used, the stress in the middle part of the joint increases while the stress concentration at the point near the end of the lap zone decreased, so that the peak stress decreases markedly.
Acknowledgements The authors would like to acknowledge the financial Supported by the Major Research Programs of Hubei Provincial Department of Education (2003Z001), China.
References [1] Adams RD, Wake WC. Structural adhesive joints in engineering. London: Elsevier Applied Science Publishers Ltd.; 1984. [2] Pires I, Quintino L, Durodola JF, Beevers A. Performanceof bi-adhesive bonded aluminium lap joints. Int J Adhes Adhes 2003;23(3):215–23. [3] Fitton MD, Broughton JG. Variable modulus adhesives: an approach to optimized joint performance. Int J Adhes Adhes 2005;25(4): 329–36. [4] Broughton WR, Mera RD, Hinopoulos G. Environmental degradation of adhesive joints single-lap joint geometry. Project PAJ3— combined cyclic loading and hostile environments 1996–1999 report no 69, 1999.
ARTICLE IN PRESS Z.-M. Yan et al. / International Journal of Adhesion & Adhesives 27 (2007) 687–695 [5] Lang TP, Mallick PK. Effect of spew geometry on stresses in single lap adhesive joints. Int J Adhes Adhes 1998;18:167–77. [6] You M, Zheng Y, Zheng XL, et al. Effect of metal as part of fillet on the tensile shear strength of adhesively bonded single lap joints. Int J Adhes Adhes 2003;23:365–9. [7] You M, Zheng Y, Zheng XL, et al. Failure analysis of adhesively bonded single lap joints embedded with metal component as part of fillet. Key Eng Mater 2006;324–325:727–30. [8] Avila AF, Bueno PO. Stress analysis on a wavy-lap bonded joint for composites. Int. J Adhes Adhes 2004;24:407–14. [9] Sancaktar E, Nirantar P. Increasing strength of single lap joints of metal adherends by taper minimization. J Adhes Sci Technol 2003; 17(5):55–67. [10] Oterkus E, Barut A, Madenci E, et al. Bonded lap joints of composite laminates with tapered edges. Int J Solids Struct 2006;43:1459–89.
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[11] Belingardi G, Goglio L, Tarditi A. Investigating the effect of spew and chamfer size on the stresses in metal/plastics adhesive joints. Int J Adhes Adhes 2002;22:273–82. [12] Sancaktar E, Simmons S. Optimization of adhesively bonded single lap joints by adherend notching. J Adhes Sci Technol 2000;14(11): 1363–404. [13] Shokrieh MM, Lessard LB. An assessment of the double-notch shear test for interlaminar shear characterization of a unidirectional graphite/epoxy under static and fatigue loading. Appl Composite Mater 1998;5:289–304. [14] Pettersson KB, Neumeister JM. A tensile setup for the IDNS composite shear. Composites: Part A 2006;37:229–42. [15] You M, Yan ZM, Zheng Y, et al. Effect of fillet on bi-adhesive bonded aluminum lap joints. Trans Nonferrous Met Soc China 2005;15(S3):344–8.
International Journal of Adhesion & Adhesives 27 (2007) 687–695 www.elsevier.com/locate/ijadhadh
A numerical study of parallel slot in adherend on the stress distribution in adhesively bonded aluminum single lap joint Zhan-Mou Yana, Min Youa,, Xiao-Su Yib, Xiao-Ling Zhenga, Zhi Lia a
College of Mechanical and Material Engineering, China Three Gorges University, Yichang 443002, China National Key Laboratory of Advanced Composites, Beijing Institute of Aeronautical Materials, Beijing 100095, China
b
Accepted 17 February 2007 Available online 3 March 2007
Abstract The effect of the length and depth of a parallel slot as well as the elastic modulus of the adhesive on the stress distribution at the midbondline and in the adherend was investigated using the elastic finite element method. The results showed that the peak stress in midbondline decreased markedly when there were two of parallel slots located in the outside of the adherend, corresponding to the middle part of the lap zone and the original low stress in this zone of the joint increases. The peak stress decreased at first, and then increased again as the length of the parallel slot was increased. The stress distribution in the mid-bondline at the position corresponding to the parallel slot decreased significantly as the depth of the parallel slot was increased. The high peak stresses caused by the tensile load occurred close to the edge of the parallel slot in the adherend. Almost all the peak values of stresses at the mid-bondline increased when the elastic modulus of the adhesive was increased. The effect of the parallel slot on the peak stress at the mid-bondline with a low elastic modulus adhesive was negligible, but the peak stress decreased markedly for adhesives with a high elastic modulus. r 2007 Elsevier Ltd. All rights reserved. Keywords: Epoxy; Aluminum and alloy; Finite element analysis; Lap joint
1. Introduction Adhesively bonded joints are widely used in the aeronautics and astronautics industry as a result of their high strength–weight ratio and convenience in using the single lap joint is the most common one, although it is geometrically nonlinear due to the non-collinear load path. The eccentricity causes a significant stress concentration at the ends of the lap zone, where cracks may initiate, and this has a negative effect on the strength of joint [1]. In general, there are two kinds of method to reduce the stress concentration, using changes in the material or geometry. Material modifications are mainly optimizing the properties of both adhesive and adherend. Pires et al. [2] showed that the use of a bi-adhesive system was advantageous to the joint: the more flexible the adhesive, the more uniform the stress distribution in single lap joint and the smaller the stress concentration. Fitton and Broughton [3] studied the 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.2007.02.003
effect of variable modulus adhesive as an approach to optimize the performance of the joint. The results of Broughton [4] showed that the use of a rigid adherend made the stress distribution more uniform. Geometrical modifications mainly include fillet, pre-bending the adherend, tapering, chamfering and notching, etc. Lang and Mallick [5] concluded that the larger the fillet size and angle, the lower is the peak stress. The experimental and numerical simulation results from You et al. [6,7] showed that the existence of metal component in the fillets increases the strength of a single lap joint. Avila and Bueno [8] showed that the stress distribution was more uniform by using a wavy-lap bonded joint, giving a higher strength from their experiments and numerical simulation. The conclusions drawn by Sancaktar and Nirantar [9] were the smaller the taper angle of adherend at the ends of lap zone, the higher the strength of the joint. Oterkus et al. [10] investigated the effect of tapered edges on the performance of the joint. Belingardi et al. [11] discussed the results from the finite element analysis as the smaller the inner chamfering angle in the unloaded ends of the adherend,
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the lower the peak stress in single lap joint. Sancaktar [12] also reported that a top and bottom notch at the ends of the lap zone increased the strength of the joint. Shokrieh and Lessard [13] verified the double-notch test method with the finite element technique, and found an optimal geometry for the specimen. Pettersson and Neumeister [14] reported they developed the inclined double notch shear (IDNS) test further and achieved accurate interlaminar shear strength values. Therefore, it can be seen that if we shift the top and bottom notch at the ends of lap zone (as in Ref. [12]) to the middle of the lap zone, the stress concentrations might be decreased. The object of this work is to study the parallel slot at the middle of the lap zone on the stress distribution of adhesively bonded single lap joints using the elastic finite element method. 2. Finite element model and mesh The model and mesh were built using the ANSYS finite element software as shown in Figs. 1 and 2. The load applied was taken as 3 kN and the constraint of the model is also shown in Fig. 1. The properties of the materials used in this study are listed in Table 1.The dimensions of the aluminum adherend is in accordance with the Chinese standard GB 7124 (equivalent to ISO 4587) with a length of 100 mm, width of 25 mm, and a thickness of 2 mm. In the outside of the joint there were two parallel slots in the middle of the lap zone. Because the element PLANE183 of ANSYS is a higher order 2-D, 8-node element and has quadratic displacement behavior and has a very good mixed formulation capability for quadrilateral elements and triangular elements (such as triangle for fillet and quadrilateral for adherend) and it may be used as a plane element (plane stress, plane strain and generalized plane
strain), it was used for both the adherend and the adhesive (0.2 mm thick). The bondline was divided into four layers through the thickness, and the smallest element length of fillets and the neighboring adherend is 0.05 mm. Fillets were divided into triangular elements, and the others were divided into quadrilateral element, as shown in Fig. 2. 3. Finite element analysis 3.1. Effect of parallel slot When the length and depth of the parallel slot was 7 and 1.5 mm and the adherends bonded with an epoxy adhesive XH-11, the effect of the parallel slot was investigated. The origin of coordinate y is at the bottom of the upper adherend and the origin of coordinate x is located at the left edge of the fillet or free end of lower adherend as shown in Fig. 1. In Fig. 3(a)–(e) the effect of parallel slot on the stress distribution of joint in the mid-bondline (y ¼ 0.1 mm) and in the adherend near the interface (y ¼ 0.25 mm) is presented. All the peak stresses in the mid-bondline decrease markedly for the adherend with a parallel slot, and the original low stress in the middle of the lap zone increases especially for the longitudinal stress Sx (Fig. 3(a)) and the peel stress
Table 1 Materials properties Material
Elastic modulus E (GPa) Poisson’s ratio g
Aluminium sheet LY12 71 Acrylate adhesive 0.05 Epoxy resin adhesive 1.89 Epoxy resin adhesive XH-11 2.88
Fig. 1. Finite element model.
Fig. 2. Mesh of (a) lap zone and (b) fillet.
0.32 0.45 0.33 0.42
ARTICLE IN PRESS Z.-M. Yan et al. / International Journal of Adhesion & Adhesives 27 (2007) 687–695
Sy (Fig. 3(b)) though the change of each stress at the edges of the fillets is smaller. The reason may be that the stiffness of the middle part of adherend was reduced after the adherend had been processed into a parallel slot so that the high level of the stress concentration occurred at the left and right ends was decreased and much stress transferred through the middle part, corresponding to a parallel slot in the mid-bondline. The stress distribution in the adherend near the interface also shows that tendency in Fig. 3(f)–(j). The distribution of the longitudinal stress Sx (Fig. 3(f)) and the 1st principal stress S1 (Fig. 3(i)) are similar to that of the von Mises equivalent stress Seqv (Fig. 3(j)). The stress increases greatly near the parallel slot, especially for Sy (Fig. 3(g) and Seqv (Fig. 3(j)). Similar to what happened in the mid-bondline, the original low stress in the middle part of the joint increase, so the middle of joint is subjected to high loads and the value of peak stress at the end of the overlap is decreased. It is the same as the result from that of biadhesive bonded single lap joint in Ref. [2]. There is almost no difference to the distribution of the von Mises equivalent stress Seqv in the lower adherend near the right end of the lap zone between the joint with or without a parallel slot (Fig. 3(j)).
3.2. Effect of parallel slot length When the parallel slot depth was kept constant at 1.5 mm, the parallel slot length L was set as 1, 7 and 12 mm, respectively, and the effect of the parallel slot length on the stress distribution in the mid-bondline (y ¼ 0.1 mm) and in the adherend near the interface (y ¼ 0.25 mm) are presented in Fig. 4. For the longitudinal stress Sx in the mid-bondline, the peak stress and the stress near the parallel slot decreases as the parallel slot length increases and the minimum value of the peak stress is achieved when the slot length is approximately equal to 7 mm (Fig. 4(a)). The distribution tendency of the shear stress Sxy (Fig. 4(c)), the 1st principal stress S1 (Fig. 4(d)) and the von Mises equivalent stress Seqv (Fig. 4(e)) was similar to that of the longitudinal stress Sx (Fig. 4(a)) as the parallel slot length was increased. When the length of the parallel slot increased to 12 mm close to the boundary of the adherend end and the fillet, the peak stress increases again (Fig. 4(a)). The reason is where the stress concentration occurred. However, for the peel stress Sy, the peak stress, and the stress near the parallel slot decrease as the parallel slot length was increased (Fig. 4(b)). The distribution of longitudinal stress Sx (Fig. 4(f)) and the 1st principal stress
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Fig. 3. Effect of the parallel slot on the stresses distribution in the joint: longitudinal stress Sx in (a) mid-bondline and (f) adherend; peel stress Sy in (b) mid-bondline and (g) adherend; shear stress Sxy in (c) mid-bondline and (h) adherend; 1st principal stress S1 in (d) mid-bondline and (i) adherend and von Mises equivalent stress Seqv in (e) mid-bondline and (j) adherend.
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Longitudinal stress Sx (MPa)
von Mises equivalent stress Seqv (MPa)
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14 Peel stress Sy (MPa)
6 12 Distance from the edge (mm)
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-6
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von Mises equivalent stress Seqv(MPa)
1st principal stress S1 (MPa)
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Notched
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45
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Fig. 3. (Continued)
S1 (Fig. 4(i)) are also similar to that of the von Mises equivalent stress Seqv (Fig. 4(j)). For the peel stress Sy, the peak stress changed markedly from positive to negative at the left end of the lap zone (Fig. 4(g), which was beneficial and improved the load bearing ability of the joint [13]. The stress increases greatly near the parallel slot, especially for the peel stress Sy (Fig. 4(g)). 3.3. Effect of parallel slot depth The effect of the parallel slot depth on the stress distribution of the joint in the mid-bondline (y ¼ 0.1 mm) and the adherend near the interface (y ¼ 0.25 mm) along
the length of the lap zone is shown in Fig. 5 when the parallel slot length was kept constant at 7 mm and the parallel slot depth was taken as 1, 1.5 and 1.7 mm, respectively. As the parallel slot depth increased, the peak value of the longitudinal stress Sx in the mid-bondline near the free end of the adherend decreased and the stress level in the middle part corresponding to the parallel slot increased (Fig. 5(a)). The distribution of the 1st principal stress S1 (Fig. 5(d)) is also similar. For the peel stress Sy, the peak stress at the point corresponding to the edge of the parallel slot increases greatly as the depth of the slot increases, but the stresses in the middle zone are nearly the same (Fig. 5(b))
ARTICLE IN PRESS Z.-M. Yan et al. / International Journal of Adhesion & Adhesives 27 (2007) 687–695
and it is similar to what shows in Fig. 5(g) in the adherend near the interface. The stress distribution of the longitudinal stress Sx (Fig. 5(f)) and the 1st principal stress S1 (Fig. 5(i)) are also similar to that of the von Mises equivalent stress Seqv (Fig. 5(j)). On the whole, each peak stress near the end of the lap zone increases gradually as the slot depth increases while the peel stress Sy decreases a little. When the parallel slot depth was taken as 1.7 mm, all the peak stresses of Sx, S1 and Seqv in the adherend at the point corresponding to the edge of the slot reached a value over 170 MPa.
3.4. Effect of the elastic modulus of the adhesive When the parallel slot length and depth were kept at 7 and 1.5 mm, respectively, the effect of the elastic modulus of the adhesives on the stress distribution of joint in the mid-bondline was studied and the results from the FEM analysis are shown in Fig. 6 where the letter ‘‘N’’ means from the normal specimen (without a parallel slot). All the peak stresses increase as the elastic modulus of the adhesive increases for the joint with a parallel slot. The reason may be that the smaller the elastic modulus of the adhesive, the
20 1mm
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Longitudinal stress Sx (MPa)
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12 mm 1st principal stress S1 (MPa)
Shear stress Sxy (MPa)
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12 mm Longitudinal stress Sx (MPa)
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von Mises equivalent stress Seqv (MPa)
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12 mm
150
100
50
0 0
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12
Distance from the edge (mm)
16
0
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Distance from the edge (mm)
Fig. 4. Effect of the parallel slot length on the stresses distribution in the joint: longitudinal stress Sx in (a) mid-bondline and (f) adherend; peel stress Sy in (b) mid-bondline and (g) adherend; shear stress Sxy in (c) mid-bondline and (h) adherend; 1st principal stress S1 in (d) mid-bondline and (i) adherend and von Mises equivalent stress Seqv in (e) mid-bondline and (j) adherend.
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692
0 Shear stress Sxy (MPa)
Peel stress Sy (MPa)
16 8 0 -8
-6
-12 1mm
7mm
12 mm
-18 1mm
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4
7mm 8
12 mm 12
16
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4
Distance from the edge (mm) 200
12
16
200 1mm
7mm
von Mises equivalent stress Seqv (MPa)
1st principal stress S1 (MPa)
8
Distance from the edge (mm)
12 mm
150
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50
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Distance from the edge (mm)
Fig. 4. (Continued)
smaller is the stiffness of the joint and the stress concentration at the end of lap zone is also decreased. The longitudinal stress Sx (Fig. 6(a)) and the peel stress Sy (Fig. 6(b)) corresponding to the parallel slot increase as the elastic modulus of the adhesive increases. When a low elastic modulus adhesive was used, the effect of the parallel slot on each peak stress and the stress distribution in the mid-bondline was negligible. The reason is that the stress distribution along the bondline of the joint with a low elastic modulus adhesive was very smooth, and the stress concentration at the end is lower [15]. When a high elastic modulus adhesive was used, both the peak stresses and the stress distribution varied markedly. For the aluminum joint bonded with an adhesive of high elastic modulus, the original low stresses as well as their peaks in the middle of joint increased and much load was carried by that part while the stress concentration and the peak stress at the end of the lap zone was seem to decrease. 4. Conclusion When two parallel slots were arranged in the adherend, the peak values of the longitudinal stress Sx, the shear stress Sxy, the 1st principal stress S1 and the von Mises equivalent stress Seqv in the mid-bondline decreased
markedly and the stress level in the middle part of the overlap zone also increased. In the adherend near the interface, the peak stresses of the longitudinal stress Sx, the shear stress Sxy, the 1st principal stress S1 and the von Mises equivalent stress Seqv of the joint are almost the same at the point near the two ends of the overlap zone whether there is or is not a slot. When the slot existed, the stress level in the middle part of the overlap zone is higher than that of the normal joint. For the peel stress Sy, the peak stress changed markedly from positive to negative at the left end of the lap zone and it is of benefit to restrict the harmful effect of the peel stress on the joint. The values of the peak stresses in the mid-bondline decrease when the parallel slot length is increased, except that the peak peel stress Sy decreases all the time. As the parallel slot depth was increased, the stress in the midbondline at the point near the end of the lap zone decreases gradually while the stress in the middle part of the lap zone corresponding to the parallel slot also increases. The stress in the adherend with the parallel slot increases gradually as the parallel slot depth increases. In the joint with a parallel slot, the peak stress increases as the elastic modulus of the adhesive increases. The effect of a parallel slot on the peak stress and the stress distribution at the mid-bondline is negligible when a low
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693
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1st principal stress S1 (MPa)
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1.7mm
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Fig. 5. Effect of the parallel slot depth on the stresses distribution in the joint: longitudinal stress Sx in (a) mid-bondline and (f) adherend; peel stress Sy in (b) mid-bondline and (g) adherend; shear stress Sxy in (c) mid-bondline and (h) adherend; 1st principal stress S1 in (d) mid-bondline and (i) adherend and von Mises equivalent stress Seqv in (e) mid-bondline and (j) adherend.
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694
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12
0.05
Peel stress Sy (MPa)
Longitudinal stress Sx (MPa)
18 1.89 2.88-N
6
0.05
1.89 2.88-N
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-8
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4 8 12 Distance from the edge (mm)
1st principal stress S1 (MPa)
-4 -8 -12 -16
0.05-N 2.88
0.05
0
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0 Shear stress Sxy (MPa)
0.05-N 2.88
1.89 2.88-N
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32 0.05-N 2.88
0.05
1.89 2.88-N
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0 4 8 12 Distance from the edge (mm)
on Mises equivalent stress Seqv (MPav)
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16
32
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0.05
4 8 12 Distance from the edge (mm)
16
1.89 2.88-N
24 16 8
0
4 8 12 16 Distance from the edge (mm)
Fig. 6. Effect of the elastic modulus of the adhesive on the stress distribution in the joint with a parallel slot at the mid-bondline (unit: GPa): (a) longitudinal stress Sx; (b) peel stress Sy; (c) shear stress Sxy; (d) 1st principal stress S1 and (e) von Mises equivalent stress Seqv.
elastic modulus adhesive was used. When a high elastic modulus adhesive was used, the stress in the middle part of the joint increases while the stress concentration at the point near the end of the lap zone decreased, so that the peak stress decreases markedly.
Acknowledgements The authors would like to acknowledge the financial Supported by the Major Research Programs of Hubei Provincial Department of Education (2003Z001), China.
References [1] Adams RD, Wake WC. Structural adhesive joints in engineering. London: Elsevier Applied Science Publishers Ltd.; 1984. [2] Pires I, Quintino L, Durodola JF, Beevers A. Performanceof bi-adhesive bonded aluminium lap joints. Int J Adhes Adhes 2003;23(3):215–23. [3] Fitton MD, Broughton JG. Variable modulus adhesives: an approach to optimized joint performance. Int J Adhes Adhes 2005;25(4): 329–36. [4] Broughton WR, Mera RD, Hinopoulos G. Environmental degradation of adhesive joints single-lap joint geometry. Project PAJ3— combined cyclic loading and hostile environments 1996–1999 report no 69, 1999.
ARTICLE IN PRESS Z.-M. Yan et al. / International Journal of Adhesion & Adhesives 27 (2007) 687–695 [5] Lang TP, Mallick PK. Effect of spew geometry on stresses in single lap adhesive joints. Int J Adhes Adhes 1998;18:167–77. [6] You M, Zheng Y, Zheng XL, et al. Effect of metal as part of fillet on the tensile shear strength of adhesively bonded single lap joints. Int J Adhes Adhes 2003;23:365–9. [7] You M, Zheng Y, Zheng XL, et al. Failure analysis of adhesively bonded single lap joints embedded with metal component as part of fillet. Key Eng Mater 2006;324–325:727–30. [8] Avila AF, Bueno PO. Stress analysis on a wavy-lap bonded joint for composites. Int. J Adhes Adhes 2004;24:407–14. [9] Sancaktar E, Nirantar P. Increasing strength of single lap joints of metal adherends by taper minimization. J Adhes Sci Technol 2003; 17(5):55–67. [10] Oterkus E, Barut A, Madenci E, et al. Bonded lap joints of composite laminates with tapered edges. Int J Solids Struct 2006;43:1459–89.
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[11] Belingardi G, Goglio L, Tarditi A. Investigating the effect of spew and chamfer size on the stresses in metal/plastics adhesive joints. Int J Adhes Adhes 2002;22:273–82. [12] Sancaktar E, Simmons S. Optimization of adhesively bonded single lap joints by adherend notching. J Adhes Sci Technol 2000;14(11): 1363–404. [13] Shokrieh MM, Lessard LB. An assessment of the double-notch shear test for interlaminar shear characterization of a unidirectional graphite/epoxy under static and fatigue loading. Appl Composite Mater 1998;5:289–304. [14] Pettersson KB, Neumeister JM. A tensile setup for the IDNS composite shear. Composites: Part A 2006;37:229–42. [15] You M, Yan ZM, Zheng Y, et al. Effect of fillet on bi-adhesive bonded aluminum lap joints. Trans Nonferrous Met Soc China 2005;15(S3):344–8.