The effect of adherend alignment on the behaviour of adhesively bonded double lap joints

Int. J. Adhesion and Adhesives 16 (1996) 241-247

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~, 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved 0143-7496/96/$15.00 ELSEVIER

PII: S0 ! 43-7496(96)00012-7

The effect of adherend alignment on the behaviour of adhesively bonded double lap joints L. Tong Department of Aeronautical Engineering, University of Sydney, Sydney, NSW 2006, Australia

A. Sheppard Cooperative Research Centre for Aerospace Structures, 361 Milperra Road, Bankstown, NSW 2200, Australia

D. Kelly School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, NSW 2050, Australia (Accepted 15 February 1996)

For an adhesively bonded double lap joint, end mismatch between the two outer adherends can not be removed completely although it can be controlled within a manufacturing tolerance. This paper shows that the end mismatch introduces local bending and, consequently, results in a significant effect on the surface normal displacement. Furthermore, the end mismatch also affects the shear and peel stresses in the adhesive. To include the end mismatch effect, a modified equation is developed to characterise the peel stress in the adhesive layer in terms of the surface normal displacement measured using the holographic interferometry technique. The surface normal displacement predicted by the FEM is validated experimentally. A good correlation is also noted between the adhesive peel stress computed using the FEM and that calculated using the modified equation and the measured surface normal displacement. (Keywords: C. finite element stress analysis; D. fracture; stress distribution; adherend alignment)

INTRODUCTION Adhesively bonded lap joints have been investigated by many researchers using various methods 1. It was shown that the peel and shear stresses in the adhesive are not uniform along the overlap length and their gradients are very steep close to the ends of the joint overlap. To confirm this prediction experimentally, a variety of techniques have been used by various researchers ~7. Dillard et al. 2 and Anderson e t al. 3 developed a piezoelectric sensor and embedded it in the adhesive layer to measure the average peel stress over the sensor area for a single lap joint and a butt joint. Although the technique requires a dynamic loading and has temperature restrictions, it provided a reasonable point-wise correlation between the measured and calculated peel stresses. Tuttle e t al. 4 embedded strain gages in the bonded joints to measure the strain in the joints. Tsai and Morten 5 used the Moire fringe technique to measure the displacement fields from a sideview of a single lap joint. A correlation was obtained only for the shear stress in adhesive between the experimental and the theoretical predictions. Measurement

for the peel stress was not in agreement with the prediction close to the end of the overlap. Tong et al. 16 proposed an approach that can be used to confirm the peel stress prediction for an adhesively bonded double lap joint. In this approach, the surface normal displacement of the outer adherend was assumed to be measured using holographic interferometry technique 7 9. It was also assumed that the two outer adherends are perfectly aligned and there is no end mismatch. However, in practical manufacturing, it is difficult to perfectly align the two outer adherends during the bonding process although their lengths can be kept within a tight tolerance. In this paper, a numerical study is first presented to show the effect of the end mismatch on the mechanical behaviour of adhesively bonded double lap joints. Parametric results show that the end mismatch has a noticeable effect on the adhesive peel and shear stresses and a significant effect on the surface normal displacement. Secondly, the effect of end mismatch was then included in the peel stress formula developed by Tong et al. 6 Finally, the surface normal displacement and the peel stress in the adhesive layer were validated by

INT. J. ADHESION AND ADHESIVES Volume 16 Number 4 1996

241

Adhesively bonded double lap joints: L. Tong et al. comparing them with the experimental results measured using the holographic interferometry technique.

N U M E R I C A L M O D E L L I N G A N D RESULTS In the manufacturing of the adhesively bonded double lap joint specimens, it was found that the two outer adherends could not be aligned appropriately during the bonding process although their lengths were cut to an acceptable tolerance. It was found that it was difficult to remove the end mismatch between the two outer adherends. It is assumed in this study that the lengths of the two outer adherends are the same and there only exists an end mismatch between the two outer adherends because an end mismatch between the two adherends seems to be inevitable during the bonding process. As a result, a modified specimen geometry was used as shown schematically in Figure 1. The nominal dimensions of a specimen with an end mismatch are: the outer adherend thickness t is 1 mm, the inner adherend thickness 2t is 2mm, the adhesive thickness ta is 0.19mm, the overlap length 2l is 6 0 m m and the width of the specimen is 25mm. The end mismatch was varied to see its effect. The specimen adherends were made of Aluminium 2024-T3, and the adhesive used was FM300-K. The material properties of Aluminium 2024-T3 and adhesive FM300-K were detailed in Table 1. For all parametric studies, a tensile load P of 7 K N was applied. Finite element analyses were conducted using MSC/ N A S T R A N 1°. The plane strain finite element models of the joint specimen were generated using four node isoparametric quadrilateral elements. The whole joint specimen was modelled because the presence of the end mismatch nullifies the geometrical symmetry. Through the adhesive thickness of the models, i.e. y-direction, one element was used. To reduce the number of elements in the models a relatively coarse mesh was used along the length (i.e. x-direction, see Figure 2) but was refined in regions where the stress gradients were expected to be high. The elastic-plastic material nonlinear analysis was incorporated by assuming that both the adhesive and the adherend were isotropic and using the data given in Table 1. The Von Mises yield criterion was used for both the adhesive and adherends.

P.m----[ I~ L - - ~ X Figure I

242

Geometric configuration of the double lap joint

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Table 1 Material property Item

Adhesive (FM300-K)

Adherend (2024-T3)

Elastic Young's modulus Elastic Poisson's ratio apl MPa col %2 MPa ep~ ap3 MPa F,,p3 trp4 MPa ep4 ap5 MPa co5

2.515 GPa 0.36 30.2 0.012 45.1 0.0201 57.8 0.031 67.9 0.05 71.3 0.092

70.34 GPa 0.3 338 0.0048 355 0.006 362 0.0098 -----

To illustrate the effect of the end mismatch on the adhesive stresses and surface normal displacement, a parametric study was conducted using a number of finite element models, as shown in Figure 2, for the specimen with the end mismatch d (see Figure 1) varying from 0 to l mm. The effect of the end mismatch on the peel stress and shear stress as well as the surface normal displacement are addressed. Figure 3 (a) depicts the peel stress distribution along the adhesive layer in the overlap for the joints with the end mismatch of 0 and 1 mm. Obviously, when there is no end mismatch peel stress distribution is symmetric about the midpoint and when there is an end mismatch of 1 mm, the peel stress at the left end decreases while the peel stress at the other end increases. The maximum increase and decrease are depicted in Figure 3(b) for a variety of joints with the end mismatch ranging from 0 to 1 mm. The maximum increase and decrease are about 15% and 24% of the peak peel stress for perfect aligned specimens, respectively. Figure 4(a) shows the shear stress distribution in the adhesive layer along the overlap for the joints with the end mismatch being 0 and 1 mm. The variations of the peak shear stresses at both ends of the joints with the end mismatch ranging from 0 to 1 mm are depicted in Figure 4(b). The maximum increase is about 5%, while the maximum decrease is about 9%. It is evident that the end mismatch has less influence on the shear stress than it does on the peel stress when the end mismatch varies from 0 to 1 mm. Figure 5 shows the surface normal displacement distributions along the overlap for the joints with the end mismatch being 0, 0.5 and 1 mm. It is shown that a small end mismatch between the top and bottom doublers due to the manufacturing tolerance have an important effect on the distribution pattern of the outof-plane surface displacement. An end mismatch produces a local bending moment that can be approximated as a constant across the overlap length. The bending moment creates an additional out-of-plane displacement similar to a single-lap joint. Thus, the total normal displacement can be approximated as the sum of the displacement of the perfect joint and this additional displacement. For the specimen with a small

INT. J. ADHESION AND ADHESIVES Volume 16 Number 4 1996

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INT. J. ADHESION A N D ADHESIVES Volume 16 Number 4 1996

243

Adhesively bonded double lap joints: L. Tong et al. EEa trpl - (E + kEa)t, (wsr -

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where tr = P / 2 b t and E, v and Ea, va are the Young's modulus and the Poisson's ratio for the adherend and the adhesive, respectively. To validate equation (1) numerically, let us compare the peel stresses given by the finite element analysis with those computed using equation (1) and the surface normal displacement of the finite element analysis. Figures 6(a) and 6(b) compare the peel stress distributions given by the finite element analysis and these computed using equation (1) with k = 0 or 1 for the specimen with an end mismatch of 0.1 mm. A reasonable correlation is noted between the stresses given by the finite element analysis and equation (1).

o -0.15 '~

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EXPERIMENTAL VALIDATION

-0.25

End mismatch (mm)

Figure 3(b)

Effect of end mismatch on maximum peel stresses at x = 0 and x = 60mm

end mismatch, this extra surface normal displacement can be approximated as a rigid body rotation by an angle about the midpoint. The angle can be determined as the slope of the surface normal displacement at the midpoint along the overlap. Similar to the surface normal displacement caused by the Poisson's ratio effects, this extra surface normal displacement needs to be subtracted from the total displacement.

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MODIFIED PEEL STRESS EQUATION Tong et a116 presented an equation that can be used to characterise the peel stress in the adhesive in terms of the surface normal displacement for a perfectly aligned double lap joint. However, when the end mismatch is present, a modified equation is needed to include the effect of end mismatch. As shown numerically in the previous section, total surface normal displacement is the sum of the displacement of the perfect joint and the extra displacement caused by the end mismatch, thus the surface normal displacement contributing to the peeling behaviour should be the total displacement minus the extra displacement and minus the displacement created by the Poisson contraction. As a result, the equation for characterising the peel stress in the adhesive layer developed by Tong et al. 6 can be modified as"

244

Overlap position (ram) Figure 4(a)

Effect of end mismatch on shear stress distribution along the overlap

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INT. J. ADHESION AND ADHESIVES Volume 16 Number 4 1996

Adhesively bonded double lap joints: L. Tong e t

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Overlap position (mm) Figure 5 Effectof end mismatch on the distribution of the surface normal displacementalong the overlap 2024-T3, and the adhesive used was FM300-K. The specimen was bonded following the manufacturer's recommendation with special effort to control the adhesive thickness and to minimise the end mismatch. It was discovered that a mismatch of 0.1 mm had developed. The PHITS (portable holographic interferometry technique system) experimental set-up 9 was used to measure the surface normal displacement of the outer adherend of the specimen 11, =2. The technique uses singlebeam reflective holographic interferometry to obtain interferograms of displacement between two load states. The PHITS set-up contained a laser unit and a 2O

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Overlap length (nun) Figure 6(a) Comparison betweenpeel stresses predicted by the FEM and Eqn (l) (k = 1)

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Overlap length (ram) Figure 6(b) Comparison between peel stresses predicted by FEM and equation (1) (k = 0)

INT. J. A D H E S I O N

holographic plate. The laser unit, mounted on a conventional camera tripod, consisted of a spatial filter, a beam expander and a laser source. A holographic plate was attached to one side of the bonded joint at two locations using double-sided adhesive tape. The laser light absorbed by the plate on its first pass represents the reference beam while the light reflected from the surface of the measured object is the object beam. Through double exposure, the change in out-of-plane surface displacement between two load steps can be picked up by the fringes in the hologram. Thus the relative out-of-plane surface movement can be computed using the following equations11: For bright fringe:

n2 W = ~-

(3(a))

For dark fringe:

W - (2n +4 1)2

(3(b))

Where W denotes the out-of-plane surface displacement, n is an integer and 2 is the wave-length of the laser light (0.633/~m). However, determination of the absolute displacement requires the absolute displacement of a fringe and the sign of the gradient fringe to be known. In general, it is difficult to define the absolute displacement and to determine the sign of each fringe without a physical understanding of the problem. However, a closing U-shape contour can indicate the change of the gradient associated with the maximum (hill) or minimum (valley). To minimise the effect of the end mismatch, a rig to hold the specimen was used to shorten the free length of the central adherend in order to reduce the local bending effect. In addition, the specimen was carefully installed on the Instron machine to ensure appropriate alignment. After installation, the specimen was loaded and two exposures were taken at different load levels. The first exposure was taken at a load level of 1.0 kN, and the second exposure taken at 7.0kN. The holographic plate was then developed and dried to obtain the interferometric fringes. The fringes were then analysed using equation (3) and the surface normal displacement

AND ADHESIVES Volume

16 N u m b e r

4 1996

245

Adhesively bonded double lap joints: L. Tong et al.

~ 1.2

. 1.2

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Overlap length (mm)

Figure 7 Experimental and numerical correlation for Surface displacement along centreline of the overlap

Figure 9 Experimental and numerical correlation for Surface displa-

was obtained. In the following results the displacement distributions are only given for half of the specimen along the centreline (half width of the specimen) and along the edge of the specimen. Figure 7 depicts the surface normal displacement distribution measured using the holographic technique l~ along the centreline (half width of the specimen) of the overlap and also that computed using the finite element method 1°. A reasonable correlation between the test data and the numerical prediction is observed. The peel stress is computed using equation (1) and the measured surface normal displacement and then compared with these given by the finite element method. These comparisons are shown in Figure 8(a)

(with k = 1) and Figure 8(b) (with k --- 0). Figures 8(a) and 8(b) show a good correlation between the stresses measured and computed using FEM. Figure 9 depicts the surface normal displacement distribution along the edge of the overlap measured using the holographic technique and that computed using the finite element method. A better correlation between the test data and the numerical prediction is observed. The peel stress is computed using equation (1) and the measured surface normal displacement and then compared with these given by the finite element method. These comparisons are shown in Figure lO(a) (with k = 1) and Figure lO(b) (with k = 0). A good correlation is noted for the peel stress.

cement along one edge of the overlap

20

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N

8

Experimental

4 0 10

15

20

25

10

30

15

20

25

30

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-4

Overlap length (mm)

Overlap length (mm)

Figure 8(a)

Experimental and numerical correlation for peel stress (k = 1) along centreline of the overlap

'6i

Figure I0(a)

Experimental and numerical correlation for peel stress (k = 1) along one edge of the overlap 20

20

161

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:: 1'0"

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"

20

25

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~4

Overlap length (mm)

Overlap length (ram)

Figure 8(b) Experimental and numerical correlation for peel stress

Figure lO(b) Experimental and numerical correlation for peel stress

(k = 0) along centreline o f the overlap

(k = O)

246

INT. J. ADHESION AND ADHESIVES Volume 16 Number 4 1996

Adhesively bonded double lap joints: L. Tong et al. 2

CONCLUSIONS

3 This p a p e r investigates the effect o f end m i s m a t c h o n the b e h a v i o u r o f an adhesively b o n d e d d o u b l e lap joint. T h e results indicate t h a t an end m i s m a t c h causes local b e n d i n g a n d thus has a significant effect on the surface n o r m a l d i s p l a c e m e n t o f the o u t e r a d h e r e n d a n d the stresses in the adhesive layer. Increase in adhesive stresses, especially in peel stress, d u e to presence o f an end m i s m a t c h is n o t desirable as it can cause p r e m a t u r e failure. Hence end m i s m a t c h in d o u b l e lap j o i n t s s h o u l d be minimised. T o include the end m i s m a t c h effect, a m o d i f i e d f o r m u l a was d e v e l o p e d that c h a r a c terises the peel stress in terms o f the surface n o r m a l d i s p l a c e m e n t . U s i n g the P H I T S e x p e r i m e n t a l set-up, surface n o r m a l d i s p l a c e m e n t was m e a s u r e d for a specimen, a n d then used to v a l i d a t e the m o d i f i e d f o r m u l a . A g o o d c o r r e l a t i o n was observed.

4 5

6 7 8 9

10 11

12

REFERENCES 1

Dillard, D.A., Anderson, G.L. and Davis Jr, D.D. Journal ~f Adhesion 1989, 29, 235

Adams, R.D. and Wake, W.C. 'Structural Adhesive Joints in Engineering', Elsevier, London, 1984

Anderson, G.L., Robertson, R.C., Peterson, B.L. and Dillard, D.A. Experimental Mechanics 1994, September, 194~201 Tuttle, M.E., Barthelemy, B.M., Brison, H.F. Experimental Mechanics 1984, 8, 31 Tsai, M.-Y. and Morton, J. Mechanics of the adhesive-bonded single-lap joint specimen. Con. Pro.." Pacific Int. Conf. on Aerospace and Technology, Vol. II, P1CAST'I 1993, December 1993, Taiwan, pp. 936-944 Tong, L., Sheppard, A. and Kelly, D. Int. J. Adhes. Adhes. 1995, 15, 4348. Vallat, M.F., Martz, P., Fontaine, I. and Schultz, S. J. Appl. Polymer Science, 1986, 31,309-321 Gregory, D.A. NDTInt. 1979, 12(2), 71 70 Baird, J.P., Williamson, H.M., Clark, R.K. and Brown, G. A new holographic technique for the detection of fatigue cracks in riveted aircraft structures, Int. Conf. on Aircraft Damage Assessment and Repair, Melbourne, 26-28 August 1991 MSC/NASTRAN V67 'User's Manual' Vol. 1, MacNealSchwendler Corporation, 1992 Zhuang, W.Z.L., Baird, J.P., Clark, R.K., Williamson, H.M. and Heslehurst, R.B. 'Peel displacement measurement of bonded double lap joints by holographic interferometry', Research report, Department of Aerospace and Mechanical Engineering, Australian Defence Force Academy, Canberra, 1994 Tong, L., Kelly, D., Chalkley, P., Sheppard, A., Zhuang, W. and Baird, J. 'Test programs for joints in thin skins', Proc. of the 2nd Pacific Int. Conf. on Aerospace Science and Technology--Sixth Australian Aeronautical Conference 2(~23

March 1995, Melbourne, Australia, pp. 663-668

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