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The effect of a spew fillet on adhesive stress distributions in laminated composite single-lap joints
Composite Stmchms 32 (1995) 123-13 1 0 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved 0263~8223/95/$9.50 0263-8223(95)00059-3
The effect of a spew fillet on adhesive stress distributions in laminated composite single-lap joints M. Y. Tsai Department of Engineering Science and Mechanics, T/irginiaPolytechnic Institute and State University, Blacksbutg, VA 24061-0219, USA
&
J. Morton Structural Materials CenteG DRA, Famborough, Hampshire GU14 6TD, UK
A laminated composite single-lap joint without a spew fillet, subjected to tensile loading, is investigated experimentally and numerically. By directly comparing the experimentally- and numerically-determined deformations of the single-lap joints with and without a fillet, the effect of a spew fillet on adhesive stress distributions is discussed. Moire interferometry is used to measure the in-plane surface deformation of the overlap region of the test specimens. The deformation interactions of the laminated adherends, adhesive layer and a fillet are documented in the form of orthogonal components of the displacement fields (u and v). Two-dimensional, geometrically linear and nonlinear finite element analyses are performed to simulate the mechanical response of the laminated composite single-lap joint and the effect of a spew fillet. Experimental and numerical results indicate that the adhesive shear and peel strain (stress) concentrations can be reduced greatly by introducing a fillet at the end of the overlan, and by the geometrically no&near these concentrations are affected deformation of the single-lap joint.
theoretically, numerically and experimentally for more than half a century,3-7 single-lap joints with laminated composite adherends have also received some attentions-10 due to the increasing use of laminated composite structures. By comparing and evaluating several theoretical and numerical models, Oplingerl’ pointed out that factors such as transverse shear deformation, transverse normal strain, material nonlinear behaviour of adherends and adhesives, viscoelastic behaviour, thermal effect, and fracture mechanism should be incorporated in modeling any configurations of composite bonded joints. In addition, general reviews related to the composite joints have been provided by several researchers.1z-14 Despite the research efforts on composite joints, the mechanics of laminated composite adhesive joints have not been comprehensively
INTRODUCTION Adhesive bonded joints offer advantages over mechanically fastened and riveted joints in time and cost savings, higher strength to weight ratios, corrosion and fatigue resistance, crack retardance, damping characteristics and so ‘,’ Adhesive bonding of composite structures :zs additional merits in avoiding the drilled holes (and broken fibres) and reducing stress concentrations. However, factors such as the inherent material heterogeneity, residual stresses, free-edge effects, and relatively low transverse strength and shear stiffness, impose greater complexity to the case of adhesive bonded composite structures as opposed to homogenous isotropic structures. Although the problem of the single-lap joint with isotropic adherends has been investigated 123
124
M. Y Tsai, J. Morton
the adherend is 25.4 mm. The material for the adherend is graphite/epoxy (XAW914C). The lay-up is [O/45/-45/0],, with fiber orientation defined in Fig. 2. For the purpose of subsequent numerical analysis, the material properties in each unidirectional lamina are taken as longitudinal elastic modulus El = 138 GPa, transverse E2=9.4 GPa, in-plane shear G12=6.7 GPa and Poisson’s ratio v12=0.32. Note that the subscripts 1 and 2 represent the fiber and matrix directions in a single lamina. The two adherends are bonded together with a thin adhesive layer (~=0.13 mm). The material for the adhesive is epoxy resin (Redux 308A) with elastic modulus E,=3 GPa and Poisson’s ratio v,=O.31. Two end tabs were used for loading applied and easy alignment. Nonlinear behavior for this adhesive appears in deformations beyond about 3% shear strain and about 1.5% normal strain. Shear plastic deformation occurs after 10% shear strain. A moire grating with a frequency of 1200 lines/mm was replicated on the edge surface of the overlap, shown in Fig. 2. Moire inteferometry is an optical method for measuring in-plane surface deformation.15 The moire fringe patterns u and v represent the horizontal and vertical displacement contours, respectively. The governing equations for strain determination from the displacement fields are,
treated. The specific problem of a laminated composite single-lap joint with a 45” spew fillet has been investigated and the results have been The objective of this study is to published.” investigate a composite single-lap joint with and without a spew fillet experimentally and numerically and thus understand the role of a spew fillet in the laminated composite single-lap joint.
EXPERIMENTAL
PROGRAM
A two-dimensional schematic of the single-lap joint is shown in Fig. 1. For the geometric parameters, 1 is the length of the outer adherend, 2c the length of the overlap, t the thickness of the adherend, q the thickness of the adhesive and a, a force-eccentricity angle. E, and v, respectively represent the adhesive elastic modulus and Poisson’s ratio. The resultant force per unit width, T’, is approximately equal to the longitudinally applied force per unit width, T, when a, < 1 (usually LX,~0.1). An applied force, F, is defined as T x b, in which b is the width of the adherend. p is an applied stress which is denoted as TJt. A laminated composite single-lap specimen without a fillet is shown in Fig. 2 where Z=101.6 mm, 2c=254 mm, t=2 mm and the width of
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Geometry
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1
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Moire surface grating
(0/45/-451O)zs
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of the composite
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and moirC grating replication.
Effect of spew fillets on stress dhributions
au f%=-=ax
,y=-=-
1 aN, f ax
av
1 alv,
aY
f
-
(1)
aY
au av ‘“=y +-=ax
1 f
aiv, arv, (F+T)
where f=2400 lines/mm in the system used and N, and NY denote the fringe orders in the u and v fields. The sensitivity of measurement is 0.417 pm per fringe order. A portable achromatic was employed in the moire interferometer-l6 experiment. This system features vibration insentivity which allows the specimen to be tested in a conventional testing machine. This system also provides simultaneous measurement of u and v displacements so that the shear deformation of the loaded body can be resolved. The moire technique was used to obtain the surface deformations of the adherends and adhesive in the region, located on the edge surface of the overlap, covered with the moire
125
grating shown in Fig. 2. Typical fringe patterns are shown in Fig. 3 which contains the horizontal (u) and vertical (v) deformations of half an overlap for the specimen without a fillet, under an applied load, F=3202 N (720 lb). In order to provide a direct comparison of moire fringes, the u-field fringe patterns in regions, distance 3t away from the end of the overlap (in Fig. 4) and around the end of the overlap (in Fig. 5) are shown for the specimens with and without a 45” spew fillet, under the same load (F~4448 N or 1000 lb). It is apparent in Fig. 4 that the u-field fringe patterns away from the fillet-affected region for both specimens are almost the same. Both longitudinal normal strain distributions across the thickness of the overlap, extracted from these moire fringes, are also in a very good agreement. Good agreement in the deformation of the far fields for two different specimens (with and without a fillet) provide confidence for further comparing deformations in the near fields around the end of the overlap for both specimens, which are shown in Fig. 5. The resulting adhesive strain distributions for both specimens are shown in Fig. 6.
(a) u-field
(b) v-field
Fig. 3.
Typical moire fringe patterns: (a) u displacement field (b) v displacement field, for a laminated composite singlelap joint, without a fillet, under an applied load, F=3202 N (720 lb).
126
M. Y Tsai, J. Morton
u-field with a fillet
u-field without a fillet
0
0.05
0.1
0.15
0.2
qw Fig. 4.
Comparisons of u-field moirC fringe patterns and longitudinal away from the end of the overlap, for the specimens with and without 1000 lb).
FINITE ELEMENT
ANALYSIS
Geometrically linear and nonlinear two-dimensional finite element analyses using the ABAQUS code were performed to model the deformation of the laminated composite singlelap joint. Two entire single-lap joint models (joints with and without fillet), shown in Fig. 7, were analyzed. The geometric boundary conditions include a hinge on the center line of the adherend at one end and a roller at the other. A force is applied horizontally at the roller end. For these end conditions, the resultant force generated always passes through the center of the overlap, so that antisymmetrical loading and deformed conditions are achieved. The plane strain condition assumed in these analyses fails to capture/represent the effect of in-plane shear and bending-twisting coupling which are gen-
strain, cx, distributions at the region, 3t distance a spew fillet under a similar load (Fz4448 N, or
erated by the presence of +45” layers. Constant-strain (stress) elements were used for the adherends and adhesive. There were two elements across the thickness of the adhesive layer, except for the spew fillet, and one element for each lamina of the laminated composite adherends. The material of each lamina is modelled as orthotropic, while the material of the adhesive as isotropic. Due to the use of two the constant-strain (stress) elements across the thickness of the adhesive, the strain (stress) values calculated siong the center line of the adhesive represent approximately the average values over the thickness. To increase the accuracy of the numerical calculation, the finer meshes were adopted near and at the end of the overlap. The geometry, dimensions and material properties of the adherend and adhesive in the numerical analyses are the data
Effect of spew fillets on stress distributions
127
(b) Fig. 5. Moirt fringe patterns in the region near the end of the overlap: (a) u displacement field, for a laminated corn posite single-lap joint, without a fillet, under an applied load, F=4337 N (975 lb) (b) u displacement field,” for a laminated composite single-lap joint, witha 45” spew fillet, under an applied load, F=4448 N(1000 lb).
128
M. Y Tsai, J. Morton
described in the experimental program, and it is assumed that Es=Ez, Gr3=Gi2 and ~13=~12.
RESULTS AND DISCUSSION 0.5
-2.5
-3
-3.5
I ,
1.2
1.4
Fig. 6. Comparisons of adhesive strain cnstrmuttons determined from moire experiments for the laminated composite single-lap joint specimens with and without a spew fillet under a similar load (FE 4448 N, or 1000 lb).
The global bending deformation of the test specimen is verified by comparing the results from experimental measurement and finite element analyses. The longitudinal strain response at points 1 and 2, where back-to-back adherend surfaces are at positions about 25 t away from the end of the overlap, are shown in Fig. 8 for various applied loads per unit width (T=F/b) from the finite element analyses (linear and nonlinear) and strain gauge measurement. It is apparent .that the experimental results are in good agreement with those from the nonlinear finite element analysis, rather than from the linear analysis. Thus the specimen deformed geometrically nonlinearly and the bending
Ec ,vc
Fig. 7.
Finite
element
model; geometry,
boundary conditions and detailed with and without a spew fillet.
meshes used the composite
single-lap
joints
Effect of spew fillets on stress distributions
0.61
I
I
T, load (N/mm) Fig. 8. Comparisons of longitudinal normal strain responses at the points near the end of the overlap from experimental measurement and finite element analyses (linear and nonlinear models).
strains near the end of the overlap predicted from the linear analysis are larger than that from the nonlinear analysis. A detailed comparison of moire u-displacement field near the end of the overlap for the joints with and without a spew fillet is shown in Fig. 5. Both joints have the same lay-up and are under similar loads. The numbers marked on the fringe patterns are the u-field fringe order, Nx. These fringe patterns are obtained by optically reducing the number of v-field fringes as much as possible, at the center point of the overlap by introducing a carrier pattern of rotation. Thus, the term of au/ay in the calculation of shear strain in eqn (1) becomes dominant. That is, the u displacement gradient in the y direction ((aNx/ay)lf) approximately represents the shear strain component. It is observed that the aNxli3y for the joint without a spew fillet in the adhesive near and at the end of the overlap is larger than that for the joint with a spew fillet. The 45” spew fillet carries a portion of shear strains which are used to transfer the longitudinal load from the lower adherend to the upper. This argument can be confirmed by observing that the fringes for the joint without a fillet, at the upper adherend near the end of the overlap are almost horizontal and parallel, while the fringes for the joint with a fillet are inclined. Thus the upper adherend for the joint
129
with a fillet near the end of the overlap carries the longitudinal normal strains (.sx) unlike the joint without a fillet. This existence of a, indicates that the fillet does help transfer a part of the longitudinal load from the lower adherend to the upper through shear. The adhesive strain distributions obtained from the moire experiment are shown in Fig. 6 for the composite joints with and without a spew fillet under a load, Fr4448 N. These strain values are calculated by averaging the value over the thickness of the adhesive. The E, components are not shown, because of the difficulty of extracting zXdata from the joint without a fillet, due to high density of the fringes near and at the end of the overlap. For the peel strain (a,,) distributions, the location of tensile strain on the free surface moves from the end of the overlap to the end of the spew fillet as a result of the presence of the spew fillet. Note that the adhesive peel strain is very sensitive to three-dimensional effects.17 E,, measured from the free surface does not represent that in the interior, since E,, is more compressive than that in the interior. For the shear strain (yV) distributions, the maximum shear strain occurs at the end of the overlap for both cases. However, the value of the maximum shear strain for the joint with a fillet is only about 40% of that for the joint without a fillet. And the 45” spew fillet carries a certain degree of shear. Apparently the spew fillet is able to reduce significantly the adhesive shear strain concentration at the end of the overlap. Since the surface deformation recorded from the moire experiment does not fully represent that in the interior (especially for the peel strain component), the two-dimensional plane strain finite element analysis, however, does provide the deformation in the interior. Note that the adhesive shear strain (yxy) distributions for the joint without a fillet are insensitive to threedimensional effects,17 while those with a fillet are not near and at the spew fillet.18 Accordingly, a comparison of the adhesive shear distributions from numerical and experimental results can be used to confirm the validity of both results. The adhesive shear strain distributions determined from the moire experiment and two-dimensional finite element analysis are shown in Fig. 9 for joints with and without a fillet, under Fr4448 N. A very good agreement for the adhesive shear distributions is found in the joint without a spew fillet, while a partially
M. Y Tsai, J. Morton
130
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’
’
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Fig. 9. Comparisons of the adhesive shear strain distributions, obtained from the moire experiment and the nonlinear finite element analysis for the composite joints with and without a spew fillet, under F=4448 N (1000 lb).
disagreement near the end of overlap and at the spew fillet is shown in the joint with a fillet. This disagreement between on the surface and in the interior is expected, according to the three-dimensional analysis.” After validating the geometrically nonlinear finite element model which represents the stress (strain) state in the interior, the resulting adhesive strain and stress distributions are shown in Fig. 10(a) and (b), respectively, for composite joints with and without a spew fillet, under F=7619 N. In Fig. 10(a) the position of maximum aY moves from the end of the overlap to the end of the spew fillet, as observed in moire experiment, and the value decreases significantly due to the presence of the spew fillet. The spew fillet carries appreciable amounts of shear strains. Thus, the spew fillet helps reduce the maximum shear strain in the end of the overlap. E,, especially for the joint with a fillet, is not small enough to be neglected in terms of its contribution to initial failure. For the adhesive stress distributions in Fig. 10(b), the maximum values of oY and zV which are dominant in failure initiation in the joint without a fillet decrease greatly in the presence of the spew fillet. The maximum 0x located near and inside the end of the overlap for the joint without a fillet moves to the position outside of the overlap with a fillet. This maximum o, in the joint with a fillet is comparable to other stresses (cry and z~), so that it cannot be excluded in a failure analysis. Due to the nature of geometrically nonlinear deformation in the single-lap joint, the adhesive
’ 0.6
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0.6
0.4
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0.2
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’ 0
’ 0.2
’
’ 0.4
’
’ 0.6
’
’ 0.8
’
1
’ 1.2
x/c
Fig. 10.
(a) Adhesive strain distributions and (b) adhesive stress distributions, determined from the nonlinear finite element analyses for the composite single-lap joints with and without a spew fillet, under F=7619 N (1713 lb) or p= 150 MPa (21.7 ksi).
stress concentrations vary with the change of an applied load, and are affected by introducing a fillet. The maximum adhesive stresses normalized by the applied stress, p, are plotted against the applied stresses for composite joints with and without a 45” spew fillet in Fig. 11, which is determined from nonlinear finite element analyses. The values of o,, and “.V are plotted at the end of the overlap for the joints with and without a fillet. Note that the sign of z_ is ignored. The plotted values of a, are located 1.5 adhesive thicknesses inside the end of the overlap for the joint without a fillet, and outside the end of the overlap for the joint with a fillet. It is apparent that the nonlinear deformation greatly affects the adhesive stress concentrations for both joints with and without a fillet. The stress concentrations from the linear analysis, (approximately equivalent to those at p=O)
EfSect of spew fillets on stress distributions
131
the financial support under the contract USDOT/FAA 93-G-064. The authors also thank Mr F. L. Matthews of the Center for Composite Materials, Imperial College for providing the test specimens.
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REFERENCES
v
0.6
1. National 0.5
_______________~
0.4
OY
0.3
” __.__.___________.______._.______.
2.
0.2 -
0.2
:Io:
O.l
50
100
150
200
250
3.
3000
P (MPa)
4. Fig. 11. Normalized maximum adhesive stresses vs applied stresses, p, for the composite single-lap joints with and without a spew fillet.
5. 6.
would be overestimated. The values of c,, and zV decrease significantly due to the effect of the spew fillet, while gX has a mild drop. After the large decrease of the oY and zqxy,the crXand rxy would become the dominant components for the joint with a fillet, rather than aY. CONCLUSIONS From the experimental and numerical studies, it is concluded that, in the laminated composite single-lap joint, the adhesive shear and peel strain (or stress) concentrations, generally occurring at the end of the overlap, are reduced significantly by introducing a fillet. This reduction of the stress concentration is attributed to the ability of the spew fillet to carry some of the shear stresses and thus plays a part in transferring an element of longitudinal load from one adherend to the other. The geometrically nonlinear deformation greatly affects the adhesive stress (strain) concentrations which, unlike the linear deformation, varies with the change of the applied load.
7.
8.
9.
10.
11.
12.
13. 14.
15.
16.
17.
ACKNOWLEDGEMENT The authors would like to express their gratitude to the Federal Aviation Administration for
18.
Material Advisory Board National Research Council. Structural adhesives: with emphasis on aerospace applications. Marcel Dekker Inc. New York, 1976. Kuno, J. K., Structural adhesives continue to gain foothold in aerospace and industrial use. In Structural Adhesives and Bonding, Proc. Structural Adhesives Bonding Conf., Technology Conference Associates, El Segundo, California, 1979. Volkersen, O., Die nietkraftverteilung in zugbeannietverbindungen mit konstanten spruchten laschenquerschnitten, Luftfahrtforschung, 15 (1938) 41-7. Goland, M. & Reissner, E., The stresses in cemented joints. J. Appl. Mech., 11 (1944) A17-A27. Hart-Smith, L. J., Adhesive-bonded single-lap joints. NASA. CR-112236, 1973. Oplinger, D. W., Effects of adherend deflections in single-lap joints. ht. .I. Solids & Struct., 31 (1994) 2565-87. Tsai, M. Y. & Morton, J., An evaluation of analytical and numerical solutions to single-lap joint. Znt. J. Solids & Struct., 31 (1994) 2537-63. Renton, W. J. & Vinson, J. R., Analysis of adhesively bounded joints between panels of composite materials. J. AppZ. Mech., (1977) 101-6. Mignery, L. A. & Schapery, R. A., Viscoelastic and nonlinear adherend effects in bonded composite joints. J. Adhesion, 34 (1991) 17-40. Tsai, M. Y., Morton, J. & Matthews, F. L. Experimental and numerical studies of a laminated composite single-lap adhesive joint. J. Comp. Mat., (in press). Oplinger, D. W., Stress analysis of composite joints. In Proc. Fourth Army Materials Technology Conference - Advances in Joining Technology, 1975. Matthews, F. L., Kilty, P. F. & Godwin, E. W., A review of the strength of ioints in fiber-reinforced plastics: part 2: adhesively bonded joints. Comp., (1982) 29-37. Vinson, J. R., Adhesive bonding of polymer composites. Polymer Eng. & Sci., 29 (1989) 1325-31. Adams, R. D., Strength predictions for lap joints especially with composite adherends: a review. J. Adhesion, 30 (1989) 219-42. Czarnek, R., Moire interferometry. Structural Testing, Society of Experimental Mechanics, 30 (1990) 195-200. Czarnek, R., High sensitivity moire interferometry with compact achromatic interferometer. Optics and Lasers in Engng, 13 (1990) 99-115. Tsai, M. Y. & Morton, J., Three-dimensional deformations in a single-lap joint. J. Strain AnaZysis, 29 (1994) 137-45. Tsai, M. Y. & Morton, J., Mechanics of the single-lap adhesive joint with laminated composite adherends. 17th Annual Meeting of Adhesion Society, Orlando, Florida, Feb. 1994.
The effect of a spew fillet on adhesive stress distributions in laminated composite single-lap joints M. Y. Tsai Department of Engineering Science and Mechanics, T/irginiaPolytechnic Institute and State University, Blacksbutg, VA 24061-0219, USA
&
J. Morton Structural Materials CenteG DRA, Famborough, Hampshire GU14 6TD, UK
A laminated composite single-lap joint without a spew fillet, subjected to tensile loading, is investigated experimentally and numerically. By directly comparing the experimentally- and numerically-determined deformations of the single-lap joints with and without a fillet, the effect of a spew fillet on adhesive stress distributions is discussed. Moire interferometry is used to measure the in-plane surface deformation of the overlap region of the test specimens. The deformation interactions of the laminated adherends, adhesive layer and a fillet are documented in the form of orthogonal components of the displacement fields (u and v). Two-dimensional, geometrically linear and nonlinear finite element analyses are performed to simulate the mechanical response of the laminated composite single-lap joint and the effect of a spew fillet. Experimental and numerical results indicate that the adhesive shear and peel strain (stress) concentrations can be reduced greatly by introducing a fillet at the end of the overlan, and by the geometrically no&near these concentrations are affected deformation of the single-lap joint.
theoretically, numerically and experimentally for more than half a century,3-7 single-lap joints with laminated composite adherends have also received some attentions-10 due to the increasing use of laminated composite structures. By comparing and evaluating several theoretical and numerical models, Oplingerl’ pointed out that factors such as transverse shear deformation, transverse normal strain, material nonlinear behaviour of adherends and adhesives, viscoelastic behaviour, thermal effect, and fracture mechanism should be incorporated in modeling any configurations of composite bonded joints. In addition, general reviews related to the composite joints have been provided by several researchers.1z-14 Despite the research efforts on composite joints, the mechanics of laminated composite adhesive joints have not been comprehensively
INTRODUCTION Adhesive bonded joints offer advantages over mechanically fastened and riveted joints in time and cost savings, higher strength to weight ratios, corrosion and fatigue resistance, crack retardance, damping characteristics and so ‘,’ Adhesive bonding of composite structures :zs additional merits in avoiding the drilled holes (and broken fibres) and reducing stress concentrations. However, factors such as the inherent material heterogeneity, residual stresses, free-edge effects, and relatively low transverse strength and shear stiffness, impose greater complexity to the case of adhesive bonded composite structures as opposed to homogenous isotropic structures. Although the problem of the single-lap joint with isotropic adherends has been investigated 123
124
M. Y Tsai, J. Morton
the adherend is 25.4 mm. The material for the adherend is graphite/epoxy (XAW914C). The lay-up is [O/45/-45/0],, with fiber orientation defined in Fig. 2. For the purpose of subsequent numerical analysis, the material properties in each unidirectional lamina are taken as longitudinal elastic modulus El = 138 GPa, transverse E2=9.4 GPa, in-plane shear G12=6.7 GPa and Poisson’s ratio v12=0.32. Note that the subscripts 1 and 2 represent the fiber and matrix directions in a single lamina. The two adherends are bonded together with a thin adhesive layer (~=0.13 mm). The material for the adhesive is epoxy resin (Redux 308A) with elastic modulus E,=3 GPa and Poisson’s ratio v,=O.31. Two end tabs were used for loading applied and easy alignment. Nonlinear behavior for this adhesive appears in deformations beyond about 3% shear strain and about 1.5% normal strain. Shear plastic deformation occurs after 10% shear strain. A moire grating with a frequency of 1200 lines/mm was replicated on the edge surface of the overlap, shown in Fig. 2. Moire inteferometry is an optical method for measuring in-plane surface deformation.15 The moire fringe patterns u and v represent the horizontal and vertical displacement contours, respectively. The governing equations for strain determination from the displacement fields are,
treated. The specific problem of a laminated composite single-lap joint with a 45” spew fillet has been investigated and the results have been The objective of this study is to published.” investigate a composite single-lap joint with and without a spew fillet experimentally and numerically and thus understand the role of a spew fillet in the laminated composite single-lap joint.
EXPERIMENTAL
PROGRAM
A two-dimensional schematic of the single-lap joint is shown in Fig. 1. For the geometric parameters, 1 is the length of the outer adherend, 2c the length of the overlap, t the thickness of the adherend, q the thickness of the adhesive and a, a force-eccentricity angle. E, and v, respectively represent the adhesive elastic modulus and Poisson’s ratio. The resultant force per unit width, T’, is approximately equal to the longitudinally applied force per unit width, T, when a, < 1 (usually LX,~0.1). An applied force, F, is defined as T x b, in which b is the width of the adherend. p is an applied stress which is denoted as TJt. A laminated composite single-lap specimen without a fillet is shown in Fig. 2 where Z=101.6 mm, 2c=254 mm, t=2 mm and the width of
C
d-
‘1
t
d-
I‘
C
I
I
I
t
i
t
!
9
1
Geometry
c ,vc and related parameters
l-101.6
I_ L101.6
2c-25.4
\
Materials: Adhenxdsz Graphite/f$oxy, Ahsive: Fig. 2.
Geometry
of a single-lap joint.
r,
!: 25.4
#SF
t
an Fig. 1.
1
25.4
Moire surface grating
(0/45/-451O)zs
Epoxy (Redux 308A) and material
of the composite
test specimen,
and moirC grating replication.
Effect of spew fillets on stress dhributions
au f%=-=ax
,y=-=-
1 aN, f ax
av
1 alv,
aY
f
-
(1)
aY
au av ‘“=y +-=ax
1 f
aiv, arv, (F+T)
where f=2400 lines/mm in the system used and N, and NY denote the fringe orders in the u and v fields. The sensitivity of measurement is 0.417 pm per fringe order. A portable achromatic was employed in the moire interferometer-l6 experiment. This system features vibration insentivity which allows the specimen to be tested in a conventional testing machine. This system also provides simultaneous measurement of u and v displacements so that the shear deformation of the loaded body can be resolved. The moire technique was used to obtain the surface deformations of the adherends and adhesive in the region, located on the edge surface of the overlap, covered with the moire
125
grating shown in Fig. 2. Typical fringe patterns are shown in Fig. 3 which contains the horizontal (u) and vertical (v) deformations of half an overlap for the specimen without a fillet, under an applied load, F=3202 N (720 lb). In order to provide a direct comparison of moire fringes, the u-field fringe patterns in regions, distance 3t away from the end of the overlap (in Fig. 4) and around the end of the overlap (in Fig. 5) are shown for the specimens with and without a 45” spew fillet, under the same load (F~4448 N or 1000 lb). It is apparent in Fig. 4 that the u-field fringe patterns away from the fillet-affected region for both specimens are almost the same. Both longitudinal normal strain distributions across the thickness of the overlap, extracted from these moire fringes, are also in a very good agreement. Good agreement in the deformation of the far fields for two different specimens (with and without a fillet) provide confidence for further comparing deformations in the near fields around the end of the overlap for both specimens, which are shown in Fig. 5. The resulting adhesive strain distributions for both specimens are shown in Fig. 6.
(a) u-field
(b) v-field
Fig. 3.
Typical moire fringe patterns: (a) u displacement field (b) v displacement field, for a laminated composite singlelap joint, without a fillet, under an applied load, F=3202 N (720 lb).
126
M. Y Tsai, J. Morton
u-field with a fillet
u-field without a fillet
0
0.05
0.1
0.15
0.2
qw Fig. 4.
Comparisons of u-field moirC fringe patterns and longitudinal away from the end of the overlap, for the specimens with and without 1000 lb).
FINITE ELEMENT
ANALYSIS
Geometrically linear and nonlinear two-dimensional finite element analyses using the ABAQUS code were performed to model the deformation of the laminated composite singlelap joint. Two entire single-lap joint models (joints with and without fillet), shown in Fig. 7, were analyzed. The geometric boundary conditions include a hinge on the center line of the adherend at one end and a roller at the other. A force is applied horizontally at the roller end. For these end conditions, the resultant force generated always passes through the center of the overlap, so that antisymmetrical loading and deformed conditions are achieved. The plane strain condition assumed in these analyses fails to capture/represent the effect of in-plane shear and bending-twisting coupling which are gen-
strain, cx, distributions at the region, 3t distance a spew fillet under a similar load (Fz4448 N, or
erated by the presence of +45” layers. Constant-strain (stress) elements were used for the adherends and adhesive. There were two elements across the thickness of the adhesive layer, except for the spew fillet, and one element for each lamina of the laminated composite adherends. The material of each lamina is modelled as orthotropic, while the material of the adhesive as isotropic. Due to the use of two the constant-strain (stress) elements across the thickness of the adhesive, the strain (stress) values calculated siong the center line of the adhesive represent approximately the average values over the thickness. To increase the accuracy of the numerical calculation, the finer meshes were adopted near and at the end of the overlap. The geometry, dimensions and material properties of the adherend and adhesive in the numerical analyses are the data
Effect of spew fillets on stress distributions
127
(b) Fig. 5. Moirt fringe patterns in the region near the end of the overlap: (a) u displacement field, for a laminated corn posite single-lap joint, without a fillet, under an applied load, F=4337 N (975 lb) (b) u displacement field,” for a laminated composite single-lap joint, witha 45” spew fillet, under an applied load, F=4448 N(1000 lb).
128
M. Y Tsai, J. Morton
described in the experimental program, and it is assumed that Es=Ez, Gr3=Gi2 and ~13=~12.
RESULTS AND DISCUSSION 0.5
-2.5
-3
-3.5
I ,
1.2
1.4
Fig. 6. Comparisons of adhesive strain cnstrmuttons determined from moire experiments for the laminated composite single-lap joint specimens with and without a spew fillet under a similar load (FE 4448 N, or 1000 lb).
The global bending deformation of the test specimen is verified by comparing the results from experimental measurement and finite element analyses. The longitudinal strain response at points 1 and 2, where back-to-back adherend surfaces are at positions about 25 t away from the end of the overlap, are shown in Fig. 8 for various applied loads per unit width (T=F/b) from the finite element analyses (linear and nonlinear) and strain gauge measurement. It is apparent .that the experimental results are in good agreement with those from the nonlinear finite element analysis, rather than from the linear analysis. Thus the specimen deformed geometrically nonlinearly and the bending
Ec ,vc
Fig. 7.
Finite
element
model; geometry,
boundary conditions and detailed with and without a spew fillet.
meshes used the composite
single-lap
joints
Effect of spew fillets on stress distributions
0.61
I
I
T, load (N/mm) Fig. 8. Comparisons of longitudinal normal strain responses at the points near the end of the overlap from experimental measurement and finite element analyses (linear and nonlinear models).
strains near the end of the overlap predicted from the linear analysis are larger than that from the nonlinear analysis. A detailed comparison of moire u-displacement field near the end of the overlap for the joints with and without a spew fillet is shown in Fig. 5. Both joints have the same lay-up and are under similar loads. The numbers marked on the fringe patterns are the u-field fringe order, Nx. These fringe patterns are obtained by optically reducing the number of v-field fringes as much as possible, at the center point of the overlap by introducing a carrier pattern of rotation. Thus, the term of au/ay in the calculation of shear strain in eqn (1) becomes dominant. That is, the u displacement gradient in the y direction ((aNx/ay)lf) approximately represents the shear strain component. It is observed that the aNxli3y for the joint without a spew fillet in the adhesive near and at the end of the overlap is larger than that for the joint with a spew fillet. The 45” spew fillet carries a portion of shear strains which are used to transfer the longitudinal load from the lower adherend to the upper. This argument can be confirmed by observing that the fringes for the joint without a fillet, at the upper adherend near the end of the overlap are almost horizontal and parallel, while the fringes for the joint with a fillet are inclined. Thus the upper adherend for the joint
129
with a fillet near the end of the overlap carries the longitudinal normal strains (.sx) unlike the joint without a fillet. This existence of a, indicates that the fillet does help transfer a part of the longitudinal load from the lower adherend to the upper through shear. The adhesive strain distributions obtained from the moire experiment are shown in Fig. 6 for the composite joints with and without a spew fillet under a load, Fr4448 N. These strain values are calculated by averaging the value over the thickness of the adhesive. The E, components are not shown, because of the difficulty of extracting zXdata from the joint without a fillet, due to high density of the fringes near and at the end of the overlap. For the peel strain (a,,) distributions, the location of tensile strain on the free surface moves from the end of the overlap to the end of the spew fillet as a result of the presence of the spew fillet. Note that the adhesive peel strain is very sensitive to three-dimensional effects.17 E,, measured from the free surface does not represent that in the interior, since E,, is more compressive than that in the interior. For the shear strain (yV) distributions, the maximum shear strain occurs at the end of the overlap for both cases. However, the value of the maximum shear strain for the joint with a fillet is only about 40% of that for the joint without a fillet. And the 45” spew fillet carries a certain degree of shear. Apparently the spew fillet is able to reduce significantly the adhesive shear strain concentration at the end of the overlap. Since the surface deformation recorded from the moire experiment does not fully represent that in the interior (especially for the peel strain component), the two-dimensional plane strain finite element analysis, however, does provide the deformation in the interior. Note that the adhesive shear strain (yxy) distributions for the joint without a fillet are insensitive to threedimensional effects,17 while those with a fillet are not near and at the spew fillet.18 Accordingly, a comparison of the adhesive shear distributions from numerical and experimental results can be used to confirm the validity of both results. The adhesive shear strain distributions determined from the moire experiment and two-dimensional finite element analysis are shown in Fig. 9 for joints with and without a fillet, under Fr4448 N. A very good agreement for the adhesive shear distributions is found in the joint without a spew fillet, while a partially
M. Y Tsai, J. Morton
130
.
I
- 4' 0
w wl fillet l 0.2
w/o
fillet
0.4
MOh
t
I
0.6
0.6
1
-
-6l
A 1.2
.
’
0
1.4
’
’
0.2
’
’
’
’
0.8
’ 1
’
’
’
’ 1.2
x/c
XIC
Fig. 9. Comparisons of the adhesive shear strain distributions, obtained from the moire experiment and the nonlinear finite element analysis for the composite joints with and without a spew fillet, under F=4448 N (1000 lb).
disagreement near the end of overlap and at the spew fillet is shown in the joint with a fillet. This disagreement between on the surface and in the interior is expected, according to the three-dimensional analysis.” After validating the geometrically nonlinear finite element model which represents the stress (strain) state in the interior, the resulting adhesive strain and stress distributions are shown in Fig. 10(a) and (b), respectively, for composite joints with and without a spew fillet, under F=7619 N. In Fig. 10(a) the position of maximum aY moves from the end of the overlap to the end of the spew fillet, as observed in moire experiment, and the value decreases significantly due to the presence of the spew fillet. The spew fillet carries appreciable amounts of shear strains. Thus, the spew fillet helps reduce the maximum shear strain in the end of the overlap. E,, especially for the joint with a fillet, is not small enough to be neglected in terms of its contribution to initial failure. For the adhesive stress distributions in Fig. 10(b), the maximum values of oY and zV which are dominant in failure initiation in the joint without a fillet decrease greatly in the presence of the spew fillet. The maximum 0x located near and inside the end of the overlap for the joint without a fillet moves to the position outside of the overlap with a fillet. This maximum o, in the joint with a fillet is comparable to other stresses (cry and z~), so that it cannot be excluded in a failure analysis. Due to the nature of geometrically nonlinear deformation in the single-lap joint, the adhesive
’ 0.6
0.4
0.6
0.4
a
0.2
_I .
-.__.-. without
fillet
w&h f&t
-0.4 -0.6’
’ 0
’ 0.2
’
’ 0.4
’
’ 0.6
’
’ 0.8
’
1
’ 1.2
x/c
Fig. 10.
(a) Adhesive strain distributions and (b) adhesive stress distributions, determined from the nonlinear finite element analyses for the composite single-lap joints with and without a spew fillet, under F=7619 N (1713 lb) or p= 150 MPa (21.7 ksi).
stress concentrations vary with the change of an applied load, and are affected by introducing a fillet. The maximum adhesive stresses normalized by the applied stress, p, are plotted against the applied stresses for composite joints with and without a 45” spew fillet in Fig. 11, which is determined from nonlinear finite element analyses. The values of o,, and “.V are plotted at the end of the overlap for the joints with and without a fillet. Note that the sign of z_ is ignored. The plotted values of a, are located 1.5 adhesive thicknesses inside the end of the overlap for the joint without a fillet, and outside the end of the overlap for the joint with a fillet. It is apparent that the nonlinear deformation greatly affects the adhesive stress concentrations for both joints with and without a fillet. The stress concentrations from the linear analysis, (approximately equivalent to those at p=O)
EfSect of spew fillets on stress distributions
131
the financial support under the contract USDOT/FAA 93-G-064. The authors also thank Mr F. L. Matthews of the Center for Composite Materials, Imperial College for providing the test specimens.
L .
I.
0.8 0.5 -
‘*-. *.__
-_
_-__
-.._
-.._
----ma__
0.4 -
.---_._
-----
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-
Wlth Fillet
-.-___
-A----______
----__
-6-
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1; -------_-____________
--------z
REFERENCES
v
0.6
1. National 0.5
_______________~
0.4
OY
0.3
” __.__.___________.______._.______.
2.
0.2 -
0.2
:Io:
O.l
50
100
150
200
250
3.
3000
P (MPa)
4. Fig. 11. Normalized maximum adhesive stresses vs applied stresses, p, for the composite single-lap joints with and without a spew fillet.
5. 6.
would be overestimated. The values of c,, and zV decrease significantly due to the effect of the spew fillet, while gX has a mild drop. After the large decrease of the oY and zqxy,the crXand rxy would become the dominant components for the joint with a fillet, rather than aY. CONCLUSIONS From the experimental and numerical studies, it is concluded that, in the laminated composite single-lap joint, the adhesive shear and peel strain (or stress) concentrations, generally occurring at the end of the overlap, are reduced significantly by introducing a fillet. This reduction of the stress concentration is attributed to the ability of the spew fillet to carry some of the shear stresses and thus plays a part in transferring an element of longitudinal load from one adherend to the other. The geometrically nonlinear deformation greatly affects the adhesive stress (strain) concentrations which, unlike the linear deformation, varies with the change of the applied load.
7.
8.
9.
10.
11.
12.
13. 14.
15.
16.
17.
ACKNOWLEDGEMENT The authors would like to express their gratitude to the Federal Aviation Administration for
18.
Material Advisory Board National Research Council. Structural adhesives: with emphasis on aerospace applications. Marcel Dekker Inc. New York, 1976. Kuno, J. K., Structural adhesives continue to gain foothold in aerospace and industrial use. In Structural Adhesives and Bonding, Proc. Structural Adhesives Bonding Conf., Technology Conference Associates, El Segundo, California, 1979. Volkersen, O., Die nietkraftverteilung in zugbeannietverbindungen mit konstanten spruchten laschenquerschnitten, Luftfahrtforschung, 15 (1938) 41-7. Goland, M. & Reissner, E., The stresses in cemented joints. J. Appl. Mech., 11 (1944) A17-A27. Hart-Smith, L. J., Adhesive-bonded single-lap joints. NASA. CR-112236, 1973. Oplinger, D. W., Effects of adherend deflections in single-lap joints. ht. .I. Solids & Struct., 31 (1994) 2565-87. Tsai, M. Y. & Morton, J., An evaluation of analytical and numerical solutions to single-lap joint. Znt. J. Solids & Struct., 31 (1994) 2537-63. Renton, W. J. & Vinson, J. R., Analysis of adhesively bounded joints between panels of composite materials. J. AppZ. Mech., (1977) 101-6. Mignery, L. A. & Schapery, R. A., Viscoelastic and nonlinear adherend effects in bonded composite joints. J. Adhesion, 34 (1991) 17-40. Tsai, M. Y., Morton, J. & Matthews, F. L. Experimental and numerical studies of a laminated composite single-lap adhesive joint. J. Comp. Mat., (in press). Oplinger, D. W., Stress analysis of composite joints. In Proc. Fourth Army Materials Technology Conference - Advances in Joining Technology, 1975. Matthews, F. L., Kilty, P. F. & Godwin, E. W., A review of the strength of ioints in fiber-reinforced plastics: part 2: adhesively bonded joints. Comp., (1982) 29-37. Vinson, J. R., Adhesive bonding of polymer composites. Polymer Eng. & Sci., 29 (1989) 1325-31. Adams, R. D., Strength predictions for lap joints especially with composite adherends: a review. J. Adhesion, 30 (1989) 219-42. Czarnek, R., Moire interferometry. Structural Testing, Society of Experimental Mechanics, 30 (1990) 195-200. Czarnek, R., High sensitivity moire interferometry with compact achromatic interferometer. Optics and Lasers in Engng, 13 (1990) 99-115. Tsai, M. Y. & Morton, J., Three-dimensional deformations in a single-lap joint. J. Strain AnaZysis, 29 (1994) 137-45. Tsai, M. Y. & Morton, J., Mechanics of the single-lap adhesive joint with laminated composite adherends. 17th Annual Meeting of Adhesion Society, Orlando, Florida, Feb. 1994.