- Email: [email protected]
plastics adhesive joints
International Journal of Adhesion & Adhesives 22 (2002) 273–282
Investigating the effect of spew and chamfer size on the stresses in metal/plastics adhesive joints Giovanni Belingardi, Luca Goglio*, Andrea Tarditi Dipartimento di Meccanica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy Accepted 4 December 2001
Abstract Regarding the optimisation of adhesive lap joints, several authors have proposed the use of adhesive spews (i.e. shoulders of adhesive connecting the unloaded ends of the adherends) and of chamfers at the ends of the adherends to reduce stress concentrations. Considering a hybrid joint between steel and FRP, this paper analyses in detail the effect of such solutions on the stress field, in order to identify the optimal condition and to assess design rules. It has been found that spew and chamfer angles of about 451 are sufficient to obtain a considerable reduction of the stress peaks. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: B. Plastics; C. Finite element stress analysis; E. Joint design; Optimisation
1. Introduction The simplest and most popular solution for adhesively bonding two sheets is the single-lap joint. From the structural viewpoint, this is characterised by two harmful features: (a) the offset of the two sheets causes a bending action in the joint, adding additional stress components; (b) the stress distribution in the lap is not constant and displays peaks at its ends. After the simplified solution of Volkersen [1] (developed for riveted joints but applicable also to bonds) and the more complete study of Goland and Reissner [2] (which accounted for the peel stress) much effort has been spent over six decades to determine the stress field and to obtain the ‘‘optimal’’ design of the joint. The analytical approach has been progressively refined until recent times [3–7]. In general terms it makes use of the plate theory to model the sheets while some simplified assumption is made for the adhesive layer behaviour. The analysis is bidimensional, since it involves a strip of unit width in transverse direction, assuming plane strain conditions. Volkersen [3] improved his previous work by including the peeling stress and assuming a relationship between shearing strain and displacement more correct than that of Goland and *Corresponding author. Tel.: +39-011-564-6934; fax: +39-011-5646999. E-mail address: [email protected] (L. Goglio).
Reissner. Segerlind [4] pointed out that as the lap length increases the stresses are in general reduced, but the stress peaks at the lap ends are more marked. Conversely, in case of short lap length the stresses are everywhere higher but more uniform. Renton and Vinson [5] developed an analytical solution for the case of an adhesive joint of orthotropic plates. Ojalvo and Eidinoff [6] accounted for the variation of the stresses through the adhesive thickness and investigated on the adhesive layer thickness effect. Bigwood and Crocombe [7] developed an analytical solution capable to describe not only simple lap joints but also more complicated geometries. Structural optimisation of the joint tries to modify the geometry of the adhesive layer and also of the adherend parts, with the scope of reducing the intensity of the stress peaks and therefore increase the strength of the joint. This approach has been made possible by the numerical analysis to treat cases with geometrical features that are beyond the analytical approach, such as fillets introduced at the ends of the overlap zone. This line of research has been explored over the last two decades [8–14], accounting also for the non-linearities occurring during collapse (material inelasticity, large displacements). The effects occurring at the ends of the overlap are extensively discussed in [8], on the basis of previous papers of Adams and co-workers. Dorn and Weiping Liu [10] performed a number of FEM analysis and some experimental measurements in order to study
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G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
Fig. 1. Geometrical features of the single-lap joint considered in the study.
the effect of spew fillets for joints with different couples of plastic and metal parts. In that work the spew angles are not considered design variables, their values are assumed at the beginning and maintained fixed for the whole article. Hildebrand [12] studied different shapes (obtained by tapering, rounding or denting) of the extremities of the adhesive layer in joints of metal with fibre-reinforced plastics parts; also in this case, the analysis was performed by the FE method. He considered the shape of the extremities as design variables and developed an optimisation study, but did not discuss the peeling and shear stress patterns in the adhesive layer. A comparative analysis of the effect of the spew geometry, considering triangular and rounded profiles, has been developed by Lang and Mallick [13] by the FE method. The spew is considered as the result of the adhesive squeezed out of the lap region at the moment of the joint manufacture. Detailed analysis has been devoted to study the effect of the adhesive thickness, while the effect of the spew angle is only addressed very briefly and their conclusions on the subject do not explain the reported maximum peel stress dependency. Very recently [14] they also investigated the effect of a recess (i.e. lack of adhesive in the central portion of the lap) in the joint. In both studies the joint concerns adherends equal in material and thickness. The present work deals with the case of a steel/fibrereinforced plastics lap joint. Its aim is to improve the understanding of the effect played by the geometry (namely the spews and chamfers) on the stress field in order to optimise the design, identifying the geometrical configuration that minimises the stress peaks. The study has been performed numerically, by means of the finite element method, assuming linear elastic behaviour of all of the joint components. The latter limiting assumption is justified by the argument that, even if it is well known that the ultimate strength of the joint largely depends on non-linear phenomena (e.g. large rotation, plasticity), the reduction of the elastic stress peaks is often beneficial in case of low ductility and essential in case of fatigue loading. The activity has been developed within a research program concerning the design and development of a new type of doors for the baggage
Table 1 Dimensional data L1 ¼ 120 mm h1 ¼ 1:5 mm
L2 ¼ 120 mm h2 ¼ 3 mm
L ¼ 20 mm t ¼ 0:1 mm
Table 2 Material properties Steel
FRP
Epoxy adhesive
E1 ¼ 206 GPa n1 ¼ 0:30
E2 ¼ 40 GPa n2 ¼ 0:22
Ea ¼ 3300 MPa na ¼ 0:31
Fig. 2. Finite element model of the basic configuration (detail).
compartment of the buses. Up to now, these are usually completely made of metal (steel or aluminium). The desired new component consists in panels made of plastics joined by bonding to the metallic reinforcing frame, hinges, locks, etc.
2. Analysis and results 2.1. Reference case (basic configuration) The considered joint is schematised in Fig. 1 and the dimensional data are listed in Table 1. The geometry
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
sketched in the figure must be regarded as a basic configuration from which different solution can be derived and compared. The plates are made of different materials, namely steel for plate 1 and fibrereinforced plastics for plate 2, and have different thickness. The adhesive is an epoxy resin (Ciba AV138). The material properties are listed in Table 2. The tensile load applied to the joint corresponds to 10 MPa in the steel plate. All the study has been performed by means of the ANSYS finite element code assuming plane strain
condition, as usually done and justified in [11]. The four-noded element type 42 has been used for all zones. The total number of elements is about 10,000, the adhesive layer contains six elements along its thickness (0.1 mm). The boundary conditions sketched in Fig. 1 are applied to the mid-thickness node of each end. Fig. 2 shows a detail of the finite element model. For comparison, mainly to assess whether the level of mesh refinement was enough to give correct results, also the simplified solution of Bigwood and Crocombe [7] has been calculated in this case. This is accomplished by
Basic configuration / adhesive-steel interface 20 15
MPa
10
peel stress
5 0 -5
shear stress -10 -15
-10
-5
0
5
10
15
mm
Basic configuration / adhesive half thickness 20
solid lines: FEM dashed lines: theoretical
15
MPa
10
peel stress
5 0 -5
shear stress -10 -15
-10
-5
0
5
10
15
mm
Basic configuration / adhesive-composite interface 20 15
MPa
10
peel stress
5 0 -5
shear stress -10 -15
-10
-5
275
0
5
10
15
mm
Fig. 3. Basic configuration: stresses on three levels in the joint and comparison with the simplified theoretical solution [7].
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
276
solving the two differential equations:
where syy and txy are the peel and shear stress components, K5 and K6 are constants related to the material properties and to the thickness values. Eqs. (1) and (2) hold exactly if the adherends are identical, in our case they are reasonably approximate since the stiffness values of the adherends are not too different.
4
d sy þ 4K54 sy ¼ 0; dx4
ð1Þ
d3 txy K62 txy ¼ 0; dx3
ð2Þ
Adherend 1
Adhesive
Adherend 1
Adherend 2
α
Adhesive
Adherend 2
(a)
(b)
Fig. 4. Different solutions for the lap end: (a) fillet at the end of the adhesive layer; (b) spew covering also the adherend end.
α = 75˚
α = 45˚
α = 15˚
Fig. 5. Detail views of the finite element models for the spew solution.
α = 60˚
α = 30˚
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
composite) the highest peak occurs at the overlap end corresponding to the loaded adherend. This is particularly true for the peel stress.
Fig. 3 shows the behaviour of the peel and shear stress in the joints. The stress fields are evaluated on three levels: the interface between steel and adhesive, the midplane of the adhesive layer, and the interface between adhesive and composite. The central diagram (adhesive mid-plane) also contains the curves given by the solutions of Eqs. (1) and (2), the good accordance is evident. This also leads to assume that the adopted finite element discretisation is adequate. In general terms, the stress field is affected by the typical peaks at the ends of the overlap zone, both for the peel and for the shear stresses. On each interface (adhesive-steel, adhesive-
2.2. Effect of the adhesive spew Starting from the basic configuration, both solutions in which a fillet made of adhesive covers the end of the adhesive layer only (Fig. 4a), and solutions in which a spew made of adhesive covers the end of the adhesive layer and of the adherend (Fig. 4b) have been analysed similarly to [10,12,13]. Here the attention is focussed on
Spew / adhesive-steel interface
peak value 6.1 MPa
5
6
6
75˚
75˚
5
60˚
MPa
75˚
60˚ 3
4
45˚
60˚ 3
3
2
60˚
30˚
45˚
45˚
45˚
2
2 1
4
5 75˚
4
30˚
1 -10.5
1
30˚ 15˚ -10
30˚ 15˚
0 -9.5
9.5
10
10.5
0
15˚
-1
15˚
Peel stress
-2 -15
-10
-5
0
5
10
15
mm
Spew / adhesive half thickness 75˚
75˚
5
3 MPa
75˚
60˚ 3
4
45˚
45˚ 2
30˚
1 -10.5
0 -1
45˚ 2
3
45˚
2
60˚
60˚
60˚
75˚
4
5
4
1
5
6
6
1
30˚ 15˚ -10
30˚
30˚ 15˚
0 -9.5
9.5
10
10.5
Peel stress
15˚
15˚
-2 -15
-10
-5
0
5
10
15
mm
Spew / adhesive-composite interface 75˚
75˚
4 MPa
3
2
2 1
60˚
3 60˚
45˚
2
60˚
75˚
3
60˚
45˚
45˚
30˚ 45˚ 15˚
1
30˚ 0 -10.5
0 -1
75˚
4
4
5
1
peak value 8.3 MPa
5
5
6
9.5
-9.5
30˚
30˚ 15˚
0 -10
10
10.5
Peel stress
15˚
15˚
-2 -15
-10
-5
277
0
5
10
mm
Fig. 6. Effect of the spew: peel stress field on three levels in the joint.
15
278
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
additional stress peaks that occur at the ends of the spews can even exceed the peaks occurring at the end of the overlap, when a is lower such additional stress peaks tends to disappear. Nevertheless, the dependence of the stress on the angle is fairly complicated:
the spew case, to identify the angle that minimises the stress peaks. Fig. 5 shows in detail the finite element meshes of the lap, at the end of the thinner adherend (steel), for the different cases. Figs. 6 and 7 show, for the different configurations, the behaviour of the peel and shear stress components on three levels in the joint, as it has been done for the basic configuration. The effect of the adhesive spew on the stress field can be appreciated. In general terms, the amplitude of the stresses decreases with a under high values of a the
*
considering the peel component on the adhesive–steel interface, the highest stress peaks always appear (except for the case 151) at the left overlap end or at the left spew end, i.e. at the loaded end, as in the reference case;
Spew / adhesive-steel interface 15˚
0 Shear stress
-1 -2
30˚
-1
MPa
45˚ 60˚
-4
60˚
-3
60˚ 75˚
-3
75˚
-4
75˚
30˚
45˚
-5
-4
-5
30˚ 45˚
15˚
-2
15˚ 30˚ 45˚
-2
-3
15˚
-1
0
60˚
-6 -15
-10
75˚
-6
-5 -10.5
-10
9.5
-9.5
-5
10
0
10.5
5
10
15
mm
Spew / adhesive half thickness 15˚ 0
Shear stress -1
MPa
-2
15˚
-1
0
30˚ -1
45˚ 60˚ 75˚
-3
-2 -3
-4
-2
15˚ 30˚ 45˚
30˚
15˚
45˚
-3
60˚
60˚ 75˚
-4 45˚
30˚ -4
-5
-5 -10.5
-6
60˚
-5 -6 -15
-10
-10
-9.5
-5
75˚
75˚ 9.5
10
0
10.5
5
10
15
mm
Spew / adhesive-composite interface
15˚
0 Shear stress
-1
-1
45˚ 60˚
-3
15˚
15˚
30˚
MPa
-2
-2 60˚ -3
75˚
-5
45˚
-3
75˚
60˚
-4 45˚
-4
-5
-5 -10.5
-6 -10
-9.5
-5
60˚
9.5
-6 -10
30˚
30˚
-2 30˚ 45˚
-4
-15
15˚
-1
0
0
75˚
75˚ 10
10.5
5
10
mm
Fig. 7. Effect of the spew: shear stress field on three levels in the joint.
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G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
Adherend 1
h1
α
α
h2 / 3
279
h1 / 3
α
α
Adhesive h2 Adherend 2
Fig. 8. Chamfering of the unloaded ends of the adherends.
*
*
conversely, for the peel component on the adhesive– composite interface the highest stress peaks usually appear (except for the case 151) at the unloaded end, that is, again at the left end; only in the case 751 the right spew end causes the highest peak; as far as the shear component is concerned, on both interfaces the highest peaks appear always at the right end.
It can be noticed that, with respect to the basic configuration, the stress reduction due to the spews is more pronouced for the peel than for the shear component, being of about five times for the peel stress and two times for the shear stress. As a synthetic rule, it can be concluded that for a equal to 451 the stress is well reduced and the additional peaks at the ends of the spew do not exceed those at the ends of the overlap. The use of lower values of a; much more difficult to obtain in practice, does not seem worthwhile.
5.3
Fig. 9. Detailed view of the finite element model for the 451 spew and chamfer solution.
*
2.3. Adhesive spew and chamfer of the adherends *
In order to further reduce the stress peaks, an improvement that has been tested in addition to the spew consists in chamfering the unloaded ends of the adherends on the inner side, as shown in Fig. 8. This idea, yet considered in [12], is here further developed to find the best configuration. For the sake of simplicity, the same angle value is adopted both for the spew and for the chamfer, the latter concerns two-thirds of the thickness, whilst the remaining third is square. For the sake of brevity, Fig. 9 shows in detail the finite element mesh of the lap, at the end of the thinner adherend (steel), for the case 451 only. The results are presented in the same way as for the case of the spew; Figs. 10 and 11 show the stress field at three levels in the joint. The behaviour can be summarised as follows: *
*
each peak is shifted inwards, at the location where the chamfer starts; for the peel component, the highest peaks appear at the left spew end on the adhesive–steel interface, and at the right spew end on the adhesive–composite interface, that is, they are always at the loaded end (for low-angle values the peaks tend to be equal and very small);
for the shear component on the adhesive–composite interface, the highest peaks always appear at the right spew end (a high) or right overlap end (a low); for the shear component on the adhesive–steel interface the highest peaks occur at the right overlap end (unloaded) except for the case 751, in which the peak at the left spew end is the highest.
With respect to the case of spew only (Figs. 6 and 7) it can be noticed that: (a) the stresses are, in general, lower; (b) when the angle a assumes values below 451 the peaks of the peel stress occurring at the ends of the spews tend to zero and those at the ends of the overlap even disappear. The latter result is of considerable relevance, since these stress peaks are the most harmful for the joint.
3. Conclusions The work deals with the optimal design of adhesive joints when a glass fibre plastic composite part has to be structurally connected to a metallic frame. The adhesive joint is characterised by stress peaks (both shear and peeling components) due to the peculiar structure of the joint: geometrical and stiffness factors are concurrent in determining the entity of these peaks.
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Chamfer and spew / adhesive-steel interface 6 75˚
5
peak value 7.9 MPa
60˚
4
75˚ Peel stress
60˚
MPa
3
45˚
45˚
2
30˚
30˚
1 0 15˚
15˚
-1 -2 -15
-10
-5
0
5
10
15
mm
Chamfer and spew / adhesive half thickness 6 75˚
75˚
5
60˚
4
60˚
Peel stress
MPa
3 2
45˚
45˚ 30˚
30˚
1 0 15˚
-1
15˚
-2 -15
-10
-5
0
5
10
15
mm
Chamfer and spew / adhesive-composite interface 6 75˚
4
60˚
Peel stress
60˚
3 MPa
75˚
peak value 10.5 MPa
5
45˚
45˚
2
30˚
30˚
1 0 -1
15˚
15˚
-2 -15
-10
-5
0
5
10
15
mm
Fig. 10. Effect of the chamfer and of the spew: peel stress field on three levels in the joint.
Starting from the well-known literature studies, the present paper shows that interesting results in terms of stress reduction can be achieved not only if the spew type adhesive extremity is adopted but, by varying properly the geometry of spews, an optimal solution can be devised. Further improvement can be obtained by adopting the spew and chamfer-type adhesive extremity.
The finite element method has been used to analyse the stress state in the adhesive, through the discretisation of a number of different solutions both of the linear spew type and of the spew and chamfer type, exploring a wide range of spew angles, from 901 (i.e. square edge) to 151. The magnitude of the stress peaks (for both shear and peeling components) decrease in entity with the decrease
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
281
Chamfer and spew / adhesive-steel interface
15˚
0 15˚
-1 30˚
30˚
-2 MPa
45˚
45˚ 60˚
-3 60˚
-4
Shear stress
75˚
75˚
-5 -6 -15
-10
-5
0
5
10
15
mm
Chamfer and spew / adhesive half thickness
15˚
0 15˚
-1 30˚
30˚
-2 MPa
45˚ 60˚
-3
45˚ 75˚
60˚ Shear stress
-4
75˚
-5 -6 -15
-10
-5
0
5
10
15
mm
Chamfer and spew / adhesive-composite interface 15˚
0 -1 -2
15˚ 30˚
30˚
MPa
45˚
45˚
60˚
-3
75˚
-4
60˚
Shear stress
75˚
-5 -6 -15
-10
-5
0
5
10
15
mm
Fig. 11. Effect of the chamfer and of the spew: shear stress field on three levels in the joint.
of the spew angle, although the most of the advantage is obtained within the 451 solution. The stress distribution in the adhesive, in the cases of spew solution, shows the presence of a secondary peak whose entity can exceed the primary peak magnitude when the spew angle is large but tends to disappear as the spew angle decreases. The study has, however, pointed out that yet for angles of 451 the peak stress reduction is adequate and of the order of five times for the peel component (which is
usually the most harmful for the adhesive) and of two times for the shear component with respect to the basic solution. The stress distribution in the adhesive, in the cases of spew and chamfer solution, shows again the presence of a secondary peak whose magnitude can exceed that of the primary peak when the spew angle is large, but tends to disappear as the spew angle decreases. The study has, however, pointed out that yet for angles of 451 the peak
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G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
stress reduction is adequate and of the order of two times for the peel component (which is usually the most harmful for the adhesive) and of two times for the shear component with respect to the previous spew solution. In conclusion, adopting the spew and chamfer solution, an advantage of one order of magnitude for the peel stress component and of one half order of magnitude for the shear stress component can be gained in the maximum stress values in the adhesive layer. With respect to other solutions presented in the literature, those considered here are feasible and geometrically simple. Obviously, the obtained result concerns the elastic behaviour, thus it cannot be directly inferred that the ultimate strength of the joint increases as much as the peak stress is reduced.
[2] [3] [4] [5]
[6] [7]
[8] [9]
Acknowledgements
[10]
The work has been carried out with the financial support by the Italian Ministry of the University and of the ResearchFMIUR (cooperative research project approved for the year 1999).
[11]
[12]
[13]
References [14] [1] Volkersen O. Die Nietkraftverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten (Rivet
strength distribution in tensile-stressed rivet joints with constant cross section). Luftfahrtforschung 1938;15:41–7. Goland M, Reissner E. The stresses in cemented joints. J Appl Mech 1944;11:A17. Volkersen O. Research on the theory of cemented joints. Constr M!et 1965;4:3–13. Segerlind LJ. On the shear stress in bonded joints. J Appl Mech 1968;35:177–8. Renton WJ, Vinson JR. Analysis of adhesively bonded joints between panels of composite materials. J Appl Mech 1977;44: 101–6. Ojalvo IU, Eidinoff HL. Bonded thickness effects upon stresses in single-lap adhesive joints. AIAA J 1978;16:204–11. Bigwood DA, Crocombe AD. Elastic analysis and engineering design formulae for bonded joints. Int J Adhes Adhesives 1989;9:229–42. Adams RD, Comyn J, Wake WC. Structural adhesive joints in engineering. Kluwer Academic Publishers: Dordrecht, 1997. Bigwood DA, Crocombe AD. Non-linear adhesive bonded joint design analysis. Int J Adhes Adhesives 1990;10:31–41. Dorn L, Weiping L. The stress state and failure properties of adhesive-bonded plastic/metal joints. Int J Adhes Adhesives 1993;13:21–31. Richardson G, Crocombe AD, Smith PA. A comparison of twoand three-dimensional finite element analyses of adhesive joints. Int J Adhes Adhesives 1993;13:193–200. Hildebrand M. Non-linear analysis and optimisation of adhesively bonded single-lap joints between fibre-reinforced plastics and metals. Int J Adhes Adhesives 1994;14:261–7. Lang TP, Mallick PK. Effect of spew geometry on stresses in single-lap adhesive joints. Int J Adhes Adhesives 1998;18:167–77. Lang TP, Mallick PK. The effect of recessing on the stresses in single-lap adhesively bonded single-lap joints. Int J Adhes Adhesives 1999;19:257–71.
Investigating the effect of spew and chamfer size on the stresses in metal/plastics adhesive joints Giovanni Belingardi, Luca Goglio*, Andrea Tarditi Dipartimento di Meccanica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy Accepted 4 December 2001
Abstract Regarding the optimisation of adhesive lap joints, several authors have proposed the use of adhesive spews (i.e. shoulders of adhesive connecting the unloaded ends of the adherends) and of chamfers at the ends of the adherends to reduce stress concentrations. Considering a hybrid joint between steel and FRP, this paper analyses in detail the effect of such solutions on the stress field, in order to identify the optimal condition and to assess design rules. It has been found that spew and chamfer angles of about 451 are sufficient to obtain a considerable reduction of the stress peaks. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: B. Plastics; C. Finite element stress analysis; E. Joint design; Optimisation
1. Introduction The simplest and most popular solution for adhesively bonding two sheets is the single-lap joint. From the structural viewpoint, this is characterised by two harmful features: (a) the offset of the two sheets causes a bending action in the joint, adding additional stress components; (b) the stress distribution in the lap is not constant and displays peaks at its ends. After the simplified solution of Volkersen [1] (developed for riveted joints but applicable also to bonds) and the more complete study of Goland and Reissner [2] (which accounted for the peel stress) much effort has been spent over six decades to determine the stress field and to obtain the ‘‘optimal’’ design of the joint. The analytical approach has been progressively refined until recent times [3–7]. In general terms it makes use of the plate theory to model the sheets while some simplified assumption is made for the adhesive layer behaviour. The analysis is bidimensional, since it involves a strip of unit width in transverse direction, assuming plane strain conditions. Volkersen [3] improved his previous work by including the peeling stress and assuming a relationship between shearing strain and displacement more correct than that of Goland and *Corresponding author. Tel.: +39-011-564-6934; fax: +39-011-5646999. E-mail address: [email protected] (L. Goglio).
Reissner. Segerlind [4] pointed out that as the lap length increases the stresses are in general reduced, but the stress peaks at the lap ends are more marked. Conversely, in case of short lap length the stresses are everywhere higher but more uniform. Renton and Vinson [5] developed an analytical solution for the case of an adhesive joint of orthotropic plates. Ojalvo and Eidinoff [6] accounted for the variation of the stresses through the adhesive thickness and investigated on the adhesive layer thickness effect. Bigwood and Crocombe [7] developed an analytical solution capable to describe not only simple lap joints but also more complicated geometries. Structural optimisation of the joint tries to modify the geometry of the adhesive layer and also of the adherend parts, with the scope of reducing the intensity of the stress peaks and therefore increase the strength of the joint. This approach has been made possible by the numerical analysis to treat cases with geometrical features that are beyond the analytical approach, such as fillets introduced at the ends of the overlap zone. This line of research has been explored over the last two decades [8–14], accounting also for the non-linearities occurring during collapse (material inelasticity, large displacements). The effects occurring at the ends of the overlap are extensively discussed in [8], on the basis of previous papers of Adams and co-workers. Dorn and Weiping Liu [10] performed a number of FEM analysis and some experimental measurements in order to study
0143-7496/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 7 4 9 6 ( 0 2 ) 0 0 0 0 4 - 0
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G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
Fig. 1. Geometrical features of the single-lap joint considered in the study.
the effect of spew fillets for joints with different couples of plastic and metal parts. In that work the spew angles are not considered design variables, their values are assumed at the beginning and maintained fixed for the whole article. Hildebrand [12] studied different shapes (obtained by tapering, rounding or denting) of the extremities of the adhesive layer in joints of metal with fibre-reinforced plastics parts; also in this case, the analysis was performed by the FE method. He considered the shape of the extremities as design variables and developed an optimisation study, but did not discuss the peeling and shear stress patterns in the adhesive layer. A comparative analysis of the effect of the spew geometry, considering triangular and rounded profiles, has been developed by Lang and Mallick [13] by the FE method. The spew is considered as the result of the adhesive squeezed out of the lap region at the moment of the joint manufacture. Detailed analysis has been devoted to study the effect of the adhesive thickness, while the effect of the spew angle is only addressed very briefly and their conclusions on the subject do not explain the reported maximum peel stress dependency. Very recently [14] they also investigated the effect of a recess (i.e. lack of adhesive in the central portion of the lap) in the joint. In both studies the joint concerns adherends equal in material and thickness. The present work deals with the case of a steel/fibrereinforced plastics lap joint. Its aim is to improve the understanding of the effect played by the geometry (namely the spews and chamfers) on the stress field in order to optimise the design, identifying the geometrical configuration that minimises the stress peaks. The study has been performed numerically, by means of the finite element method, assuming linear elastic behaviour of all of the joint components. The latter limiting assumption is justified by the argument that, even if it is well known that the ultimate strength of the joint largely depends on non-linear phenomena (e.g. large rotation, plasticity), the reduction of the elastic stress peaks is often beneficial in case of low ductility and essential in case of fatigue loading. The activity has been developed within a research program concerning the design and development of a new type of doors for the baggage
Table 1 Dimensional data L1 ¼ 120 mm h1 ¼ 1:5 mm
L2 ¼ 120 mm h2 ¼ 3 mm
L ¼ 20 mm t ¼ 0:1 mm
Table 2 Material properties Steel
FRP
Epoxy adhesive
E1 ¼ 206 GPa n1 ¼ 0:30
E2 ¼ 40 GPa n2 ¼ 0:22
Ea ¼ 3300 MPa na ¼ 0:31
Fig. 2. Finite element model of the basic configuration (detail).
compartment of the buses. Up to now, these are usually completely made of metal (steel or aluminium). The desired new component consists in panels made of plastics joined by bonding to the metallic reinforcing frame, hinges, locks, etc.
2. Analysis and results 2.1. Reference case (basic configuration) The considered joint is schematised in Fig. 1 and the dimensional data are listed in Table 1. The geometry
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
sketched in the figure must be regarded as a basic configuration from which different solution can be derived and compared. The plates are made of different materials, namely steel for plate 1 and fibrereinforced plastics for plate 2, and have different thickness. The adhesive is an epoxy resin (Ciba AV138). The material properties are listed in Table 2. The tensile load applied to the joint corresponds to 10 MPa in the steel plate. All the study has been performed by means of the ANSYS finite element code assuming plane strain
condition, as usually done and justified in [11]. The four-noded element type 42 has been used for all zones. The total number of elements is about 10,000, the adhesive layer contains six elements along its thickness (0.1 mm). The boundary conditions sketched in Fig. 1 are applied to the mid-thickness node of each end. Fig. 2 shows a detail of the finite element model. For comparison, mainly to assess whether the level of mesh refinement was enough to give correct results, also the simplified solution of Bigwood and Crocombe [7] has been calculated in this case. This is accomplished by
Basic configuration / adhesive-steel interface 20 15
MPa
10
peel stress
5 0 -5
shear stress -10 -15
-10
-5
0
5
10
15
mm
Basic configuration / adhesive half thickness 20
solid lines: FEM dashed lines: theoretical
15
MPa
10
peel stress
5 0 -5
shear stress -10 -15
-10
-5
0
5
10
15
mm
Basic configuration / adhesive-composite interface 20 15
MPa
10
peel stress
5 0 -5
shear stress -10 -15
-10
-5
275
0
5
10
15
mm
Fig. 3. Basic configuration: stresses on three levels in the joint and comparison with the simplified theoretical solution [7].
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
276
solving the two differential equations:
where syy and txy are the peel and shear stress components, K5 and K6 are constants related to the material properties and to the thickness values. Eqs. (1) and (2) hold exactly if the adherends are identical, in our case they are reasonably approximate since the stiffness values of the adherends are not too different.
4
d sy þ 4K54 sy ¼ 0; dx4
ð1Þ
d3 txy K62 txy ¼ 0; dx3
ð2Þ
Adherend 1
Adhesive
Adherend 1
Adherend 2
α
Adhesive
Adherend 2
(a)
(b)
Fig. 4. Different solutions for the lap end: (a) fillet at the end of the adhesive layer; (b) spew covering also the adherend end.
α = 75˚
α = 45˚
α = 15˚
Fig. 5. Detail views of the finite element models for the spew solution.
α = 60˚
α = 30˚
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
composite) the highest peak occurs at the overlap end corresponding to the loaded adherend. This is particularly true for the peel stress.
Fig. 3 shows the behaviour of the peel and shear stress in the joints. The stress fields are evaluated on three levels: the interface between steel and adhesive, the midplane of the adhesive layer, and the interface between adhesive and composite. The central diagram (adhesive mid-plane) also contains the curves given by the solutions of Eqs. (1) and (2), the good accordance is evident. This also leads to assume that the adopted finite element discretisation is adequate. In general terms, the stress field is affected by the typical peaks at the ends of the overlap zone, both for the peel and for the shear stresses. On each interface (adhesive-steel, adhesive-
2.2. Effect of the adhesive spew Starting from the basic configuration, both solutions in which a fillet made of adhesive covers the end of the adhesive layer only (Fig. 4a), and solutions in which a spew made of adhesive covers the end of the adhesive layer and of the adherend (Fig. 4b) have been analysed similarly to [10,12,13]. Here the attention is focussed on
Spew / adhesive-steel interface
peak value 6.1 MPa
5
6
6
75˚
75˚
5
60˚
MPa
75˚
60˚ 3
4
45˚
60˚ 3
3
2
60˚
30˚
45˚
45˚
45˚
2
2 1
4
5 75˚
4
30˚
1 -10.5
1
30˚ 15˚ -10
30˚ 15˚
0 -9.5
9.5
10
10.5
0
15˚
-1
15˚
Peel stress
-2 -15
-10
-5
0
5
10
15
mm
Spew / adhesive half thickness 75˚
75˚
5
3 MPa
75˚
60˚ 3
4
45˚
45˚ 2
30˚
1 -10.5
0 -1
45˚ 2
3
45˚
2
60˚
60˚
60˚
75˚
4
5
4
1
5
6
6
1
30˚ 15˚ -10
30˚
30˚ 15˚
0 -9.5
9.5
10
10.5
Peel stress
15˚
15˚
-2 -15
-10
-5
0
5
10
15
mm
Spew / adhesive-composite interface 75˚
75˚
4 MPa
3
2
2 1
60˚
3 60˚
45˚
2
60˚
75˚
3
60˚
45˚
45˚
30˚ 45˚ 15˚
1
30˚ 0 -10.5
0 -1
75˚
4
4
5
1
peak value 8.3 MPa
5
5
6
9.5
-9.5
30˚
30˚ 15˚
0 -10
10
10.5
Peel stress
15˚
15˚
-2 -15
-10
-5
277
0
5
10
mm
Fig. 6. Effect of the spew: peel stress field on three levels in the joint.
15
278
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
additional stress peaks that occur at the ends of the spews can even exceed the peaks occurring at the end of the overlap, when a is lower such additional stress peaks tends to disappear. Nevertheless, the dependence of the stress on the angle is fairly complicated:
the spew case, to identify the angle that minimises the stress peaks. Fig. 5 shows in detail the finite element meshes of the lap, at the end of the thinner adherend (steel), for the different cases. Figs. 6 and 7 show, for the different configurations, the behaviour of the peel and shear stress components on three levels in the joint, as it has been done for the basic configuration. The effect of the adhesive spew on the stress field can be appreciated. In general terms, the amplitude of the stresses decreases with a under high values of a the
*
considering the peel component on the adhesive–steel interface, the highest stress peaks always appear (except for the case 151) at the left overlap end or at the left spew end, i.e. at the loaded end, as in the reference case;
Spew / adhesive-steel interface 15˚
0 Shear stress
-1 -2
30˚
-1
MPa
45˚ 60˚
-4
60˚
-3
60˚ 75˚
-3
75˚
-4
75˚
30˚
45˚
-5
-4
-5
30˚ 45˚
15˚
-2
15˚ 30˚ 45˚
-2
-3
15˚
-1
0
60˚
-6 -15
-10
75˚
-6
-5 -10.5
-10
9.5
-9.5
-5
10
0
10.5
5
10
15
mm
Spew / adhesive half thickness 15˚ 0
Shear stress -1
MPa
-2
15˚
-1
0
30˚ -1
45˚ 60˚ 75˚
-3
-2 -3
-4
-2
15˚ 30˚ 45˚
30˚
15˚
45˚
-3
60˚
60˚ 75˚
-4 45˚
30˚ -4
-5
-5 -10.5
-6
60˚
-5 -6 -15
-10
-10
-9.5
-5
75˚
75˚ 9.5
10
0
10.5
5
10
15
mm
Spew / adhesive-composite interface
15˚
0 Shear stress
-1
-1
45˚ 60˚
-3
15˚
15˚
30˚
MPa
-2
-2 60˚ -3
75˚
-5
45˚
-3
75˚
60˚
-4 45˚
-4
-5
-5 -10.5
-6 -10
-9.5
-5
60˚
9.5
-6 -10
30˚
30˚
-2 30˚ 45˚
-4
-15
15˚
-1
0
0
75˚
75˚ 10
10.5
5
10
mm
Fig. 7. Effect of the spew: shear stress field on three levels in the joint.
15
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
Adherend 1
h1
α
α
h2 / 3
279
h1 / 3
α
α
Adhesive h2 Adherend 2
Fig. 8. Chamfering of the unloaded ends of the adherends.
*
*
conversely, for the peel component on the adhesive– composite interface the highest stress peaks usually appear (except for the case 151) at the unloaded end, that is, again at the left end; only in the case 751 the right spew end causes the highest peak; as far as the shear component is concerned, on both interfaces the highest peaks appear always at the right end.
It can be noticed that, with respect to the basic configuration, the stress reduction due to the spews is more pronouced for the peel than for the shear component, being of about five times for the peel stress and two times for the shear stress. As a synthetic rule, it can be concluded that for a equal to 451 the stress is well reduced and the additional peaks at the ends of the spew do not exceed those at the ends of the overlap. The use of lower values of a; much more difficult to obtain in practice, does not seem worthwhile.
5.3
Fig. 9. Detailed view of the finite element model for the 451 spew and chamfer solution.
*
2.3. Adhesive spew and chamfer of the adherends *
In order to further reduce the stress peaks, an improvement that has been tested in addition to the spew consists in chamfering the unloaded ends of the adherends on the inner side, as shown in Fig. 8. This idea, yet considered in [12], is here further developed to find the best configuration. For the sake of simplicity, the same angle value is adopted both for the spew and for the chamfer, the latter concerns two-thirds of the thickness, whilst the remaining third is square. For the sake of brevity, Fig. 9 shows in detail the finite element mesh of the lap, at the end of the thinner adherend (steel), for the case 451 only. The results are presented in the same way as for the case of the spew; Figs. 10 and 11 show the stress field at three levels in the joint. The behaviour can be summarised as follows: *
*
each peak is shifted inwards, at the location where the chamfer starts; for the peel component, the highest peaks appear at the left spew end on the adhesive–steel interface, and at the right spew end on the adhesive–composite interface, that is, they are always at the loaded end (for low-angle values the peaks tend to be equal and very small);
for the shear component on the adhesive–composite interface, the highest peaks always appear at the right spew end (a high) or right overlap end (a low); for the shear component on the adhesive–steel interface the highest peaks occur at the right overlap end (unloaded) except for the case 751, in which the peak at the left spew end is the highest.
With respect to the case of spew only (Figs. 6 and 7) it can be noticed that: (a) the stresses are, in general, lower; (b) when the angle a assumes values below 451 the peaks of the peel stress occurring at the ends of the spews tend to zero and those at the ends of the overlap even disappear. The latter result is of considerable relevance, since these stress peaks are the most harmful for the joint.
3. Conclusions The work deals with the optimal design of adhesive joints when a glass fibre plastic composite part has to be structurally connected to a metallic frame. The adhesive joint is characterised by stress peaks (both shear and peeling components) due to the peculiar structure of the joint: geometrical and stiffness factors are concurrent in determining the entity of these peaks.
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Chamfer and spew / adhesive-steel interface 6 75˚
5
peak value 7.9 MPa
60˚
4
75˚ Peel stress
60˚
MPa
3
45˚
45˚
2
30˚
30˚
1 0 15˚
15˚
-1 -2 -15
-10
-5
0
5
10
15
mm
Chamfer and spew / adhesive half thickness 6 75˚
75˚
5
60˚
4
60˚
Peel stress
MPa
3 2
45˚
45˚ 30˚
30˚
1 0 15˚
-1
15˚
-2 -15
-10
-5
0
5
10
15
mm
Chamfer and spew / adhesive-composite interface 6 75˚
4
60˚
Peel stress
60˚
3 MPa
75˚
peak value 10.5 MPa
5
45˚
45˚
2
30˚
30˚
1 0 -1
15˚
15˚
-2 -15
-10
-5
0
5
10
15
mm
Fig. 10. Effect of the chamfer and of the spew: peel stress field on three levels in the joint.
Starting from the well-known literature studies, the present paper shows that interesting results in terms of stress reduction can be achieved not only if the spew type adhesive extremity is adopted but, by varying properly the geometry of spews, an optimal solution can be devised. Further improvement can be obtained by adopting the spew and chamfer-type adhesive extremity.
The finite element method has been used to analyse the stress state in the adhesive, through the discretisation of a number of different solutions both of the linear spew type and of the spew and chamfer type, exploring a wide range of spew angles, from 901 (i.e. square edge) to 151. The magnitude of the stress peaks (for both shear and peeling components) decrease in entity with the decrease
G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
281
Chamfer and spew / adhesive-steel interface
15˚
0 15˚
-1 30˚
30˚
-2 MPa
45˚
45˚ 60˚
-3 60˚
-4
Shear stress
75˚
75˚
-5 -6 -15
-10
-5
0
5
10
15
mm
Chamfer and spew / adhesive half thickness
15˚
0 15˚
-1 30˚
30˚
-2 MPa
45˚ 60˚
-3
45˚ 75˚
60˚ Shear stress
-4
75˚
-5 -6 -15
-10
-5
0
5
10
15
mm
Chamfer and spew / adhesive-composite interface 15˚
0 -1 -2
15˚ 30˚
30˚
MPa
45˚
45˚
60˚
-3
75˚
-4
60˚
Shear stress
75˚
-5 -6 -15
-10
-5
0
5
10
15
mm
Fig. 11. Effect of the chamfer and of the spew: shear stress field on three levels in the joint.
of the spew angle, although the most of the advantage is obtained within the 451 solution. The stress distribution in the adhesive, in the cases of spew solution, shows the presence of a secondary peak whose entity can exceed the primary peak magnitude when the spew angle is large but tends to disappear as the spew angle decreases. The study has, however, pointed out that yet for angles of 451 the peak stress reduction is adequate and of the order of five times for the peel component (which is
usually the most harmful for the adhesive) and of two times for the shear component with respect to the basic solution. The stress distribution in the adhesive, in the cases of spew and chamfer solution, shows again the presence of a secondary peak whose magnitude can exceed that of the primary peak when the spew angle is large, but tends to disappear as the spew angle decreases. The study has, however, pointed out that yet for angles of 451 the peak
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G. Belingardi et al. / International Journal of Adhesion & Adhesives 22 (2002) 273–282
stress reduction is adequate and of the order of two times for the peel component (which is usually the most harmful for the adhesive) and of two times for the shear component with respect to the previous spew solution. In conclusion, adopting the spew and chamfer solution, an advantage of one order of magnitude for the peel stress component and of one half order of magnitude for the shear stress component can be gained in the maximum stress values in the adhesive layer. With respect to other solutions presented in the literature, those considered here are feasible and geometrically simple. Obviously, the obtained result concerns the elastic behaviour, thus it cannot be directly inferred that the ultimate strength of the joint increases as much as the peak stress is reduced.
[2] [3] [4] [5]
[6] [7]
[8] [9]
Acknowledgements
[10]
The work has been carried out with the financial support by the Italian Ministry of the University and of the ResearchFMIUR (cooperative research project approved for the year 1999).
[11]
[12]
[13]
References [14] [1] Volkersen O. Die Nietkraftverteilung in zugbeanspruchten Nietverbindungen mit konstanten Laschenquerschnitten (Rivet
strength distribution in tensile-stressed rivet joints with constant cross section). Luftfahrtforschung 1938;15:41–7. Goland M, Reissner E. The stresses in cemented joints. J Appl Mech 1944;11:A17. Volkersen O. Research on the theory of cemented joints. Constr M!et 1965;4:3–13. Segerlind LJ. On the shear stress in bonded joints. J Appl Mech 1968;35:177–8. Renton WJ, Vinson JR. Analysis of adhesively bonded joints between panels of composite materials. J Appl Mech 1977;44: 101–6. Ojalvo IU, Eidinoff HL. Bonded thickness effects upon stresses in single-lap adhesive joints. AIAA J 1978;16:204–11. Bigwood DA, Crocombe AD. Elastic analysis and engineering design formulae for bonded joints. Int J Adhes Adhesives 1989;9:229–42. Adams RD, Comyn J, Wake WC. Structural adhesive joints in engineering. Kluwer Academic Publishers: Dordrecht, 1997. Bigwood DA, Crocombe AD. Non-linear adhesive bonded joint design analysis. Int J Adhes Adhesives 1990;10:31–41. Dorn L, Weiping L. The stress state and failure properties of adhesive-bonded plastic/metal joints. Int J Adhes Adhesives 1993;13:21–31. Richardson G, Crocombe AD, Smith PA. A comparison of twoand three-dimensional finite element analyses of adhesive joints. Int J Adhes Adhesives 1993;13:193–200. Hildebrand M. Non-linear analysis and optimisation of adhesively bonded single-lap joints between fibre-reinforced plastics and metals. Int J Adhes Adhesives 1994;14:261–7. Lang TP, Mallick PK. Effect of spew geometry on stresses in single-lap adhesive joints. Int J Adhes Adhesives 1998;18:167–77. Lang TP, Mallick PK. The effect of recessing on the stresses in single-lap adhesively bonded single-lap joints. Int J Adhes Adhesives 1999;19:257–71.