Strength Improvement of Adhesively-Bonded Joints Using
a Reverse-Bent Geometry
R. D. S. G. Campilho, A. M. G. Pinto, M. D. Banea, R. F. Silva
and L. F. M. da Silva
Abstract
Adhesive bonding of components has become more efficient in recent years due to the developments in ad-
hesive technology, which has resulted in higher peel and shear strengths, and also in allowable ductility up
to failure. As a result, fastening and riveting methods are being progressively replaced by adhesive bonding,
allowing a big step towards stronger and lighter unions. However, single-lap bonded joints still generate
substantial peel and shear stress concentrations at the overlap edges that can be harmful to the structure,
especially when using brittle adhesives that do not allow plasticization in these regions. In this work, a nu-
merical and experimental study is performed to evaluate the feasibility of bending the adherends at the
ends of the overlap for the strength improvement of single-lap aluminium joints bonded with a brittle and a
ductile adhesive. Different combinations of joint eccentricity were tested, including absence of eccentricity,
allowing the optimization of the joint. A Finite Element stress and failure analysis in ABAQUS
®
was also
carried out to provide a better understanding of the bent configuration. Results showed a major advantage
of using the proposed modification for the brittle adhesive, but the joints with the ductile adhesive were not
much affected by the bending technique.
Keywords
Bonded joint, structural adhesive, finite element analysis, strength prediction
1.
Introduction
Adhesive bonded joints have become more efficient in the last few decades due
to the developments in adhesive technology, which has resulted in higher peel
and shear strengths, and also in allowable ductility up to failure. As a result of
the reported improvement in the mechanical characteristics of adhesives, adhesive
bonding has progressively replaced traditional joining methods such as fastening
or riveting, allowing a big step towards stronger and lighter unions between com-
ponents. Compared to these traditional techniques, adhesive bonded joints also
benefit from smaller stress concentrations, absence of fretting between materials
to be joined, improved fatigue behaviour, easier conformance to complex shapes,
amongst many other factors. However, it is common knowledge that stress concen-
trations still subsist in bonded joints along the bond length owing to the gradual
transfer of load between the two adherends in the overlap region (also known as
differential straining along the overlap), especially in single-lap joints [1]. As a re-
sult, shear stresses concentrate at the overlap edges, with only a very small amount
of load being carried in the central region. Peel stresses also develop in the same
regions owing to the joint rotation and curvature of the adherends [2]. Both of these
can be harmful to the structure, especially when using relatively brittle adhesives,
which do not allow redistribution of stresses at the loci of higher concentrations,
i.e., the overlap edges, leading to premature failures.
To overcome these limitations, considerable research has been carried out in re-
cent years on the development of more efficient adhesively-bonded techniques that
are able to suppress the concentrations of stresses as well as on adhesive technology
[3–6]. One of the most commonly applied techniques is the use of adhesive fillets
at the overlap edges. Fillets allow the redistribution of stresses in the mentioned
regions and, as a result, they increase the strength of bonded unions [7–9]. Fillets
usually extend over all the adherends thickness, minimizing peak peel and shear
stresses at the overlap edges [10]. Rispler et al. [11] developed a numerical algo-
rithm to find the optimal fillet shape in adhesively-bonded reinforced plates. In each
iteration of the optimization process, the low stressed fillet elements were deleted in
order to optimize their shapes. The optimal solution (a 45
◦
flat fillet) was achieved
when all fillet representative elements were stressed by at least 20% of the structure
maximum stress. A two-dimensional Finite Element study was published by Lang
and Mallick [12], concerning the effect of the fillet shape on peel and shear stresses
in a single-lap joint loaded in tension. Reductions in peel and peak shear stresses of
87 and 60% were achieved at the overlap edges using a curved fillet. These results
are consistent with the work of Quaresimin and Ricotta [13], whose experimental
data revealed that efficiency improvements from 11.6 to 25.2% could be achieved
with a 45
◦
straight fillet, depending on the overlap length and surface condition of
the carbon-epoxy adherends (with or without peel-ply).
Outer and inner tapering of the patches can also be effective in reducing peak
peel stresses at the overlap edges [14–16], eventually increasing the load bearing
capability of the repairs. Kaye and Heller [17] emphasized that patch outer tapering
distributes the loads more uniformly between the laminates and patches, which re-
flects in a strength improvement of bonded structures. Hu and Soutis [18] showed
that peak shear strains can be markedly reduced by increasing the adhesive thick-
ness at the patch edges. Therefore, a joint with patches tapered from inside was
considered to reduce stress concentrations in the adhesive layer and consequently
to increase the joint strength. da Silva and Adams [19] studied for double-lap joints
the effects of internal patch tapering and filleting on peel stresses and on the joint
strength under varying temperatures. Stresses along the bondline greatly diminished
with this modification under tensile loads. The experimental results showed that, as
a rule, tapering and filleting increased the joint strength at ambient temperatures.
At low temperatures, the differences were not significant.
Ganesh and Choo [20] evaluated Young’s modulus grading of the adherends
in single-lap joints under tension to reduce stress concentrations. Finite Element
results showed a 20% reduction in peak shear stresses in the adhesive layer, concur-
rently with an increased load transfer in the central region of the bondline. Boss et
al. [21] followed an alternate route, considering in addition to the aforementioned
technique an edge chamfer to improve the joint strength. A reduction in peak shear
stresses was achieved with modulus grading and chamfering. However, only the
chamfering technique was able to reduce peel stresses. Ávila and Bueno [22] tested
a wavy geometry (with a sinusoidal adherend shape at the overlap). This approach
increased the joint strength by approximately 40%, which was justified by the uni-
formity of shear and peel stress distributions in the adhesive layer. An identical
solution was tested by Zeng and Sun [23], which showed that this technique allows
a large improvement in load capacity of the joints, mainly due to the development
of compressive through-thickness stresses at the edges of the overlap.
Campilho et al. [24] evaluated by Finite Elements coupled with cohesive mod-
elling the tensile strength of adhesively-bonded single and double-strap repairs.
Several geometric alterations, such as fillets, chamfering the patch outer and in-
ner faces, plug filling and chamfering the outer and inner plate edges, were tested.
For the single-strap repairs, the best results (26.8% strength improvement) were
achieved by filleting the patch ends and chamfering the outer and inner edges of the
adherends. Using the double-strap technique, the strength improvement was highest
by using a flat fillet at the patch ends and plug filling with adhesive the gap between
the adherends (strength improvement of 11.9%).
The work of McLaren and MacInnes [25] is considered as the pioneering work on
the subject of single-lap joints with a bent edge at the overlap for the optimization of
stress distributions by elimination of the joints eccentricity. The bent modification
to the lap joint with flat adherends was proposed and analysed by photoelastic-
ity, showing the effectiveness of this technique to reduce stress gradients along the
bondline. The most impressive results were attained for certain negative values of
adherends eccentricity. Related studies performed a couple of decades later by Das
Gupta and Sharma [26] and Das Gupta [27] led to similar conclusions, but consider-
ing the adherends bent outside the overlap region, i.e., keeping a constant thickness
bondline. Sancaktar and Lawry [28] evaluated the use of single-lap joints with pre-
bent adherends by photoelasticity, considering resin adherends bonded with a liquid
plastic cement. Photoelasticity was used to experimentally ascertain the magnitude
±
±
±
±
of tear stresses. Experimental testing also revealed that for the joint materials se-
lected for the study, the failure strength of the joints could be increased up to 71%,
compared with the flat joint. Fessel et al. [29] performed an experimental and Finite
Element study on tensile loaded steel single-lap joints, with emphasis on wavy and
bent geometries. These modifications diminished peak peel and shear stresses at the
overlap edges. The experimental tests showed strength improvements for the bent
joint from 8 to 40%, compared to a flat geometry.
In this work, a parametric study was performed on single-lap aluminium joints
bonded with two adhesives, a brittle (Araldite
®
AV138) and a ductile one (Araldite
®
2015), to evaluate the feasibility of bending the adherends at the ends of the overlap
(configuration known as bent joint) for the strength improvement of these joints.
The experimental study comprises different combinations of joint eccentricity, in-
cluding absence of eccentricity, for strength optimization. A Finite Element stress
and failure analysis in ABAQUS
®
was also carried out to provide a deeper insight
into the effect of the bent configuration on the joint behaviour. Failure was predicted
with two straightforward failure criteria, each one particularly suited to one of the
adhesives, as they capture the essence of the respective failure process while giving
acceptable results.
2.
Characterization of the Materials
The aluminium alloy AW6082 T651 was selected for the adherends, character-
ized by a high tensile strength (340 MPa as specified by the manufacturer) ob-
tained through artificial ageing at a temperature of approximately 180
◦
C [30].
This specific alloy was chosen due to its wide use in Europe for several struc-
tural applications under different extruded shapes. The bulk stress–strain (σ –ε)
response of the aluminium adherends, obtained according to the ASTM-E8M-04
standard [31], is presented in Fig. 1. The aluminium alloy has a Young’s modulus
(E) of 70.07 0.83 GPa, a yield stress (σ
y
) of 261.67 7.65 MPa, a maximum
strength (σ
f
) of 324 0.16 MPa and a failure strain (ε
f
) of 21.70 4.24%. The
bilinear approximation of Fig. 1 was used for input in the simulations. The two
Figure 1. σ –ε curves of the aluminium AW6082 T651 and respective approximation for the Finite
Element analysis.
(a)
(b)
Figure 2. σ –ε curves of the Araldite
®
AV138 (a) and Araldite
®
2015 with approximation for the
Finite Element analysis (b).
adhesives, Araldite
®
AV138 and Araldite
®
2015, were also characterized for sub-
sequent input in the Finite Element analysis that will make possible the analysis of
the results and comparison with the experiments. The tests were carried out under
tension (mode I loading; bulk tests) and shear (mode II loading; Thick Adherend
Shear Test (TAST)), which allowed the determination of the yield strengths and
moduli in both loading modes. The bulk specimens for both adhesives were fabri-
cated according to the French standard NF T 76-142 [32] to prevent the formation
of porosities. Thus, the specimens were made of 2 mm plates, cured under pressure
in a sealed mould, followed by machining to produce the dogbone shape described
in the standard. The TAST tests followed the guidelines of the ISO 11003-2:1999
standard [33], using DIN Ck 45 steel for the adherends. Particular attention was paid
to the surface preparation and bonding procedures to guarantee a cohesive failure
of the adhesive, which followed entirely the specifications of the standard. Figure 2
shows, as an example, typical stress–strain curves in pure mode I of the Araldite
®
AV138 (a) and Araldite
®
2015 (b). For the Araldite
®
2015, a bilinear approxima-
tion was made for the subsequent Finite Element failure analysis. The difference
between these two adhesives concerning the allowable ductility is notorious, as the
AV138 is extremely fragile, while the 2015 undergoes large plasticization prior to
failure. A higher deviation between specimens was also found for the AV138 since,
due to its brittleness, it is more sensitive to fabrication defects [34]. The failure
strength of the AV138 is nearly twice that of the 2015. Table 1 summarizes the data
on these materials [34], which will be subsequently used for the Finite Element
simulations and strength predictions. The initial yield strength was calculated for a
plastic deformation of 0.2% for both adhesives.
3.
Experimental Work
The eccentricity parameter of a single-lap joint, K, is defined as
