MP 110521
MATERIALS TESTING FOR JOINING TECHNOLOGIES
Experimental and Numerical
Strength Analysis of Double Lap
Joints Subjected to Tensile Loads
Hamit Adin and Şemsettin Temiz,
Batman, Turkey
In this paper, the mechanical behavior of the Double Lap Joints (DLJs)
bonded with adhesive was analyzed. The stress-strain behaviors were
investigated along the overlap length and adherend thickness in DLJs
subjected by tensile loads. The stress analyses were performed via
Finite Element Method (FEM). The FEM calculations were performed
with ANSYS (12.0.1). Experimental results were compared with the
FEM results and were found quite reasonable. The results show that the
failure loads were increased with an increase in adherend thickness.
The stress-strains were changed depending on adherend thickness and
overlap length. Both FEM stress analyses and experimental results
revealed that failure occurred around at the edge zones of the overlap
length due to the effect of shear stresses, while the failure at the edges
of the adhesive layer originated from the peel strain in tensile.
Adhesive bonding technology is widely
used today in almost all the industries
fields of the world and this is mainly due to
its high strength–weight ratio, low cost and
high efficiency [1].
The potential use of adhesive joints as
fasteners in machine and structure components has been increasing gradually. Adhesive joints supersede, especially in longtime periods, conventional joining methods
such as bolting, riveting, soldering and
welding from day to day in aviation, space,
automotive, substructure, medicine, electronic packaging, sport, building and marine industrials, for which the security of
the joints is needed [2-4].
Adams and Harris [5] have studied the
influence of the geometry of the ends of the
overlap of adhesively bonded joints on the
stresses. They showed that rounding the
corners removes the mechanical singularity point and these roundings have considerable effect on the magnitude of the stress
reduction.
The reduction of transverse shear and
normal stress concentrations along the
edges of adhesive bondlines is important in
order to prevent premature failure of the
bonded joint. Due to differential straining
in the substrates, adhesively-bonded joints
inevitably experience stress concentrations, especially in the adhesive layer near
the ends of overlap where the load transfer
takes place. Among the many factors affecting the strength of a bonded joint, the
stresses in both adhesive layer and substrates are probably most crucial for designing of bonded joints [6-8].
Structural designers are interested in
the strength evaluation under service conditions. A reliable prediction of stresses at
locations where a high risk of crack initiation exists is thus a necessary step in designing mechanical structures. Simplified
models [9-11] and solid finite element calculations [12, 13] showed that in adhesive
joint, both shear and normal stresses reach
their maximum value in the vicinity of the
bond edges. These stress concentrations
often lead to the joint failure. In an adhesive joint, three kinds of failure are possible. The first is adhesive failure,
which °Ccurs at the adherend/adhesive interface. The second is cohesive failure,
which °Ccurs in the adhesive. The last
kind of failure is mixed: it starts out as an
56 (2014) 1 © Carl Hanser Verlag, München Materials Testing
adhesive crack and then quickly becomes a
cohesive failure.
Different approaches were recently employed to predict the mechanical behaviour
of bonded assemblies. In the early stages of
bonded structures analyses, theoretical
studies were popular [14-16], which employed simplifying assumptions in the
structures geometry, materials behaviour,
loading, and boundary conditions, to formulate efficient closed-form elasticity solutions for the local fields in the adhesive region. The main advantage of analytical
modelling is that the structure can be analysed quickly, although with lot of embedded simplifications [17].
In the computer age, FEM codes to simulate the mechanical behaviour of structures
were rapidly implemented, providing a
more accurate insight on this subject. In
the FEM, each component of the adhesive
joint is treated as a continuum and the analysis of large displacements, such as those
seen in the single lap joints, is also available. Accounting for the materials plasticity
was also made easier, since FEM codes actually incorporate several complex material
laws. One of the first FEM works on bonded
1
Hinweis Table 2 fehlt!
2
MATERIALS TESTING FOR JOINING TECHNOLOGIES
assemblies dates back to the 1970s when
Wooley and Carver [18] conducted a stress
analysis on single-lap joints.
On the strength prediction of bonded assemblies, two different lines of analyses
were developed over the years: the strength
of materials and fracture mechanics-based
methods. The strength of materials approach is based on the evaluation of allowable stresses [19, 20] or strains [21, 22], by
theoretical formulations or the FEM. The
assemblies strength can be predicted by
comparing the respective equivalent
stresses or strains at the critical regions,
obtained by stress or strain-based criteria,
with the properties of the structure constituents [23-25].
The purpose of this research is to investigate strength of joint along different the
overlap lengths in double lap joints (DLJs)
subjected by tensile load. A hard adhesive
was used as adhesive. The mechanical behaviors of DLJs were analyzed, both experimentally and numerically. The numerical
analysis of stress-strain in the DLJs was performed via Finite Element Method (FEM).
FEM was carried out to predict failure loads,
to assist the geometric design and to identify
effective ratios of properties to maximize
joint strength. The joint strengths were estimated using the obtained interface stressstrain distributions. The FEM results were
also compared with experimental results.
Experimental
The determination of mechanical properties of adhesive. In the study, the 2214
regular produced by 3M was chosen as adhesive and AA2024-T3 alloy was utilized
as adherend which widely used in the aircraft industry. To determine mechanical
properties of adhesive bulk specimen
method was performed. The bulk specimens used in this study were prepared as
described in Ref. [26].
The stress–strain (σ – ε) behaviors of the
adhesive was determined by bulk specimens tested under specified the conditions.
The experiments of bulk specimen were
performed using video extensometer, Shimadzu (Shimadzu Corporation, Tokyo, Japan) (100 kN) machine at room temperature and relative humidity 50 % ± 5. During
tensile tests, the crosshead speeds were
maintained at 1 mm/min. Four specimens
were tested. Typical tensile stress–strain
curves for the adhesives and adherend are
shown in Figure 1. It can be seen in Figure
1.a that the maximum stress of the adhesive is measured as 72 MPa.
Production of DLJs. DLJs were made of
AA2024-T3 alloy bonded using 2214 regular type adhesive. The dimensions of adherend are shown in Table 1. The thicknesses
of adhesive and outer adherend (cover plate)
were chosen as 0.25 mm and 1.6 mm, respectively. In addition, the width of adherend was chosen as 25 mm. The other dimensions of the DLJs are shown in Figure 2.
Since effects of thickness and overlap length
were examined, the same element dimension was used in all models as often as practicable (see in Table 1 and Figure 3a). The
upper and lower cover plates have the same
dimensions and materials. The thickness of
upper and lower patches was 1.6 mm.
Four different adherend thickness and
overlap length were used. The DLJs were
manufactured as four different specimens
for each condition of adherend thicknesses
Figure 1. Tensile stress–strain behaviors of adhesive and adherend: (a) SBT 9244 adhesive;
(b) AA2024-T3 alloy [26]
Adherend thickness (mm) Overlap length (mm)
Adherend width (mm) Adhesive thickness (mm)
3.2
24.8
25
0.25
4.8
26.8
25
0.25
6.4
28.8
25
0.25
8.0
30.8
25
0.25
Table 1. Geometrical parameters of the DLJs used in experimental and numerical studies
(all dimensions in mm)
Figure 2. Double Lap Joints (DLJs) configuration under tensile loading: (a) geometry and loading
(all dimensions in mm); b) Mesh details and boundary conditions
56 (2014) 1
MATERIALS TESTING FOR JOINING TECHNOLOGIES
and overlap lengths. The mechanical properties of adherend and adhesive are given
in Tables 1. Before bonding, the adherend
surfaces were degreased with acetone,
etched with H2SO4 + Na2Cr2O7.2H2O for
30 minutes at 60-65 °C, washed in running
tap water and dried in an oven for 30 minutes at 60 °C. Then, the adhesive was prepared. It was applied at the joint surface
and the adherend were clamped for curing
as cure of adhesives were waited.
The tensile load was applied in the x direction. DLJs experiments were performed
under the same conditions with bulk specimen experiments as mentioned above.
Finite Element Modeling of the DLJs. In
this step, Finite Element Method (FEM) was
employed in order to analyze the behaviors
of stress and strain of the DLJs. The FEM calculations were the ANSYS (Academic Teaching Advanced, Ver. 12.0.1) software [27].
Additionally, the stress-strain analysis was
obtained according to von Mises yield criterion. Because, Gali et al. [28] showed that
the von Misses yield criterion was suitable
to model the stress-strain behavior of the
adhesives used in the joint. By means of this
criterion, the stress-strain distributions in
the adhesive layer were calculated.
Loading, boundary conditions and mesh
conditions were presented in Figure 3. In
this study, Plane 82 elements were used.
The elements are composed of eight different nodes with two degrees of freedom.
Baylor and Sancaktar [29] showed that if
the mesh density along the transverse direction of the overlap was greater than
3 elements per mm, then the variation in
maximum principal stress and von Mises
stress with mesh density would be effectively removed. It was also shown that for
an adhesive thickness of 0.2 mm, 25 elements per mm in the peel direction would
result in the uncoupling of these stresses
with mesh density.
The mesh density can effect the strain
predictions in the adhesive layer. A smaller
element size will generally give a higher
strain. For this reason, the size of elements
in the mesh was reduced until a stable
strain value had been achieved. Eventually,
25 elements through the adhesive thickness (0.25 mm) were used in the models,
as shown in Figure 3b. The adherend thickness was meshed with 100 layers. The
cover plate thickness (1.6 mm) was meshed
with 12 layers. So, the smallest element
sizes were used as 0.01 mm in the adhesives and 0.133 mm in the adherends. The
total number of nodes and elements were
chosen 26889 and 8810, respectively.
56 (2014) 1
(σeqv) was calculated using the von Mises
failure criterion and it was assumed that
the failure occurred when the equivalent
stress calculated at any point of adhesive
layer reached the ultimate strength of adhesive. In addition, the effects of thickness
and overlap length at the interfaces of adherends were examined.
As the maximum von Mises stress values at adhesive interface approach to these
values, then they were multiplied by the
frontal area of specimens (t × b = thickness
of specimen × breadth of specimen) from
which the failure loads were obtained, as
shown in Table 3.
When the results that calculated from
FEM approach near to the maximum stress
of bulk specimen, the adhesive interfaces
were turned on. Paths were defined
Results and discussion
Experimental results. Four different specimens were tested in experiments for each
condition of adherend thickness and overlap length. The specimens were carefully
and closely observed to understand failure
mechanism during the tensile experiments. All failures of the joints were catastrophic failure and occurred at the interface without breaking the adherends. The
average values of failure loads were presented in Table 3. It is clearly seen from
table that the lowest failure load was determined at t = 3.2 mm for each specimen.
The FEM calculations. To find out the
failure loads of the specimens in the FEM
calculations, ultimate strength of adhesives (σ*) were used. The equivalent stress
Figure 3. Comparison of failure loads for DLJs; (a) The effects of different adherend thicknesses
(L = 24.8 mm); (b) The effects of different overlap lengths (h = 4.8 mm)
AA2024-T3 (Adherend)
2214 (Adhesive)
E (MPa)
71875
5171
ν
0.33
0.35
σ* (MPa)
482
72
ε*(mm/mm)
0.159
0.02
Table 2. Material properties of the adherend and
adhesives [26]
E, Young’s modulus; ν, Poisson’s ratio;
σ*, ultimate strength; ε* Ultimate strain.
Adherend
thickness (mm)
Overlap length
(mm)
FEM Failure Load
(FFEM) (kN)
Experimental Failure
Load (FEXP) (kN)
FR (FFEM/FEXP)
3.2
24.8
5.771
5.398
1.069
4.8
24.8
8.705
8.436
1.032
6.4
24.8
11.637
11.027
1.055
8.0
24.8
14.608
14.273
1.023
4.8
24.8
8.705
8.436
1.032
4.8
26.8
8.733
8.455
1.033
4.8
28.8
8.747
8.475
1.032
4.8
30.8
8.762
8.491
1.032
Table 3. Comparison of failure loads obtained from FEM and experimental for different adherend
thickness and overlap length
3
4
MATERIALS TESTING FOR JOINING TECHNOLOGIES
a)
b)
c)
d)
Figure 4. Stress distributions along the A-B bond-line on the adhesive side of the DLJs for different
adherend thickness (L: 24.8 mm): (a) Sx (σx ) stress distributions; (b) Sy (σy ) stress distributions;
(c) Sxy (τxy ) stress distributions; (d) Seqv (σeqv ) von-Mises stress distributions
a)
c)
b)
d)
Figure 5. Stress distributions along the C-D bond-line on the adhesive side of the DLJs for different
adherend thickness (L: 24.8 mm): (a) Sx (σx ) stress distributions; (b) Sy (σy ) stress distributions;
(c) Sxy (τxy ) stress distributions; (d) Seqv (σeqv ) von-Mises stress distributions
through the lines A-B and C-D. After that,
path values were separately found for each
adhesives and specimen. The stress and
strain values (σx, σy, τxy, σeqv, εx, εy, γxy,
εeqv) were selected for each specimen and
their results were found. The figures were
drawn using Matlap.
Effect of the adherend thickness and
overlap length on failure load. The failure
loads of experimental and FEM calculation
were shown in Table 3. As it can be seen
from the above mentioned tables, the failure loads from the FEM calculations and
the experimentally measured values seem
to be quite close to each other. In addition,
it was found that the FEM results of stress
were well consistent with the experimental
results. In the last columns of the tables,
the convergence ratios were found by dividing the experimental loads (FEXP) with
failure loads (FFEM) found by the FEM calculations. In general, the values of FR were
found to be very close to 1. As a result, the
values of experimental results were consistent with the values of FEM calculations.
Additionally, FR ratios were found between
1.023 and 1.069.
The effects of adherend thickness and
overlap length in failure loads were showed
in Figure 3. It can be seen from Figure 3a
that when the adherend thicknesses were
increased, the failure loads were increased.
The adherend thicknesses were played a
significant role in failure initiation and
loads. So, these results have been consistent with Ref. [26]. The adhesion area of the
butt region increased gradually with an increase in adherend thickness, therefore,
the failure load increased.
The effect of overlap lengths on the failure load for the DSJs with 2214 adhesive
are given in Figure 3b.10. It can be seen in
both FEM and experimental results that
the increase in overlap length was increased less than Figure 3a in the load carried by the DSJs. In addition, the failure
loads were maximum when the adherend
thickness and overlap length was around
t = 8 mm, L = 30.8 mm, respectively. So, it
was shown that this dimensions were affected the performance of the DLJs.
Stress and strain distribution results.
The stress and strain distributions of DSJs
subjected to a tensile load are given in the
following figures. For the stress strain distributions between adherend and cover
plate, adhesive-cover plate interface along
line A-B were selected and for the stress
and strain distributions in the butt region,
the mid-line of adhesive along line C-D was
selected as given in Figure 2a.
56 (2014) 1
MATERIALS TESTING FOR JOINING TECHNOLOGIES
Effect of the adherend thickness on
stress distribution. The stress distributions along the line A-B for different adherend thickness obtained from FEM analyses
is presented in Figure 4. The longitudinal
stress (σx) and peel stress (σy) distributions along the bond-line A-B for different
adherend thickness are given in Figure 4a
and b, respectively. The σx and σy stresses
were maximum at the edges of x/L (point A
and B). The stresses increased when close
to points A and B. In addition, σx and σy
increased with increasing of adherend
thickness. Note that both the σx and σy
stresses were symmetric along the horizontal centerlines of the adhesive.
The shear stress (τxy) and equivalent
stress (σeqv) distributions along the bondline A-B for different adherend thickness
are depicted in Figure 4c and d, respectively. The τxy was maximum at point A,
whereas it was minimum at point B. The
σeqv was symmetric and maximum at
point A and B. The σeqv stress also increased when the adherend thickness increased.
Contrary to Figure 4a and 4b, the adherend thickness had a considerable effect on
τxy stress distributions, and τxy stress decreased when the adherend thickness increased. Except for t : 3.2 mm adherend
thickness the τxy was symmetric. σx, σy and
σeqv were also maximum at point A and B
point. They were more uniform at the end
of the overlap length. The comparison indicates close agreement for the stress distribution of σx, σy and σeqv as shown in Figure
4a, 4b and 4d, respectively. Both the peeling and shear stresses were increased with
increasing of adherend thickness. Due to
these stresses, failures were initiated at A
and B points.
The stress distributions along the line
C-D for different adherend thickness obtained from FEM analyses is showed in Figure 5. The σx, σy and σeqv stress distributions along the bond-line C-D for different
adherend thickness are illustrated in Figure 5a, 5b and 5d, respectively. The σx, σy
and σeqv stresses were minimum at the
edges of x/L (point A and B) but the stresses
were higher close to middle point of x/L.
The values of σx, σy and σeqv increased with
increasing of adherend thickness. The normal and equivalent stresses were high for
thick adherend and those stresses increased with an increase in adherend
thickness. The reason of this is that when
the adherend thickness gets thinner, the
adhesive in the butt region is exposed to
more strain in the loading direction and
56 (2014) 1
a)
c)
b)
d)
Figure 6. Stress distributions along the A-B bond-line on the adhesive side of the DLJs for different
overlap length (h: 4.8 mm): (a) Sx (σx ) stress distributions; (b) Sy (σy ) stress distributions;
(c) Sxy (τxy) stress distributions; (d) Seqv (σeqv ) von-Mises stress distributions
a)
b)
c)
d)
Figure 7. Stress distributions along the C-D bond-line on the adhesive side of the DLJs for different
overlap length (h: 4.8 mm): (a) Sx (σx ) stress distributions; (b) Sy (σy ) stress distributions;
(c) Sxy (τxy) stress distributions; (d) Seqv (σeqv ) von-Mises stress distributions
5
6
MATERIALS TESTING FOR JOINING TECHNOLOGIES
a)
b)
c)
d)
Figure 8. Strain distributions along the A-B bond-line on the adhesive side of the DLJs for different
adhesive thickness (L: 24.8 mm): (a) Ex (εx ) strain distributions; (b) Ey (εy ) strain distributions;
(c) Exy (γxy) strain distributions; (d) Eeqv (εeqv ) von-Mises strain distributions
a)
c)
b)
d)
Figure 9. Strain distributions along the C-D bond-line on the adhesive side of the DLJs for different
adhesive thickness (L: 24.8 mm): (a) Ex (εx ) strain distributions; (b) Ey (εy ) strain distributions;
(c) Exy (γxy) strain distributions; (d) Eeqv (εeqv ) von-Mises strain distributions
this causes an increase in the normal and
equivalent stresses.
The shear stress (τxy) distributions along
the bond-line C-D for different adherend
thickness are showed in Figure 5c. The τxy
was maximum at point C, whereas it was
minimum at point D. Contrary to Figure 5a,
5b and 5c; the τxy shear stress also decreases when the adherend thickness increases. The σx, σy, τxy and σeqv stresses
were also symmetric along the horizontal
centerlines of the x/L. Except for τxy distribution the σx, σy and σeqv were more uniformly along the bond-line C-D.
Effect of the overlap length on stress
distribution. In Figure 6, as a result of the
FEM, normal (σx and σy), shear (τxy) and
equivalent (σeqv) stress distributions obtained from the adhesive layers A-B bondline throughout at t = 4.8 mm adherend
thickness have been given. This figure
clarified that maximum values of all stress
located at the edges of x/L. It was observed
in Figure 6a that maximum and minimum
values of σx occurred in the edges. As overlap length were increased, the values of
σxincreased as well. But, when overlap
length were increased, the σeqv decreased.
The peeling stresses (σy) along the A-B
bond-line were determined by means of
Figure 6b. Maximum and minimum values
of the peeling stress were determined in
edges and in the middle of x/L. Similar to
the σy components in the middle of the adhesive layer, the σy at the interface was almost constant across the x/L, but increased
near the edges. The peel stresses at the
edges of the overlap were very important
because of cause initiation and propagation
of failure in this region. This argument is
consistent with Hart-Smith’s argument [1].
Figure 6c showed that the overlap length
had a considerable effect on τxy stress distributions, and the stresses of τxy were decreased when the overlap length was increased until the middle of x/L. But, τxy,
after this point was decreased. As seen can
be in Figure 6d, σeqv stress distribution has
almost the same characteristics with σy
peeling stress distribution. Maximum and
minimum values of the equivalent stress
were obtained in edges and middle of x/L.
In addition, it should be noted that σx, σy,
τxy and σeqv distributions were symmetric
along the horizontal and vertical centerlines axis of x/L.
The longitudinal (σx) stress, peel (σx)
stress and equivalent (σeqv) stress distributions along the bond-line C-D for different
overlap lengths are given in Figure 7a, b
and d, respectively. In these figures, the
56 (2014) 1
MATERIALS TESTING FOR JOINING TECHNOLOGIES
stress distributions σx, σy, and σeqv are
similar to each other qualitatively. The σx,
σy and σeqv stresses were maximum at the
ends of the overlap length (point A and
point B). The stresses points far from A and
B were low. It can be seen from Figure 7a
and d that the values σx and σeqv were decreased with increase of the overlap length.
That’s way the load carried by the bondline decreases depending on decreased in
overlap length. Consequently, the load was
carried more by the butt region in short
overlap length and, therefore, this situation
accelerated an increase in the longitudinal
and peel stresses. In addition, the overlap
length longitudinal (σx) stress had no significant effect of on stress distributions as
value along the C-D bond-line.
The shear (τxy) stress distribution along
line C-D on the adhesive different overlap
lengths is given in Figure 7c. Contrary to
σx, σy and σeqv stresses, the overlap length
had a considerable effect on τxy stress distribution, and τxy stresses until the middle
of x/L were decreased when the overlap
length was increased. Then, τxy was increased. τxy was also maximum at point A
and minimum near B point. The joint distributes the shear stress (τxy) from the ends
of the overlap towards the centre more uniformly than the longitudinal (σx), peel (σy)
and von Mises equivalent (σeqv) stresses.
Effect of the adherend thickness on
strain distribution. The strain distributions
along the line A-B for different adherend
thickness are presented in Figure 8. The εx,
εy, γxy and εeqv distributions along the bondline A-B for different adherend thickness
are given in Figure 8a, b, c and d, respectively. Similar to Figure 8b and d that, the εy
and εeqv strains were maximum at the ends
of the overlap (point A and B). The strain of
εy was decreased with increase of the adherend thickness along A-B line. Contrarily, the
equivalent strains (εeqv) were increased. The
εx strain was maximum at the end of the
x/L, and was decreased when near point A
and B. Figure 8c showed that the overlap
length had a considerable effect on γxy
strain distributions, and the values of γxy
were decreased when the overlap length
was increased until the middle of x/L. But,
γxy after this point they were decreased.
Maximum and minimum values of the shear
strain were obtained in edges and middle of
x/L. In addition, notes that εx, εy, γxy and εeqv
distributions were symmetric along the vertical centerline axis of x/L.
The εx, εy, γxy and εeqv distributions along
the bond-line C-D for different adherend
thickness are shown in Figure 9a, b, c and
56 (2014) 1
d, respectively. Figure 9a and d are similar.
A comparison of the εx peeling strain and
the εeqv equivalent strain evaluated along
the C-D these strains were increased with
increase of the adherend thickness. Maximum and minimum values of the εx and
εeqv strains were obtained in edges of x/L
whereas, the εy peeling strain distribution
was minimum in edges. The peeling strain
distribution along C-D was also decreased
with an increased in adherend thickness.
The shear strain (γxy) distribution along the
bond-line C-D for different adherend thickness is illustrated in Figure 9c. The γxy was
maximum at point C, whereas it was minimum at point D. Contrary to Figure 9a, 9b
and 9d, the γxy shear strain was increased
in the middle point of C-D bond-line and
then it was decreased when the adherend
thickness increases. The values of γxy away
from C were approached to zero. It can be
seen from Figure 9 that εx, εy, γxy and εeqv
distributions were symmetric along the
vertical centerline axis of x/L.
Effects of the overlap length on strain
distribution. The strain distributions along
the line A-B for different overlap length are
illustrated in Figure 10. Figure 8 and Figure 10 are similar except for Figure 8c and
10c. The εx, εy, γxy and εeqv distributions
along the bond-line A-B for different overlap length are given in Figure 10a, b, c and
d, respectively. The εy and εeqv strains were
maximum at the ends of the overlap (point
A and B). The strain of εy was decreased
with increase of the adherend thickness
along A-B line. Contrarily, the equivalent
strains (εeqv) were increased. The εx strain
was maximum in the middle of the x/L, and
was decreased when far from point A and
B. Figure 8c showed that the overlap length
had a considerable effects on γxy strain distributions, and the values of γxy were decreased when the overlap length was increased until the middle of x/L. But, after
this point γxy was decreased. Maximum
and minimum values of the shear strain
were obtained in edges and middle of x/L.
It can be seen from Figure 10a, b and d that
the strains were increased when the overlap length was increased. In addition, note
that the εx, εy and εeqv strain distributions
were symmetric along the vertical centerline axis of x/L.
The εx, εy, γxy and εeqv distributions along
the bond-line C-D for different overlap
length are shown in Figure 11a, b, c and d,
respectively. Figure 11a and d are similar.
a)
b)
c)
d)
Figure 10. Strain distributions along the A-B bond-line on the adhesive side of the DLJs for
different overlap length (h: 4.8 mm): (a) Ex (εx ) strain distributions; (b) Ey (εy ) strain distributions;
(c) Exy (γxy) strain distributions; (d) Eeqv (εeqv ) von-Mises strain distributions
7
8
MATERIALS TESTING FOR JOINING TECHNOLOGIES
A comparison of the εx peeling strain and
the εeqv equivalent strain were evaluated
along the C-D. These strains were decreased again with increase of the overlap
length. Maximum and minimum values of
the εx and εeqv strains were obtained at
edges of x/L whereas, the εy peeling strain
distribution was minimum at edges. It is
observed from Figure 11b that the peeling
strain distribution along C-D was also increased with increase in overlap length.
The shear strain (γxy) distribution along the
bond-line C-D for different overlap length is
illustrated in Figure 11c. The γxy was maximum at point C, whereas it was minimum
at point D. Contrary to Figure 11a, 11b and
11d, the γxy shear strain was increased in
the middle point of C-D bond-line and then
was decreased when the overlap length increased. The values of γxy away from C
were approached to zero. Figure 11 b and c
showed that the overlap length had no significant effect on strains distributions as
value along the C-D bond-line. It can be
seen from Figure 11 that εx, εy, γxy and εeqv
distributions were symmetric along the
vertical centerline axis of x/L.
As seen from Figure 9 and Figure 11,
while all strains in the DLJs were close to
each other, εx alone was considerably. All of
the strains were maximum at the ends of the
overlap length except for γxy shear strain.
When the magnitude of the equivalent
stresses is considered, it is clearly that the
equivalent stresses have very important
influence on the initiation and the propagation of failure at the edges of DLJs. Consequently, failure initiation was probably occurred on the edges of overlap (the line
A-B) at the interface of adhesives. Then, the
failure at ends promotes to the centre of
overlap before joining each other.
Conclusions
This work is about the effects of the adherend
thickness and overlap length on DLJs subjected to static tensile loadings. In the calculations Finite Element Method (FEM) was
used. The following results were obtained:
•Comparing the failure loads estimated
by the analysis of FEM with the failure
loads obtained by tensile test, it was
seen that they were in a considerable
harmony with each other.
•The failure loads were increased with an
increase in adherend thickness. The effect of overlap lengths on the failure loads
a)
b)
c)
d)
Figure 11. Strain distributions along the C-D bond-line on the adhesive side of the DLJs for
different overlap length (h: 4.8 mm): (a) Ex (εx ) strain distributions; (b) Ey (εy ) strain distributions;
(c) Exy (γxy) strain distributions; (d) Eeqv (εeqv ) von-Mises strain distributions
was less than adherend thickness. The
load carried was increased with an increase in adherend thickness due to the
increased adhesion area. In addition, the
failure loads were maximum when the
adherend thickness and overlap length
was around t = 8 mm, L = 30.8 mm, respectively. Namely, the dimensions were
affected the performance of the DLJs.
•The stress-strains were changed depending on the adherend thickness and overlap length. When adherend thickness
was increased, the values of normal, peel
and equivalent stress-strains were increased. These stresses along A-B bondline were also higher in the ends of the
interface. The effect of the adhesive
thickness on stress-strain along A-B was
higher than that of along C-D bond-line.
•The equivalent stress and strain has
very important influence on the initiation and the propagation of failure at the
edges of DLJs. Equivalent stress and
strain transferee from the end to the
center of the DLJs with increasing of
both adherend thickness and overlap
length. This is the reason for increase in
the strength of joints. In addition, the effect of equivalent strain increases with
increasing of adherend thickness and
overlap length. Eventually, failure initiation occurred on the edges of overlap at
the interface of adhesives.
•The joint distributes the shear stressstrain from the ends of the overlap towards the centre more uniformly than the
longitudinal, peel and equivalent stresses.
The normal and equivalent stresses are
high for thick adherend and those stresses
increase with an increase in adherend
thickness. The reason of this is that when
the adherend thickness gets thinner, the
adhesive in the butt region is exposed to
more strain in the loading direction and
this causes an increase in the normal and
equivalent stresses.
•The peel stresses at the edges of the overlap length was very important because of
causes initiation and propagation of failure in this region. Both FEM stress analyses and experimental results presented
that failure occurred around at the edges
zone of the overlap length due to the effect of shear stresses, while the failure at
the edges of the adhesive layer originated
from the peel strain in tensile.
•The stress and strain distributions were
symmetric along the horizontal and vertical centerlines axis of x/L. They are
more uniformly at the end of the overlap
length.
56 (2014) 1
MATERIALS TESTING FOR JOINING TECHNOLOGIES
References
1L. J. Hart-Smith: R. D. Adams (Ed.), Aerospace,
Adhesive bonding, Cambridge England: Woodhead Publishing Ltd., (2005), pp. 489-494
2M. K. Apalak, R. Davies R.: Analysis and design of adhesively bonded corner joints, Int. J.
Adhesion Adhesives, 13 (1993), pp. 219-235
3M. D. Aydın: Experimental and theoretical
investigation of mechanical properties of the
adhesive bonded single lap joint, Ph.D. Thesis,
Mechanical Engineering, Atatürk University,
Erzurum, Turkey (2003)
4M. D. Aydın, Ş. Temiz, A. Özel: Machine and
Engineer 536 (2004), pp.18-24
5R. D. Adams, J. A. Harris: The influence of local
geometry on the strength of adhesive joints,
Int. J. Adhesion Adhesives 7 (1987), pp. 69-80
6L. J. Hart-Smith: Adhesive-bonded Single-lap
Joints, NASA Technical Report CR-112236.
NASA, Houston, TX (1973)
7R. D. Adams, J. Comyn, W. C. Wake: Structural
Adhesive Joints in Engineering. Elsevier,
Amsterdam, ISBN 0-412-70920 (1997)
8A. J. Kinloch: Adhesion and Adhesives, Science
and Technology, Chapman and Hall, London,
(1993)
9O. Volkersen: Die Nietkraftverteilung in
zugbeanspruchten Nietverbindungen mit
konstanten Laschenquerschnitten, Luftfahrtforschung 15 (1938), pp. 41-47
10F. Delale, F. Erdogan, M. N. Aydinoglu:
Stresses in Adhesively Bonded Joints:
A Closed Form Solution, J. Composite
Materials 15 (1981), pp. 249-259
11P. A. Gustafson, A. Bizard, A. Waas: Dimensionless parameters in symmetric double lap
joints: An orthotropic solution for thermomechanical loading, Int. Journal Solids Structure
44 (2007), pp. 5774-5795
12R. D. Adams, W. C. Wake: Structural adhesive
joints in engineering. Elsevier Applied Science, London and New York, 1984
13K. Shahin, F. Taheri: Analysis of Deformations
and Stresses in Balanced and unbalanced
Adhesively Bonded Single-Strap Joints. Int. J.
of Composite Structure 81 (2007), pp. 511-524
14M. Goland, E. Reissner: The stresses in cemented joints. Journal of Applied Mechanics
66 (1944), pp. 17-27
15F. Szépe: Strength of adhesive-bonded lap
joints with respect to change of temperature
and fatigue. Experimental Mechanics 6 (1966),
pp. 280-286
16J. Pirvics: Two dimensional displacement–
stress distributions in adhesive bonded composite structures. The Journal of Adhesion 6
(1974), pp. 207-228
17S. K. Panigrahi, B. Pradhan: Three dimensional
failure analysis and damage propagation behavior of adhesively bonded single lap joints in laminated FRP composites, Journal of Reinforced
Plastics and Composites 26 (2007), pp. 183-201
18G. R. Wooley, D. R. Carver: Stress concentration
factors for bonded lap joint, Journal of Aircraft
8 (1971), pp. 817-820
19J. A. Harris, R. D. Adams: Strength prediction
of bonded single-lap joints by non-linear finite
element methods. International Journal of
Adhesion & Adhesives 4 (1984), pp. 65-78
56 (2014) 1
Abstract
Übersetzung deutscher Abstract fehlt. Übersetzung deutscher Abstract
fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher
Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung
deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt
Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract
fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher
Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung
deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt Übersetzung deutscher Abstract fehlt.
20D. A. Bigwood, A. D. Crocombe: Non-linear adhesive bonded joint design analyses, International Journal of Adhesion and Adhesives 10
(1990), pp. 31-41
21A. D. Crocombe, R. D. Adams: An elastoplastic
investigation of the peel test, The Journal of
Adhesion 13 (1982), pp. 241-267
22S. J. Lee, G. L. Lee: Development of a failure
model for the adhesively bonded tubular
single lap joint, The Journal of Adhesion 406
(1992), pp. 1-14
23Z. Q. Qian, A. R. Akisanya: An investigation of
the stress singularity near the free edge of
scarf joints, European Journal of Mechanics A/
Solids 18 (1999), pp. 443-463
24E. Dragoni, P. Mauri: Intrinsic static strength
of friction interfaces augmented with anaerobic adhesives, International Journal of Adhesion and Adhesives 20 (2000), pp. 315-321
25S. Feih, H. R. Shercliff: Adhesive and composite
failure prediction of single L joint structures
under tensile loading, International Journal of
Adhesion & Adhesives 25 (2005), pp. 47-59
26Ş. Temiz: Application of bi-adhesive in doublestrap joints subjected to bending moment,
J. Adhesion Sci. Technol. 20 (2006),
pp. 1547-1560
27ANSYS, The general purpose finite element
software, Swanson Analysis Systems,
Houston, TX
28S. Gali, G. Dolev, O. Ishai: An effective stress/
strain concept in the mechanical characteriza-
tion of structural adhesive bonding, Int. J. of
Adhesion and Adhesives 1 (1981), pp. 135-140
29J. S. Baylor, E. Sancaktar: Reliability, Stress
Analysis and Failure Prevention Issues in
Emerging Technologies and Materials 87
(1995), ASME-DE, pp. 41-48
The Authors of This Contribution
Bios fehlen •••• Autor ••• Bios fehlen ••••
Autor ••• Bios fehlen •••• Autor ••• Bios fehlen •••• Autor ••• Bios fehlen •••• Autor
••• Bios fehlen •••• Autor ••• Bios fehlen
•••• Autor ••• Bios fehlen •••• Autor •••
Bios fehlen •••• Autor ••• Bios fehlen ••••
Autor ••• Bios fehlen •••• Autor ••• Bios fehlen •••• Autor ••• Bios fehlen •••• Autor
••• Bios fehlen •••• Autor ••• Bios fehlen
•••• Autor ••• Bios fehlen •••• Autor •••
Bios fehlen •••• Autor •••
Bios fehlen •••• Autor ••• Bios fehlen
•••• Autor ••• Bios fehlen •••• Autor •••
Bios fehlen •••• Autor ••• Bios fehlen ••••
Autor ••• Bios fehlen •••• Autor ••• Bios fehlen •••• Autor ••• Bios fehlen •••• Autor
••• Bios fehlen •••• Autor ••• Bios fehlen
•••• Autor ••• Bios fehlen •••• Autor •••
Bios fehlen •••• Autor ••• Bios fehlen ••••
Autor ••• Bios fehlen •••• Autor ••• Bios fehlen •••• Autor ••• Bios fehlen •••• Autor
••• Bios fehlen •••• Autor ••• Bios fehlen
•••• Autor •••
You will find the article and additional material by entering the document number MP110521
on our website at www.materialstesting.de
9