chapter 3 design, fabrication and analysis of bolted...
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CHAPTER 3
DESIGN, FABRICATION AND ANALYSIS OF
BOLTED JOINTS
3.1 INTRODUCTION
Composites like other structural materials must be joined to create
useful assemblies. The manner, in which this operation performed is a
determining factor on the efficiency of the structure produced. Hence the need
to understand the joint behavior of these materials becomes important. In
relation to use conventional joints on composite structure a lot of
investigation has been done both theoretically and experimentally. Generally
there are two major features of composite material joining that need to be
known, the first is the joint strength and the second is the failure mode. Both
of them were influenced by various parameters.
The work presented in this chapter covers a design, fabrication,
analysis and experimental study of bolted joints. The experimental study was
focused on the influence of joint parameters, clearance between the bolt and
the hole, clamping pressure, washer size, adherent thickness, stacking
sequence, joint strength and failure modes.
3.2 WET LAY-UP PROCESS
A large proportion of all manufactured advanced composite
components consist of laminates. As the term implies, they are manufactured
31
by bonding together a number of layers of reinforcements using a polymer
matrix. There are, however, many variations on the theme, the choice of a
particular process involves an assessment of the required performance, the
production rate, quality, and acceptable cost. The choice is further influenced
by the nature of the matrix polymer and by the form of the reinforcement.
In the early days, the wet lay-up process was the dominant
fabrication method for the making of composite parts. It is still widely used in
the marine industry as well as for making prototype parts. This process is
labor intensive and has concerns for styrene emission because of its open
mold nature (Jhones 1990). In this process, liquid resin is applied to the mold
and then reinforcement is placed on top. A roller is used to impregnate the
fiber with the resin. Another resin and reinforcement layer is applied until a
suitable thickness builds up. It is a very flexible process that allows the user to
optimize the part by placing different types of fabric and mat materials.
Because the reinforcement is placed manually, it is also called the hand lay-up
process. This process requires a little capital investment and expertise and is
therefore easy to use. A schematic of the wet lay-up process is shown in
Figure 3.1(Jhon Wheeton 1986).
3.2.1 Basic Raw Materials
Woven fabrics of glass, Kevlar, and Carbon fibers are used as
reinforcing material, with E-glass predominating in the commercial sector.
Epoxy, polyester, and vinylester resins are used during the wet lay-up process,
depending on the requirements of the part.
32
Figure 3.1 Schematic of the wet lay-up process
The mechanical properties and manufacturing possibilities of
composite laminates are controlled by the use of reinforcing fibers. The
principal mechanical properties such as stiffness and strength are determined
by the properties of the chosen fiber, the volume fraction (Vf) of the fiber, and
the over all fiber architecture.
E-glass is a low alkali borosilicate glass originally developed for
electrical insulation applications. It is manufactured as continuous filaments
in bundles or strands each containing typically between 200 and 2000
individual filaments of 10-30 μm diameters. The glass filaments have
relatively low stiffness (70 GPa) but very high strength (3GPa). Woven cloth
rovings are widely used in the manufacture of laminated structures. They are
available in a variety of weights and weaves and may be woven from yarns
(twisted) or roving (untwisted). The fibers are aligned in the two orthogonal
directions and may be balanced proportions in the two directions or have up
to 90% of the fiber in one direction (unidirectional woven roving).
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3.2.2 Tooling Requirements
The mold design for the wet lay-up process is very simple as
compared to other manufacturing processes because the process requires a
room temperature cure environment with low pressures. Steel, wood and other
materials are used as mold materials for prototyping purposes. To fabricate a
flat laminates, glass plate or finely polished steel plate will be used.
3.2.3 Advantages of the Wet Lay-Up Process
The wet lay-up process has the following advantages:
1. Very low capital investment is required for this process
because there is negligible equipment cost as compared to
other processes.
2. The process is very simple and versatile. Any fiber type
material can be selected with any fiber orientation.
3. The cost of making a prototype part is low because a simple
mold can be used to make the part. In addition, the raw
material used for this process is liquid resin, mat, and fabric
material, which are less expensive than prepreg materials.
3.2.4 Fabrication of the laminates
GFRP composite laminates with stacking sequence 0°/90°, 300/600
and ±450 with various layers (8, 12, and 16) and Quasi-Isotropic laminate
with 16 layers were fabricated by using woven mat glass/epoxy composites
with hardener HY-951. Woven cloth rovings with 360 GSM was used for
laminate preparation. To make a laminates using this process, a release agent
34
is applied to the mold surface (flat steel plate) to facilitate the demolding
operation. A gel coat is then applied using a brush. A polyester gel coat is
commonly used. The gel coat is then cured to avoid print-through of the
laminate. The gel coat improves the quality of surface finish.
The lay-up of the fiber reinforcement in the mold is a crucial step in
any technique of processing of composites because fiber volume fraction and
fiber orientation in the fiber reinforcement are important factors in the control
of mechanical properties of the composite product. During lay-up, each layer
is then laid up at a certain orientation, as required, as the layers are stuck on
top of each other. The thickness of the composite part is built up by applying
a series of reinforcing layers and liquid resin layers. A roller is used to
squeeze out excess resin and create uniform distribution of the resin
throughout the surface. By the squeezing action of the roller, homogeneous
fiber wetting is obtained. The part is then cured at room temperature and once
solidified, it is removed from the mold. The overall process cycle time is
dictated by the size of the component as well as the resin formulation used.
Quality control in the wet lay-up process is relatively difficult. The quality of
the final part is highly dependent on operator skill. Fabricated large sized
Quasi-Isotropic laminate is shown in Figure 3.2. Figure 3.3 shows the test
specimens cut out of the laminate. CFRP laminates were fabricated using high
modulus carbon fiber T 300 -12K (using the autoclave available with M/s
Valeth High tech Composites, Chennai).
3.3 ESTIMATION OF MECHANICAL PROPERTIES OF THE
GFRP AND CFRP COMPOSITES
The woven mat and unidirectional carbon–epoxy composite
material is fabricated with a fiber volume fraction of approximately 63%,
using T 300-12 K, high modulus carbon fiber. GFRP laminates were
35
fabricated with an approximate fiber volume fraction of 60% by using
360 GSM woven mat and epoxy resin. Mechanical properties of the laminated
composite plate are obtained from standard tests. The obtained mechanical
properties of the material are used in numerical analysis.
Figure 3.2 Fabricated quasi-isotropic laminates
Figure 3.3 Preparation of test specimens (00/90
0, 30
0/60
0, ±45
0 and
quasi-isotropic stacking sequence)
36
To find E1, γ12, two strain gauges are stuck on a specimen whose
fiber direction coincides with the loading direction shown in Figure 3.4. One
of them is in the loading direction while the other is in the transverse
direction. The specimen was loaded step by step up to rapture by Zwick
Tensile Machine. For all steps, ε1 and ε2 were measured by an indicator in
1 direction and 2 directions, respectively. By using these strains E1, E2 and γ12
were obtained. Tensile strength (Xt) and Compressive strength (Xc) are
calculated by dividing the failure load by the cross-section area of specimen
under tensile loading and compression loading respectively. Similarly shear
strength (Xs) is calculated by dividing the shear failure load by the shearing
area. G12 is calculated by the known formula,
1
12
211
12 2114
1
EEEE
G ν+−−
= (3.1)
Figure 3.4 Direction of fibers on tensile specimen
Figure 3.5 shows the experimental set-ups for GFRP and CFRP test
specimen to find mechanical properties. Elastic properties of laminates are
estimated based on micromechanics of laminates and by using PROMAL
software and compared with experimental values. The mechanical properties
of carbon–epoxy composite plate which were obtained from the experimental
study have been given in Table 3.1. The properties of GFRP laminates made
of woven mat glass fiber have been listed in Table 3.2.
37
Figure 3.5 Experimental set-ups for GFRP and CFRP test specimen
Table 3.1 Elastic properties of carbon–epoxy composite materials
Type Vf (%) E1 (GPa) E2 (GPa) G12 (GPa) γ12
Woven mat 63% 85.6 85.6 51.34 0.15
Unidirectional 63% 145.5 7.48 4.16 0.22
Table 3.2 Mechanical properties of woven mat GFRP laminates at
60% Vf
Type Vf
(%)
E 1= E2
(Gpa)
G12
(Gpa)
Xt = Yt
(Mpa)
Xc = Yc
(Mpa)
Xs
(Mpa) γxy
Glass/Epoxy
Woven mat 60% 22.7 3.9 412 264 73 0.16
38
3.4 DESIGN CONSIDERATION OF BOLTED JOINTS
In view of obtaining enhanced strength and efficiency of bolted
joints, bolted joint parameters were obtained by analytical and experimental
technique. These parameters were used for the fabrication of bolted joints.
Experimentally and analytically obtained joint parameters are presented in
section 3.4.1 to 3.4.2.3.
3.4.1 Design of bolted joints parameters for maximum efficiency
Hart-Smith equations of elastic stress concentration factor and
efficiency are used to evaluate the w/d and e/d values for all types of bolted
joints configurations.
Hart-Smith (1980) suggested that the elastic stress concentration
factor Kic in orthotropic material is given by
θ
+
−−
−+
−+=1
1
5.1111
41.22
nd
w
nd
w
nd
w
w
ndK ic (3.2)
where, w - width of plate, n - number of bolts, d - diameter of hole and
e - edge distance. θ is defined as,
−=
w
en.
5.05.1θ (3.3)
The Structural efficiency for composite materials of a bolted
connection is given by the equation
39
Efficiency=[ ]
−+− w
nd
KC ic
111
1 (3.4)
where C is correlation coefficients
The correlation coefficients C for the different configurations, as
per Hassan (1995) are as bellow and different bolted joints configurations are
as shown in Figure 3.15 in section 3.5.1.
For connection type S, C = 0.22
For connection type B, C = 0.40
For connection type C, C = 0.16
For connection type D, C = 0.50
By using equation (3.1), (3.2) and (3.3) efficiency of the joints was
predicted for various values of e/d and w/d ratios. Variation of the efficiency
with respect to the ratio d/w with different constant e/d ratio, was plotted as
shown in Figure 3.6. From these graphs we can predict the optimal values of
the geometric parameters for maximum efficiency. Table 3.3 shows the
obtained optimal values of joint parameters for maximum efficiency.
Table 3.3 Optimal joint parameters for maximum efficiency
Type Parameters Efficiency
(%) e/d w/d
Joint-S
Joint-B
Joint-C
Joint-D
3
4
4
4
6
8
7
9
36.8
38.8
35.7
43.0
40
Relation between efficiency and d/w (Joint C)
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0 0.1 0.2 0.3 0.4
d/w ratio
Eff
icie
ncy
e/d=2
e/d=3
e/d=4
Figure 3.6 Relation between efficiency and d/w ratio (Joint–C)
3.4.2 Design of GFRP bolted joints for ultimate bearing strength
This study deals with the bearing strength, failure mode and failure
load in a woven laminated glass–epoxy composite plate with circular hole
subjected to a tensile force by a rigid pin. These were investigated for two
variables; the distance from the free edge of the plate-to-the diameter of the
hole (e/d) ratio and the width of rectangular plate-to-the diameter of the hole
(w/d) ratio. The strength of pinned joints was determined experimentally and
verified numerically. The results of the numerical and experimental analysis
are presented in section 3.4.2.1 and 3.4.2.3 respectively.
3.4.2.1 Damage analysis and failure modes at pin loaded holes using
FEA
The numerical study is performed by using 3D finite element
analysis program by NISA.Tsai-Wu failure criteria is used in the failure
41
analysis. Modeling was done using NKTP-4, NORDR-1, 3D brick element.
The element has three degrees of freedom per node (UX, UY, and UZ). The
state of stress is characterized by six components (SXX, SYY, SZZ, SXY,
SYZ, and SXZ) and is modeled as a half model and symmetry boundary
conditions to reduce the size of the model. The symmetrical surface of the
half model is supported on symmetry XZ plane, with the hole surface of the
plate supported in radial direction. After that, a tensile load test is carried out.
Figure 3.7 shows the boundary conditions applied. The analysis results are
shown in Figure 3.8 indicating failure modes of the GFRP composite
material. Experimental results concerning damage progression and ultimate
strength of the joints are discussed in section 3.3.2.3. These are investigated
for two variables; the distance from the free edge of the plate-to the diameter
of the hole (e/d) ratio, and the width of rectangular plate-to-the diameter of
the hole (w/d) ratio. Comparisons of experimental and numerical failure
modes and loads of the glass–epoxy composite material is shown in
Table 3.4.
Figure 3.7 Boundary conditions applied
42
e/d = 2, w/d = 2, Failure mode = N e/d = 1, w/d = 2, Failure mode = N
e/d = 2, w/d = 4, Failure mode = S e/d = 3, w/d = 3, Failure mode = B, S
e/d = 5, w/d = 5, Failure mode = B e/d = 4, w/d = 4, Failure mode = B
Figure 3.8 Failure modes of the GFRP composite material (B = Bearing
mode, S = shear-out mode, N = net-tension mode)
3.4.2.2 Bearing strength test specimens
The test specimen is prepared as shown in Figure 3.9 and according
to ASTM D5961 standard. The test specimen is a composite rectangular plate
of length (l + e) and width w and with a hole of diameter d. The hole diameter
(d) was fixed at a constant value of 6mm. The hole is at a distance e, from the
free edge of the plate. A rigid pin is located at the centre of the hole. Different
edge distance-to-diameter (e/d) and width-to-diameter (w/d) ratios in the plate
were considered for experimentation.
43
Figure 3.9 Geometry of a bearing test specimen
3.4.2.3 Experimental analysis on bearing strength of pinned joints
This study deals with the bearing strength, failure mode and failure
load in a woven laminated glass–epoxy composite plate with circular hole
subjected to a tensile force by a rigid pin. These are investigated for two
variables; the distance from the free edge of the plate-to-the diameter of the
hole (e/d) ratio (1, 2, 3, 4, 5), and the width of rectangular plate-to-the
diameter of the hole (w/d) ratio (2, 3, 4, 5). Experimental results concerning
damage progression and ultimate strength of the joint are obtained. A good
agreement is obtained between experimental results and numerical
predictions. The numerical results have been discussed in section 3.3.2.1. The
strength of pinned joints was determined experimentally according to ASTM
D5961. The bolted joint test fixture is shown in Figure 3.10.
In the experimental study, every composite joint was loaded until
failure. In these experiments, three basic failure modes were observed for the
different geometries. Some specimens tear immediately. This failure mode is
called as net-tension which is the weakest and the most dangerous mode. For
some specimens, the load decreased with increasing pin displacement and
specimens tear. This failure mode is known as shear-out. But the other
specimens continued to sustain loading. This failure mode is named as
l
w
e
d
t
44
Figure 3.10 Experimental setup for pin-joint
bearing which is the best mode of the resisting load and desired mode. Three
types of basic failure modes are shown in Figure 3.11. All the failure modes
and failure loads results of experimental and numerical study are presented in
Table 3.4. Also bearing test was conducted on GFRP specimens to observe
the failure mode and failure load for a hole dia 4 mm and 5 mm. The results
were tabulated as shown in Table 3.5. Few failed test specimens are as shown
in Figure 3.12(A). The surface plot of experimental results for pin-loaded
glass–epoxy composite is shown in Figure 3.13.
Figure 3.11 Three of basic failure modes in bolted joints
45
Table 3.4 Comparisons of experimental and numerical failure modes,
loads and bearing stress of the glass–epoxy woven-mat
composite material (B = bearing mode, S = shear-out mode,
N = net-tension mode, NA = not acceptable, A = acceptable)
e/d
( d=6 mm)
Failure
load
(kN)
Bearing stress
(MPa)
Failure mode
Experimental FEA Remarks
w/d=2
1
2
3
4
5
w/d=3
1
2
3
4
5
w/d=4
1
2
3
4
5
w/d=5
1
2
3
4
5
5.85
8.61
8.70
9.38
9.48
7.53
9.38
9.89
10.35
11.63
7.58
9.38
10.56
10.99
11.57
7.96
9.45
10.94
11.41
11.63
186.5
275.9
278.8
300.6
303.8
241.3
300.6
316.9
331.7
372.7
274.9
300.6
338.4
352.2
370.8
255.1
302.8
350.6
365.7
372.7
N
N
N
N
S and N
N
B and S
B
B
B
S
S
B
B
B
B and S
B
B
B
B
N
N
N
N
N
N
B and S
B and S
B
B
N
S
B
B
B
N
S
B
B
B
NA
NA
NA
NA
NA
NA
NA
NA
A
A
NA
NA
A
A
A
NA
NA
A
A
A
46
a
a
d
a b
c
Table 3.5 Comparisons of experimental failure modes and loads of the
glass–epoxy composite material for pin diameter
4 and 5 mm
Test Piece Dia
(mm)
e/d
Minimum
w/d
Minimum
Failure load
(kN)
Failure
mode
B11
B12
B13
4
3
3
3
5
5
5
10.90
10.66
10.58
B
B
B
B21
B22
B23
5
3
3
3
5
5
5
11.10
10.68
10.65
B
B
B
Figure 3.12 (A) Failed test specimens (a) S and N, (b) & (c) B and S, (d) B
Figure 3.12 (B) Load displacement behaviour of laminates failing by
net-section and bearing failure modes
Bearing failure
(w/d=5, e/d=3) Net-section failure (w/d=2, e/d=3)
47
Figure 3.13 Experimental results for pin-loaded glass–epoxy composite
3.4.2.4 Discussion and failure mode analysis
The bearing strength values are dependent on e/d ratio. Generally,
while the w/d ratio is constant, bearing strength values increase with
increasing e/d ratio (Figure 3.13). The plate is the weakest for e/d = 1, which
indicates that the hole is too close to the specimen edge. The bearing strength
values are close each other for 4 and 5 ratios of e/d. For low values of e/d, the
failure types are net-tension or shear-out and high values of e/d, except
w/d = 2, the failure type is bearing.
Mixed mode of failure ie. combination of tearing and shearing has
been observed at e/d=2 and w/d=4 with enhanced strength. Where as only
tearing mode of failure has been observed by increasing simply e/d with slight
reduction in load bearing capability. Pinned joint bearing strength decreases
with decreasing w/d ratio, while e/d ratio is constant. The plate is the weakest
for ratio w/d = 2 and the critical w/d ratio is 3. As the width of the specimen
increases, the failure mode changes from net-tension to shear-out for ratio
e/d = 1. For other e/d ratios, failure mode changes to bearing mode.
48
It is observed from load displacement behaviour curves shown in
Figure 3.12 (B), for higher loads, a continuous reduction in stiffness was
noted, as the damage developed at the bearing surface. The load continued to
increase until the maximum load was attained and failure was characterized
by a minor drop in the load, while the net-section failed specimens failed
catastrophically. Thus we observe that the deformation of the bolt-hole in the
laminate significantly influences the stiffness and strength of a mechanically
fastened joint.
It is observed from Tables 3.4 and 3.5 that simply changing the
diameter of the hole while having the same e/d and w/d ratio does not affect
bearing strength capability of laminate. At value of e/d=3 and w/d=6 there
may be increase in strength of laminate failed by bearing failure followed by
tearing mode of failure.
3.5 FABRICATION OF BOLTED JOINTS
The adherends were fabricated from using GFRP and CFRP
laminates for the preparation of bolted joints. Test specimens were prepared
as per ASTM standard D 5961 M-96 and based on joint parameters obtained
for maximum bearing strength and efficiency. The transverse pitch is adjusted
based on determined values of w/d ratios for different types of joints and
longitudinal pitch is maintained at three times the diameter of the bolt as the
safety factor. The laminates were machined to size using a diamond tipped
saw and final finish is given with fine emery paper. The end tabs were
designed as doublers to avoid eccentricity of loading for all types of joints
configurations by using glass/epoxy or aluminum with 35-38 mm length.
Minimum thickness of end tabs is maintained at 3.2 mm. End tabs are bonded
to the specimens with epoxy adhesive. Figure 3.14 shows the schematic
diagram of single bolted joint of type-S with end doublers.
49
Line of action of load
Figure 3.14 Schematic diagram of joint S with end doublers
3.5.1 Bolted joints configurations and fabrication
The S-type of test specimens were prepared by taking ratios w/d=6
and e/d=3. For multi bolted connections like type-B, C and D pitch distance
and edge distance is maintained at three times the diameter. For fastener
connections the 8 mm diameter hole is prepared using high speed CNC
drilling machine with drilling fixtures, 7.0 mm diameter drill bit is used for
this purpose. The reamers were used to finish the hole to the required
diameter of 8 mm, with out much delamination. Laminates with 8, 12 and
16 layers were used for specimen preparation with stacking sequence
00/900, ±450and 300/600. The proposed rational models of four different
configurations of bolted connections for fiber-reinforced plastic structural
members are shown in Figure 3.15.
3.5.2 Clearance effect test specimen
The joint considered was single-lap, single bolt carbon fiber/epoxy
material laminate with the test procedure and joint geometry based on the
ASTM standard D 5961 M-96. The laminate thickness was 5.2 mm, while all
ratios were in accordance with the joint parameters obtained for maximum
bearing strength and efficiency. The relatively large thickness was chosen so
as to maximize the three-dimensional effects introduced to the joint during
loading. In order to avoid premature bolt failure and obtain bearing mode as
the primary mode of failure, an 8 mm diameter bolt was chosen.
50
Figure 3.15 Bolted joints configurations
The varying bolt-hole clearances were obtained by using constant
diameter bolts and different diameter reamers. The nominal clearance values
obtained in different cases are shown in Table 3.6. Clearance Cl was intended
to be a neat-fit and Clearance C2 is larger than normally found in aerospace
structures but was studied to examine an out of tolerance situation (e.g. due to
manufacturing defects or in-service undetected damage). A low torque level
of 5 N-m was applied to the bolts using a calibrated torque wrench so as to
continue the failure to bearing mode. For each clearance value six test
specimens were fabricated, and the study was carried out.
w = 48
e =
24
L =
154
w = 72
e =
24
L =
154
P = 24
w = 48
Joint S
Joint C
Joint B
w = 72
e
L =
154
P = 24
Joint D
All dimensions are in mm
P
P
51
Table 3.6 Nominal hole clearance
Hole Clearance code Nominal Bolt Hole Clearance (μm)
C1
C2
0 ±10
200 ±10
3.5.3 Load sharing analysis specimen
The joint considered was single-lap, multi bolted with the joint
geometry based on the designed joint parameters as discussed in 3.4.2.1 and
3.4.2.3. The fabricated specimen is shown in Figure 3.16. In order to avoid
premature bolt failure and obtain bearing as the primary mode of failure, an
8 mm (nominal) diameter bolt was chosen.
Figure 3.16 Fabricated test specimen for load sharing analysis
3.5.4 Surface strain measurement test specimen
It is required to analyse the effect of eccentricity due to off axis
loading. This effect is studied by observing surface strain technique. The joint
considered was a single-lap, single bolt joint with the test procedure and joint
52
geometry based on the ASTM standard D 5961 M-96. The specimen
geometry is shown in Figure 3.17. The configurations were with
C1 clearances (i.e. neat fit). Figure 3.18 shows the positions of the strain
gauges, which had a 3 mm gauge length. All gauges were aligned with the
loading direction except gauge 7, which was aligned in the transverse
direction. The gauge 2 was on the inner face of the laminate (i.e. on the shear
plane of the joint) while the other gauges were on the outward-facing surface.
Considering the washer outer diameter the strain gauges location was
identified.
Figure 3.17 Strain gauge locations on test specimen
53
Figure 3.18 Fabricated surface strain measurement test specimen with
strain gauges
3.6 TESTING OF BOLTED SINGLE SHEAR LAP JOINT OF
TYPE-S
Preparation of test specimens have been discussed in detail in
section 3.5 and 3.5.1. Test were performed by considering clearance and with
out clearance and also with and with out clamping torque. Experimentation is
performed on both GFRP and CFRP laminates. In addition isotropic material
like steel and aluminium plates were also tested and results were compared
with its counter parts orthotropic materials.
All joints were loaded in tension, in a stroke control at a rate of
0.1 mm/min. All the specimens were tested up to failure. Figure 3.19 shows
the test set-up for isotropic and orthotropic joints of type-S. Table 3.7 shows
test results of single bolted joints up to failure load for GFRP, CFRP and
isotropic materials by considering various layers, stacking sequence,
clearance and clamping torque.
54
Figure 3.19 Test set-up for a) Aluminium b) GFRP joints of type-S
a
b
55
Table 3.7 Comparison of failure loads of single bolted joint for GFRP,
CFRP and isotropic materials, by considering different
layers, stacking sequence, clearance and clamping torque
Materials,
Stacking sequence
and adherend
layers *16 Layers =
5.2 mm thickness
Experimental load (kN)
Clamping torque, 5 N-m
Experimental load (kN)
Clamping torque, 15 N-m
Neat-fit
Clearance
(0 ± 10 μm)
Clearance
(200 ± 10 μm)
Neat-fit
Clearance
(0 ± 10 μm)
Clearance
(200 ± 10 μm)
Number of tests
Composites
GFRP (00/90
0)
8 layers
12 layers *16 layers
3
9.63
11.32
18.82
3
-
-
18.21
3
10.20
11.80
19.94
3
-
-
19.00
GFRP (±450)
8 layers
12 layers *16 layers
9.98
11.74
20.12
-
-
19.92
10.52
12.31
20.91
-
-
20.42
GFRP (300/60
0)
8 layers
12 layers *16 layers
9.84
11.70
19.90
-
-
19.81
10.50
12.20
20.87
-
-
20.36
GFRP(00/900 ±
450)2S
*16 layers
20.64
-
21.82
-
CFRP (00)
8 Layers
CFRP (00/90
0)
8 Layers *16 Layers
12.85
11.72
28.30
-
-
27.20
13.6
12.43
29.82
-
-
28.41
Isotropic material
Thickness =5.2 mm
1) Steel plate
2) Aluminium plate
52.84
16.92
52.13
16.52
-
-
-
-
56
3.6.1 Discussion
All types of GFRP test specimens failed without much yielding
when compared with CFRP laminates. All types of joints with low thickness
constraints (with less clamping pressure) showed larger displacement to
failure and higher energy absorption during damage processes and resulted in
initial bearing damage followed by final net-section failure.
Load–displacement curves gave important information concerning properties
of joints. Beyond the initial linear ranges, all load-displacement curves
seemed to exhibit two different types of profiles that could be categorized as
ductile and brittle type. In all types of GFRP laminates failed in brittle-type
curve, while CFRP laminates exhibit ductile-type curve. Since ratio w/d = 6
and ratio e/d = 3 were imposed to all joints in order to have bearing damage
initially, accordingly all composite joints investigated in the present study
started failure with initial bearing damage prior to ultimate net–section
failure.
From the experimental analysis it is concluded that, increasing the
laminate layer/thickness enhances the load bearing capability of bolted joints
for all types of joint configurations, but no significant difference was
observed between 8 and 12 layers from strength point of view. Laminates
with quasi-isotropic stacking sequence joints are stronger then the joints with
other stacking sequence.
3.6.2 Studies on Clearance Effect
The specimen geometry and fabrication of specimens with neat-fit
and with clearance is explained in detail in section 3.5.2. Testing was
performed on CFRP laminates by using ZWICK universal testing machine.
The test setup is shown in Figure 3.20. An experimental study, which
57
involved over 12 tests to failure, was carried out on the effects of clearance in
single-lap, single-bolt joints. For each series 2 tests were conducted, average
values of load and displacement have been considered for plotting
load-displacement curves. The clearances chosen for this study are of two
types (neat-fit (0 ± 10 microns) and 200 ± 10 microns). The bolts were
torqued to 5 N-m in the experiments, to ensure firm gripping of the bolted
joint assembly. All joints were loaded in tension. Figure 3.21 shows the load
versus machine stroke for bolted joint specimens tested to failure. The figure
covers two distinct configurations, protruding head bolts with a) neat-fit (C1)
and with b) clearance (C2).
Figure 3.20 Test setup for bolted joint tests (CFRP), showing a) initial
setup b) At 17kN load showing bolt rotation
a b
58
0
5
10
15
20
25
30
35
0 0.5 1 1.5 2 2.5 3 3.5
Displacement (mm)
Load (
kN
)
C1 (I)
C1 (II)
C1 (III)
a) C1 clearance (neat-fit)
0
5
10
15
20
25
30
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Displacement (mm)
Load
(k
N)
C2 (I)
C2 (II)
C2 (III)
b) C2 clearance fit
Figure 3.21 a) and b) Load-deflection curves for protruding head bolts
at 5 N-m clamping torque
59
3.6.2.1 Discussion
The following general observations can be made. For all tests, the
load-deflection curves possess a region that appears linear, and for tests at a
given clearance, the slope of this region is repeatable. Looking closely reveals
that the slope reduces with increasing clearance. There is a delay in initial
load take up, dependent on the clearance. The C2 curves exhibit a delay in
load take-up of approximately the same size as the clearance (0.20 mm),
while the C1 curves do not exhibit any delay.
Referring to Figure 3.21 the C1 curves exhibit linearity up to
approximately 10-13 kN, and thereafter become non-linear, indicating the
initiation of bearing failure. Significant stiffness loss occurs at approximately
18-20 kN, and further stiffness loss occur on route to final failure. The C2
curves show linearity up to about the same load level, but with a reduced
slope. The first significant stiffness loss occur at a lower load level (15 kN).
The tested specimens were sectioned and analysed with scanning
and inspection using digital camera for possible damage in hole region.
Figures 3.22, 3.23 and 3.24 show the damaged region of the holes with
clearances C1 and C2 respectively. Damage in the C1 joint comprised matrix
chip out in the resin rich surface layer formed during curing of the laminate
adjacent to the peel ply. For clearance C2 damage was more significant
involving both fibre fracture and matrix chip-out. This is most likely due to
increased bolt rotation (depicted in Figure 3.20 (b)), thereby inducing more
localized contact stresses in this region.
The sectioned specimen was examined for contact area as shown in
Figure 3.25. This provided a clear image of the impression left by the bolt on
the surface of the hole, particularly for the C2 joints. For the C2 clearance the
60
contact angle was of the order of 1300–140
0 at the shear plane and reduced
markedly through the thickness, resulting in a significantly lower contact area.
For clearance C1 the contact angle at the shear plane was of the order of
approximately 1600–170
0, and was fairly constant through the thickness.
The C1 clearance joint exhibited localized crushing of the surface
ply. The C2 joint also showed localized crushing of the surface ply, and
delamination propagated further away from the bolt-hole contact region.
More fibre and matrix chip out occurred through the thickness of the
laminate. The damage comprised matrix chip out in the resin rich surface
layer. The Figure 3.23 shows significant damage around the bearing region
for clearance C2, resulting in a region of broken fiber ends and chip out.
Figure 3.22 Damage developed at 17 kN applied load a) C1 clearance
b) C2 clearance
a b
61
Figure 3.23 Damage in the Surface Ply of the shear plane of C1 hole
after Loading
Figure 3.24 Damage in the Surface Ply of the shear plane of C2 hole
after Loading
Figure 3.25 Contact area for hole with Clearance C1 and C2
C2 C1
62
3.6.3 Effect of clearance on joint stiffness and bearing strength
To provide a consistent comparison of joint stiffness, the slope was
measured between 2 and 10 kN, over which all the curves were close to
linear. The average slopes calculated from load-displacement diagram for all
specimens are shown in Tables 3.8 and 3.9 shows the effect of clearance on
stiffness of bolted joints based on extensometer reading at 5 N-m clamping
torque.
The bearing stress was calculated from:
kdt
Pbr=σ (3.5)
where P- bearing load, d - diameter of hole, t - coupon thickness, and
k - load per hole factor ( 1.0 for single-fastener).
In accordance with the standard, the actual thickness (in the vicinity
of the hole) and hole diameters for each individual joint were used in the
calculations rather than nominal values. The obtained results are shown in
Table 3.10. The-bearing stress was calculated for woven-mat lay-ups for
5 N-m clamping torque joints condition.
Table 3.8 Effect of clearance on stiffness of bolted joints based on
stroke reading at 5 N-m clamping torque
Configuration Protruding head (woven mat)
Clearance C1 C2
No. of tests
Average value (kN/mm)
3
20.43
3
18.31
63
Table 3.9 Effect of clearance on stiffness of bolted joints based on
extensometer reading at 5 N-m clamping torque
Configuration Protruding head (woven mat)
Clearance C1 C2
No. of tests
Average value (kN/mm)
3
35.44
3
30.57
Table 3.10 Effect of clearance on ultimate bearing strength of bolted
joints at 5 N-m clamping torque
Configuration Protruding head (woven mat)
Clearance C1 C2
No. of tests
Average value (MPa)
3
680.28
3
637.84
3.6.3.1 Discussion
The hole deformation behaviour was investigated for laminates
failing by bearing failure mode. The hole deformation was found to be
slightly larger for clearance fit laminates in comparison to neat fit laminates
for a given load level. The stiffness of the joint was also shown to decrease in
clearance fit laminates as a result of the reduced contact area and larger hole
deformation. Bolt-hole clearance should be minimized in order to achieve
maximum bearing strength of the joint. The deformation of the bolt-hole in
the laminate influences the stiffness and strength of a mechanically fastened
64
joint. Permanent deformation of the hole results in slackness in the joint,
which can results in significant strength reduction.
3.6.4 Effect of tightening torque
The specimen geometry and fabrication of specimens with net-fit is
explained in section 3.5.1. Testing was performed on ZWICK universal
testing machine. Figure 3.26 shows tightening of bolt with torque wrench and
Figure 3.27 shows the failed CFRP joints subjected to bearing failure under
clamping torque.
Figure 3.26 Tightening of bolt with
torque wrench (clamping
torque,15 N-m)
Figure 3.27 Bearing failure of
laminates under
clamping torque
5 N-m
3.6.4.1 Discussion
Figure 3.28 shows the load –displacement diagram for the applied
torque of 5 N-m and 15 N-m (neat-fit clearance). The experimental results
65
0
5
10
15
20
25
30
35
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Displacment (mm)
Load (
kN
)
C1 (5 Nm)
C1 (15 Nm)
Figure 3.28 Influence of tightening torque on the behavior of
load-displacement diagram of bolted joint specimens
(Neat-fit)
show that, 15 N-m tightening torque has the maximum strength. As a result of
increasing the tightening torque (contact pressure), the slope of the
load-displacement curve (stiffness) increases with increasing the tightening
torque. The bearing strength of bolted joint increases with increasing
tightening torque. The load-displacement curve of bolted joint specimen with
5 N-m tightening torque has the less slope/stiffness.
It is clear that from the study the ultimate loads increases with
increasing the clamping torque from lower level to higher level (5 to 15 N-m).
At the applied clamping torque of 20 N-m, on the surface of top ply around
and below the washer area matrix cracking damage was observed. So analysis
has been limited up to a clamping torque of 15 N-m.
66
The bearing strength of CFRP could be improved by increasing the
lateral (i.e. through thickness) compressive stress around the loaded hole.
Equation (5.7) gives relationship between tightening and lateral compression
pressure. The stress (constraint pressure), which is assumed constraint over
the washer area, was obtained using the following expression.
σ = T/ [0.2d π/4(D2-d
2)] (3.6)
D and d are, the washer and hole diameter respectively and T is the applied
torque.
σ is lateral compressive pressure.
3.6.5 Effect of washer size on the performance of bolted joints
In the present work, the effects of washer outer diameter size
(Dwo = 14, 18, 22 and 27 mm) at constant tightening torque (T = 15 N-m) and
different tightening torque levels (T = 0,5,10 and 15 N-m) on the strength of
bolted joints in composite GFRP materials are investigated experimentally.
The angle-ply [00/900, ±450]s glass fiber reinforced epoxy composite
laminates with 5.2 ±0.1 mm thicknesses were used for this purpose. The
specimen geometry and fabrication of specimens with neat-fit clearance is
explained in section 3.5.1. Testing was performed on GFRP laminates by
using ZWICK universal testing machine. Three specimens were tested for
each test condition and the average values were considered.
67
3.6.5.1 Discussion
From the load–displacement diagrams of bolted joint specimens
tested at constant torque (15 N-m) and various outer diameter washer sizes, it
is observed that, the slope of these diagrams (stiffness of the joint) increase
with decreasing washer size. The failure load of bolted joints decreases with
increasing washer size from 18 mm to 27 mm. The load–displacement
diagrams behave in a nonlinear fashion.
Figure 3.29 illustrates the effect of washer outer diameter on the
bearing strength of bolted joint tested at constant tightening torque, T= 5 N-m.
The results in this figure show that the maximum bearing strength was
obtained at 18 mm washer size. Although bolted joint with 14 mm washer
size has the minimum contact area, i.e. maximum contact pressure, its bearing
strength is less than the joint with 18 mm washer size. This behavior was due
to the lateral constrained area of 14 mm washer is less than that of 18 mm
washer. Also increasing the contact pressure, i.e. the lateral compressive
stress under the washer in bolted joint with Dwo = 14 mm.
This behavior indicates that the bolt bearing strength not only
depends on the contact pressure but also on the lateral constrained area of the
washer. Although the lateral constrained areas of bolted joint specimens with
22 and 27 mm washer sizes are higher than that of bolted joint specimen with
18 mm washer size, their bearing strength is lower than the latter specimen.
This result is due to the decreasing of contact pressure with increasing washer
sizes on these specimens. Therefore, for the fabricated composite laminates,
bolted joint specimen with 18 mm washer size and 15 N-m tightening torque
has optimum contact pressure and lateral constrained area that give maximum
bearing strength. Hence, the influence of tightening torque on the bearing
strength will be investigated at constant washer size, Dwo = 18 mm.
68
Figure 3.30 illustrates the relationship between tightening torque
and the bearing strength of bolted joint specimens with Dwo = 18 mm. The
results in this figure indicate that, in the range of the investigated tightening
torques, the bolt bearing strength increases with increasing the tightening
torque.
Figure 3.31 (a) and (b) shows photograph of some failed bolted
joint specimens. Most of the test specimens failed in the same manner.
Failures occurred on the following sequences:
– First, delamination between the layers occurred. This was
attributed to the different strains in the 00/900, ±450 layers.
– After delamination, the ‘‘shear-out’’ failure mode was
observed for 00/ 900 layers. These layers had the minimum
Figure 3.29 Effect of washer size on
bearing strength
Figure 3.30 Effect of tightening torque
on bearing strength
69
strength compared with the other layers. The final failure of
bolted joints specimens was nearly catastrophic.
Figure 3.31 Photograph illustrates the damage in bolted joint
specimens:(A) specimens tested at different washer sizes,
(B) specimens tested at different tightening torques
3.7 FINITE ELEMENT ANALYSIS ON SINGLE BOLTED
JOINT
In ANSYS due to the assumption of linear response in this work
bolted joints were analysed using SOLID46 element. Figure 3.32 shows the
SOLID46 3-D layered structural solid element. SOLID46 is a layered version
of the 8-node structural solid element designed to model layered thick shells
or solids. The element allows up to 250 different material layers. If more than
250 layers are required, a user-input constitutive matrix option is available.
The element may also be stacked as an alternative approach. The element has
three degrees of freedom at each node: translations in the nodal x, y, and z
directions.
A B
70
Figure 3.32 SOLID46 3-D Layered Structural Solid element
The three-dimensional finite element models have been developed
using ANSYS to study the variations in the stress distribution and
displacement in the laminate. Each ply in the composite laminate was
modeled with the layered solid element (SOLID 46) and the bolt with solid
element (SOLID 45). The bolt, washer, and nut are modeled as one unit in
order to limit the number of contact surfaces in the model. The bolt head and
nut are modeled as a cylinder. Contact between the two composite laminates
and the bolt-nut unit was modeled using the contact pair approach in ANSYS.
The surface-to-surface ANSYS friction contact elements have been
used for computations. The friction coefficient is expected to be different at
different contact surfaces due to different material combinations or surface
treatment. Therefore, a friction coefficient of 0.2 is assumed at all contact
surfaces in all models, which is available in the literature (McCarthy 2000).
The most important contact surface in the model is the interface between the
composite laminates.
71
3.7.1 Without clearance between hole and bolt
Typical finite element mesh of the composite plate with protruding
head bolt and displacement is shown in Figure 3.33.The mesh is divided into
two major regions, a square corresponding to the overlap area with a fine
mesh surrounding the bolt hole and a rectangle with a coarser mesh away
from the bolt hole. The mesh of the lower part is partitioned in the same way
as for the upper part so as to match the mesh of the lower surface of the upper
part. Figures 3.34 and 3.35 shows the Von-Mises and shear stress respectively
in bolted joints.
Figure 3.33 Meshed model of bolted joints with boundary condition
and deflection of bolt
Figure 3.34 Von-Mises stresses
in bolted joint
Figure 3.35 Shear stresses in
bolted joint
72
The development of contact area between the bolt and the laminate
in C1 (neat fit) clearance single bolted joint is shown in Figure 3.36. It can be
seen that the contact area gets up to its final value quickly4 with a fairly
constant contact angle throughout the thickness. Figures 3.37 and 3.38 shows
the effect of tightening torque and induced compressive stress below the
washer region due to applied clamping pressure of 15 N-m.
Figure 3.36 Development of contact area in C1 (neat fit) clearance
bolted joint
Figure 3.37 Deformation due to
applied clamping
torque of 15 N-m
Figure 3.38 Induced
compressive stress
73
3.7.2 With clearance between hole and bolt
The development of contact area between the bolt and the laminate
in the C2 (200 μm) joint, shown in Figure 3.39. Contact is not made until
clearance is taken up, and initial contact is over a small contact arc. Several
investigators in the past simplified the contact stress problem at the pin-hole
interface by assuming the load transfer on a semi-circular arc of contact and a
cosine distribution of the pin load. This has also been used freely, for the case
of clearance fits (Hart- smith 1993, McCarthy 2000) Stress distribution
around the hole is as shown in Figure 3.40. Induced shear and Von-Mises
stresses in the bolt due to clearance C2 is shown in the Figures 3.41 and 3.42
respectively.
Figure 3.39 Development of contact area in C2 (200 μm) clearance
bolted joint
Figure 3.40 Radial stress distributions around the hole
74
Figure 3.41 Shear stresses in
bolted joint
Figure 3.42 Von-Mises stresses in
bolted joint
The peak radial stress increases with increasing clearance (due to
the load being distributed over a smaller contact area). The location of the
maximum tangential stress varies with clearance, generally being near the end
of the contact region. The magnitude of the peak tangential stress increases
slightly with increasing clearance. In addition, it can be seen that compressive
tangential stress exists at the back of the hole. It can be seen that in both cases
the hole deforms from a circular to a more oval shape, while in the C2 case a
localised reduction in radius of curvature under the bolt occurs.
The experimentally obtained displacements are compared with the
results from finite element analysis. Only linear portion of the experimental
load displacement curve is modeled in ANSYS. The safe load and deflection
obtained for clamping pressure of 5 N-m for both C1 and C2 clearances is
shown in Table 3.11.
75
Table 3.11 Comparison of loads, deflections, Von- Mise stress and
shear stress for applied clamping torque of 5 N-m
Neat fit clearance
(0 ± 10 µm)
With clearance
(200 ± 10 µm)
Experimental FEA Experimental FEA
Load (kN) 18.82 18.82 18.21 18.21
Deflection (mm) 1.82 2.217 2.05 2.665
Von-Mises stress
(MPa)
- 219 - 374
Shear stress (MPa) - 122 - 211
3.8 TESTING OF BOLTED JOINTS OF TYPE-B, C AND D
Test were performed by considering without clearance and also
with and with out clamping torque. The experimentation is done for two
different tightening torques (5 N-m and 15 N-m). Testing was performed on
CFRP laminates by using ZWICK universal testing machine and on GFRP
laminates by using computerized UTM. Tensile load was applied at constant
stroke rate of 0.1 mm/min. To determine the influence of the bolt pattern and
the number of bolts three different connections were used. They are
designated as joints .B, C and D. The configurations of the bolted joints were
illustrated in Figure 3.15 in section 3.5.1. The ratio of the edge distance to the
hole diameter (e/d) is maintained as 3 so as to avoid the net tension failure of
composites joints. The holes are finished with the reamer and the edges are
rounded using a smooth file. The test setup is shown in Figure 3.43. GFRP
and CFRP test specimens are as shown in Figure 3.44. In addition isotropic
material like steel and aluminium plates were also tested and results were
compared with its counter parts orthotropic materials. Tables 3.12 and 3.13
shows test results up to failure load for GFRP and CFRP laminates
respectively.
76
Figure 3.43 Experimental set up for testing of joints
77
Figure 3.44 GFRP and CFRP test specimens
78
Table 3.12 Comparison of test results for bolted joints (woven mat
E-glass/epoxy) *Average value of 3 tests
Joints
type
No. of
layers
Clamping torque
(5 N-m)
Clamping torque
(15 N-m)
*Load
(kN)
*Displacement
(mm)
*Load
(kN)
*Displacement
(mm)
B
8 22.4 4.7 24.23 4.5
12 23.6 4.0 24.12 3.9
16 24.8 3.1 25.30 2.8
C
8 22.9 8.8 23.19 8.6
12 23.4 8.1 23.74 7.9
16 25.9 8.7 26.19 8.5
D
8 26.4 6.0 27.32 5.7
12 27.2 6.5 28.12 6.3
16 29.6 5.5 29.2 5.4
Table 3.13 Comparison of test results for bolted joints (woven mat
carbon/epoxy) *Average value of 3 tests
Joints
type
No. of
layers
Torque (5 N-m) Torque (15 N-m)
*Load
(kN)
*Displacement
(mm)
*Load
(kN)
*Displacement
(mm)
B 8 13.4 4.0 14.2 3.9
C 8 22.4 8.1 23.1 7.9
D 8 34.5 6.5 36.3 6.4
79
3.8.1 Discussion
Effects of thickness constraints, stacking sequence effect and
number of layers have been discussed in section 3.5.1. From the experimental
analysis on multi-row joints, it can be concluded that bearing strength is same
for the joint types B and C. While joint D was found to exhibit high strength,
when compared to B and C type joints. Uniform load sharing of the joints
could made joint D to take more load than other joints with higher efficiency.
3.9 LOAD SHARING ANALYSIS FOR MULTIBOLTED JOINTS
NUMERICALLY
In this work, the analysis for the determination of the load sharing
between individual bolts in a line of bolts in a symmetrical lap joint is
outlined. The existing mathematical equations developed by Niklewich et al
(1999) for isotropic materials with double lap joints have been used to analyse
the orthotropic multibolted single lap joint with modification by considering
orthotropic material properties. The analytical results were verified with
experimentally obtained data.
A schematic diagram of the bolted joint is shown in Figure 3.45.
The upper part of the diagram shows co-linear bolts in a strap of width w in
line with the total applied load P. The lower part of the diagram shows the
construction of the joint in which a plate of uniform thickness tp and straps of
uniform thickness ts. The assumptions of the model are as follows:
• The ratio of stress to strain is constant.
• The stress is uniformly distributed over the cross sections of
main plate.
80
1 2 i –1 N
• The effect of friction is negligible
• The bolts fit the holes initially, and the material in the
immediate vicinity of the holes is not damaged or Stressed in
making the holes or inserting the bolts.
• The relationship between bolt deflection and bolt load is linear
in the elastic range.
Figure 3.45 Symmetrical lap joint with bolts in line of applied load
The relative displacement of main plate between the ith and (i+l)th
bolts yields for i=l, 2,.... (n-1) is given by the equation as
λ
λµ
+
−+=
∑−
+
1
**1
1
1
i
i
i
RPR
R (3.7)
where
C
Kp=µ and
C
KKsp
+=λ (3.8)
81
Ri is the ith
bolt load and P the external applied load. C denotes a constant
dependent upon material properties, plate and strap dimensions and includes
effects of bending, shear and bearing. Kp and Ks are given by:
pp
pEwt
pK = ;
ss
sEwt
pK = (3.9)
Ep and Es denote Young's modulus for the plate and strap respectively.
C - Shear effect + Bearing effect + Bending effect
bb
ppspss
psb
ps
bb
ps
IE
tttttt
ttE
tt
AG
ttC
192
88
3
3223 ++++
++
+= (3.10)
where
4
2dAb
π= ,
64
4dIb
π= and d is the bolt diameter.
The solutions for these equations are obtained by using Gauss
Seidel iteration numerical method and the flow chart is shown in Figure 3.46.
Figures 3.47 and 3.48 shows the load distribution among bolts obtained
numerically.
82
Gauss-Siedal Algorithm out put for four bolted connection
Enter the values of λ=4.037 and μ= 2.692
Enter the value of load applied in KN: 10
2500.000000 0.000000
2500.000000 0.000000
2500.000000 0.000000
2500.000000 0.000000
5841.460449 1159.710327 230.238235 2769.868408
5575.380371 922.356323 686.941833 2816.615479
5528.259766 1050.793335 631.300293 2790.943359
5553.757812 1019.309875 629.743347 2798.483887
5547.507324 1024.010376 630.985657 2798.791504
5548.440430 1023.509155 630.639465 2798.705811
5548.340820 1023.520264 630.710388 2798.723389
5548.343262 1023.532349 630.698792 2798.720459
5548.345703 1023.528076 630.700256 2798.720947
5548.344727 1023.529175 630.700134 2798.720947
83
Start
Read I/P
Roi=P/n
λ
λµ
+
−+=
∑−
+
1
**1
1
1
i
i
i
RPR
R
|Roi – Rni| <= 0.0001
Print Ri
Stop
Assign Rni to Roi
No
Yes
Figure 3.46 Algorithm for Gauss-Siedal iteration method
84
0
5
10
15
20
25
0 1 2 3 4 5
Bolt number
Lo
ad
(k
N)
10 kN
20 kN
30 kN
40 kN
Figure 3.47 Load shared by four
bolts for various load
steps
0
5
10
15
20
25
0 1 2 3 4 5 6 7 8 9 10
Bolt numbers
Lo
ad
(k
N)
10 kN
20 kN
30 kN
40 kN
Figure 3.48 Load shared by nine
bolts for various
load steps
3.9.1 Measurement of load shared by bolts in multi bolted
connections
To predict the possible failure load and mode of failure of the
mechanically fastened joints, it is need to develop numerical methods to
analyse the load distribution among the bolts and compare with experimental
results for the sake of validation. Numerical model and algorithm is explained
in section 3.9. This also helps us to design the efficient joints with out failure
by considering the data arrived from the numerical methods. The fabrication
of test specimen as per standard has been explained in section 3.5.3. In this
present work, the analysis for the determination of the load sharing between
individual bolts in a line of bolts in a symmetrical lap joint is outlined. The
main objective of using multi-row joints is to minimize the peak-bearing load,
avoiding the cut-off due to bearing. The experiments were carried out using
microprocessor controlled Zwick UTM. The experimental set up is shown in
Figure 3.49. The Table 3.14 shows comparison of load shared by multi bolted
joints obtained experimentally and numerically.
85
Figure 3.49 Experimental set up for load sharing analysis
Table 3.14 Comparison of load shared by multi bolted joints obtained
experimentally and numerically
Bolt
number
Load applied: 10 kN
Numerical Load
(N)
Experimental Load Error
% Strain (μm) N
1
2
3
4
5548.3
1023.5
630.7
2798.7
5138
872
817
2943
11.39
18.41
-23.80
-0.618
11.39
18.41
-23.80
-0.618
86
3.9.2 Discussion
The results could be summarized as load shared by each bolt
obtained from numerical methods by considering possible failure in the model
equations have good agreement with experimentally determined data. The
percentage error varies from -23.8 to18 % among experimental and numerical
data. This may be due to the mounting of strain gauges on the laminate
bearing region, instead of mounting on the bolt axis, by using instrumented
bolt. Hence this method can be used as a preliminary design for a composite
laminate, which is designed to fail in net tension.
It is observed from the Figures 3.47 and 3.48 that unevenness in
load sharing among the bolt is more, if the number bolts in a row exceeds four
bolt. Hence it is suggested that for good design and to avoid irregularity in
load sharing among the bolts in a multibolted joints, number of bolts can be
restricted to four in a row.
3.10 MEASUREMENT OF BENDING EFFECT OF ADHERENTS
The experimental measurement of strains at selected points on the
joint surface is presented in this section. Joints were strain gauged and loaded
to a level that did not cause detectable damage to the laminates (5 kN). The
configurations were with C1 clearances (i.e. neat fit). The positions of the
strain gauges, gauges alignment with the loading direction and specimen
preparation has been discussed in section 3.5.4. The specimen under testing is
shown in Figure 3.50. Test was repeated 2 times (dissembling the joint
between each test), and the average strains were considered. Experimentally
measured surface strains are plotted as shown in Figure 3.51.
87
Figure 3.50 Surface strain measurement specimen under testing
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
-800 -600 -400 -200 0 200 400 600 800
Microstrain
Lo
ad
(K
N)
G1
G2
G3
G4
G5
G6
G7
G8
Figure 3.51 Experimental surface strains for the C1 clearance joint
88
3.10.1 Observations
The following observations can be made from the experimentally
measured strains.
• Gauge 2 indicate a bending at this location in the form of
tensile strain due to the applied load
• The outer surface of the overlap region (gauges 1, 3, 4, 5, 6
and 8) is in compression despite the fact that a tensile load is
being applied to the joint. This is due to bending of the joint.
Gauge 4, which is located near the edge of the washer displays
the highest compressive strains of all the longitudinally-
oriented gauges
• The transverse gauge 7 also shows significant transverse
compressive strains. This may be due to double curvature
effect
• The result indicates that there is a significant bending effect
due to eccentricity
• The measured surface strains could be used to compute elastic
properties and stiffness of the composite laminates