bearing strength of carbon fibre/epoxy laminates: effects of bolt-hole clearance
TRANSCRIPT
Bearing strength of carbon fibre/epoxy laminates:
effects of bolt-hole clearance
Gordon Kelly, Stefan Hallstrom*
Division of Lightweight Structures, Department of Aeronautical and Vehicle Engineering, Kungl Tekniska Hogskolan, S-100 44 Stockholm, Sweden
Received 17 March 2003; revised 10 November 2003; accepted 12 November 2003
Abstract
The bearing strength of carbon fibre epoxy laminates manufactured from non-crimp fabric from heavy tow yarn has been investigated. The
effects of laminate stacking sequence and geometry on the bearing strength have been determined experimentally together with the effect of
initial bolt-hole clearance on the bearing strength at 4% hole deformation and at ultimate load. Significant reduction in bearing strength at 4%
hole deformation was found for both pin-loaded and clamped laminates as a result of bolt-hole clearance. It was concluded that the effect of
bolt-hole clearance is significant with regard to the design bearing strength of mechanically fastened joints. A three-dimensional non-linear
finite element model was developed to investigate the effects of bolt-hole clearance on the stress field in the laminate adjacent to the hole. The
magnitude and distribution of stress at the hole was found to be significantly dependent on the level of clearance.
q 2004 Elsevier Ltd. All rights reserved.
Keywords: Composite; Bolted joint; Bearing strength; Experimental investigation; Finite element analysis
1. Introduction
The introduction of composite materials in the auto-
motive industry, places new demands on the materials and
manufacturing processes in terms of cost, cycle time and
automation. Manufacture and assembly of composite
structures require knowledge of reliable joining techniques.
Mechanical fastening is a common method used to join
composite materials. Mechanically fastened joints com-
monly adopted in aerospace structures are characterised by
tight tolerances on both the fasteners and on the machined
holes. However, if composite materials are to be used in
mass production, different tolerance levels may be necess-
ary for the joining and attachment of components to allow
shorter cycle times and minimise production costs. As a
consequence, knowledge of the effect of tolerances between
the fastener and the hole on the strength and fatigue life of
mechanically fastened joints will be required for design and
selection of manufacturing processes. The aim of this paper
is to investigate the effect of bolt-hole clearance on the static
bearing strength of composite laminates.
A common method used to determine the strength of
mechanically fastened joints is through pin-loading, where
the bolt is replaced by a pin. The pin-loading condition is most
representative of the middle laminate in a balanced double-
lap joint configuration where the effects of load eccentricity
and secondary bending are omitted. The pin-bearing strength
of the composite laminates has been the focus of a significant
research effort. The strength and failure modes of mechani-
cally fastened joints have been shown to be significantly
effected by relations between geometrical parameters such as
the bolt-hole diameter d; laminate thickness t; width w and
edge distance e [1–5]. Other factors such as the laminate
stacking sequence [2,6–8], lateral clamping force [1–4,6,
9–12] and material non-linearity [13,14] have been investi-
gated and shown to be important for the joint strength.
While the main part of the published literature regarding
pin-loaded joints has focussed on strength characterisation
and prediction, literature regarding the effect of manufactur-
ing aspects on joint structural performance is limited. Persson
et al. [15] investigated the effect of hole machining techniques
and manufacturing defects on the static strength and fatigue
life of carbon fibre/epoxy joints. Manufacturing defects
relating to hole machining were found to significantly reduce
the static strength and fatigue life of pin-loaded joints in
comparison to defect-free laminates.
Another important manufacturing- and assembly-
related issue is the hole machining tolerance and fit
1359-8368/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compositesb.2003.11.001
Composites: Part B 35 (2004) 331–343
www.elsevier.com/locate/compositesb
* Corresponding author. Tel.: þ46-70-349-6440; fax: þ46-8-20-78-65.
E-mail address: [email protected] (S. Hallstrom).
between the bolt and the hole. This is discussed in more
detail Section 2.
2. Effect of bolt-hole clearance
The dimensional tolerance of the machined holes and
fasteners can lead to large clearances in mechanically
fastened joints. The effect of bolt-hole clearance has been
studied by several researchers [16–19]. Hyer et al. [16]
investigated the effects of pin elasticity, clearance and
friction on the stress state of pin-loaded joints. The effects of
friction and clearance were found to be most significant
affecting both the distribution and magnitude of the stresses
around the hole. Clearances of 0 (neat fit) and 40 mm were
considered for a nominal hole diameter of 4 mm. The 40 mm
clearance resulted in a reduction of the contact angle by 22%
with a corresponding reduction in the predicted joint strength
of 12%. The bolt-hole contact angle is illustrated in Fig. 1. A
shift in the maximum tangential stress from the net-section
plane (908) towards the bearing plane (08) was also noted.
Eriksson [17] conducted a numerical investigation on the
effects of the laminate elastic properties, clearance, friction,
load magnitude and bolt stiffness on the contact stresses in
pin-loaded joints. The results were in general agreement with
Ref. [16], highlighting the importance of including these
parameters in stress analysis and strength prediction models.
Naik and Crews [20] studied the effects of clearance
between a rigid pin and quasi-isotropic laminate using an
inverse formulation. A two-dimensional finite element
analysis (FEA) was performed assuming frictionless contact
between the pin and the laminate. The contact angle and
maximum radial and hoop stresses around the hole were
shown to be dependent on the pin-hole clearance.
DiNicola and Fantle [18] investigated the effects of
clearance on pin-loaded quasi-isotropic carbon fibre epoxy
laminates. Specimens with bolt-hole clearances of 0 (neat
fit), 76, 152 and 276 mm for nominal hole diameters of 3.18
and 6.35 mm were compared and the bearing strength
determined as the stress at 4% deformation of the hole
diameter and the stress at the ultimate bearing load.
The bearing strength at 4% hole deformation was found to
decrease significantly with the increase in clearance but the
ultimate bearing strength exhibited limited dependence on
the clearance. The ultimate bearing strength was reached
after complex damage propagation around the bolt-hole and
it was concluded that the ‘design’ bearing load is clearance
dependent.
Lanza Di Scalea et al. [19] investigated the effect of
clearance and interference fit pin-loaded joints in cross-ply
glass fibre reinforced epoxy laminates. Larger tolerances
were examined than in any of the previous studies. Clearances
of 0 (neat fit), 0.35 and 2.35 mm were investigated for a
nominal hole diameter of 6.35 mm. From a linear elastic FEA,
the peak bearing stresses were found to increase by 900% for
the 0.35 mm clearance and 3000% for the 2.35 mm clearance
relative to the neat fit case. In support of the previous studies
[16], the magnitude of the maximum tangential stress
remained unchanged but was found to shift location with
increasing clearance. A shift of 148 towards the bearing plane
was observed for the case of 0.35 mm clearance but no further
shift was noted for the 2.35 mm clearance.
The prior numerical investigations of the effects of
clearance or interference effects in mechanically fastened
joints in composite materials have been limited to two-
dimensional analysis where an assumption of plane stress
has been assumed. However, the stress field in the region of
bolt-hole contact is three-dimensional and several research-
ers have identified the need for three-dimensional analysis
in order to include the effects of the through-thickness stress
[21,22]. The three-dimensional model developed in the
current work is used to study the effects of the bolt-hole
clearance and the through-thickness stress field in the
vicinity of the hole.
3. Experimental program
A comprehensive experimental program has been
undertaken to study the load bearing behaviour of the
laminates and the effect of the geometrical parameters such
as width to hole diameter ratio ðw=dÞ; edge distance to hole
diameter ratio ðe=dÞ and the thickness to hole diameter ratio
ðt=dÞ on the bearing strength. A series of specimens were
manufactured with a range of geometrical parameters as
listed in Table 1. The effect of lateral clamping on the
bearing strength and joint failure mode was also investi-
gated with a series of joint specimens being clamped with a
torque of 5 Nm. A nominal pin diameter of 6.35 mm and
a neat fit between the bolt and the hole was used for all of the
initial pin-bearing tests.
The effect of bolt-hole clearance on the laminate bearing
strength was investigated for both pinned and clamped
Fig. 1. Contact angle for bolt-hole loading.
Table 1
Test specimen configurations for static pin-bearing tests
Stacking sequence w=d e=d t=d
[0/45/90/245]s 2–6 1.5–6 0.236
[0/45/90/245]s2 2–6 1.5–6 0.519
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343332
joints under static loading. The specimen width and edge
distance values were selected after the first series of tests to
ensure that bearing failure occurred in the specimens. Three
different clearance levels were investigated with the
clearance l being defined as
l ¼fhole 2 fpin
fhole
ð1Þ
where fhole and fpin are the nominal diameters of the hole
and the pin, respectively. The specimen configurations
which were manufactured to investigate the bolt-hole
clearance effects are listed in Table 2.
3.1. Specimen preparation
Specimens were machined from carbon fibre epoxy
laminates manufactured by resin transfer moulding (RTM).
A continuous carbon fibre (Toray T700) non-crimp fabric
from heavy tow yarn was used together with epoxy resin
(Shell Epicote LV 828). Two different laminate thicknesses
were considered with stacking sequences [0/45/90/245]s
and [0/45/90/245]s2, respectively. Specimens were
machined from laminates of size 1800 mm £ 600 mm to
the geometry illustrated in Fig. 2 using a diamond tip saw.
Three specimens were tested per configuration with a total
of 100 experiments being performed.
Holes were machined in the specimens using a
Twinspinw machine based on a new orbital drilling
technique [23]. The technique involves a cutting tool
revolving at high speed around its own axis and at a lower
speed eccentrically around a principal axis. The method
allows for a hole to be machined axially and radially
simultaneously. The hole diameter is machined accurately
by controlling the eccentricity of the cutting tool and the
technique has been shown to be able to produce high
precision, delamination free holes in carbon fibre reinforced
plastics [15]. The technique has the advantage of allowing
holes to be drilled with different diameters using the same
cutting tool, which in this study has been used to assess the
effect of clearance or hole machining tolerance.
3.2. Testing procedure
Static tests were conducted using a universal testing
machine (Instron 4505) with a load capacity of 100 kN.
The system is fully computer controlled and allows for
acquisition of load, displacement and strain data. The
specimens were mounted in the pin-loading fixture at one
end and clamped within the grips of the testing machine
at the opposite end. The tests were run in displacement
control at a rate of 1 mm/min. Loading was stopped after
the first significant load drop. Selected specimens were
instrumented with uniaxial strain gauges to determine the
strain field around the bolt-hole and provide verification
data for numerical simulations.
A pin-loading fixture which allowed for the testing of
pinned and clamped joints was used to test the laminates as
shown in Fig. 3. The specimens were loaded with a steel pin
of diameter 6.35 mm and washers of inner diameter
6.35 mm and outer diameter 12 mm were used for the
clamped joint specimens.
The strain in the laminate was measured using a strain
gauge extensiometer with agauge lengthof50 mm. Thestrain
was measured at the laminate mid-point as shown in Fig. 2.
Fig. 3. Test setup and schematic of the pin-loading structure.
Table 2
Test specimen configurations used to investigate clearance effects
Stacking sequence w (mm) e (mm) t (mm) l (%)
[0/45/90/245]s 32 32 1.61 0, 1.55, 3.05
[0/45/90/245]s2 32 32 3.3 0, 1.55, 3.05
Fig. 2. Test specimen geometry for pin-loaded laminates.
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343 333
4. Experimental results
4.1. Static load displacement behaviour
Typical load displacement behaviour of pinned and
clamped laminates is shown in Fig. 4. In the case of the pin-
loaded laminate, the load displacement relationship was
relatively linear up to 60% of the failure load. A slight non-
linearity occurred as a result of damage at the hole edge.
Failure of the pin-loaded laminate was sudden with a drop in
load occurring after the maximum load was reached. Visual
inspection of the laminate revealed a ‘brooming’ type
failure at the edge of the hole with local through-thickness
expansion evident over the region of the bolt-hole contact.
The load displacement behaviour of the clamped
laminate was similar to the pin-loaded laminate for load
levels below 40% of the failure load. For higher loads, a
continuous reduction in stiffness was noted as damage
developed at the bearing surface in the region beneath the
washers. The load continued to increase until the maximum
load was attained and failure was characterised by a minor
drop in the load. Visual inspection of the clamped speci-
mens revealed that internal damage within the laminate
surfaced at the edge of the washers. The washers acted to
suppress the brooming failure found in pin-loaded laminates
and shifted the out-of-plane expansion associated with pin-
bearing failure away from the hole edge [10,11].
The load displacement behaviour was also found to be
dependent on the geometry of the test specimens and the
resulting failure mode. Fig. 5 illustrates typical load
displacement curves for specimens failing in bearing and
net-section failure modes. The load displacement curve for
specimens failing by net-section mode illustrates a linear
load displacement relation prior to catastrophic failure.
At failure, the laminate fractured across the net-section
perpendicular to the direction of the applied load with
the fracture originating at the hole edge. In contrast, the
specimens failing by bearing failure mode underwent
progressive damage accumulation as illustrated by the
non-linearity in the load displacement curve. While a clear
indication of the damage was evident in the current material
at approximately 40% of the failure load, Camanho et al.
[21] found that for laminates made from pre-impregnated
(pre-preg) carbon epoxy (Hexcel T300/914), damage
initiation occurred at load levels approximately 60% of
the final failure load with no apparent loss of stiffness
evident from the load displacement curve. The authors also
reported that damage in specimens failing by net-section
failure mode did not occur until 80% of the ultimate failure
load was reached.
The load displacement behaviour of the specimens
failing by shear-out failure mode exhibited a combination
of initial bearing failure followed by a sudden reduction in
load carrying capability. Pure shear-out failure, as found in
laminates made from pre-preg material, did not occur in any
of the laminates used in the current study. This is assumed to
be due to the microstructure of the laminates and the high
percentage of ^458 plies.
Similar dependence on the lateral clamping load and
specimen geometry was noted for the load displacement
behaviour of both the [0/45/90/245]s and [0/45/90/245]s2
laminates.
4.2. Effect of parameter variations w=d; e=d and t=d
on the static bearing strength
The effects of the geometrical parameters w=d; e=d and t=d
on the laminate’s ultimate bearing strength are illustrated in
Figs. 6 and 7. The ultimate bearing strength ðsubÞ of the hole
is defined as
sub ¼
Pu
dtð2ÞFig. 4. Load displacement behaviour of pinned and clamped
[0/45/90/245]s2 laminates.
Fig. 5. Load displacement behaviour of [0/45/90/245]s2 laminates failing
by bearing and net-section failure modes.
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343334
where Pu is the ultimate failure load, d the hole diameter and
t the thickness of the laminate. The nominal hole diameter
d ¼ 6:35 mm was used throughout this investigation.
Fig. 6 illustrates the effect of the width to hole diameter
ratio ðw=dÞ on the ultimate bearing strength of the laminates.
For pinned joints, bearing failure occurred for w=d values
$2. At lower values of w=d; the laminates failed in net-
section mode. Similar behaviour was noted for the [0/45/90/
245]s and [0/45/90/245]s2 laminates.
The transition from net-section to bearing failure
occurred at a higher value of w=d for clamped joints in
comparison to pinned joints. This was due to the lateral
support at the hole edge which inhibited the through-
thickness expansion.
A significant increase in the ultimate bearing strength
was noted for the laminates subject to a lateral clamping
load. An increase in strength of over 100% was found in
comparison to the pin-loaded laminates. The increase in
strength due to the clamping load is in agreement with the
results from other authors [1–4,6,9–12].
The effect of e=d on the bearing strength is illustrated in
Fig. 7. For low edge distances e=d , 1:5; the failure mode
was a combination of bearing failure and shear-out failure.
The laminates sheared through the thickness and there was
no evidence of individual plies shearing out which is
a common occurrence for 08 plies in pre-preg laminates. Full
bearing strength was achieved in laminates with e=d $ 2 for
the pin-loaded laminates and e=d $ 3 for the clamped
laminates. A similar increase in the ultimate bearing
strength was noted between the pin-loaded and clamped
laminates as discussed previously.
4.3. Hole deformation
The deformation of the bolt-hole in the laminate
significantly influences the stiffness and strength of a
mechanically fastened joint. The interaction between the
bolt and the hole at different load levels governs the contact
area over which load is transferred. Permanent deformation
of the hole results in looseness in the joint, which can result
in significant strength reduction, especially during cyclic
loading.
The deformation of the bolt-hole can be used to define a
design load limit for mechanically fastened joints. The
testing standard ASTM STD D953-87 [24] outlines a
procedure for determining the bearing strength defined as
the stress at 4% hole deformation. In this paper, the bearing
strength at 4% hole deformation will be referred to as s4%b :
Assuming that the measured displacement ðdtotalÞ is the
sum of the elastic deformation ahead of the hole ðdspecimenÞ
and the deformation of the hole itself ðdholeÞ; the hole
deformation at a given load can be determined as
dhole ¼ dtotal 2 dspecimen ð3Þ
or substituting for the deformation of the specimen,
dhole ¼ dtotal 2 eLo 2ðL2e
Lo
P
AðxÞEdx ð4Þ
where L is the specimen length, e the edge distance, Lo the
free length of the specimen ahead of the hole (see Fig. 2) and
e is the far-field strain. The last term in Eq. (4) accounts for
the reduction of the net-section at the hole where P is the
applied load, E is the modulus in the length direction of the
laminate and AðxÞ is the effective cross-sectional area of a
strip of material in the laminate length direction x:
The bearing stress ðP=dtÞ versus hole deformation for
specimens with different bolt-hole clearance subject to pin-
loading is illustrated in Fig. 8. The bolt was located at the
centre of the hole at the start of each test. For clearance fit
specimens, the initial portion of the curve corresponds to the
bolt movement within the hole prior to contact between the
bolt and the laminate. The initial displacement prior to
contact is equal to the radial clearance between the bolt and
the hole measured from the centre of the hole.
The bolt-hole clearance is shown to influence the hole
deformation behaviour as shown in Fig. 8. The neat fit
specimens ðl0Þ immediately transfer load in comparison to
the clearance fit specimens where the initial clearance
results in a delay in the load transfer. The slope of the
bearing stress versus hole deformation curves indicates
Fig. 6. Bearing strength of the [0/45/90/245]s and [0/45/90/245]s2
laminates versus w=d ratio.
Fig. 7. Bearing strength of the [0/45/90/245]s and [0/45/90/245]s2
laminates versus e=d ratio.
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343 335
a slightly lower stiffness associated with the clearance fit
specimens. For a given bearing stress, the hole deformation
in clearance fit specimens is slightly larger in comparison to
that of neat fit specimens. This is physically reasonable
given that the contact area between the bolt and the hole is
reduced for clearance fit specimens resulting in higher local
contact stress. The hole deformation versus bearing stress
behaviour was found to be thickness independent below
certain bearing stress levels for a given clearance (see points
A in Fig. 8). The stress level where the [0/45/90/245]s and
[0/45/90/245]s2 curves diverge is shown to decrease with
increasing bolt-hole clearance. It is assumed that this
reduction is due to the earlier onset of damage in specimens
with larger clearance.
A thickness effect is evident when considering the
ultimate failure of both laminates with the thicker
[0/45/90/245]s2 laminates illustrating a higher ultimate
bearing strength. Similar thickness dependent behaviour
was reported by Collings [1] who found that the ultimate
bearing strength decreased with increasing values of d=t:
Collings also reported that the effect of d=t on the ultimate
bearing strength can be reduced through application of high
lateral clamping load around the hole.
The bearing stress versus hole deformation is signifi-
cantly different for pin-loaded and clamped laminates as
shown in Fig. 9. The initial slope of the curve for the
clamped laminate is dictated by the friction between the
washers and the laminate. When the friction is overcome,
the deformation behaviour follows that of the pin-loaded
laminate. The clamped laminate is shown to withstand
higher bearing stress and larger hole deformation in
comparison to the pin-loaded laminate. Above 50% of the
failure load, a continuous reduction in stiffness is evident as
damage accumulates within the laminate. Failure of
the clamped laminate is non-catastrophic with the hole
deformation increasing steadily without any increase in
load. The bearing stress at 4% hole deformation, s4%b ; is also
illustrated in the figure.
In order to investigate the micromechanical failure
modes, which contribute to the bearing failure of the
laminates, and the effects of bolt-hole clearance, a series of
specimens loaded to failure were sectioned along the bearing
plane and polished to allow inspection under a microscope.
Inspection of the bearing plane of the laminates revealed the
micromechanical failure modes and the extent of damage
within each specimen. Earlier investigations of failure modes
and damage development in pin-loaded laminates by Wang
et al. [25] and Camanho et al. [21] have found the primary
failure mode in pin-loaded laminates to be shear cracking
comprising of matrix compression, fibre kinking and fibre-
matrix shearing. The previous investigations were, however,
limited to laminates made from pre-impregnated material
which has a different microstructure compared to laminates
made from non-crimp fabric.
The damage in the bearing plane of [0/45/90/245]s2
laminates is illustrated in Fig. 10(a)–(c). Inspection of the
laminates revealed the dominant micromechanical failure
modes as matrix compression, interlaminar and intralaminar
matrix shear cracking, fibre microbuckling and fibre shear
fracture. Fibre microbuckling in the restrained 08 oriented
plies located within the laminate (plies 8 and 9) resulted
in eventual fibre compressive fracture as illustrated in
Fig. 11(a) and (b).
The damage in the bearing plane was found to be more
extensive for laminates with larger bolt-hole clearance. The
higher stress levels in the bearing plane resulted in a large
network of shear cracks propagating from the hole edge.
Delamination was noted to be more pronounced towards the
outside of the laminate through the resin rich interface
between the 45 and 908 ply bundles. Fibre failure in the 08
oriented plies located within the laminate (plies 8 and 9)
extended almost 1 mm from the hole edge for the l3:05%
laminate. The greater extent of damage in the bearing plane
correlated with the increased hole deformation found in
specimens with larger clearances for a given load level.
Fig. 8. Bearing stress versus hole deformation for pin-loaded laminates. Fig. 9. Bearing stress versus hole deformation for pinned and clamped
laminates ðl ¼ 1:55%Þ:
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343336
Fig. 10. Micrographs of sections cut through the bearing plane of [0/45/90/245]s2 laminates. (a) l0; (b) l1:55%; (c) l3:05%:
Fig. 11. Micrographs of local failure modes in [0/45/90/245]s2 laminates. (a) Fibre microbuckling and shear cracking in the centre of the laminate (plies 8 and
9). (b) Fibre compressive fracture in a 08 oriented ply. (c) Interlaminar shear failure between plies at the outer edge of the bolt-hole.
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343 337
Inspection of damage in the bearing plane of the
thinner [0/45/90/245]s laminates revealed the primary
failure modes as matrix compression and shear failure
(see Fig. 12(a) and (b)). Fibre splitting was present in the 08
oriented outer plies together with a limited degree of fibre
microbuckling. At ultimate failure, shear cracks from the
hole edge propagated and merged with delaminations
between the 0 and 458 plies.
The increase in the ultimate strength of the
[0/45/90/245]s2 laminates may occur as a result of the
increased load carried by the restrained 08 oriented plies at
the centre of the laminate. The outer 08 oriented plies are
unconstrained at one side allowing for a ‘brooming’ type
deformation at failure which results in interlaminar shear
failure (see Fig. 11(c)) or fibre splitting.
4.4. Effect of bolt-hole clearance on the static bearing
strength
The effect of bolt-hole clearance on the static bearing
strength of pin-loaded CFRP laminates at 4% hole
deformation ðs4%b Þ and at ultimate load ðsu
bÞ is illustrated
in Fig. 13.
The bearing strength at 4% hole deformation of the
[0/45/90/245]s laminate was shown to decrease by 7 and
19% for bolt-hole clearances of l1:55% and l3:05%;
respectively. The corresponding ultimate bearing strength
ðsubÞ was found to be similar for clearances of l0 and
l1:55% with a reduction of 12% being noted for the
clearance of l3:05%:
The corresponding decrease in bearing strength at 4%
hole deformation for the [0/45/90/245]s2 laminate was 1.3
and 6% for bolt-hole clearances of l1:55% and l305%;
respectively. The ultimate bearing strength levels remained
almost constant and independent of the clearance between
the bolt and the hole.
The s4%b values for the neat fit joints in both the
[0/45/90/245]s and [0/45/90/245]s2 laminates were found
to be similar. However, as the clearance increased, a
significant reduction in strength was noted in the
[0/45/90/245]s laminate in comparison to the
[0/45/90/245]s2 laminate. This result has important impli-
cations regarding the determination of design bearing
strength values for mechanically fastened joints in laminates
made from similar materials. Design bearing strengths must
be determined for both a given bolt-hole clearance and
laminate thickness.
The variation in strength was found to be slightly larger for
the [0/45/90/245]s laminates in comparison to the
[0/45/90/245]s2 laminates. This may be attributed to the
thinner laminates havinga smaller contact areaand being more
sensitive to misalignment. The larger variation in strength of
the clearance fit laminates may be due to the contact conditions
and friction between the bolt and the hole surface.
The effect of the bolt-hole clearance on the bearing
strength of clamped joints is illustrated in Fig. 14. The lateral
clamping load was found to increase the s4%b values of the
laminates by approximately 20% in comparison to pin-
loaded laminates. However, the most significant increase in
strength was evident in the sub values which increased by
approximately 110%. The variation in strength due to
clearance was found to be smaller than for the pin-loaded
laminates. The ultimate bearing strength was shown to be
independent of the bolt-hole clearance for both the [0/45/90/
245]s and [0/45/90/245]s2 laminates. With the application
of a lateral clamping load, the [0/45/90/245]s laminates
were found to have slightly higher bearing strengths at 4%
hole deformation than the [0/45/90/245]s2 laminates. In a
similar manner to the pin-loaded laminates, the bearing
strength at 4% hole deformation for the clamped [0/45/90/
245]s laminates was found to decrease with bolt-hole
clearance, with reductions in the bearing strength of 4
and 12% for clearance levels of l1:55% and l3:05%; respec-
tively. The corresponding reduction in the s4%b strength of
[0/45/90/245]s2 laminate was 10 and 22%, respectively.
Fig. 12. Micrographs of the bearing plane of [0/45/90/245]s laminates at ultimate failure.
Fig. 13. Effect of bolt–hole clearance on the static bearing strength of pin-
loaded [0/45/90/245]s and [0/45/90/245]s2 laminates.
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343338
While the effect of the clearance on the stress field
around the hole can be determined analytically [26] or
numerically [16–19], the influence on the bearing strength
is complex given the progressive nature of damage
development during bearing failure. In Section 5, the finite
element method is used to investigate the multi-axial stress
state which exists around the hole, and the effect of
clearance on the stress magnitudes.
5. Finite element modelling
The finite element method was used to determine the
stress field around a hole in a pin-loaded laminate. The stress
field around a hole in a laminate when subject to pin or bolt
loading has been shown to be three-dimensional [21,22] and
thus a three-dimensional finite element model is necessary to
compute the multi-axial stress state which exists at the hole
and the surrounding area. This is particularly important for
laminates exhibiting bearing failure where the through-
thickness stress is extremely important.
Finite element models of the pin-loaded laminates were
developed using the ABAQUS [27] finite element code.
Each ply was modelled using a layer of linear isoparametric
three-dimensional solid brick elements (C8D3), with the
mesh being refined around the region adjacent to the hole in
order to allow for two elements per ply. Elements further
afield from the hole where the aspect ratio of the elements
was poorer were modelled using the reduced integration
element (C8D3R) as reduced integration scheme alleviates
the over-stiffened behaviour of such elements. A symmetry
boundary condition was used to model the [0/45/90/245]s2
laminate with a displacement constraint being applied in the
thickness direction to nodes lying on the symmetry plane.
No other symmetry planes exist due to the presence of
the ^458 plies which produce a non-symmetric stress
distribution around the boundary of the hole. A half section
of the finite element model is illustrated in Fig. 15.
No a priori assumptions were made regarding the contact
stress distribution and the full three-dimensional contact
problem was solved in order to determine the actual contact
pressure distribution and contact area. The master–slave
contact algorithm was used based on small sliding
conditions [27]. The pin was modelled using an analytical
rigid surface based on the work of Hyer et al. [16] and
Eriksson [17] who concluded that the effect of pin modulus
of elasticity was minor on the resulting contact stress
distribution in the laminate. The use of an analytical contact
surface is more computationally efficient and limits
geometric discretisation error in comparison to modelling
the pin using solid finite elements.
A friction coefficient of 0.2 was assumed between the pin
and the laminate with the friction being modelled using a
Coulomb friction model. The coefficient was selected
through comparison of the experimentally determined strain
field and the strain from the finite element model.
Geometrically linear analysis was performed as both the
pin and the laminate are stiff bodies which do not undergo
large rotations.
Each ply of the finite element model was modelled as an
orthotropic solid. The in-plane properties of the lamina were
experimentally determined [28] and the through-thickness
properties estimated values (see Table 3).
5.1. Comparison with experimental results
Verification of the finite element model was performed
through comparison of predicted radial strain distributions
and experimentally determined values. Uniaxial strain
gauges (Showa N11-FA-1-120-11, gauge length 1 mm)
were located around the bolt-hole along the bearing plane
Fig. 15. A section of the finite element model of the pin-bearing specimen.
Table 3
Elastic properties for the unidirectional lamina [28]
E11
(GPa)
E22
(GPa)
E33
(GPa)
G12
(GPa)
G13
(GPa)
G23
(GPa)
n12 n13 n23
98 7.8 7.8 4.7 4.7 3.2 0.34 0.34 0.44
Fig. 14. Effect of bolt–hole clearance on the static bearing strength of
clamped [0/45/90/245]s and [0/45/90/245]s2 laminates.
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343 339
and at an angle of 458 to the bearing plane. The locations of
the strain gauges are shown in Fig. 16 together with a
comparison of the measured and predicted radial strains.
The predicted radial strains from the finite element model
are shown to compare reasonably well with the measured
strains. The predicted strains are somewhat lower than
measured strains in the gauges adjacent to the hole where
the stress gradients are high and thus difficult to measure
accurately. The predicted strains at locations further a field
from the hole compare well with the measured values and
thus the model is deemed to be in good agreement with the
measured response.
5.2. Results and discussion of the finite element analysis
The three-dimensional stress field around the bolt-hole
in the [0/45/90/245]s laminate is illustrated in
Fig. 17(a)–(d). The radial and tangential stresses are
normalised with the bearing stress for an applied load of
1.2 kN. The load level was selected to ensure that the
stress levels were compared at a point where the
material remained undamaged. The bolt-hole contact
problem is, however, highly non-linear with the stress
distribution changing as the load and contact surface are
increased.
Fig. 16. Comparison between measured and predicted strains for
[0/45/90/245]s pin-loaded laminate ðl0; P ¼ 1:2 kNÞ:
Fig. 17. Stress distribution around the bolt-hole of the [0/45/90/245]s laminates at an applied load of P ¼ 1:2 kN:
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343340
The radial and tangential stress distributions on ply level
were found to be similar for both the [0/45/90/245]s and
[0/45/90/245]s2 laminates for a given tolerance and hence
only the results from the [0/45/90/245]s laminate are
presented.
The radial and tangential stresses in each ply direction for
the laminate with the neat fit bolt-hole clearance ðl0Þ
are illustrated in Fig. 17(a) and (b). The radial stresses are
predominantly compressive while the tangential stresses are
tensile, regardless of ply orientation. The highest radial stress
occurs in the 08 plies at the bearing plane ðu ¼ 0Þ which
corresponds to the direction of the applied load. The radial
stress in the 08 plies decreases around the circumference of
the hole with increasing angle towards the net-section where
no radial load is carried by the 08 plies. High stress levels are
also evident in the ^458 plies with the peak load occurring
close to the respective ply fibre directions. The radial stress
distribution in these plies is non-symmetric about the bearing
plane. The high stress in these plies is a result of the neat fit
allowing for the load to be distributed over the maximum
contact area. The maximum radial stress in the 908 plies is
shown to occur at an angle of 188 from the net-section plane.
The radial stress in the 908 plies is significantly lower than in
the 08 and ^458 plies which is physically reasonable given
that the effective stiffness in the load direction is an order of
magnitude lower there than for the 08 plies. The location of
the peak stress in the 908 plies shifts from the net-section
plane towards the bearing plane as the load is increased and
the hole is deformed.
The tangential stress around the circumference of the
hole for each ply orientation is illustrated in Fig. 17(b). The
peak tangential stress is shown to be almost equal in each
ply regardless of the orientation. The location of the peak
stress coincides with the angle where the ply orientation is
tangential to the hole edge. The magnitude of the peak
tangential stresses is generally lower in comparison to the
magnitude of the peak radial stresses around the hole.
The radial and tangential stresses around the hole of the
clearance fit laminate ðl3:05%Þ are illustrated in Fig. 17(c)
and (d), respectively. The clearance between the bolt and
Fig. 18. Through-thickness stress distributions in the [0/45/90/245]s and [0/45/90/245]s2 laminates.
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343 341
the hole is shown to significantly increase the radial stress in
the bearing plane. The peak bearing stress in the 08 plies
increases by 100% in comparison to the neat fit case. The
peak radial stress in the ^458 plies increases by 25% with
the location of the peak stress shifting 238 towards the
bearing plane. The peak radial stresses in the 908 plies,
which occurred close to the net-section plane for the neat fit
case are significantly reduced due to the absence of contact
in that region. The radial stresses in the 908 plies at the
bearing plane are increased by 100% but the stress levels
remain significantly lower than in the other plies.
The magnitude of the tensile tangential stresses is
shown to alter as a result of the clearance. The location of
the peak tangential stress in the 08 plies remains at the net-
section plane while the location of the peak tensile stresses in
the ^458 plies shift 108 towards the net-section plane. In the
bearing plane, there is a marked increase in the compressive
tangential stress in the ^458 plies and a reduction in the
tensile stress in the 908 plies. In general, the magnitude of
the tangential stresses is not significantly changed as a result
of the increased clearance. This result implies that the net-
section failure mode, which is dependent on the tangential
stress in the net-section plane, does not show significant
dependency on the bolt-hole clearance. Similar conclusions
have been drawn by other authors based on the result from
two-dimensional analysis with homogenised material prop-
erties [16,19].
The through-thickness stresses ðszzÞ at the hole edge
contributes significantly to the bearing failure of the
laminates. The through-thickness stress distribution in the
[0/45/90/245]s and [0/45/90/245]s2 laminates are shown
in Fig. 18(a)–(d) where the stresses are evaluated at the
mid-surface of each ply. The through-thickness stress
distribution at the bearing plane of the [0/45/90/245]s
laminate is illustrated in Fig. 18(a). At this location the
through-thickness stress is tensile with the maximum stress
occurring at the centre of the laminate. The tensile stress is
caused by the laminate expansion in the thickness direction
as the bolt load is applied. The distribution of szz around the
hole circumference is illustrated in Fig. 18(b). The tensile
component of the through-thickness stress is confined to
the region 2288 # u # 458 for the neat fit case with the
region reducing to 2188 # u # 328 for a clearance level of
l3:05%: The magnitude of the through-thickness stress is
shown to increase by 60 and 100% for bolt-hole clearances
of l1:55% and l3:05%; respectively. The presence of tensile
through-thickness stress serves to promote intralaminar
and interlaminar fracture of the plies, resulting in the loss
of strength.
The through-thickness stress distribution at the bearing
plane of the [0/45/90/245]s2 laminate is illustrated in
Fig. 18(c). The through-thickness stress distribution differs
from that of the [0/45/90/245]s laminate with the maximum
tensile stress occurring in the 908 plies. This result correlates
with the location of the damage found in the [0/45/90/245]s2
laminates as shown in Fig. 11(c). The magnitude of the peak
tensile stress at this location increases by 53 and 92% for bolt-
hole clearances of l1:55% and l3:05%; respectively. The
distribution of szz around the hole circumference is
illustrated in Fig. 18(d). The region over which the tensile
stress occurs is shown to decrease with increased clearance in
a similar manner to the [0/45/90/245]s laminate.
6. Conclusions
The bearing strength of mechanically fastened joints in
carbon fibre reinforced plastic laminates made from non-
crimp fabric was investigated both experimentally and
numerically. The effect of the geometrical parameters such
as width to hole diameter ratio ðw=dÞ; edge distance to hole
diameter ratio ðe=dÞ and the thickness to hole diameter ratio
ðt=dÞ on the ultimate bearing strength were determined. The
effect of lateral clamping load on the bearing strength was
also determined. Bearing failure occurred in pin-loaded
laminates with w=d $ 2 and e=d $ 1:5: Application of a
lateral clamping load increased the minimum width and
edge distance ratios necessary to avoid net-section failure to
w=d $ 3 and e=d $ 2: The shift in the net-section to bearing
failure mode supports the results of other authors [6,11]. The
ultimate bearing strength was shown to increase by 100%
through application of a lateral clamping load.
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.
The effect of the bolt-hole clearance was found to be
important with regard to the bearing strength at 4% hole
deformation with a significant reduction in bearing strength
noted for clearance fit specimens. However, the ultimate
bearing strength of the laminates illustrated no dependency
on the bolt-hole clearance. It is concluded that the effect of
bolt-hole clearance has more significant implications on the
design bearing strength than on the ultimate strength of
a joint. Bolt-hole clearance should be minimised in order to
achieve maximum bearing strength of the joint.
A three-dimensional non-linear finite element model was
developed to investigate the effect of bolt-hole clearance on
the stress field around the hole. The laminate stacking
sequence was shown to significantly affect the distribution of
stress through the thickness of the laminate and around the
circumference of the hole. The radial compressive stresses at
the bearing plane of the laminate were shown to increase
significantly as the bolt-hole clearance was increased. The
increase in stress is a direct result of a reduction in the contact
area between the bolt and the hole. The most significant
increase in stress was found in the plies aligned in the load
direction. Increasing clearance between the bolt and the hole
was shown to increase both the in-plane and out-of-plane
G. Kelly, S. Hallstrom / Composites: Part B 35 (2004) 331–343342
stress levels. Laminates with [0/45/90/245]s stacking
sequence were found to have tensile through-thickness
stresses in the bearing plane which increased by 60 and
100% for bolt-hole clearances of l1:55% and l3:05%;
respectively. The increase in both the compressive radial
and tensile through-thickness stress in the bearing plane
promote earlier initiation of damage in the laminate.
In comparison to previously published work [16–19], the
current work involves a more detailed representation of the
laminate in three dimensions. The through-thickness stresses,
commonly ignored in two-dimensional models, are predicted
and shown to be significant. The effect of the clearance on the
stress levels in each ply have been determined, highlighting
the non-uniform stress field within the laminate.
Acknowledgements
Dr Ingvar Eriksson and Mr Mats Jonsson at Novator AB
are gratefully acknowledged for their cooperation and
assistance with hole machining. This work has been
financially supported by the Commission of the European
Union through Growth Project GR3D-CT-2000-00102
(Technologies for Carbon Fibre Reinforced Modular
Automotive Body Structures) and by the Swedish Foun-
dation for Strategic Research through the national Swedish
research program ‘Integral Vehicle Structures’. The
TECABS partners who have contributed to this work are
gratefully acknowledged.
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