Composite Structures 71 (2005) 140–158
www.elsevier.com/locate/compstruct
Three-dimensional finite element analysis of single-bolt,single-lap composite bolted joints: part I—model
development and validation
M.A. McCarthy *, C.T. McCarthy 1, V.P. Lawlor, W.F. Stanley
Department of Mechanical and Aeronautical Engineering, Composites Research Centre, Materials and Surface Science Institute,
University of Limerick, Limerick, Ireland
Available online 5 November 2004
Abstract
Three-dimensional finite element models have been developed to study the effects of bolt–hole clearance on the mechanical
behaviour of bolted composite (graphite/epoxy) joints. The joint type studied was single-bolt, single-lap, which is a standard test
configuration in both a civilian and a military standard for composite joints. In this Part I of a two part paper the model is con-
structed in the non-linear finite element code MSC.Marc and attempts are made to validate it by comparing results with experiments
and other finite element solutions generated in a European project on composite bolted joints. Issues in modelling the contact
between the joint parts, which affect the accuracy and efficiency of the model are presented. Experimental measurements of surface
strains and joint stiffness are compared with results from a finite element parameter study involving variations in mesh density, ele-
ment order, boundary conditions, analysis type and material modelling. The ability of the models to capture three-dimensional
effects such as secondary bending and through-thickness variations in stress and strain is evaluated, and the presence of mathemat-
ical singularities in such models is highlighted. The validated model is used in Part II to investigate the effects of clearance on joint
stiffness, stress state and failure initiation.
� 2004 Elsevier Ltd. All rights reserved.
Keywords: Composite; Bolted Joints; Finite element analysis; Clearance; Validation
1. Introduction
Bolted joints are critical elements in designing safe
and efficient aerospace structures from carbon–fibre
reinforced polymer materials. Because joints represent
potential weak points in the structure, the design of
the joint can have a large influence over the structuralintegrity and load-carrying capacity of the overall struc-
ture. Due to factors such as bolt bending and tilting,
bolt pre-load (due to torquing) and secondary bending,
0263-8223/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compstruct.2004.09.024
* Corresponding author. Tel.: +353 61 202222; fax: +353 61 202944.
E-mail address: [email protected] (M.A. McCarthy).1 Present address: Materials Ireland, Department of Mechanical
Engineering, University College Dublin, Dublin 4, Ireland.
stresses and strains in bolted joints vary three-dimen-
sionally. In addition, in composite joints, the stress-field
near the hole is three-dimensional due to the presence of
interlaminar stresses at the free edges, and the bearing
mode of failure is particularly dependent on such
three-dimensional effects.
Methods for analysis of composite joints include ana-lytical methods [1–5], and finite element methods [6–25].
Despite the three-dimensional nature of the problem, to
date the majority of finite element studies have been
two-dimensional [6–14]. This is mainly due to the signif-
icant requirements for model development time and
processing power with three-dimensional analysis.
With the recent increases in computing power, three-
dimensional finite element modelling of composite
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 141
bolted joints has become feasible and such analyses have
begun to appear in the open literature [15–25]. In these
studies, to account for through-thickness variations in
stiffness, the laminates have been modelled either with
one or more orthotropic solid elements per ply
[17,20,21] or with layered solid elements representingmultiple plies [19]. Some of the earlier studies [15–
17,24] did not consider contact between the bolt and
the hole, but made simplifying assumptions to simulate
the presence of the bolt, such as fixing the radial dis-
placement of the nodes around the hole [17,24]. In later
studies, explicit modelling of contact between the bolt
and hole has been used [19–21,23]. In these cases, non-
linear finite element codes were needed to solve for thecontinuously changing boundary conditions brought
about by changes in contact between the bolt and lami-
nate. Some authors modelled the bolt as a rigid cylindri-
cal contact surface [20,21], while others considered it as
elastic and modelled it with three-dimensional finite ele-
ments [19,23].
As part of a collaborative European Union research
project, ‘‘BOJCAS—Bolted Joints in Composite Air-craft Structures’’ [26], several approaches are being
examined for modelling and designing composite bolted
joints in the future. One of these approaches is three-
dimensional finite element analysis, which currently
can be regarded as a research rather than a design tool.
In the future, processing power can be expected to in-
crease to the point where routine three-dimensional
analysis of bolted joints in a design environment willbe feasible. However, to support such advancement,
much work is needed to show that three-dimensional fi-
nite element models can provide distinct advantages
over existing design rules [27,28] or two-dimensional
analysis programs [29,30]. Furthermore, such three-
dimensional models need to be validated against exper-
iments, and the best approaches for producing accurate
yet efficient models need to be determined.The aim of this first part of a two-part paper is to
examine different approaches to three-dimensional mod-
elling of composite bolted joints, in terms of their ability
to produce accurate results with a reasonable level of
computational efficiency. For the investigation, a finite
element model of a single-bolt, single-lap composite
joint is developed in the non-linear finite element code
MSC.Marc. The accuracy of the model is criticallyexamined by comparing results with experiments and
other finite element solutions generated in the research
project BOJCAS. Attempts are made to improve the
model through a series of mesh refinements, increases
in element order, and modifications to boundary condi-
tions, material modelling and analysis type. The single-
bolt, single-lap joint was chosen as it provides a suitable
test case for three-dimensional modelling since it in-volves secondary bending and three-dimensional varia-
tions in stress and strain. It is also one of the standard
configurations for characterisation of mechanically fas-
tened composite joints in MIL-HDBK-17 [31,32], and
in ASTM standard D 5961/D 5961M-96 [33]. MIL-
HDBK-17 states that the single-lap configuration is
more representative than the double-lap configuration
of most critical aircraft bolted joint applications.In the second part of this paper, the usefulness of
three-dimensional analysis is demonstrated by studying
the effects of bolt–hole clearance in such single-lap
joints. Since clearance significantly alters the three-
dimensional stress state in the laminates it provides an
interesting topic for three-dimensional modelling. In
addition, no three-dimensional study on variable clear-
ance was found in the open literature and so this workadds to existing two-dimensional investigations
[3,9,12,14,34]. The only results on clearance presented
in Part I of this paper are those relevant to the valida-
tion exercise. Part II concentrates entirely on the effect
of clearance on joint stiffness, stress state and failure
initiation.
2. Problem description
An experimental study, which involved over 80 tests
to failure and percentages of failure, was carried out
on the effects of clearance in single-lap, single-bolt
joints. This study was reported on in [35], so only brief
details are given here. The specimen geometry is shown
in Fig. 1. The joint geometry is based on the ASTMstandard D 5961/D 5961 M-96, [33]. The geometric ra-
tios, w/d = 6, e/d = 3, d/t = 1.6, were designed to induce
bearing failure. The carbon fibre/epoxy material used
in the experiments was HTA/6376, manufactured by
Hexcel Composites, a high-strength material currently
used in the aircraft industry. Two different lay-ups were
used: one quasi-isotropic with stacking sequence [45/0/
�45/90]5s, the other zero-dominated with stacking se-quence [(45/02/�45/90)345/02/�45/0]s. The latter lay-up
is representative of lay-ups suitable for composite air-
craft wing skins. The ply thickness was nominally
0.13 mm, yielding a nominal laminate thickness of
5.2 mm when cured. The bolts used were aerospace
grade Titanium alloy fasteners with nominal diameter
8 mm. Steel nuts together with steel washers were also
used.The clearances chosen for this study are shown in
Table 1. For a nominal 8 mm hole diameter, they repre-
sent percentage clearances of 0%, 1%, 2% and 3% and
are respectively coded C1–C4. Clearances C1 and C2
are within current aerospace tolerances, while C3 and
C4 are slightly outside. The latter two are thus of inter-
est in examining the possible effects of out-of-tolerance
aerospace holes (or fasteners), and also in non-aero-space applications. For further details on the rationale
for choosing these clearances, see [35]. The clearances
Fig. 1. Specimen geometry.
Table 1
Clearances in present study
Clearance code Nominal clearance (lm)
C1 0
C2 80
C3 160
C4 240
142 M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158
were obtained experimentally using four reamers of dif-
ferent diameters, specially manufactured for this studyto a tight tolerance, by an aerospace supplier.
In the experiments modelled here, the bolts were tor-
qued to 0.5 Nm, which was regarded as the lowest,
repeatable torque that could be applied, hence repre-
senting ‘‘finger-tight’’ conditions. Finger-tight represents
the worst-case scenario of a bolt loosened during fatigue
loading from an initial fully torqued condition. To re-
move bolt position as a variable in the current study(especially for the larger clearance specimens), a mount-
ing jig was designed to locate the bolt in the centre of the
hole, prior to testing. This jig is described in more detail
in [36].
Fig. 2. Finite element model w
3. Finite element model
Several models of varying complexity were con-
structed for this study. Most of these were a refinementof a ‘‘Base Model’’ and are discussed later (Section 4).
This section describes the development of the Base Mod-
el of the bolted joint.
3.1. Finite element mesh
A typical finite element mesh for the Base Model is
shown in Fig. 2. Five separate parts were meshed—two laminates, two washers and a combined bolt-nut.
The meshing of the laminates is similar to that used by
Ireman [19] with a relatively high radial mesh density
near the hole and under the washer, where high strain
gradients exist. However, differently from [19], the wash-
ers were modelled separately. The only disadvantage of
modelling the washers separately is the increase in model
size due to the increased number of elements and contactbodies. Advantages are that including the washers al-
lows the actual contact conditions in the joint to be
modelled more accurately, including movement of the
ith boundary conditions.
Fig. 3. Instrumented bolts used for calibrating bolt pre-load—note:
gauges also affixed on opposing side of bolt (not visible): (a)
instrumented bolt, (b) schematic.
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 143
washer under load, and studies on bolt to washer clear-
ance like those carried out by Tong [37] and Herrington
and Sabbaghian [38] can be conducted. Both linear 8-
noded and quadratic 20-noded isoparametric hexahe-
dral elements have been used for comparison. Wedge
elements were used to form the core of the bolt.
3.2. Boundary conditions and loading
The boundary conditions shown in Fig. 2 were used
in most cases, i.e. the gripped part of the specimen
was assumed perfectly gripped and was not modelled.
Instead, the left end of the top laminate had all three dis-
placement degrees of freedom (DOF) fixed so as to sim-ulate the stationary grip of the tensile testing machine.
Load was introduced by applying a prescribed displace-
ment in the x-direction to the rightmost end of the
bottom laminate to mimic a quasi-static displacement-
controlled loading in the experiments. In some models,
these boundary conditions were modified, as described
later. To avoid potential rigid body modes, light springs
were applied to the components not fully constrainedsuch as the bolt, washers and bottom laminate.
To simulate bolt pre-load due to applied torque,
orthotropic thermal expansion coefficients (allowing
thermal expansion/contraction only in the direction of
the longitudinal axis of the bolt) were given to one of
the washers. This washer was then subjected to a posi-
tive temperature differential prior to mechanical loading
which had the effect of stretching the bolt and clampingthe laminates, which is essentially what happens experi-
mentally. Using this scheme, the bolt also reduces in
diameter during application of pre-load (due to the Pois-
son effect), which is what happens in practice when tor-
que is applied. For the finger-tight experiments modelled
here, a bolt pre-stress of 7.2 MPa was applied. This
value was obtained from the axial gauges in specially
manufactured instrumented bolts (Fig. 3). A loading de-vice designed to introduce a pure axial load was used to
produce a relationship between axial load and strain in
the gauges, while a second test measured the relationship
between strain and torque. From these two tests, the tor-
que versus axial load relationship was obtained. For fur-
ther details of these tests refer to [39].
3.3. Material modelling
The unidirectional stiffness properties of the compos-
ite material (HTA/6376) were obtained from an indus-
trial partner in the BOJCAS project [40] and are
Table 2
Unidirectional stiffness properties for HTA/6376 (Friberg [40])
E11 (GPa) E22 (GPa) E33 (GPa) G12 (GPa) G13
140 10 10 5.2 5.2
shown in Table 2. Two methods of modelling the lay-
ups used in the experiments were implemented. In the
first, the laminates were modelled with the layered solidcontinuum element available in MSC.Marc (Element
149). This element allows a maximum of five orthotropic
layers per element, with each layer containing four inte-
gration points in-plane. Thus, stresses in each ply can be
recovered and the correct bending-twisting coupling is
obtained. In this case, the laminates were modelled with
ten elements through the thickness, with each element
modelling four plies of the composite material. Modelsusing this method are referred to here as ‘‘layered mod-
els’’. As will be shown in Part II of this paper, these
models are important for application of failure criteria
to determine joint strength.
In the second method, homogeneous, orthotropic
material properties were derived by performing a series
of tensile and shear numerical experiments on a block
of layered material and the in-plane properties were val-idated against classical laminate theory. Homogeneous
properties obtained for the quasi-isotropic and zero-
dominated lay-ups in this study are shown in Table 3.
Models using this method are referred to as ‘‘homogene-
ous models’’ and were developed primarily to reduce
complexity to help debug contact.
Concerning the other joint components, the titanium
bolt and steel washers were modelled with isotropicmaterial properties, with material constants Eb = 110 G-
Pa, mb = 0.29 for the bolt, and Ew = 210 GPa, mw = 0.3
for the washers.
3.4. Contact description
Contact was modelled using the direct constraint
method in MSC.Marc. The method requires the defini-tion of ‘‘contact bodies’’, i.e. bodies that potentially
(GPa) G23 (GPa) m12 m13 m23
3.9 0.3 0.3 0.5
Table 3
Equivalent laminate stiffness properties
Exx (GPa) Eyy (GPa) Ezz (GPa) Gxy (GPa) Gxz (GPa) Gyz (GPa) mxy mxz myz
Derived homogeneous properties
for quasi-isotropic lay-up
54.25a 54.25a 12.59 20.72a 4.55 4.55 0.309 a 0.332 0.332
Derived homogeneous properties
for zero-dominated lay-up
77.23a 40.57a 12.47 17.62a 4.74 4.35 0.355 a 0.299 0.402
a Verified by laminate theory.
144 M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158
may come in contact with each other. Contact bodies
can simply be the physical bodies themselves (e.g. the
laminates, bolt and washers), but it was found that it
is more efficient to select subsets of the physical bodies
which are likely to be involved in contact (see Fig. 4)
since less checking for contact is required at each solu-
tion step.
Efficiency was improved further by using a ‘‘contacttable’’ available in MSC.Marc. Contact tables define
which contact bodies are likely to contact each other
during an analysis step. For example, it was known a
Fig. 4. Contact bodies defined by possible contacting elements only: (a) sect
bodies isolated.
priori that the two washers would never come into con-
tact, so the contact table was set to eliminate checking
for this possibility. The contact table used here is shown
in Fig. 5. Seven contact bodies are defined in this table.
Body ‘‘Top_washer_c_lap’’ is made up of the elements
in the upper washer (see Fig. 4) which can contact the
upper laminate. ‘‘Top_washer_c_bolt’’ consists of the
elements in the upper washer which can contact the bolt.The next two contact bodies in the table (‘‘Bot-
tom_washer_c_lap’’ and Bottom_washer_c_bolt’’) per-
form similar functions for the lower washer. Bodies
ion through single-bolt model highlighting contact bodies, (b) contact
Fig. 5. A contact table defined in MSC.Mentat for the bolted joint model (�T� indicates touching contact between two bodies).
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 145
‘‘lap1’’ and ‘‘lap2’’ represent the elements within the
upper and lower laminates, respectively, which can con-
tact other bodies. Finally the ‘‘bolt’’ contact body con-tains the elements in the bolt which can contact other
bodies. A blank entry indicates that no contact search
is performed between two bodies, while a ‘‘T’’ indicates
that it will. For example the ‘‘T’’ in row 5, column 7
indicates that contact will be checked between the con-
tact bodies ‘‘lap1’’ and ‘‘bolt’’. As self-contact (i.e. a
body bending over and contacting itself) was unlikely
to occur during the analysis, the leading diagonal hadno entries, thus eliminating checking for this possibility.
The lower left area of the contact table was deactivated
as a result of using a single-sided contact definition (dis-
cussed later).
With the direct constraint method, detection of con-
tact is done by checking if potential contact nodes are
‘‘in contact’’ with potential contact segments. In three-
dimensional deformable–deformable contact, contactsegments are the element faces on the surface of the con-
tact bodies. A tolerance is used to decide if a node is ‘‘in
Fig. 6. Contact searching in MSC.Marc: (a) contact tolerance showing pene
bias factor used here.
contact’’—see Fig. 6(a). If the trial position of the node
is within the contact tolerance zone, it is considered to
be in contact with the segment and is placed on that seg-ment by means of a multi-point (‘‘tying’’) constraint. If
it lies beyond the contact zone (as in Fig. 6(a)), it is con-
sidered to have penetrated and the increment is split and
a new trial position found. Too small a tolerance leads
to a lot of increment splitting (and hence high computa-
tional cost), but too large a tolerance leads to premature
contact detection. The default tolerance in MSC.Marc is
one twentieth of the smallest element edge length. How-ever, because a primary goal of this work was to exam-
ine differences between small clearances, a 10 lmtolerance (which is significantly smaller than the default
value) was used. This value was obtained by some ‘‘trial
and error’’ in a separate numerical study. This contact
tolerance was used with a ‘‘Bias Factor’’ of 0.9. This
biased the contact zone into the contacted body—thus
the contact zone ranged from (1-Bias) · tolerance (i.e.1 lm) ‘‘above’’ the body to (1 + Bias) · tolerance (i.e.
19 lm) ‘‘into’’ the body, as shown in Fig. 6(b). Again,
tration (which leads to increment splitting), (b) contact tolerance with
146 M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158
this bias factor was obtained by some ‘‘trial and error’’
in a separate numerical study.
In MSC.Marc, both ‘‘single-sided’’ and ‘‘double-
sided’’ contact is available. For this type of analysis, sin-
gle-sided contact was found to be more suitable because
double-sided contact led to holes and gaps occurring insome contact interfaces. In single-sided contact, when
two contact bodies come into contact, the contact body
defined first is the ‘‘contacting’’ body and supplies the
contacting nodes, while the other body is the ‘‘con-
tacted’’ body and provides the contacted segments.
Thus, the order in which contact bodies are defined is
important and this places restrictions on the mesh. For
example, the MSC.Marc documentation [41] recom-mends that the body with the finer mesh should be de-
fined first, i.e. should be the contacting body. As can
be seen in the contact table (Fig. 5), this guideline has
been generally followed as the washers (finest
meshes—see Fig. 2) were defined before the laminates
(medium meshes) which themselves were defined before
the bolt (coarse mesh). One exception is the contact be-
tween the two laminates. Both these contact bodies haveidentical meshes so the order in which they were defined
was arbitrary.
A problem with single-sided contact arises when a
contacting body ‘‘overhangs’’ a contacted body as shown
for contact between the two laminates in Fig. 7. Lami-
nate 1 is defined first and therefore is the contacting
body (i.e. supplies contacting nodes), while Laminate 2
Fig. 7. Issues with single-sided contact: (a) penetration due to
overhanging contacting body, (b) reduced by refined radial mesh in
this area.
is the contacted body (i.e. supplies contacted segments).
When the joint is deformed, the ‘‘overhanging’’ contact-
ing node on Laminate 1 in Fig. 7(a) does not interface
with a contacted segment and so meets no restraint. This
allows penetration as shown. Reversing the order of def-
inition of the two contact bodies would only shift theproblem to the other side of the joint. This problem can-
not be fully eliminated but can be reduced to a negligible
level by radial refinement of the mesh, as shown in Fig.
7(b).
The final issue with contact was the use of so-called
‘‘analytical’’ contact rather than ‘‘discrete’’ contact.
The tying constraint applied when a node contacts a seg-
ment, uses information regarding the segment�s outward
Fig. 8. Radial strain distribution, err, with different contact algorithms:
(a) discrete contact, (b) analytical contact.
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 147
normal. In ‘‘discrete’’ contact, the finite element piece-
wise linear representation of the surface is used for cal-
culating this normal, leading to unique normals
emanating from each element face. A problem then oc-
curs when a contacting node slides from one face to an-
other because it tends to get ‘‘stuck’’ due to thesediscontinuous normals. This has an adverse effect on
the quality of the solution. For example, Fig. 8(a) shows
the radial strain distribution, err, in the bottom laminate
from a model with homogeneous orthotropic material
properties (defined in Section 3.3). As can be seen, the
result is seriously flawed since peaks in radial strain oc-
cur not just at the 0� position in the hole (i.e. the bearing
plane), but also at other locations; the err distribution isalso not symmetric which it should be with these mate-
rial properties.
When ‘‘analytical’’ contact is implemented,
MSC.Marc fits a smooth Coons surface through the
nodes of the contacted body. This analytical surface is
then used to generate a continuous normal over the sur-
face of the body, thus removing the problem with con-
tacting nodes getting stuck. This procedure also resultsin a more accurate representation of the physical geom-
etry, especially curved geometries. Fig. 8(b) shows the
radial strain distribution in the bottom laminate when
using the analytical contact algorithm. Comparing to
the discrete contact algorithm (Fig. 8(a)), it can be seen
that the strain distribution is symmetric and much
smoother, and a peak only occurs once at the expected
location (i.e. the bearing plane or 0� location).
Fig. 9. Strain gau
4. Model validation
In this section, results from the three-dimensional fi-
nite element model developed in the previous section
are compared with results from experiments and also re-
sults from other finite element solutions generated in theBOJCAS project. The relevant experimental results are
first presented, and then results from the Base Model
are given. Following that a parameter study to improve
model behaviour is discussed, and finally a comparison
is made between the improved model and finite element
results from other project partners.
4.1. Experimental results
Two different metrics are used to compare the exper-
iments and simulations:
1. Strains at selected points on the joint surface
2. Joint stiffness
The experimental measurements for these two quan-tities are now presented.
4.1.1. Surface strains
Four joints were strain gauged and loaded to a level
that did not cause detectable damage to the laminates
(5 kN). The four configurations were quasi-isotropic
lay-up with C1 and C4 clearances (i.e. neat-fit and 240
lm), and zero-dominated lay-up, also with C1 and C4
ge locations.
148 M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158
clearances. Only the quasi-isotopic results are presented
here. Fig. 9 shows the positions of the strain gauges,
which had a 3 mm gauge length; note that all gauges
were aligned with the loading direction except gauge 7,
which was aligned in the transverse direction. Note also
that 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. Each test was re-
peated 3–4 times (dissembling the joint between each
test), and results were repeatable within approximately
±15 microstrain. Fig. 10 shows the experimental results
for the quasi-isotropic, C1 clearance joint and the fol-
lowing observations can be made from this figure:
• Gauges 1 and 2 indicate a significant amount of bend-
ing at this location. For gauge 1, the tensile strain due
to the applied load is virtually balanced by the com-
pressive strain due to bending, giving a near-zero
output.
• The axial strain in the laminate, obtained by averag-
ing the strains in gauges 1 and 2, is 379.3 microstrain
at an applied load of 5 kN, or a gross-section stress of20.0 MPa. Thus, the measured axial strain indicates a
material modulus of 52.8 GPa, which compares well
with the theoretical value (see Exx for the quasi-iso-
tropic lay-up in Table 3). This provided some confi-
dence that the gauges were reading correctly.
• The bending strain at the same location, obtained by
differencing the strains in gauges 1 and 2, and divid-
ing by two, is 380.9 microstrain.• The outer surface of the overlap region (gauges 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 (termed ‘‘secondary bend-
ing’’). Gauge 4 (which is in line with the edge of the
washer) displays the highest compressive strains of
all the longitudinally-oriented gauges.
0
1
2
3
4
5
-800 -600 -400 -200 0Micros
Lo
ad(k
N)
G1G2G3G4G5G6G7G8
Fig. 10. Experimental strain gauge readings from
• Gauges 5 and 8 differ slightly at higher loads indicat-
ing some possible twisting of the joint about its longi-
tudinal axis, but the amount of the difference is within
the scatter band of the test repeats.
• The transverse gauge 7 shows significant compressive
strains. If the surface of the laminate possessed single-curvature only (flat across the width) this strain
would be expected to be tensile due to Poisson�s effect(since the longitudinal strain on the surface is com-
pressive). The fact that it is compressive indicates that
a ‘‘saddling effect’’ is occurring (i.e. the surface has
double curvature).
Concerning the effects of clearance, the experimentalstrains at 5 kN are listed for both the C1 and C4 quasi-
isotropic joints in Table 4. As can be seen, since differ-
ences of less than 30 microstrain are within the scatter
band, the most significant difference due to clearance
was in gauge 6 and, to a lesser extent, gauge 7.
4.1.2. Joint stiffness
The experimental load–deflection curves were foundto be essentially linear between applied loads of 2–
7 kN, so the stiffness of the joint was measured over this
range. The joint load was obtained directly from the
load cell of the testing machine. However, an accurate
measurement of joint displacement for this single-lap
configuration proved difficult. A number of procedures
were carried out to try and estimate the displacement
of the free length of the joint, and hence the true stiffnessof the joint, as listed below:
1. From a series of tests on unnotched laminates
with known stiffnesses determined from laminate the-
ory, a ‘‘machine stiffness’’, lumping all the compli-
ance effects of the cross-head components, was
determined. This stiffness was then used to apply a
200 400 600 800train
quasi-isotropic, C1 (neat-fit) clearance joint.
Table 4
Experimental and numerical strains at 5 kN applied load (quasi-isotropic lay-ups)
Gauge number Experimental results Finite element results
C1 clearance
(microstrain)
C4 clearance
(microstrain)
Base Model C1
clearance (microstrain)
Improved Model C1
clearance (microstrain)
Improved Model C4
clearance (microstrain)
1 �1.8 �11.6 231 149 132
2 760 757 548 633 606
3 �349 �346 �209 �244 �219
4 �488 �482 �374 �438 �427
5 �400 �381 �302 �346 �362
6 �218 �313 �191 �182 �339
7 �367 �438 �430 �414 �427
8 �353 �385 �302 �346 �362
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 149
correction to the stiffness of joint specimens calcu-
lated from the cross-head displacement, using a sim-
ple springs in series analysis.2. Extensometers were attached to the joint in the over-
lap region as shown in Fig. 11(a) and used to measure
the stiffness of this region. Hand calculations were
then carried out to estimate the stiffness of the ends
of the joint (outside the overlap region). Finally, these
quantities were combined using a springs in series
approach and an estimate of the joint stiffness was
obtained.3. Small steel blocks were attached to the side of the
specimen as shown in Fig. 11(b). Linear variable dis-
placement transducers (LVDTs) were then used to
measure the displacement of these blocks and from
this the joint stiffness was determined. The method
was also used on flat, unnotched laminates of known
stiffness to test its accuracy.
After quite a lengthy study involving several repeats
of experiments on a number of different specimens (for
further details, see [39]), it was found that procedure 3
above gave the most consistent results so this was taken
as the most appropriate measurement technique. The
joint stiffness was determined to be 28 kN/mm.
Fig. 11. Methods used to determine the joint stiffness: (a) extensom-
eters attached across over-lap region, (b) LVDT measuring displace-
ment of attached block.
4.2. Results from the base model
This section presents strain and stiffness results from
the Base Model developed in Section 3. For this calibra-
tion study small changes were made to the mesh in Fig. 2
to ensure nodes existed at the centre of each gauge loca-
tion. Fig. 12 shows the axial strain distribution on the
outer surface of the laminate. The Base Model had
homogeneous material properties, which allowed theuse of a half-model. From this figure, it can be seen that,
as in the experiments, the surface of the overlap region is
in compression, with the maximum compressive values
being in line with the edge of the washer. Table 4 lists
the numerical strain values from this model (obtained
from the node at the centre of each gauge) at 5 kN
Fig. 12. Distribution of axial strain exx in upper layer of elements.
Fig. 13. Saddle effect observed in the finite element model.
150 M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158
applied load. Examining the values in Table 4 for the
Base Model, the following is evident:
• From gauges 1 and 2, the axial strain is 389.3 micro-
strain, which compares well with the experiment
(379.3).
• However, the bending strain from gauges 1 and 2 is
158.5 microstrain, which is considerably less than
the experimental value (380.9).
• Gauges 3, 4, and 5 show compressive strains, as in the
experiment, and the trend in going from gauge 3 to 4to 5 is the same as the experiment (maximum com-
pressive strain at gauge 4). However, the size of these
strains is underestimated by 100–140 microstrain.
• Gauge 6 (behind the hole) shows good agreement
with the experiment.
• Gauge 7 shows a slight overestimation of the trans-
verse compressive strain.
• Gauge 8 is the same as gauge 5 because of the use of ahalf model with homogeneous properties.
Overall, behaviour involving tension and compres-
sion (i.e. axial strain in the laminate, compressive strain
behind the hole) appeared to give quite good agreement,
but the model was stiffer in bending than the experi-
ment. In addition, the axial joint stiffness was 34.6 kN/
mm, which is 23.6% higher than the experimentallymeasured stiffness. Note that the stiffness from the lay-
ered model (see Section 3.3) was virtually identical to
that from the homogeneous model.
Fig. 13 shows that the saddling effect noticed in the
experimental results also occurred in the model; the fig-
ure shows the deformation of the upper laminate at a
magnification factor of 10. This effect is characteristic
of bending in wide beams [42]. Interestingly, the trans-verse bending changes from concave about half way be-
tween the hole and the clamped end to convex near the
end of the laminate. The concave transverse bending
(observed experimentally with the strain gauges) is a re-
sult of high, localised contact forces from the washer
acting in the thickness direction, while the convex
transverse bending is due to the wide beam effect.This phenomenon could be referred to as ‘‘tertiary
bending’’.
4.3. Parameter study to improve model behaviour
To try and improve the base model a parameter
study, which involved varying the element order, mesh
density, boundary conditions, material modelling andanalysis type, was carried out. The first parameter exam-
ined was number of degrees of freedom. Three varia-
tions were examined:
1. increasing the element order to second order (20-
noded brick elements);
2. refining the non-overlap region (see Fig. 14(a));
3. refining both the non-overlap and overlap regions(Fig. 14(b)).
Fig. 14. Mesh refinements: (a) Refinement 1: non-overlap region only; (b) Refinement 2: overlap region and non-overlap region.
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 151
As might be expected, these modifications improved
the bending behaviour. The strains in the second-order
model and the Refinement 2 model were almost the
same, and showed improvements in almost all gaugesover the base model. The Refinement 1 model showed
improvements in gauges 1–3 only. However, Table 5
shows that improved accuracy comes at increased com-
putational cost, which is not linearly related to number
of degrees of freedom. In fact, of most significance to
run-time are the changes brought about in the contact
conditions (increased number of elements in contact or
second-order elements in contact), so Refinement 1 ischeap, but the others are not.
A much less expensive way of improving bending
behaviour was found to be to use the ‘‘assumed strain’’
formulation in MSC.Marc. The ‘‘assumed strain’’ for-
mulation is similar to that used in the ‘‘incompatible
modes’’ elements in ABAQUS and it improves the bend-
ing performance of 8-noded brick elements. Standard
8-noded brick elements do not represent bendingcorrectly, since their sides remain straight and cannot
therefore represent the curvature that exists when a
block of material is loaded in pure bending. As a result,
Table 5
CPU times on 1 GHz Pentium 4 with 1 GB RAM
Model DOF CPU time (h)
Base model, Fig. 2 19,536 1.02
Refinement 1, Fig. 14(a) 25,146 1.15
Refinement 2, Fig. 14(b) 51,336 5.56
Second-order elements, mesh as in Fig. 2 58,062 14.78
right angles in the element are not preserved, and spuri-
ous shear strains are introduced. This makes the element
too stiff in bending because applied bending moments
are resisted by the expected flexural stress plus spurious
shear stresses. To improve this behaviour, the displace-
ment field is augmented by so-called incompatible
modes, which add additional internal degrees of free-dom, and allow a state of constant curvature to be
described. This allows bending to be represented cor-
rectly, without using second-order elements. It was
found that using assumed strain in addition to Refine-
ment 1 gave virtually identical results to the second-or-
der model, with only a small increase in run time over
the Base Model (1.4 h CPU time).
Some of the other variables in the parameter studywere
• use of reduced integration elements;
• use of geometrically non-linear analysis;
• use of separate tensile and compressive elastic mod-
uli: Data from the industrial partners in the BOJCAS
project [43] indicated that the tensile modulus for the
unidirectional material was 140 GPa, while the com-pressive modulus was 130 GPa. A user-defined sub-
routine was written to implement this in
MSC.Marc. The decision as to whether the element
was in tension or compression was based on the sign
of the volumetric strain tensor;
• modelling the clamped area of the joint as shown in
Fig. 15. By fixing only the surface of the clamped
region, some ‘‘flow’’ of the interior material in the
Fig. 15. Modified ‘‘gripping’’ boundary conditions.
152 M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158
clamped region is allowed, which is closer to the true
situation than assuming all the clamped material is
completely fixed.
Using reduced integration elements slightly improved
gauges 1, 2 and 7 but dis-improved gauges 3, 4 and 5.
Using geometric non-linear analysis had little effect since
the joint was relatively thick and short, so out-of-plane
displacements tended to be small. The most improve-
ment was provided by the use of separate tensile/com-
pressive properties and modelling the clamped area.The procedures above that independently improved
the behaviour of the model were combined in a so-called
‘‘Improved Model’’. This model thus included a refined
non-overlap region, use of assumed strain, separate ten-
sile/compressive properties and modelling of the
clamped area of the joint. The strain results are listed
in Table 4. Comparing with the experimental values, sig-
nificant improvements over the Base Model are seen inalmost all gauges. In addition, the joint stiffness de-
creased to 31.5 kN/mm, which is only 12.6% higher than
the experimental value. Fig. 16 shows the strains in the
Improved Model as the applied load increases from 0
to 5 kN, which compares well with the experimental val-
ues in Fig. 10. Shown also in Table 4 is the improved
0
1
2
3
4
5
-800 -600 -400 -200 0Micros
Lo
ad(k
N)
G1G2G3G4G5G6G7
Fig. 16. Numerical strain gauge readings from quasi-isotr
model with a C4 clearance. Similarly to the experiments,
the main effect of clearance in the models was on gauge 6
(i.e. the gauge behind the hole).
4.4. Comparison with other FE solutions
The above validation exercise was presented to the
BOJCAS [26] consortium and the neat-fit (C1) clearance
joint subsequently became a ‘‘benchmark’’ for compari-
son of three-dimensional modelling efforts in the project.
Andersson [44] of the Aeronautical Research Institute ofSweden (FFA) used an in-house h-p finite element code
entitled STRIPE to model the benchmark joint. Exten-
sive computational resources were available for running
STRIPE and so the joint models had very refined
meshes with up to fourth-order elements (giving up to
1.2 million degrees of freedom), thus providing accurate
reference solutions. Ekh [45] from the Royal Institute of
Technology—Stockholm modelled the benchmark jointusing the commercially available finite element code
ABAQUS. The number of degrees of freedom used
was similar to that used here, but the in-plane meshing
scheme was different.
An initial comparison between these alternative mod-
els and the Base Model developed here in terms of joint
200 400 600 800train
opic, C1 (neat-fit) clearance joint (improved model).
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 153
stiffness, revealed a close agreement between the three
models, with the refined model of Andersson [44] show-
ing slightly lower stiffness than the Base Model. Consid-
ering three different contact schemes are used in these
codes, this result was encouraging. The modifications
in material properties and boundary conditions madeto the Improved Model, described above were not made
to the models of [44,45], so no further comparisons
regarding stiffness were made. To provide a closer com-
parison between the models, three further criteria are
used here:
1. out-of-plane displacements,
2. surface strains,3. stresses in the laminates at the hole.
4.4.1. Out-of-plane displacements
The experimental strain results from gauges 5 and 8
(see Fig. 10) indicated that the joint may have been twist-
ing about its longitudinal axis (the x-axis in Fig. 2).
Ekh [45], using layered solid elements in ABAQUS,plotted out-of-plane displacements along lines on either
side of the laminate, and half-way through the thickness
(see Fig. 17a). From this he also observed that the
benchmark joint tended to twist about the x-axis since
the out-of-plane displacements on the two sides of the
joint were different. The results from Ekh�s model and
Fig. 17. Out-of-plane displacements at the sides of the joint: (a) coordin
displacement), (c) model developed here with layered solid elements (at 0.5 m
the layered model developed here are shown in Fig.
17b and c, respectively; refer to Fig. 17a for the coordi-
nate system used. The values shown are at a joint dis-
placement of 0.5 mm. As can be seen, both models are
in excellent agreement and predict considerable second-
ary bending in the laminate and some negative (usingthe right-hand rule) twisting about the x-axis of the
joint. The twisting is a result of non-uniform contact
forces from the bolt (due to bolt rotation) acting
through the thickness of the laminate, which result in
different contact pressure on the 45� plies than the
�45� plies (since they are at different positions through
the thickness). Although the degree of twisting is small,
this phenomenon could be of relevance in bolted/bondedjoints or joints in applications that require sealing.
4.4.2. Surface strains
The strains in gauges 1–7 (see Fig. 9 for gauge loca-
tions) are shown in Fig. 18 for the Improved Model
developed here and the fourth-order model developed
by Andersson [44]. Both models used the homogeneous
quasi-isotropic material properties in Section 3.3. Datawas only available at one load level from Andersson
[44] and so is represented as a single point on the graphs.
As can be seen, agreement between the Improved Model
and the fourth-order model is excellent. This suggests
that the Improved Model is approaching a converged
state (with respect to surface strains). It also appears
ate system used, (b) model developed by Ekh [45] (at 0.5 mm joint
m joint displacement).
Fig. 18. Comparison of surface strains between the Improved Model developed here and the fourth-order model developed by Andersson [44].
154 M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158
that the relatively poor agreement between the experi-
ments and the simulations in terms of bending behav-
iour will not be improved by further mesh refinements.
4.4.3. Stresses at the hole
To examine the stresses at the hole, the mesh of the
laminates shown in Fig. 2 was modified by refining ra-
dially in the washer zone. Two levels of refinement were
used, referred to here as ‘‘Refinement 3’’ and ‘‘Refine-
ment 4’’, with 12 elements and 24 elements in the washer
zone, respectively, as shown in Fig. 19(a) and (b). It
should be noted that Refinement 4 took considerable
time to run and is thus at the limit of current modelling
capabilities with the high-end single processor PCs used
here. In the next two sections, stresses are presented forboth the homogeneous and layered material properties
and comparisons are made with the fourth-order solu-
tions given by Andersson [44]. The models used for gen-
erating the layered stress results were full (not half)
models. The graphs are plotted at a joint displacement
of 0.5 mm since results were only available from Anders-
son [44] at this displacement.
Fig. 19. Mesh refinements in washer region: (a) Refinement 3: 12
elements in washer region; (b) Refinement 4: 24 elements in washer
region.
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 155
4.4.3.1. Homogeneous models. The radial stress at the
hole along a line in the bearing plane going from the
shear plane to the free face of the joint is shown inFig. 20 for a number of homogeneous models with dif-
ferent levels of mesh refinement and element orders. It
should be noted that origin of this line (i.e. the point
on the shear plane) represents a singularity in the model
since at this point, due to tipping of the bolt in the hole,
line contact exists between the bolt and the edge of the
hole. As can be seen in Fig. 20, all models (including
the fourth-order model) are in good agreement up toapproximately 0.5 mm or four ply thicknesses from this
point. As the shear plane is approached (i.e. as we move
to the base of the vertical axis in the graph), the stress
increases with increasing radial mesh density, with no
evidence of convergence. As pointed out by Andersson
Fig. 20. Radial stress distribution at the hole along a line in the bearing plan
left). Stresses calculated at a joint displacement of 0.5 mm using the homoge
[44], displacements near locations where edge contact
occurs are of the type
u � rk; Re½k� < 1 ð1Þwhere r is the distance to the edge and k is the singular
exponent which depends on the position along the edge.
Hence, stresses and strains are infinite at these locations
for arbitrarily small loads, and the quality of the finite
element solution is very poor in such regions unless very
refined meshes are employed. If refined meshes are not
feasible, great care is needed when using stresses closeto the singular region for computing failure criteria or
stress concentration factors. The stress singularities are
examined further in Part II of this paper.
4.4.3.2. Layered models. A plot of the radial stresses in
each ply at the hole along the same line as in the previ-
ous section is shown in Fig. 21. The stresses were ob-
tained from the current layered model by averaging
the radial stress values from the two integration points
nearest the bearing plane. As can be seen, agreement be-
tween the current model and the fourth-order model
with layered properties from [44] is excellent for the0�, +45� and �45� plies and not so good for the 90�plies. However, since the 90� plies are under very low
stress due to their low transverse stiffness, the result
was considered acceptable. The 0� plies are under the
highest stress in the bearing plane which is due to their
high stiffness in the loading direction. The +45� and
�45� plies are under considerably less stress, but inter-
estingly, the stresses in the +45� plies are slightly higherthan the �45� plies. This could be due to the joint twist-
ing which may cause the bolt to tilt slightly toward the
+45� direction, but is more likely due to the +45� pliesbeing located closer to the shear plane; the contact pres-
sure is highest at the shear plane and drops off through
the thickness of the joint [19]. It is interesting to note
that the average of the layered stresses in Fig. 21 is
e going from the shear plane to the free face of the joint (see picture at
neous model.
Fig. 21. Radial stress distribution at the hole along a line in the bearing plane going from the shear plane to the free face of the joint (see picture at
left). Stresses calculated at a joint displacement of 0.5 mm using layered model.
156 M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158
approximately equal to the homogeneous result in Fig.20.
5. Concluding remarks
In this first of a two-part paper, a finite element mod-
el of a single-lap, single-bolt composite joint has been
developed, and validated against experimental resultsand results from other finite element analysis solutions.
The model has been developed for a study of the effects
of bolt–hole clearance which will be presented in detail
in Part II of the paper. A number of factors were found
to affect the accuracy and efficiency of the solution.
The joint was modelled using MSC.Marc. Efficiency
was improved by defining contact bodies as sub-parts
of the joint components, and using a contact table to de-fine which contact bodies could come into contact. For
joints with very small clearances, the contact tolerance
had to be carefully chosen, and single-sided contact
needed to be used. Use of single-sided contact placed
restrictions on the meshing of the different joint parts,
and the order in which contact bodies were defined.
The mesh also had to be adjusted to minimise passing
through of ‘‘overhanging nodes’’. Finally, it was foundto be vital to choose the analytical contact option, which
fits a smooth surface through the contact body.
A number of joints were strain gauged and the fol-
lowing effects were found in both the experiments and
simulations. Significant amounts of bending of the lam-
inates occurred (termed ‘‘secondary bending’’), so that
the external surface of the joint was in compression, de-
spite the tensile loading applied to the joint. Double-cur-vature of the surface was detected, indicating the joint
was saddling like a wide beam in bending. The joint
was also found to twist slightly about its longitudinal
axis. The surface strain distribution was found to be
unaffected by bolt–hole clearance, except for close to
the loaded side of the hole.
The axial stiffness of the joint was measured using anumber of different methods. Obtaining an accurate
measure of the joint displacement proved to be difficult
for this single-lap configuration.
Comparisons between the strains from an initial
‘‘Base Model’’ and the experiments revealed good agree-
ment for axial strain in the laminate and compressive
strain behind the hole, but an overestimation of the
bending stiffness by the model. The axial joint stiffnesswas also too high in the model.
A parameter study was carried out in an effort to im-
prove the correlation with experiment, without incurring
an excessive penalty in computational cost. The factors
that most improved the model were a refined non-over-
lap region, use of the assumed strain formulation with
first-order elements, implementing a routine to allow
separate tensile and compressive properties, and model-ling the clamped area of the joint. These factors were
incorporated into an ‘‘Improved Model’’, and signifi-
cant improvement in correlation with experimental
strain values and axial joint stiffness was obtained. The
computational cost of these improvements was relatively
small. The most detrimental effect on computational
cost occurred when the number of elements in contact
was increased, or when second-order elements were incontact.
A comparison was made with two other finite element
models from partners in the BOJCAS project [26], using
different finite element codes. Axial joint stiffness was
similar for all three models, and the degree of secondary
bending and twisting about the longitudinal axis of the
joint found here was in close agreement with the model
in [44]. Surface strains from the Improved Model tied upvery closely with a model with over 106 degrees of free-
dom in [44]. Thus further mesh refinement would not
lead to improved correlation with the experiment in
terms of bending properties. Possible ways to improve
the correlation may be to modify the boundary condi-
tions to better represent the actual gripping conditions
M.A. McCarthy et al. / Composite Structures 71 (2005) 140–158 157
or to model the resin-rich layers in the composite, which
might allow some relative movement between plies.
Implementation of a non-linear shear constitutive rela-
tionship might also improve the behaviour of the off-
axis plies.
Concerning stresses at the hole, it is important to rec-ognise the presence of singularities in the model. These
singularities actually exist in several places, i.e. at the
washer–bolt, washer–laminate, and bolt–laminate inter-
faces, and interfaces between plies (at hole surfaces).
Great care is needed when using stresses close to the sin-
gular regions for computing failure criteria or stress con-
centration factors. The stresses at the hole were
compared with the very refined model in [44] using bothhomogeneous and layered properties. The values in the
present models were found to agree closely with the val-
ues in [44] at distances approximately 4 ply thicknesses
away from the shear plane where a singularity occurs.
With radial mesh refinements, the stresses at the shear
plane approached those in [44], although it should be
recognised that the stresses are in fact infinite at this
location. Radial stresses were found to be much higherin the plies oriented in the loading direction than in
other plies, as expected.
Overall, it has been found that three-dimensional fi-
nite element models of composite bolted joints capable
of being run in reasonable timeframes on standard PC
hardware, can produce results in close agreement with
experiment and much more refined models, in all re-
spects except stresses close to singular locations.Three-dimensional effects such as bolt tilting, secondary
bending and through-thickness variations in stress and
strain are well represented by such models. However,
the process is far from routine and requires careful con-
sideration of many issues.
Acknowledgements
‘‘BOJCAS—Bolted Joints in Composite Aircraft
Structures’’ is a RTD project partially funded by the
European Union under the European Commission
GROWTH programme, Key Action: New Perspectives
in Aeronautics, Contract No. G4RD-CT99-00036’’.
The authors would like to thank the following: the EU
for funding the project; and the BOJCAS partners formany helpful discussions.
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