marc mentat fem.pdf

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.


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.


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).


‘‘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


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.


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.


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


Improved Model C4


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


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.


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.


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.


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).


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].


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.


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.


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


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.

References

[1] Madenci E, Ileri L. Analytical determination of contact stresses in

mechanically fastened composite laminates with finite boundaries.

Int J Solids Struct 1993;30(18):2469–84.

[2] Xiong Y. An analytical method for failure prediction of multi-

fastener composite joints. Int J Solids Struct 1996;33(29):

4395–409.

[3] Hyer MW, Klang EC, Cooper DE. The effects of pin elasticity,

clearance, and friction on the stresses in a pin-loaded orthotropic

plate. J Composite Mater 1987;21(3):190–206.

[4] Kradinov V, Barut A, Madenci E, Ambur DR. Bolted double-lap

composite joints under mechanical and thermal loading. Int J

Solids Struct 2001;38:7801–37.

[5] Fan WX, Qiu CT. Load distribution of multi-fastener laminated

composite joints. Int J Solids Struct 1993;30(21):3013–23.

[6] Chutima S, Blackie AP. Effect of pitch distance, row spacing, end

distance and bolt diameter on multi-fastened composite joints.

Composites Part A 1996;27(2):105–10.

[7] Rowlands RE, Rahman MU, Wilkinson TL, Chiang YI. Single

and multiple bolted joints in orthotropic materials. Composites

1982;13(3):273–9.

[8] Pradhan B, Kumar R. Stresses around partial contact pin-loaded

holes in FRP composite plates. J Reinf Plastics Composites

1984;3(1):69–84.

[9] Naik RA, Crews Jr JH. Stress analysis method for a clearance-fit

bolt under bearing loads. AIAA J 1986;24(8):1348–53.

[10] Ramamurthy TS. New studies on the effect of bearing loads in

lugs with clearance fit pins. Composite Struct 1989;11:135–50.

[11] Kim SJ, Kim JH. Finite element analysis of laminated composite

plates with multi-pin joints considering friction. Comput Struct

1995;55(3):507–14.

[12] Ko HY, Kwak BM. Contact analysis of mechanically fastened

joints in composite laminates by linear complementarity problem

formulation. Composite Struct 1998;40(3–4):187–200.

[13] Lanza Di Scalea F, Cappello F, Cloud GL. On the elastic

behaviour of a cross-ply composite pin-joint with clearance fits.

J Thermoplastic Composite Mater 1999;12:13–22.

[14] Pierron F, Cerisier F, Grediac M. A numerical and experimental

study of woven composite pin-joints. J Composite Mater

2000;34(12):1028–54.

[15] Matthews FL, Wong CM, Chryssafitis S. Stress distribution

around a single bolt in fibre reinforced plastic composites. Lon-

don: Butterworth; 1982. p. 316–22.

[16] Marshall IH, Arnold WS, Wood J, Mousley RF. Observations on

bolted connections in composite structures. Composite Struct

1989;13:133–51.

[17] Benchekchou B, White RG. Stresses around fasteners in compos-

ite structures in flexure and effects on fatigue damage initiation.

Part 1: cheese-head bolts. Composite Struct 1995;33(2):95–108.

[18] Oh HH, Kim YG, Lee DG. Optimum bolted joints for hybrid

composite materials. Composite Struct 1997;38:329–41.

[19] Ireman T. Three-dimensional stress analysis of bolted composite

single-lap joints. Composite Struct 1998;43:195–216.

[20] Camanho PP, Matthews FL. A progressive damage model for

mechanically fastened joints in composite laminates. J Composite

Mater 1999;33(24):2248–80.

[21] Camanho PP, Matthews FL. Delamination onset prediction in

mechanically fastened joints in composite laminates. J Composite

Mater 1999;33(10):906–27.

[22] Chen WH, Lee SS, Yeh JT. Three-dimensional contact stress

analysis of a composite laminate with bolted joint. Composite

Struct 1995;30:287–97.

[23] McCarthy MA, McCarthy CT. Finite element analysis of

the effects of clearance on single shear, composite bolted joints.

J Plastics, Rubbers Composites 2003;32(2):65–70.

[24] Lessard BL, Shokrieh MM, Esbensen JH. Analysis of stress

singularities in laminated composite pinned/bolted joints. In: 38th

International SAMPE Symposium 1993. p. 53–60.

[25] Persson E, Madenci E, Eriksson I. Delamination initiation of

laminates with pin-loaded holes. Theor Appl Fracture Mech

1998;30:87–101.

[26] McCarthy MA. BOJCAS: bolted joints in composite aircraft

structures. Air Space Eur 2001;3/4(3):139–42.


[27] Hart-Smith LJ. Bolted joints in graphite–epoxy composites.

NASA Contractor Report, 1976 [NASA CR-1444899].

[28] Nelson WD, Bunin BL, Hart-Smith LJ. Critical joints in large

composite aircraft structures. Army Materials and Mechanics

Research Centre Manuscript Report, 1983 [AMRC MS 83-2].

[29] Garbo SP, Ogonowski JM. Effect of variances and manufacturing

tolerances on the design strength and life of mechanically fastened

composite joints: vol. 3—bolted joint stress field model (BJSFM)

computer program user�s manual. AF Wright Aeronautical

Laboratories Technical Report, 1981 [AFWAL-TR-81-3041].

[30] Rankumar RI, Tossavainen EW. Bolted joints in composite

structures: design, analysis and verification—single fastener joints.

AF Flight Dynamics Laboratory, Wright–Patterson AFB, 1984

[AFWAL-TR-84-3074].

[31] DODSSP, Polymer matrix composites, MIL-HDBK-17, DOD-

SSP, Naval Publications and Forms Center, Standardization

Documents Order Desk, Building 4D, 700 Robbins Ave., Phila-

delphia, PA [19111-5094].

[32] Shyprykevich P. Characterization of bolted joint behaviour: MIL-

HDBK-17 accomplishments at standardization. J Composites

Technol Res 1995;17(3):260–70.

[33] ASTM standard D 5961/D 5961M-96, Standard Test Method for

Bearing Response of Polymer Matrix Composite Laminates, 1996.

[34] DiNicola AJ, Fantle SL. Bearing strength behaviour of clearance-

fit fastener holes in toughened graphite/epoxy laminates. In:

Camponeshi Jr ET, editor. Composite materials: testing and

design. ASTM STP 1206, vol. 11. Philadelphia: American Soci-

ety for Testing and Materials; 1993. p. 220–37.

[35] McCarthy MA, Lawlor VP, Stanley WF, McCarthy CT. Bolt–

hole clearance effects and strength criteria in single-bolt, single-

lap, composite bolted joints. Composites Sci Technol

2002;62:1415–31.

[36] Lawlor VP, Stanley WF, McCarthy MA. DFC-6 Conference

Proceedings, 2001. p. 377–86.

[37] Tong L. Bearing failure of composite bolted joints with non-

uniform bolt to washer clearance. Composites Part A

2000;31:609–15.

[38] Herringtion PD, Sabbaghian M. Effect of radial clearance

between bolt and washer on the bearing strength of composite

bolted joints. J Composite Mater 1992;26(12):1826–43.

[39] Lawlor VP. PhD Thesis. Ireland: University of Limerick; 2004.

[40] Friberg M. Personal communication. SAAB; 2000.

[41] MSC.Marc User�s Manual, vol. A: theory and user information.

MSC.Software Corporation; 2000.

[42] Swanson SR. Anticlastic effects and the transition from narrow to

wide behaviour in orthotropic beams. Composite Struct

2001;53:449–55.

[43] Hachenberg, Personal communication. Airbus Deutschland; 2001.

[44] Andersson B. A splitting method for fast solution of 3D contact

problems in bolted joints (interim report). Deliverable Number

D4.3-5, BOJCAS, EU Contract # G4RD-CT-1999-00036, Pro-

gramme: GROWTH, New Perspectives in Aeronautics; 2001.

[45] Ekh J. Three-dimensional stress analysis (interim report).

Deliverable Number D4.1-1, BOJCAS, EU Contract # G4RD-

CT-1999-00036, Programme: GROWTH, New Perspectives in

Aeronautics; 2001.

marc mentat fem.pdf

Documents

analysis of composite

nite element methods

nite element solutions

composite graphiteepoxy

introductionbolted joints

nite element parameter

threedimensional analysis

composite bodevelopmentm