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. Ó 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 structural integrity 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, 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 Composite Structures 71 (2005) 140–158 www.elsevier.com/locate/compstruct 0263-8223/$ - see front matter Ó 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.
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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.
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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