Numerical analysis for the influence of the geometrical and mechanical parameters on the stiffness and strength of the composite bolted joints

Abstract

The paper deals with the influence of the geometric (joint clearance) and mechanical parameters (bolt preload, axial force applied to the joint) on the stiffness and strength of the single-bolt, single-shear laminated composite joints using epoxy resin and carbon fibers reinforcement. In the first part of the paper, the finite element model is presented, using three-dimensional elements for studding the influence of the geometric and mechanical parameters on the stiffness of the joint. In the second part, the microscopic failure of the constituent layers using the Hashin failure criterion for composite materials is presented, as well as the influence of the studied parameters on the occurrence of the first lamina failure and the progressive failure phenomenon from the microscopic to the macroscopic level of the joint.

Full text

INCAS BULLETIN, Volume 10, Issue 4/ 2018, pp. 21 – 33 (P) ISSN 2066-8201, (E) ISSN 2247-4528
Numerical analysis for the influence of the geometrical and
mechanical parameters on the stiffness and strength of the
composite bolted joints
Calin-Dumitru COMAN*
*Corresponding author
INCAS – National Institute for Aerospace Research “Elie Carafoli”,
B-dul Iuliu Maniu 220, Bucharest 061126, Romania,
coman.calin@incas.ro
DOI: 10.13111/2066-8201.2018.10.4.3
Received: 11 July 2018/ Accepted: 19 September 2018/ Published: December 2018
Copyright © 2018. Published by INCAS. This is an “open access” article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: The paper deals with the influence of the geometric (joint clearance) and mechanical
parameters (bolt preload, axial force applied to the joint) on the stiffness and strength of the single-
bolt, single-shear laminated composite joints using epoxy resin and carbon fibers reinforcement. In the
first part of the paper, the finite element model is presented, using three-dimensional elements for
studding the influence of the geometric and mechanical parameters on the stiffness of the joint. In the
second part, the microscopic failure of the constituent layers using the Hashin failure criterion for
composite materials is presented, as well as the influence of the studied parameters on the occurrence
of the first lamina failure and the progressive failure phenomenon from the microscopic to the
macroscopic level of the joint.
Key Words: Stiffness, Strength, FEM, Nonlinear Shear Deformation Progressive Failure Criteria,
Bolted Joints
1. INTRODUCTION
Bolted joints represent critical elements in the design of efficient and safe composite carbon
fiber (CFRP) structures. As joints may be the weak points in an aircraft structure, an inadequate
design can have a considerable influence on the integrity and sustainability of the structure.
The stresses and deformations for single-shear bolted joints are three-dimensional due to
factors such as bending and twisting of the bolt, bolt preload and secondary bending of the
joint [1]. Particularly, in the case of composite joints, the stress field is three-dimensional in
the hole vicinity due to the presence of peel stresses in composite plate and the bearing mode
of failure is influenced by these three-dimensional phenomena.
These joints were studied analytically [2], numerically [3-5] and only a few were tested
experimentally [6, 7], but despite of the three-dimensional phenomena, most of these studies
treated the composite joints two-dimensionally. From these studies some conclusions were
made regarding the stress distribution around the hole. The contact surface between the bolt
and hole was seen to be significantly reduced with the hole oversize, resulting in high radial
and bearing stresses [8, 9]. It has been noticed that the contact surface increases with the force
applied to the clearance joints, but not in the case of the neat-fit joints [8]. The location of the
maximum circumferential stress depends on the joint clearance. Generally, it was observed

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near the contact area [10-14]. Hyer et al. [15] showed that the direction on which the maximum
circumferential stress is obtained varies with the joint clearance, which could affect the joint
strength.
The influence of clearance on the circumferential stress depends on the friction between
the composite plates [16-25], this influence being less than that on the radial stress.
Negative tangential stress values were also observed in the bearing plane, in front of the
bolt, for large joint clearance [7-16].
With the increase of computing power, the 3D approach of these joints was possible, and
such studies started to appear in the literature [5-9]. In these studies, the laminated composite
plates were modeled with one or more solid elements per each lamina or with solid elements
incorporating multiple lamina layers taking into account the variation in thickness of joint
stiffness, the contact between the bolt and the hole being neglected, but with the introduction
of constraints in displacements for the nodes on the surface of the hole. For bolt-hole contact
phenomena, nonlinear analysis is used to simulate the nonlinearities at the bolt-hole contact
surface.
In some studies [9], the bolt has been modeled with a perfectly rigid contact surface, or
has been considered elastic and has been modeled with solid 3D elements.
For this study, a finite element model is developed for a single lap, single bolt, composite
joint using PATRAN-NASTRAN commercial software.
This type of composite joint was chosen because it represents very well the secondary
bending phenomenon and the three-dimensional variations of stresses and deformations
around the hole.
It is a standard configuration for mechanical joints with a single shear with composite
materials according to MIL - HDBK 17 [26] and ASTM D 5961 / D, 5961M-96 [27]. In these
standards it is considered that the single-shear joint is more representative than the double-
shear joint in terms of stiffness and strength study.
After the refinement of the FEM (Finite Element Method) model and validation with test
data and other results from the literature, a study on the influence of geometric (joint clearance)
and mechanic (bolt preload) parameters on the stiffness and strength of the joint is presented.
Among the parameters mentioned above, the one that mainly influences the three-
dimensional state of stresses is the clearance and therefore it will be the most studied parameter
in this paper, given that few studies of the influence of this parameter on the joint can be found
in the literature.
2. PROBLEM DESCRIPTION
The joint configuration presented in this paper is a single lap, single bolt composite joint and
has the two composite plates made of material coded HTA / 6376 containing carbon fiber
impregnated in an epoxy matrix, with orthotropic properties given in Table 1, a highly resistant
material used in the aerospace industry.
The stacking (lay-up) of the unidirectional layers is quasi-isotropic in the form of [45/0/-
45 /90]5s, the orthotropic axis been the same as the global coordinate axis, see Fig. 2. The
thickness of each lamina is 0.13 mm forming a 5.2 mm thick laminate.
The geometry of the joint, shown in Fig. 1, is in accordance with ASTM D 5961 M-96
[27] with w / d = 6, e / d = 3 and d / t = 1.6, (bearing failure). The bolt is a hexagonal head,
short threaded, titanium (Ti6Al4V), 8 mm diameter (LN 29943 standard), with the nut (SMS
2175 standard) and washers (LN 9025 standard) made from steel A 4181 grade 8. The torque
level of the bolt is 0.5 Nm, which is the minimum required level for installation.

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INCAS BULLETIN, Volume 10, Issue 4/ 2018
Fig. 1 - Specimen geometry, [8]
Table 1. Unidirectional stiffness properties for HTA-6376, [8]
E11(GPa)
E22(GPa)
E33(GPa)
G12(GPa)
G13(GPa)
G23(GPa)
12
13
23
140
10
10
5.2
5.2
3.9
0.3
0.3
0.5
The joint clearances considered in this study are shown in Table 2. For a hole with a
nominal diameter of 8 mm, these clearances represent approximately 0%, 1%, 2% and 3% of
the nominal bolt diameter, being coded as C1- C4.
The first two clearances are in the field of aerospace tolerances and the last two correspond
to automotive industry.
Table 2. Joint clearance codes
Code
Nominal joint clearance (µm)
C1
0
C2
70
C3
140
C4
210
The FEM model is presented in Fig. 2, where five solid bodies are modeled with HEXA
8 solid elements (brick element with 8 nodes): two composite plates, two washers and the bolt-
nut coupling.
Regarding the composite plate’s lay-up model, there are ten solid elements per plate
thickness, each element incorporates four layers in Z direction (layer number 1 is on the bottom
surface of the plate and the 40th layer is on the upper surface). The interaction between these
bodies has been modeled using rigid RBE (Rigid Bar Element) elements representing a non-
linear contact.
To ensure the convergence of the nonlinear analysis, the degree of freedom for rigid
movements of the washers, the bolt and the upper plate were blocked using special coupling
(CELAS 1) elements with very low stiffness (10 N / mm) connecting these solids to each other.
Regarding the boundary conditions of the FEM model, the nodes from the left end of the

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INCAS BULLETIN, Volume 10, Issue 4/ 2018
bottom plate have the translations degrees of freedom blocked on all axis of the Cartesian
coordinate system, while the nodes from the right end of the upper plate have the blocked
translation degree of freedom only on Y and Z axis, see Fig. 2.
Fig. 2 - FEM model, boundary conditions and load
3. INFLUENCE OF THE CLEARANCE ON JOINT STIFFNESS
This study is performed for two cases of the clearances, namely C1 and C4 for a variable
applied force between 0-14 kN. Fig. 3 shows the force-displacement curves obtained
experimentally.
The force in the diagram represents the force transmitted by the bolt (shear force of the
bolt) and the displacement is imposed by the test machine. Some conclusions can be extracted
from Fig. 3:
• The reduction of the straight line approximation slope (stiffness) is evident with the
increase of joint clearance (case C4).
• In the C4 case, the joint tends to stiffen for bolt force values between 5 and 9 kN, the
curve is above the approximate straight line.
• Both experimental and numerical simulation results show a delay for force reacting
by the bolt in C4 case. This phenomenon is due to the joint clearance, because,
initially, the shear force is transmitted by friction forces between the plates, joint being
in “friction grip” condition and, after the joint tensile load exceeds the frictional force
between the plates, their relative displacement appears until the clearance is
consumed. After consuming the clearance and establishing the contact between the
bolt and the hole surface, the bolt starts to transmit the shear force, and the joint is in
'bearing joint' condition.
• Although the numerical simulation anticipates an axial stiffness of the joint greater
than that determined by the tests, the trend of the two diagrams is the same.
• The numerical simulation does not predict the decrease of the stiffness at high force
values as a result of the occurrence of local material failure phenomenon, because the
simulation was performed in the linear elastic domain of the material properties.
Table 3 shows the variation in the axial stiffness of the joint for all C1-C4 cases of the
clearance.

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Numerical analysis for the effects of geometric and mechanic parameters on joint stiffness and strength
INCAS BULLETIN, Volume 10, Issue 4/ 2018
Fig. 3 - Load-displacement curves for C1 and C4 joint clearance cases: (a)-experiment [8], (b)-simulation
Table 3. Joint Stiffness for C1-C4 clearance cases
Case
C1
C2
C3
C4
Simulation (kN/mm)
33.25
32.86
31.15
30.27
Relative error from C1 case
-
-1.2%
-6.3%
-8.9%
From Table 3 it results that the joint axial stiffness decreases if the joint clearance
increases and the numerical simulation provides a sufficiently precise prediction of this
phenomenon.

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4. INFLUENCE OF BOLT PRELOAD ON JOINT STIFNESS
In this chapter, three values of the axial bolt preload, 100 N, 500 N and 1000 N, respectively,
are considered to avoid composite damage while the tensile force applied to the joint varies
between 0-14 kN.
The effect of bolt preload on axial stiffness is presented in Fig. 4.
Fig. 4 - Joint force-displacement curves for preload cases
From Fig. 4 the following aspects can be concluded regarding the influence of the preload
on the axial stiffness of the joint reported in Table 4.
Table 4. Prelaod effect upon joint stiffness
Preload force
100 (N)
500 (N)
1000 (N)
Stiffness
31.4 (kN/mm)
35.2 (kN/mm)
41.3 (kN/mm)
Relative error to case of preload F=100 (N)
-
12 %
31 %
It is clearly seen from Table 4 that the axial stiffness of the joint increases significantly
with the increase of the bolt preload.
5. INFLUENCE OF CLEARANCE ON THE STRESS DISTRIBUTION
AROUND THE HOLE
In this chapter the influence of the joint clearance on the three-dimensional distribution of the
stresses in the upper laminate plate around the hole boundary is presented.
The two C1 and C4 cases of the clearances are also used and the stresses are calculated in
the center of each 3D element for each layer of the laminate. The joint tensile force is 5 kN. A
cylindrical coordinate system with origin located in the center of the hole on the shear plane

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Numerical analysis for the effects of geometric and mechanic parameters on joint stiffness and strength
INCAS BULLETIN, Volume 10, Issue 4/ 2018
will be used, thus the stresses will be calculated in the radial and tangential directions on the
hole surface and the angle α varies from -900 to 900 in (R,T) shear plane.
The radial stress on to the hole surface is presented in Fig. 5.
Fig. 5 - Radial stress around the hole, C1 clearance case
As it can be seen from Fig. 5, the maximum radial stress is located in the layer number 2,
being positioned in the second layer starting from the shear plane in the Z direction and having
a0° orientation relative to the direction of the joint tensile force.
As it can be observed, all 00-oriented laminae are the most loaded in the bearing plane, in
the force direction and the other laminae oriented at + 450 / -450 are most loaded on the
directions of the respective laminae.
The tangential stresses onto the hole surface are also presented in Fig.6. Fig. 6 shows that
the tangential stress is positive for all the laminae, except for some laminae located close to
the free surface of the laminate behind the hole (α = +/- 1800) and these negative values of the
tangential stress are due to the hole deformation, as shown in Fig. 7.

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Fig. 6 - Tangential stress around the hole in C1 case
The maximum value of the tangential stress corresponds to the laminae oriented at 00 in
the transversal plane in front of the hole.
In the C1 clearance case, the maximum tangential stress for each layer in the laminate are
located along the contour of the hole in the zones where the laminae are stiffen in the tangential
direction.
The radial stresses for the C4 case of the clearance are shown in Fig.8. As in the case of
C1, the maximum values are located in the 00-oriented laminae located in the vicinity of the
shear plane, but the maximum stress value is much higher in this case.
Fig. 7 - Hole deformation: (a) C1 case, (b) C4 case

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INCAS BULLETIN, Volume 10, Issue 4/ 2018
Fig. 8 - Radial stress around the hole in C4 case
The maximum radial stresses in the + 45o / -45o layers are not located in areas with higher
stiffness, as in case of C1, but for values of angle α = + 15o / -15o as the contact pressure is
applied to a lower surface for C4 than C1 case, however, the radial stress values are higher
than C1. Laminae oriented at 90° are very little radially stressed onto the boundary of the hole.
6. EFFECT OF BOLT PRELOAD ON THE STRES DISTRIBUTION
AROUND THE HOLE
The influence of the bolt preload on the 3D distribution of the radial stress onto the upper plate
hole surface, in the C1 clearance case is shown in Fig. 9. From Fig. 9 it can be seen that the
radial stress is maximum in the vicinity of the shear plane (layer 1) and decreases towards the
outer surface of the plate (layer 40).
Fig. 9 - Radial and tangential stress, C1 case, preload F=100 N
The same Fig. 9 shows the effect of bolt preload over the tangential stresses on the surface
of the hole in the upper plate.
It can be observed that the tangential stress decreases on the thickness of the plate starting
from the shear plane to the surface of the plate.

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7. EFFECT OF BOLT PRELOAD ON JOINT STRENGTH
In this study, the Hashin failure theory [28] will be used for both fiber and matrix failure. Since
the joint geometry was chosen for bearing failure, the applied force will not exceed the value
at which this phenomenon first occurs. It is demonstrated (McCarthy et al. [8]) that bearing of
the surface of the hole is determined by the compression failure mode of the fibers, because
this failure mode has an immediate effect on the joint decreasing stiffness. Thus, the
compression of lamina’s fibers is the direct indicator of the initial failure of the joint, although
this phenomenon is accompanied by a considerable extent of a compressive matrix failure.
This study is limited to the influence of the parameters mentioned in the chapter title on the
initial failure of the joint and implicitly limits the maximum load (Limit Load) to that for which
the joint can operate safely. To determine the Ultimate Load failure of the joint, it requires a
progressive damage analysis. The Hashin failure criterion will be evaluated for the elements
located at 0.5 mm distance away from the hole boundary in the radial direction to avoid the
intersection between the shear plane and the surface of the hole where there are numerical
singularities in stress evaluation. The following four constituent failure modes are considered
[28] as follows:
• Tensile matrix failure
σ22+σ33 > 0
(1)
1
S22
T2σ22+σ33 2+1
S23
2σ232-σ22σ33 +1
S12
2σ122+σ132 = 1
(2)
• Compressive matrix failure
σ22+σ33 < 0
(3)
1
S22
CS22
C
2S232
-1σ22+σ33 +1
4S23
2σ22+σ33 2+1
S23
2σ232-
σ22σ33+1
S12
2σ122+σ132=1
(4)
• Tensile fibre failure
σ11 > 0
(5)
σ11
S11
T2
+1
S12
2σ122+σ132 = 1
(6)
• Compressive fibre failure
σ11 < 0
(7)
σ11 = - S11
C
(8)
where σij (i, j = 1, 2, 3) represents the components of the stress tensor, and Sij (i, j = 1, 2, 3) are
the components of the strength tensor of the composite material presented in Table 5.
Table 5. Material strength data for HTA 6376, [8]
S11T(MPa)
S11C(MPa)
S22T(MPa)
S22C(MPa)
S33T(MPa)
S33C(MPa)
S12(MPa)
S23(MPa)
S31(MPa)
2200
1600
70
250
50
300
120
50
120

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The first appearance of fibre and matrix compressive failure for bolt preload, F=100 N,
and joint tensile load Ftensile = 14.5 kN is presented in Fig. 10.
Fig. 10 - First compressive fiber (a) and matrix (b) failure
From Fig. 10 it can be seen that the first fiber compression is located in the fourth layer
(oriented to 450), upward from the shear plane. It can also be noticed that even compression
of the matrix has not changed its position. Fig. 11 shows the appearance of the first fiber and
matrix compression failure for bolt preload F=500 N. Although the matrix failure area is wider
than the fiber’s failure area the compression mode of the fibers is the macroscopic failure mode
of the joint, since the fibers act as reinforcement and transmits the stresses within the material.
Fig. 11 - First compressive fiber (a) and matrix (b) failure
From Fig. 11 it can be seen that the force value for the first fiber failure decreased from
14.3 kN (for bolt preload F=100 N) to 13.3 kN (for bolt preload F=500 N) and is also located
in a 450 oriented lamina. As a general conclusion of the effect of the bolt preload on material
failure at the microscopic level it can be concluded that the bolt preload limits the maximum
axial force (Limit Load) that can be transmitted by a safe joint.
8. CONCLUSIONS
The geometric (joint clearance) and mechanical (bolt preload) parameters study for the effects
on the stiffness, stress distribution on the hole surface and strength of a single lap, single bolt
composite joint is presented in this paper using a detailed 3D finite element model. This model
was validated by comparison with the experimental results. Given the stresses around the hole,
it was noted the presence of numerical singularities in the model, which implies limitations of
the model and must be treated carefully. These singularities exist at the interface between
various components of the joint such as bolt-washer, composite plates-washers, composite
plates-bolt and at lamina interfaces (on the surface of the hole) requiring the caution use of
the stresses in the vicinity of these zones for strength evaluations or local stress concentrators.
Single-shear joints have a non-uniform distribution of stresses on the thickness of the
composite plate and the joint clearance causes the three-dimensional variation of this stress
distribution. The radial and tangential stresses of each lamina were calculated using solid

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layered elements, and it was observed that as the clearance increases, the radial stress increases
in all the laminae. The tangential stress increases also and it was observed that the stress
changes in sign on the bearing plane ("α" = 0o). It was also noticed that the radial stresses are
higher in the force-oriented laminae than in the rest of the plies, which was to be expected.
The joint clearance has been seen to increase the rotation of the bolt, decreasing the contact
surface between the bolt and the hole and reducing the stiffness of the joint. Clearance joints
tend to stiffen with increasing shear force applied which does not happen to joints without
clearance. From Table 5 it can be, clearly, seen the influence of bolt preload on stiffness, the
axial stiffness of the joint increases significantly with the preload. Taking the extreme values
of bolt preload for comparison, axial stiffness is higher with 31%, which is a considerable
contribution to the overall stiffness of the joint. As a conclusion of the influence of bolt preload
on the state of stress onto the surface of the hole, it can be emphasized that the preload has a
dual effect, firstly reduces the maximum values of the tangential and radial stresses but also
reduces the area on which the most majority of these higher values of stresses develop.
Using the Hashin failure criteria, carbon fiber compression failure was studied, around
the hole, determining the Limit Load for bearing failure. For all cases of the clearance in the
joint there was a considerable failure of the composite matrix behind the hole. Matrix failure
was originally caused by negative radial stresses (compression) in front of the bolt and
negative tangential stresses behind the hole. Expanding matrix failure may affect failure
propagation phenomena within the laminate and a progressive failure analysis should be
performed to study this phenomenon. In conclusion, for single shear joints, both joint clearance
and bolt preload have a significant influence on the stiffness and the initial failure (initial
strength) of the joint, representing a reference frame for later investigation of the crack
propagation around the hole in composite material using progressive analysis. Therefore, the
two parameters chosen for the study have proved to be of major importance in the optimal
design process of a composite joint and should be used with caution in complex models such
as aerospace structures.
The novelty of the paper is determined by the few aspect as the methodology for
development of the material composite modelling using advanced tridimensional solid-layered
elements available only in SOL 400 solver from NASTRAN software. Another novel aspect
of the paper is explicit nonlinear analysis taking into account the full friction based contact
nonlinearity. As well as the conclusions regarding the bolt preload effects on the composite
joint stiffness and on the FPF (First Ply Failure) analysis contribute on the scientific value of
the article.
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