Behavior of Fastened and Adhesively Bonded Composites Under Mechanical and Thermomechanical Loads
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Transcript of Behavior of Fastened and Adhesively Bonded Composites Under Mechanical and Thermomechanical Loads
BEHAVIOR OF FASTENED AND ADHESIVELY BONDED COMPOSITES UNDER MECHANICAL AND THERMOMECHANICAL LOADS
by
VINAYSHANKAR LINGAPPA VIRUPAKSHA
A dissertation submitted in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY IN MECHANICAL ENGINEERING
2008
Oakland University Rochester, Michigan
Doctoral Advisory Committee:
Sayed A. Nassar, Ph.D., Chair LianXiang Yang, Ph.D. Meir Shillor, Ph.D. Michael P. Polis, Ph.D.
UMI Number: 3333081
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© Copyright by Vinayshankar Lingappa Virupaksha, 2008 All rights reserved
To my dearest mother and father, Sarvamangala and Virupaksha
ACKNOWLEDGMENTS
I would like to express my sincere gratitude and appreciation to my adviser,
Professor Sayed Nassar. His wide knowledge and experience have been of great value
for me. His understanding, encouraging and personal guidance have been helpful and
invaluable.
I am grateful to my advisory committee members, Professor Michael Polis,
Professor LianXiang Yang and Professor Meir Shillor, for their valuable time and
suggestions. Special thanks to Professor Garry Barber and Dr. Forest Wright for
providing me the first job in United States of America.
I would like to thank all the staff members of Department of Mechanical
Engineering for their support through out my stay at Oakland University.
I thank all my friends and student colleagues for providing me the required social
and academic challenges, and diversions. I devote special thanks to all my relatives for
their love, support, and encouragement.
Last, but not least, I am very thankful to my family: my mother, Sarvamangala,
my father Virupaksha and my brother Dr.Vijayshankar Virupaksha for their
unconditional support and encouragement to pursue my interests, even when the interests
went beyond boundaries of languages, geography and field. Their love and devotion
throughout my life gave me the strength to accomplish my goals.
Vinayshankar Lingappa Virupaksha
iv
PREFACE
This document outlines the research conducted to complete the doctoral
dissertation entitled "Behavior of fastened and adhesively bonded composites under
mechanical and thermomechanical loads". It is submitted in partial fulfillment of the
requirements for the degree of Doctor of Philosophy in Mechanical Engineering at
Oakland University. The document is organized in the following manner:
Chapter 1: Introduction and Literature Review, gives the background of adhesive
bonding and mechanical fastening of polymeric composite materials. This chapter
outlines the previous research on interfacial stress analysis in adhesive bonded joints, and
bolt bearing behavior in composite bolted joints. It briefly describes the limited
analytical and experimental work in this field of study. Finally it presents the motivation
and the objective of this work.
Chapter 2: Effect of Adhesive Thickness and Properties on the Bi-axial Interfacial
Shear Stresses in Bonded Joints Using a Continuum Mixture Model, introduces a new
analytical model which predicts the interfacial shear stresses due to thermomechanical
loading in an adhesively bonded joints. Finite Element Analysis is further carried out to
validate the analytical model results.
Chapter 3: Effect of Washers and Bolt Tension on the Behavior of Thick
Composite Joints, presents an experimental investigation of the effect of washer
geometry and initial bolt preload on the strength and stiffness of thick composite bolted
joints. Joint clamp load is monitored in real time to correlate the bearing behavior.
v
Further, failure analysis is carried out to analyze the progression of bearing failure in
composite laminates.
Chapter 4: Effect of Bolt Tightness on the Behavior of Composite Joints, presents
an experimental investigation of the effect of various bolt tightness combinations on the
strength and stiffness of double bolted single lap joints. Further a progressive failure
analysis is carried out to analyze the bearing failure for different tightening combinations.
Finally, a 3-dimensional finite element analysis is carried out to validate the behavior of
double bolted joints.
Chapter 5: Conclusions and Future Work
VI
ABSTRACT
BEHAVIOR OF FASTENED AND ADHESIVELY BONDED COMPOSITES UNDER MECHANICAL AND THERMOMECHANICAL LOADS
by
Vinayshankar Lingappa Virupaksha
Adviser: Sayed A Nassar, Ph.D.
The safety and structural integrity of composite structures are determined by their
respective joints, which may be either adhesively bonded or mechanically fastened. The
strength and reliability of adhesively bonded joints are significantly influenced by
interfacial stresses. In the same way the strength and reliability of mechanical fastened
joints depend on its laminate bolt bearing strength. In the first part of this dissertation, an
analytical model based on continuum mixture theories is developed to study the
interfacial shear stresses in adhesively bonded joints. In the second part, experimental and
finite element investigations are carried out to study the bolt bearing behavior in
composite bolted joints.
The analytical model for adhesive bonded joints predicts the effect of adhesive
thickness and properties on the bi-axial interfacial shear stresses due to
thermomechanical loading. The interfacial shear stresses between the adhesive and each
adherend is determined using the constitutive equations. Numerical results show that
both the adhesive thickness and the material properties have a significant effect on the
thermomechanically induced interfacial shear stresses between the adherends and the
vii
adhesive. The developed model inherently has the capacity for optimizing the selection
of the adhesive thickness and material properties that would yield a more reliable bonded
joint.
For the composite bolted joints, experimental and finite element investigations are
carried out to study the affect of bolt-load level, washer geometry and bolt tightness on
the bolt bearing behavior. A double lap shear joint is considered to study the effect of
bolt-load levels and washer geometry, while a double bolted single lap shear joint is
considered to study the effect of bolt tightness and joint material on the bearing behavior
of composite bolted joints. Finite element analysis using a commercially available code
ABAQUS ® is used to validate the experimental results. Failure analysis using optical
microscope and digital photography is conducted to analyze the progression of bearing
failure in composite laminates.
viii
TABLE OF CONTENTS
ACKNOWLEDGMENTS iv
PREFACE v
ABSTRACT vii
LIST OF TABLES xiii
LIST OF FIGURES xiv
CHAPTER ONE INTRODUCTION AND LITERATURE REVIEW 1
1.1 Background on Adhesively Bonded Joints and Interfacial Stresses 1
1.1.1 Failure Modes in Adhesive Bonded Joints 3
1.2 Previous Research on Interfacial Shear Stresses in Adhesively Bonded Joints 4
1.3 Background on Bolt Bearing Behavior in Polymeric Composite Bolted Joints 15
1.3.1 Failure Modes in Polymeric Composite Bolted Joints 15
1.3.2 Bolt Bearing Behavior in Polymeric Composite Joints 16
1.4 Previous Research on Bolt Bearing Behavior in Polymeric Composite Joints 17
1.4.1 Influence of Coupon Geometry and Laminate Properties on the Bolt Bearing Behavior 17
1.4.2 Effect of Bolt Tightening Torque and Clamping Pressure on Bearing Behavior 23
ix
TABLE OF CONTENTS—Continued
1.4.3 Progressive Failure Mechanism in Composite Bolted Joints 27
1.4.4 Finite Element Analysis of Composite Bolted
Joints 31
1.5 Objective of the Dissertation 34
CHAPTER TWO EFFECT OF ADHESIVE THICKNESS AND PROPERTIES ON THE BI-AXIAL INTERFACIAL SHEAR STRESSES IN BONDED JOINTS USING A CONTINUUM MDCTURE MODEL 41
2.1 Formulation of the Problem 41
2.1.1 Equilibrium and Constitute Equations 42
2.1.2 Continuity Conditions 43
2.1.3 Continuum Mixture Equations 44
2.1.4 Evaluation of the Interaction Terms 46
2.1.5 Relationship between Shear Stresses and Average Displacements 47
2.1.6 Expression for Shear Stresses in Terms of Displacements 50
2.1.7 Governing Differential Equations 5 0
2.1.8 General Solutions for Governing Partial Differential Equations 52
2.1.9 Boundary Conditions 53
2.1.10 Interfacial Shear Stresses 54
2.2 Numerical Results and Discussions 55
TABLE OF CONTENTS—Continued
2.2.1 Finite Element Verification 56
2.2.2 Effect of Elastic Properties of Adhesive 5 8
2.2.3 Effect of Adhesive Thickness 58
2.3 Summary 59
CHAPTER THREE EFFECT OF WASHERS AND BOLT TENSION ON THE BEHAVIOR
OF THICK COMPOSITE JOINTS 76
3.1 Experimental setup and Procedure 76
3.1.1 Materials 77
3.1.2 Test Fixture and Instrumentation 77
3.2 Results and Discussion 80
3.2.1 Effect of Bolt Preload 81
3.2.2 Effect of Washer Size and Thickness on
Bearing Behavior 83
3.2.3 Clamp Load Variation 84
3.2.4 Failure Analysis 86
3.3 Summary 87
CHAPTER FOUR EFFECT OF BOLT TIGHTNESS ON THE BEHAVIOR OF
COMPOSITE JOINTS 109
4.1 Experimental Set-up and Procedure 109
4.1.1 Experiments 110
XI
TABLE OF CONTENTS—Continued
4.1.2 Progressive Damage Analysis 111
4.2 Experimental Results and Discussion 112
4.2.1 Effect of Fastener Tightness Condition 112
4.2.2 Effect of Joint Materials 114
4.2.3 Failure Mode Progression 115
4.3 Finite Element Modeling 116
4.4 Summary 118
CHAPTER FIVE
CONCLUSIONS AND FUTURE STUDY 139
5.1 Conclusions 139
5.1.1 Effect of Adhesive Thickness and Properties on the Bi-axial Interfacial Shear Stresses in Bonded Joints Using a Continuum Mixture Model 139
5.1.2 Effect of Washers and Bolt Tension on the Behavior of Thick Composite Joints 139
5.1.3 Effect of Bolt Tension on the Behavior of
Composite Joints 140
5.2 Future Work 141
REFERENCES 142
xii
LIST OF TABLES
Table 2.1 Material properties of Boron and Carbon Phenolic Laminate 60
Table 3.1 Initial bolt-load and corresponding clamping pressure for
small and large washer j oints 8 8
Table 3.2 Bearing properties of single large washer composite joints 89
Table 3.3 Bearing properties of single small washer composite joints 90
Table 3.4 Bearing properties of double large washer composite joints 91
Table 3.5 Bearing properties of double small washer composite joints 92
Table 4.1 Material properties of joint components 120
xm
LIST OF FIGURES
Figure 1.1 Example of an adhesively bonded joint 36
Figure 1.2 Shear stresses and peel stresses in an adhesive bonded joint 36
Figure 1.3 Shear stresses due to difference in coefficient of thermal
expansion 37
Figure 1.4 Failure modes in adhesive bonded joints 37
Figure 1.5 Joint parameters in a typical composite bolted joint 38
Figure 1.6 Failure modes in composite bolted joints 39
Figure 1.7 Single bolted double lap shear joint subjected to in-plane
loading 40
Figure 2.1 Geometric model 63
Figure 2.2 Shear stress distribution 64
Figure 2.3 Theoretical shear stress, (xxy), at the upper interface 65
Figure 2.4 FEM shear stress, (xxy), at the upper interface 66
Figure 2.5 Theoretical shear stress, (xzy), at the upper interface 67
Figure 2.6 FEM shear stress, (xZy), at the upper interface 68
Figure 2.7 Theoretical shear stress, (xxy), at the lower interface 69
Figure 2.8 FEM shear stress, (xxy), at the lower interface 70
Figure 2.9 Theoretical shear stress, (xzy), at the lower interface 71
Figure 2.10 FEM shear stress, (x^), at the lower interface 72
xiv
LIST OF FIGURES—Continued
Figure 2.11 Effect of adhesive properties on the shear stress at the upper interface 73
Figure 2.12 Effect of adhesive properties on the shear stress at the lower interface 74
Figure 2.13 Effect of adhesive thickness on the shear stress at the
lower interface 75
Figure 3.1 Geometry of the test coupon 93
Figure 3.2 Experimental double lap-shear test fixture 94
Figure 3.3 Bearing test experimental set-up 95
Figure 3.4 Schematic representation of bearing stress distribution in a pin loaded joint 96
Figure 3.5 Bearing stress Vs. bearing strain curve for a small
washer finger tightened bolted joint 97
Figure 3.6 Bearing stress Vs. strain curve for joints with 50% preload 97
Figure 3.7 Effect of bolt preload on joint bearing stiffness 98
Figure 3.8 Effect of bolt preload on offset bearing strength 98
Figure 3.9 Effect of bolt preload on ultimate joint strength 99
Figure 3.10 Effect of bolt preload on joint strain 99
Figure 3.11 Effect of washer size on bearing stiffness of joints: single washer 100
Figure 3.12 Effect of washer size on bearing stiffness of joints: double washer 100
Figure 3.13 Effect of washer size on offset bearing strength: single washer 101
xv
LIST OF FIGURES—Continued
Figure 3.14 Effect of washer size on offset bearing strength of j oints:
double washer 101
Figure 3.15 Effect of washer area on bearing stress-strain behavior 102
Figure 3.16 Effect of washer thickness on bearing stiffness:
large washer 102
Figure 3.17 Effect of small washer thickness on joint bearing stiffness 103
Figure 3.18 Effect of washer thickness on bearing strength: large washer 103
Figure 3.19 Effect of washer thickness on bearing strength: small washer 104
Figure 3.20 Joint clamp-load variation with joint displacement:
zero bolt preload 104
Figure 3.21 Joint clamp load Vs. displacement: 50% bolt preload 105
Figure 3.22 Joint clamp load Vs. applied axial load: small washers 105
Figure 3.23 Joint clamp load Vs. applied axial load: large washers 106
Figure 3.24 Bearing damage in finger tightened joint coupons 106
Figure 3.25 Bearing damage in various joint coupons with
large washers 108
Figure 4.1 Geometry of single lap, double-bolted joint 121
Figure 4.2 Schematic representation of inspected damage regions 122
Figure 4.3 Load displacement curves for aluminum-composite joints 124
Figure 4.4 Initial portion of the aluminum-composite load-displacement curve 126
xvi
LIST OF FIGURES—Continued
Figure 4.5 Load-displacement curves showing the ultimate
failure load 127
Figure 4.6 Bearing surface delamination for TT-LB joints 128
Figure 4.7 Bearing surface delamination for LT-TB joints 128
Figure 4.8 Bearing surface delamination for LT-LB joints 129
Figure 4.9 Bearing surface delamination for TT-TB joints 129
Figure 4.10 Strength comparison of aluminum-composite and composite-composite TT-TB joints 130
Figure 4.11 Strength comparison of aluminum-composite and composite-composite LT-LB joints 130
Figure 4.12 Initial portion of the load-displacement data for LT-LB joints 131
Figure 4.13 Initial portion of the load-displacement data for
LT-TB joints 132
Figure 4.14 Initiation of bearing failure 133
Figure 4.15 Bearing failure at 70% of ultimate failure load 133
Figure 4.16 Bearing damage just before the ultimate failure 134
Figure 4.17 Finite element model of double bolted composite to
aluminum joint 135
Figure 4.18 Contact surface in the finite element model 135
Figure 4.19 Frictional effect on the load displacement curves 136
Figure 4.20 Comparison ofFEA and experimental results 138
xvii
CHAPTER ONE
INTRODUCTION AND LITERATURE REVIEW
Polymer matrix fiber reinforced laminated composites are widely used in
structural and mechanical components across various industries that include automotive,
aerospace and defense applications. The safety and structural integrity of composite
structures often depend on the integrity and reliability of their respective joints that often
are the weak link in the design. The two main commonly followed joining technologies
are adhesive bonding and mechanical fastening. The strength and reliability of an
adhesively bonded joint depends on their interfacial stresses, while that for mechanical
fastened joints depends on their laminate bolt bearing strength [1]. This dissertation deals
with both the interfacial stresses in adhesively bonded joints, and as well as the bearing
strength in composite bolted joints.
1.1 Background on Adhesively Bonded Joints and Interfacial Stresses
Adhesive bonding is a joining technology where low modulus glue is used as a
bonding agent to join materials. A typical adhesively bonded joint is shown in Figure
1.1. Adhesively bonded joints provide smoother joint surface, hence they are often
preferred in automotive applications. The use of adhesively bonded joints is steadily
increasing due to their corrosion resistance and light weight properties. One
disadvantage of adhesively bonded joints is that they are permanent and cannot be
disassembled. Another drawback of these joints is the uncertainty of long term structural
1
stability due to the lack of standard inspection methodologies for adhesive joint quality.
Joint performance largely depends on the bonded surface preparation, the adhesive
properties, and the adhesive thickness; adhesively bonded joints are also susceptible to
environmental factors such as moisture and high temperature [2].
The main purpose of an adhesively bonded joint is to transfer the loads. These
loads produce interfacial stresses and hence understanding the stress distribution is an
essential part of the design and analysis. The knowledge of stress - strain state in a
bonded joint provides an insight into the joint behavior and potential failure mechanism.
Failure due to adhesive shear stresses or adhesive peel stresses are the most common
failure modes in bonded joints. Figure 1.2 shows the typical shear stress and peel stress
distribution in an adhesive joint. Interfacial shear stresses can be due to mechanical,
thermal or thermo-mechanical loading. Figure 1.2a illustrates how the load is transferred
by shear in the adhesive layer (as seen by the forces on a section of the substrate). As the
load is transferred, the adherend loading decreases and the shear stress is induced on the
adhesive. The shear stress is maximum at the overlap edge and decreases along the
length of the adhesive [3]; shear stresses are critical in ductile failure of adhesive joints
[4]. Figure 1.2b shows the load transfer perpendicular to the adhesive layer. The
adherend deforms less as the load is transferred; this induces stress perpendicular to the
adhesive layer that is known as peel stress. The peel stress is essentially normal stress
that would be critical in brittle failure of adhesive joints. When an adhesively bonded
joint is subjected to temperature changes, the adherends and the adhesive expand and
contract differently resulting in thermal shear stresses. These thermal shear stresses
largely depend on the temperature change and coefficient of thermal expansion (CTE). A
2
material with a higher CTE contracts and compresses the other material when the
temperature is decreased and vice-versa with the increase in temperature. This transmits
the internal load inducing thermal shear stresses through the adhesive thickness, which
decays as the load is transmitted [3], as shown in Figure 1.3. The thermo-mechanically
induced shear stresses in an adhesively bonded joint are more complex due to
superimposition of mechanical and thermal loads. The adhesive and the adherend
thickness, surface topology, taper angle of the adhesive edge, properties of the adhesives
and the adherend are some of the critical factors affecting the behavior of adhesively
bonded joints. Investigating how these factors affect the stresses would help in
improving the reliability of bonded joints.
1.1.1 Failure Modes in Adhesively Bonded Joints
Adhesively bonded joints are usually designed for a bulk failure of the adherends
and not in the adhesive. Failures in laminated composite material are often at the surface
plies of the laminate material (delamination). Care should be taken to ensure that the
adhesive layer does not become the weakest link. Some of the failure modes in bonded
composite/polymer joints are: cohesive failure in the adhesive (known as the failure of
the adhesive layer), adhesive failure at the composite-adhesive interface (known as the
interfacial failure), and failure of the adherend (laminate) known as delamination [5]. The
interfacial failure and the delamination failure is mainly due to the higher interfacial
shear stress. The interfacial shear strength can be obtained from a lap shear test.
However, numerical analysis and analytical model would help understand the distribution
of shear stresses. Cohesive failure in the adhesive usually occurs when the applied loads
3
exceed the intrinsic strength of the adhesive material. This tends to be a localized effect
occurring near stress concentration areas such as the ends of joints. In the laminate
materials such as composites, delamination failure generally initiates from the matrix
between the layers due to out-of-plane peel stresses or interlaminar shear stresses [6].
Other forms of failures such as through thickness tensile cracking can occur if the
composite adherend is not a layered structure. Figure 1.4 shows the failure modes in a
typical adhesively bonded joint.
Some of the critical issues that need to be investigated in adhesively bonded joints
include the prediction of the joint strength, designing the joint parameters, optimizing the
joint performance and inspection of bonded joint quality. Stress analysis tools help
understanding the adhesive and adherend load distribution in a bonded joint [7].
Interfacial stress prediction is one important aspect in the design of an adhesively bonded
structure. Bond breakage/delamination is the most common failure mode in bonded
structures with failure initiating at the adherend adhesive interface. The failure may
occur due to the progression of existing micro cracks or by delamination developed at the
interface. Delamination may be due to thermal, mechanical or thermomechanical loading
and interfacial degradation caused by moisture and other chemical species. Delamination
also occurs when the interfacial stresses from the loading exceed the strength of the
adhesive material.
1.2 Previous Research on Interfacial Shear Stresses in Adhesively Bonded Joints
Stress analysis in an adhesively bonded structure can be carried out using two
approaches, namely, analytical and/or numerical methods such as Finite Element
4
Analysis (FEA). Analytical approaches have been based on the beam model or
continuum model, where a set of differential equations and boundary conditions are
formulated. The solution to these differential equations yields analytical expressions
which give values of the stresses in the joints [7]. The analytical approach for the solution
of interfacial stress distributions in a bonded joint has been progressively refined until
recent times. In numerical solution approach, the solutions of the differential equations
provide displacements at each point from which corresponding strains and stresses can be
computed at each node. Finite element analyses are among the numerical approaches
which have been extensively used in many applications [7]. Published work relating to
experimental, analytical and numerical approaches to evaluate the stresses in an bonded
structures is reviewed in the following section.
One of the earliest stress analysis models were derived by Timoshenko (1925) [8]
based on the elementary beam theory. Timoshenko analyzed only the normal stresses
and assumed it to be unchanged along the length of the bimetal thermostat. The
interfacial stresses were not analyzed but he just mentioned that it is higher at the ends of
the strips. Various approaches to solve for the interfacial stresses were suggested during
the last few decades, mostly in conjunction with the needs of the microelectronics
technology [9]. These approaches were mainly extension of Timoshenko theory and were
based on strength of materials and structural mechanics.
The static analysis were carried out by Nayfeh [10] to estimate the interfacial
shear stresses in composites subjected to combined mechanical and thermal loading.
Multi-cylindrical periodic fibers, single cylindrical fiber, and single planar fiber
reinforcement models were considered in the analysis. Continuum mixture theories for
5
wave propagation, in bilaminated composites by Hegemier et al. [11], yielded a set of
partial differential equations which described the displacement behavior of the
composite. The interfacial shear stresses were calculated from distribution of the
displacements, stresses and the temperatures in each individual constituent. In a
subsequent research [12], Nayfeh and Nassar used a continuum theory developed for
bilaminated composites to study the bonding material influence on the dynamic behavior
of trilaminated composites. Longitudinal wave propagating in the direction parallel to
the layers of the linear elastic, homogeneous and isotropic trilaminated composite was
considered in the problem formulation. In another study, Nayfeh [13] extended the same
methodology in [10] to study the dynamically induced interfacial shear stresses in two-
component fibrous composites.
Nayfeh and Nassar in 1982 [14] studied the influence of bonding agents on the
thermo-mechanically induced interfacial shear stresses in laminated composites. The
analysis was carried out to determine the influence of bonding material on the statically
induced interfacial shear stresses due to various mechanical and thermal loading using the
same two dimensional model they introduced in [12]. The laminate representing various
materials in the model were assumed to be infinite along the in-plane direction, and were
stacked normal to the in-plane direction in such a way that any layer of material 1 and
material 2 were sandwiched between the layers of material 0. This arrangement
simulated the case where material 0 acted as the bonding agent between material 1 and
material 2.
Equilibrium equations, constitutive relations along with the continuum mixture
relations were used to develop the formulation. A linear variation of shear stresses was
6
assumed about the mid plane of each of the two adherends; the shear stress was also
linear through the adhesive thickness. Using these conditions, a system of two coupled
differential equations describing the behavior of the two interfacial shear stresses was
derived. The solution for the shear stresses was obtained by solving these coupled
differential equations. These interfacial shear stresses demonstrated their dependence on
the geometry and material properties of the trilaminated model, as well as the combined
mechanical and thermal loadings. Various combinations of pressure loadings and
uniform temperature changes were utilized to increase, decrease and even neutralize the
state of the interfacial shear stresses. The numerical results demonstrated the effect of
various thermomechanical loadings, and the influence of the bonding agent properties
and thickness, on the interfacial shear stresses [14]. One thing to be noted here is that the
interfacial shear stresses were determined based on a two dimensional model.
Pao and Eisele [15] developed an analytical model to evaluate the interfacial shear
and peel stresses in a multilayered thin stack subjected to a uniform thermal loading. The
model was based on Suhir's bimetal thermostat model. The approach provided a system
of coupled second order linear differential equations to solve for the interfacial stresses.
The interfacial stresses were then used for determining the normal stresses in each layer
along with the deflection of the overall stack. A general two-dimensional multi-layered
stack with finite length 2L was considered for the analysis. The material behavior was
assumed to be linearly elastic, and uniform heating or cooling effect was considered.
Two examples, first a five-layered double-shear solder joint and second, a four-layered
transistor stack were used to illustrate the application of the approach. The first one
showed that the thermally induced bending might increase or decrease the stress level. It
7
was also showed that the maximum interfacial shear stresses were not necessarily at the
edges, but were located at the vicinity of the edges. The second one showed that as the
thickness of the layer decreased the solution converged to a case where such layer was
absent. This approach was considered to be useful to analyze the behavior of multilayer
thin stacks in electronic industry. This model considered only the thermal loading and
was two dimensional.
Suhir in 1998 [9] developed an analytical model for interfacial stresses in bimetal
thermostats. This model was based on the elementary beam theory, but in addition he
considered the transverse compliance (through thickness). The solution provided the
distribution of interfacial shear and normal stresses.
Hui-Shen, Teng, and Yang [16] theoretically studied the interfacial stresses in a
simply supported beam bonded with a thin fiber reinforced polymeric composite or a
steel plate. A simply supported bonded joint was subjected to a uniformly distributed
load and a uniform bending moment. A plain stress model was used for the beam and a
plain strain model was used for the slabs. The other important feature considered in the
analysis was a non-uniform stress distribution in the adhesive layer. The results showed
that the maximum normal stress always occurred at the free edges and the maximum
shear stress occurred a small distance from the free edge. The interfacial stresses
increased as the plate stiffness was increased, or as the plate length was reduced. The
location of the maximum interfacial shear stress moved towards the free edge as the plate
stiffness was reduced or as the plate length was reduced.
Ru [17] developed a non-local modified beam model to evaluate the interfacial
thermal stresses in biomaterial elastic beams. The model was based on Suhir (1986)
8
model. The model satisfied the zero shear stress boundry condition and provided the
interfacial peel stresses. The predicted interfacial shear stresses were found to be in
reasonably good agreement with some of the known numerical results. The model was
considered to be best suitable for only multilayered and two-dimensional materials or
electronic packaging.
Hyonny and Keith [18] worked on. in-plane shear loaded adhesively bonded lap
joints. A governing partial differential equation describing the in-plane shear stress in the
adherend was obtained. The differential equation was then solved for the shear stress
components in the adhesive material. The closed form solution was verified using finite
element analysis by predicting the stresses in an in-plane shear loaded bonded joint. The
effect of geometric and material parameters on the joint behavior was studied to assist the
selection of the design parameters and evaluate the manufacturing tolerance.
Yang et al. [19] developed an analytical model using laminated anisotropic plate
theory to study the stress and strain distribution in an adhesively bonded composite
single-lap joint. The composite adherends were assumed to be linearly elastic material
and the adhesive was assumed as an elastic-perfectly plastic material following Von
Mises yield criteria. The stresses in the adhesive were considered to be uniform along the
thickness direction. The entire coupled system was determined using the kinematics and
force equilibrium of the adhesive and the adherends. The system of governing equations
was then solved analytically using appropriate boundary conditions. The results from the
analytical model were verified with the finite element analysis using ABAQUS ®. The
analytical results showed a good agreement with the finite element analysis. This model
along with a failure criterion were used as a tool to evaluate joint strength under the
9
cohesive failure mode of the adhesive. The developed model showed the stress
distribution in the adhesive layer and not at the adhesive to adherend interface.
Thermal peel, warpage and interfacial shear stresses in adhesive joints were
studied by John Rossettos [20]. The author developed a closed form solution for the
stresses, in a single lap joint, that were solely due to thermal mismatch and he also
indicated the deformation mechanism. The analytical results gave the stress and
deformation patterns due to the temperature changes. The thermal mismatch stresses
were determined using a bending model. The model predicted the bond line peel stresses,
shear stresses, and the axial stresses in the adherend. The analytical solution displayed a
sinusoidal deformation consistent with the warpage (bending) of the adherends. Their
Modified Shear Lag Model (MSLM), with no adherend bending, showed peek shear
stresses at the ends of the joint. The bending model showed the peek stresses not only at
the ends of the overlap but also at the interior point of the overlap region. The results for
the aluminum adherends with epoxy adhesive showed the distribution of the peel, the
warpage and the shear stresses.
Seo et al. [21] conducted an experimental and finite element investigation to study
the effect of adhesive overlap length and the adhesive thickness on the strength and stress
distribution in adhesively bonded joints. Five different over lap lengths with different
adhesive thicknesses were considered for the study. Tensile tests with constant cross
head speed and a three-dimensional linear finite element analysis were conducted to
analyze the strength and the stress distribution for the various adhesive joint
configurations. It was found that the stresses were maximum at the ends and minimum at
10
the center of the adhesive area. The joint strength decreased as the adhesive thickness
increased.
Li, et al. [22] carried out a geometrically nonlinear two-dimensional finite
element analysis to study the stress and strain distribution across the adhesive thickness
in composite single lap joints. The effects of adhesive thickness and mechanical
properties on the stress and strain distributions were investigated. The thin bond line was
simulated using 2-element and 6-element mesh schemes, whereas the 10-element mesh
was used for thicker bond line. It was found that the maximum peel stresses and shear
stresses within the adhesive bond occurred near the adhesive to adherend interface at the
corner ends of the overlap. The peak shear and peel stresses increased with the bond
thickness and elastic modulus.
An elastic three-dimensional finite element analysis was carried out by Sawa et al.
[23] to analyze the stress-wave propagation and stress distribution in dissimilar single lap
adhesive joints. A commercial finite element software DYNA3D® was used for this
purpose. The upper end of the single-lap joint was held fixed whereas the other end
(lower end) was impacted by a weight. The effect of Young's modulus and adherend
thickness on the stress distribution and the stress-wave propagation were investigated.
The three main conclusions derived from the analysis were that the maximum principle
stress occurred near the edge of the interface of the fixed adherend, the maximum
principal stress increased with the Young's modulus of the fixed adherend, and the
maximum principal stress increased as the fixed adherend thickness was decreased.
Experiments were conducted to validate the analytical results and a good agreement was
obtained between the FEM and the experimental results.
11
Yang et al. [24] carried out finite element analysis to study the interfacial stresses
in fiber reinforced plastics (FRP) - reinforced concrete (RC) hybrid beams. The effect of
FRP thickness, adhesive thickness and the material properties on the interfacial stresses
was investigated. Results showed that the interfacial shear stresses and the normal
stresses were maximum at the edges and were the main cause for interlaminar
delamination. The stiffness of the RC and the FRP greatly influenced the interlaminar
shear and the normal stresses. The interfacial stress concentrations and their levels
increased with the increase of the FRP thickness.
Goncalves, et al. [25] used a specially developed interfacial element in numerical
finite element analysis to study the adhesive joint behavior. The element had eighteen
nodes distributed in two faces with zero thickness. The main objective of their work was
to analyze the stresses at the adherend to adhesive interface. This finite element model
was applied to a single lap joint, considering linear elastic and elasto-plastic material
properties. The results showed a three-dimensional nature of the stresses suggesting the
importance of the three-dimensional analysis. The peek stresses at the interface were
much higher than at the middle of the adhesive. This explained the reason for the
adhesive joint failures at the interfaces and the importance of the interfacial stresses in
bonded joints.
Mathias, Grediac and Balandraud [26] derived the solutions for the bi-directional
stress distribution in a rectangular composite patch under uniform in-plane loading. An
orthotropic composite patch was adhesively bonded on to an isotropic substrate. The
stress distribution in the patch, the adhesive, and the substrate showed bi-directional
behavior. The solutions were used for comparing uni-directional and bi-directional stress
12
distribution in the adhesively bonded patch. The adhesive was subjected to only
transverse shear stresses and these stresses were constant through the thickness. The
contribution of the bending moments, tearing, peeling and normal stresses were neglected
in deriving the solutions. (These assumptions were standard as they were also used by
Adams and Peppiatt, Baker et al. (2002). The bi-dimensional solutions were validated
using a finite difference model. A significant difference was noticed when comparing the
classical solutions with the bi-directional results, showing the importance of the bi
directional stress formulation.
Weijian et al. [4] developed an analytical expression for three-dimensional stress
distribution at the bonded interfaces of the dissimilar materials. The mathematical model
predicted the stress peeks at the interfaces. The interface was expressed as a general
surface in Cartesian coordinates. This was helpful to model the approximate solution for
different interface topographies. Finite element analysis was used to compare the
mathematical model results. A linear elastic behavior with perfect bonding at the
interfaces was assumed for the analysis. Their comparison of the finite element
interfacial shear stresses with the three-dimensional mathematical model results showed
similar trends in terms of the magnitude and shape, except at the edges. This was
attributed to several assumptions in the finite element analysis. The three-dimensional
stress solutions were considered more realistic than the two dimensional model [4]. The
three-dimensional stress solutions were more helpful to optimize the surface topology or
for surface preparation of the bonded surface to produce a reliable joint. This was
necessary since ductile adhesives would fail due to shear stresses, while brittle adhesives
would fail due to normal stresses. High stresses induce cracks in brittle adhesives, where
13
as a cavity induced failures in deformable adhesives. This bi-material model determined
the interfacial normal and shear stresses, but the stresses were due to normal loading on
the plane of the bonded joint. The model was more focused on the effect of surface
topology on the interfacial stresses.
Weijing, Rajesh and Erol [27] used the mathematical model in [4] to study the
three dimensional interfacial stress distribution for a scarf interface (y = x / 2) in a bonded
joint. A commercial finite element code ALGOR ® was used for the scarf interface stress
analysis. The FEA was not able to replicate the interfacial shear stress distribution
obtained from the mathematical model. This was attributed to the difference in their
methods in maintaining boundary conditions. The FEA enforced the displacement
continuity in the whole system including the interface, but did not maintain the stress free
boundaries even when required by the equilibrium conditions. When comparing the
normal stresses, it was found that the stresses obtained from FEA were approximately the
averages of the corresponding stresses obtained for the bonded materials at their interface
by the mathematical model. Based on the results, it was concluded that the mathematical
model was able to predict approximately the three dimensional stresses at the bonded
interface for various surface topographies
As evident from literature survey, most research works [8-20] focus on two
dimensional stress analysis of adhesively bonded joints. Literature shows that there are
very few three dimensional analytical models which consider the thermomechanical bi
directional loading conditions to determine the effect of adhesive material on the
interfacial stress distribution. Mathias, Grediac and Balandraud's [26] study showed the
significant difference between the classical solutions and the bi-directional solutions. To
14
understand the need and determine the bi-directional interfacial shear stresses in bonded
structures are important. Although finite element analysis is very often used for stress
analysis, analytical procedures provide more fundamental insight and helps in analyzing
the various critical parameters affecting the stress distribution.
1.3 Background on Bolt Bearing Behavior in Polymeric Composite Bolted Joints
Bolted joints for its advantages, such as the ease of assembly and disassembly, are
often preferred in many composite joining applications. Bolted joints are considered to
be the weakest link in a structure, as drilling bolt holes creates high stress concentration
[28]. The design and analysis of fiber reinforced polymeric composite bolted joints
involves high degree of complexity and requires a special attention because of the
anisotropic, inhomogeneous and viscoelastic properties. Joint geometry, stacking
sequence, fiber orientation and bolt pre-load are some of the critical factors to be
considered for a reliable joint design [29]. Figure 1.5 shows typical composite bolted
joint parameters.
1.3.1 Failure Modes in Polymeric Composite Bolted Joints
Predicting the failure load and the failure modes in a composite bolted joint is
often a challenge. Previous works have characterized the failure modes and parameters
associated with the failure of composite bolted joints [30]. Figure 1.6 shows some of the
failure modes. The tensile failure is mainly due to the reduced joint width and is
associated with the stress concentration in the fiber and matrix material. The shear out
failure is mainly due to the reduced edge distance and results primarily due to the shear
and compression failures of the fibers and the matrix materials. This type of failure in
15
most cases can be avoided by proper selection of lay-up and increasing the edge
distance. A cleavage failure is due to a combination of reduced edge distance and width
of the joint. Fastener pull through failure is due to reduced thickness to bolt diameter
ratio. Fastener failure is a secondary type of failure mode and is not common in
composite structural applications. Bearing failure is caused by a combination of
extensive compressive force exerted on the inner bolt-hole boundary by the shank of the
bolt, and the reduced hole diameter to width ratio. The net-tension and the shear-out
failures are more catastrophic failure modes, where as the bearing failure is a progressive
failure, and may not result in total reduction of load carrying capability of the joints [31].
Most bolted composite structures are designed for the bearing failure [32]; hence
methodical understanding of effects of various joint parameters on bearing failure in a
joint is of fundamental importance.
1.3.2 Bolt Bearing Behavior in Polymeric Composite Joints
FRP composite laminates used in a bolted joint configuration exhibit a complex
behavior when subjected to in-plane loading (Figure 1.7). Under the in-plane loading
condition the bolt shank compresses the cylindrical surface of the hole (composite); this
eventually deforms the composite material and may lead to bearing failure. ASTM D
5961/D 5961M [33] gives the standard bearing test procedure for a composite bolted
joint. During a bolt bearing test, load- displacement data is recorded to determine the
bearing failure load, bearing strength and the ultimate joint strength.
Mechanical fasteners (bolts and rivets) require drilling of holes in composite
materials, which ruptures the composite fiber reinforcements. This creates stress
16
concentration and may create micro-cracks and local damage around the drilled holes
inducing structural instability [34]. Even with some of these draw backs, mechanical
fastening of composites is a proven practical technology. The literature lists [35] the
design parameters and the critical factors affecting the structural integrity and reliability
of a composite bolted joint. The bearing behavior of FRP composites vary with fiber,
matrix and laminate properties (thickness and orientation). Extensive experimental data is
required for a reliable joint design, as generalized design formulas is difficult to achieve.
1.4 Previous Research on Bolt Bearing Behavior in Polymeric Composite Joints
The study of bearing behavior, bearing strength, and bearing failure in a
composite bolted joint becomes essential as bolted joints represent the weakest link in a
mechanical system. Bearing strength and bearing failure modes depend on various joint
parameters. Some of the critical parameters include joint geometry, hole clearance, type
of fasteners, bolt clamping pressure and the operating conditions. The following section
gives an overview of previous research carried out on the bolt bearing behavior in
composite structures.
1.4.1 Influence of Coupon Geometry and Laminate Properties on the Bolt Bearing Behavior
Vangrimde and Boukhili [36] studied the effect of coupon geometry and laminate
properties on the bearing stiffness of Glass fiber Reinforced Polyester (GRP) composite.
The focus was on the load-displacement response of GRP laminate in a single-bolt
double-lap composite joint. Six different laminate materials with different amounts of 0°
and 90° roving; Chopped Strand Mat (CSM) were tested to obtain the load-displacement
17
data. Different coupon geometries considered were, a standard coupon with width to
diameter ratio of 6 and edge distance to diameter ratio of 3, a long coupon, with width to
diameter ratio of 6 and edge distance to diameter ratio of 6. a small coupon, with width to
diameter ratio of 2 and edge distance to diameter ratio of 3. Bearing stress was calculated
P using obr = — ' where P= applied load, D= bolt hole diameter and h= thickness of the
Dh
laminate, and bearing strain was calculated using —- , where 8 represents the
deformation in the bolt hole. These relations were used to obtain the bearing stress verses
bearing strain curves. The bearing stress-strain curves had three distinct regions: initial
sliding, linear bearing response prior to the damage, and a non-linear post damage stress
region. The bearing stiffness was determined from the initial linear part of the curve. On
average, joints with reduced width showed 26% more yield than the standard joints. The
end distance had an insignificant effect on the bearing stiffness; an average increase of
6% stiffness was noticed in the longer end distance joints compared to the standard joints.
The bearing stiffness was higher for the smaller coupon geometry with more axial
reinforcement. The experimental observations on the influence of coupon width, the end
distance and the laminate properties on the bearing stiffness were approximately verified
by 2-D Finite Element Analysis.
Li Hou and Dahsin [37] investigated the three-dimensional size effect and
thickness constraints on the single-pin double-lap glass-epoxy composite joints. The
constraints in the thickness direction, the composite thickness, the bonding strength
through the laminate thickness and the clamping force from bolting had a significant
18
effect on the damage and the strength behavior of the joints. The experimental data
revealed that the joint strength decreased as the joint size was increased. The failure
modes also changed from an initial bearing damage, followed by net section failure to a
direct catastrophic net-section failure as the joint size was increased. Composite joints
with low thickness constraints showed fiber buckling and delamination, resulting in a
bearing failure before net section failure. These joints showed large displacement before
final failure and consumed more energy (larger area under the load-displacement curve),
hence were more ductile than those which failed by direct catastrophic net-section failure.
Cooper and Ibvey [32] experimentally studied the effect of joint geometry and
bolt torque on structural performance of the single bolted pultruded GRP (Glass
Reinforced Polymer) joints. Tests were conducted to determine the effect of geometric
ratios, edge distance to bolt hole diameter ratio and width to hole diameter, and the bolt
torque on the failure load, failure modes and stiffness of the single bolted joint. The
failure loads of the lightly clamped (3 Nm bolt torque) and the fully clamped (30 Nm bolt
torque) joints increased by 45% and 80%, respectively, when compared to pin joints. It
was also observed that by increasing the bolt torque the critical e/D and W/D ratios also
increased significantly. The initial stiffness of the single-bolt joint was affected mainly
by the W/D ratio. The e/D ratio and the bolt clamping torque had only a small effect on
the initial joint stiffness. The load vs bolt displacement graphs for each tested joint
showed an initial bolt displacement of 0 to 0.3mm despite the tight bolt fitting. After the
initial bolt displacement the load displacement response was approximately linear until
the joint either failed (small e/D or small W/D values) or the initial stiffness reduced. An
19
irreversible bearing damage was observed at the load where the joint stiffness changed,
and this was defined as the damage load.
Oh, Kim, and Lee [38] worked on bolted joints for hybrid composites made of
glass-epoxy and carbon-epoxy under tensile loading. The design parameters investigated
were laminate ply angle, stacking sequence, the ratio of glass-epoxy to carbon epoxy, the
outer diameter of the washer and the clamping pressure. Results showed that the peak
load occurred before the maximum failure load due to the delamination of the laminate
under the washer. The static test results of the hybrid composites with stacking
sequences of [0C/± 45G/± 45C/90C]S and [OG/ ±45C/90G]S (C: carbon-epoxy, G: glass-
epoxy) revealed that the bearing strength increased as the ±45 plies were distributed
evenly along the thickness direction irrespective of the joint material (glass-epoxy or
carbon epoxy) and the stacking pattern. The bolted joint of [+45C/-45C/+45C/ (OG) 2, / -
45C/+45C/ - 45C/ (90G) 2] s laminate, with 35.5% volume fraction of glass-epoxy
yielded the highest bearing strength. The bearing strength increased as the bolt clamping
pressure increased to 71.1 MPa, thereafter the bearing strength saturated to a constant
value. The failure mode changed from bearing failure to tension failure when a 20mm
diameter washer was used. The finite-element analysis predicted the first peak load;
however, it could not predict the maximum failure load. For a more accurate prediction of
the joint strength it was suggested to consider the effects of material non-linearity, the
friction between the joint materials, and the stiffness reduction due to failure.
An experimental and numerical study was carried out by Aktas and Dirikolu [39]
to investigate the strength of a pinned-joint made of carbon epoxy composite with [0/45/-
45/90] s and [90/45/-45/0]s stacking configuration. ASTM D953 standard was followed
20
for the experimentation, and a finite element analysis was performed for verifying the
experimental results. The ratio of the edge distance to the pin diameter (e/D), and the
ratio of the specimen width to the pin diameter (W/D) were systematically considered to
analyze the strength and the failure modes in the composite joints. The results from both
the analyses showed good agreement. When the e/D > 4 and the W/D > 4, bearing failure
was dominant, where as when the ratios were below four, net tension, shear out and
mixed mode failure were observed. The [90/45/-45/0]s joint configuration showed 20%
higher bearing strength than the [0/45/-45/90]s configuration. The finite element results
predicted an average 20% lower bearing strength values when compared to those from
the experiments. Yamada-Sun failure criterion was used to determine the failure loads
and failure modes in the analysis. Besides its availability in commercial FE codes such as
ANSYS ®, the criterion also gave satisfactory predictions of both failure load and failure
modes.
Alaattin [40] experimentally investigated both static and dynamic bearing
strengths of a pinned-joint carbon epoxy composite plate with [0/45/-45/90]s and [90/45/-
45/0] s stacking configurations. In order to obtain the optimum geometry the ratio of edge
distance to pin diameter (e/D), and the ratio of specimen width to pin diameter (W/D)
were varied to obtain the static bearing strength and the S-N fatigue curves. The
experiments showed [90/45/-45/0]s sequence was about 12% stronger than the [0/45/-
45/90]s sequence in terms of bearing strengths. Additionally, the optimum geometry was
attained when e/D and W/D ratios were greater than or equal to 4. The fatigue strength
reduced up to 63% of the static strength as e/D and W/D ratios increased.
21
McCarthy et al. [41] investigated the effect of bolt-hole clearance on the strength
and stiffness of single-lap, single bolted composite joint. The graphite/epoxy with quasi-
isotropic [45/0/-45/90]5s and zero dominated [(45/02/-45/90)345/02/-45/0]s stacking
sequence were considered for the study. Bolt-hole clearanceses of Oum, 80(j.m, 160um
and 240um with various torque levels and different bolt types were investigated. The
joint stiffness, 2% offset joint bearing strength, the ultimate bearing strength and the
ultimate bearing strain were analyzed for various joint configurations. An increase in
clearance was found to reduce the joint stiffness and increase the ultimate strain for all
test configurations. The finger tightened bolts with negligible clamp load showed a
relation between the bolt-hole clearance and the joint strength, where as this was absent
for the counter sunk and the torque tightened joints.
V.P. Lawlor, et al. [42] continued their experimental investigation on the effect of
bolt-hole clearance on the single-bolt, single-shear bolted composite joints. The varying
bolt-hole clearance was obtained by using a constant bolt diameter and varying the hole
diameter. The same four hole clearances used in [41] (Oum, 80um, 160um and 240um)
were used for the analysis with countersunk and protruding head bolts. The initial delay
in the load take up was observed in the load-displacement data showing the bolt-hole
clearance effect. Two main regions, linear and nearly linear were observed in the load-
displacement curves. The bolt-hole clearance had an insignificant effect on the
maximum load taken by the composite bolted joint. The maximum displacement
decreased with the decrease in clearance. All tested joints initially failed by bearing
failure and exhibited a drop in stiffness with an increase in bolt-hole clearance. The
22
p (& + f\ V2 bearing stress - bearing strain were plotted using obr = and sb r = — ^— ,
k D h K D
where P = load, D = diameter, h - coupon thickness, and k = load per hole factor (1.0 for
single fastener or pin tests and 2.0 for double fastener tests ), 81 and 82 are
displacements, respectively, in extensometers 1,2, and K=l for double shear tests and
K=2 for single shear tests. For the protruding bolt-head joints, the bolt-hole clearance
effect on the ultimate strength was essentially negligible. Unlike the ultimate strength,
ultimate strain was significantly affected by the bolt-hole clearance. An increase in bolt-
hole clearance increased the ultimate strain. This was due to the extensive laminate
damage by the concentrated load on the laminate hole. The bolt hole clearance had a
significant effect on the joint stiffness and ultimate strain and less effect on the joint
strength. The bolt-hole clearance showed a delay in load take up and this was considered
to be a significant factor in multiple bolted joints.
1.4.2 Effect of Bolt Tightening Torque and Clamping Pressure on Bearing Behavior
Claire et al. [43] studied the effect of stacking sequence and clamping pressure on
the carbon/epoxy bolted composite joints. Three different symmetric lay-ups, cross-ply
[(0/90)4] s, angle-ply [(+45/-45)4]s and quasi-isotropic [(0/±45/90)2]s were used in the
study. The bolt displacement and the local strains around the bolt-hole edge were
recorded for the analysis. Bearing stress Vs hole elongation curves and the bearing stress
Vs strain curves showed significant effect of clamping pressure on the initial bearing
stress and the maximum bearing stress. Tightening the bolt increased the initial bearing
stress by 22% and the maximum bearing stress by 105%. The angle ply and the quasi-
23
isotropic lay-ups showed similar bolt-hole elongation which was larger than the cross-ply
bolt-hole elongation. A significant increase in strain was observed for the dowel pin
joints when compared to the finger tightened bolted joints. The increase in clamping
pressure increased the post-peak stiffness, where as the initial stiffness and the bolt-hole
elongation decreased significantly. The bearing stress vs. hole elongation curves showed
that the angle ply lay-ups had the lowest initial stiffness and the cross-ply lay-up had the
highest initial and post-peak stiffness. Orienting the fibers at an angle of 45° improved the
bearing behavior. The results from the rosette strain gage positioned on the bearing zone
showed a linear behavior for the angle-ply laminate, where as a nonlinear behavior was
observed for the cross-ply and the quasi-isotropic lay-ups. This non-linear behavior was
mainly due to the stresses corresponding to the initiation of damage due to local
delamination around the hole. This study investigated some of the most significant
parameters affecting the bearing behavior in bolted composite joints, and the data from
this could be used for the failure mechanism study and for validation of the numerical
finite element model.
Park [44] investigated the effect of stacking sequence and clamping force on
delamination bearing strength and ultimate bearing strength of mechanically fastened
carbon/epoxy composite joints using an acoustic emission (AE) and load-displacement
technique. Orthotropic and quasi-isotropic laminate lay-up configurations with four
different clamping forces were considered for the study. The stacking sequence and the
clamping pressure had a significant effect on the delamination and ultimate bearing
strength of the mechanically fastened composite joint. The comparison of orthotropic
laminate pinned joints, with stacking sequence [9(V06]s and [(V906]s, showed similar
24
ultimate bearing strengths for both lay-ups, but the laminate with [90g/06]s lay-ups had
almost twice the delamination bearing strength as compared to laminates with [0^906] s
lay-ups. The trends of variation of the delamination and ultimate bearing strengths of
bolted joints were similar to that of the pinned joints for different stacking sequences.
The laminate with [903/+453/-453/03]s lay-ups had the highest ultimate bearing strength,
whereas, the laminate with [903/03/+453/-453]s lay-ups had the highest delamination
bearing strength. The 90° layers had an important role in delamination bearing strengths;
the laminate with 90° layers on the surface had higher delamination bearing strength than
the laminate with 90° layers in the center. An increase in clamping pressure increased the
ultimate bearing strength to saturation, whereas the delamination bearing strength
increased progressively. The clamping pressure suppressed the delamination and the
interlaminar cracks. The failure mode changed from catastrophic fracture to a
progressive failure as the clamping pressure was increased.
Sun, Chang and Qing [45] experimentally studied the effect of lateral supports on
the bearing failure in composite bolted joints. Graphite/epoxy composite coupons were
investigated for various washer sizes and clamping forces. The clamping load history was
recorded as the tensile load was applied to the joint. The clamp load increased with the
applied tensile load; Poisson's ratio contributed for the initial increase in the clamping
force until the bearing failure, and the lateral constraints preventing the material damage
increased the clamping force after the bearing failure. The pinned joints had the lowest
joint strength compared to the bolted joints with lateral clamping force. The experimental
25
results were compared with the predictions from the 3DBOLT code included in
ABAQUS ®. The comparison included failure load, joint response, the failure modes for
the joints with various clamping configurations and clamping loads. The predictions
from the code agreed well with the experimental results.
Yan et al. [46] conducted an experimental study to investigate the effects of
clamp-up pressure on the net tension failure of bolt-filled laminated composite plates.
The tensile strength and the failure behavior of both open bolt-hole and bolt-filled hole
were evaluated for graphite-epoxy composite plates. The effect of washer size on the
bolt filled-hole net tension strength, and the net tension failure behavior of composite
bolted joints were also investigated. X-rayradiographs were used to analyze the
specimens after preloading and at different stress levels for the purpose of characterizing
the failure modes and damage progression inside the composite. The bolt filled-hole
composite laminate was prone to fiber matrix splitting and delamination due to its
sensitivity to the bolt clamp up effect. Higher the clamping pressure lower was the
tensile strength of the bolt filled-hole laminate. The tensile strength reduced by about
20% with the bolt clamping pressure. The washer to bolt-hole diameter ratio (Dw/D) (less
than 2) had negative effect on the tensile strength of the bolt filled-hole laminate. Unlike
bolt filled-hole laminate, the tensile strength of the bolted composite joints increased with
clamping pressure.
Khashaba et al. [47] investigated the effect of bolt tightening torque and washer
size on the bearing behavior of glass fiber reinforced epoxy composite ([0/±45/90]s)
bolted joints. Damage analysis was carried out to understand the failure mechanism.
26
Tightening torques of T = 0 Nm, 5 Nm, 10 Nm and 15 Nm and the washer sizes of D w o =
14 mm, 18 mm, 22 mm and 27 mm were used in the study. Mechanical properties such
as tensile, compressive, and in-plane shear were determined both experimentally and
theoretically. The joint stiffness increased with decreasing the washer sizes under
constant tightening torque. This was mainly due to the increase in the clamping pressure
resulting from reduced washer size. The washer size of 18 mm and the tightening torque
of 15 Nm produced the optimum clamping pressure. The composite bolted joints with 14
mm washers had higher clamping pressure but showed reduction in maximum bearing
strength. The load displacement curves of the finger tightened bolt joint showed least
stiffness with non-linear behavior that indicated the unstable development of internal
damage. Most of the tested specimens failed in a sequence, delamination, and net tension
failure at 90 ° laminate, shear out failure at 0° layers and final failure which was nearly
catastrophic due to the bearing failure of ±45 ° layers.
1.4.3 Progressive Failure Mechanism in Composite Bolted Joints
Lawlor, Stanley and McCarthy studied the effect of bolt-hole clearances on the
damage development in carbon-epoxy bolted composite joints [48]. Single-lap single-
bolted joints subjected to tensile load were considered in the analysis. The load-
displacement data was recorded for determining the bearing failure load and the ultimate
failure load of the bolted joints. The bolt-hole clearances of 0 urn, 80 urn, 160 |j,m and
240 urn were selected for the 8mm bolt-hole. The joint initially failed due to bearing
damage before the final failure. For the larger clearance bolt-boles, the load Vs
displacement data showed a delay in load take-up, initial non-linearity after the load take-
27
up, a lower slope in the linear portion of the force Vs deflection curve, and a significant
loss of stiffness. The low clearance joints failed by bolt failure, whiles, the larger
clearance joints had no bolt failure but a large joint displacement. Further examination of
the failed specimen showed significant damage at the shear plane of the laminate for all
clearances
Claire et al. [49] studied the failure mechanisms of bolted carbon epoxy
composite joints under tensile loading. They studied the effect of stacking sequence and
clamping force on the failure mechanism. The evaluation of the external macroscopic
damage was done using digital photographs, and the internal damage using the optical
microscopy. The damage analysis showed that the fiber orientation around the bolt-hole
boundary had an influence on the failure initiation. The matrix cracking, the interlaminar
shear delamination and the compressive failure were the prominent failure modes
observed in all configurations. The shear cracks in the tight bolted joints (finger
tightened and torque tightened) were seen on the surface of the laminates. The
micrographs of same specimens showed a severe internal damage over the entire bearing
zone. The damage pattern for the angle ply was different than the quasi-isotropic
laminate for similar clamping pressure. The quasi-isotropic laminate showed multiple
shear cracks spreading over the bearing zone, where as, the damage was more severe and
spread over a large area for the angle-ply laminates. For the specimens subjected to
higher stresses, the prominent shear cracks appeared on a plane distant from the bearing
plane and reached the laminate surface.
Yi Xiao [50] investigated the bearing strength and failure process in double-lap
single-bolted composite joints. The load displacement data was recorded using the load
28
cell and a non-contact electro-optical extensometer. The bearing strength was based on
the bearing load at which the pin relative displacement was deformed by 4% of the pin
diameter; the ultimate failure load was determined from the peak point of the load-
displacement data. The load-displacement data had two prominent regions, an initial
linear region and a non-linear region before it reached the load at 4% displacement; this
indicated the micro damage beginning in the tested coupon. During the static tests, along
with the load displacement data the acoustic emission was recorded for the fracture
analysis of the specimen. A sharp change in the AE signal observed at the start of the
nonlinear behavior indicated the beginning of the damage. The photographs of the
specimen surfaces and the X-ray-radiographs of bearing damage were recorded for the
investigation of failure mechanism. The local delamination under the washer, the out-of-
plane shear cracks, and the fiber matrix splitting cracks progressed with the increase in
the tensile load. These failure modes were responsible for the final failure of the bolted
joints. Further the study was extended for double bolted joints to investigate the bearing
load proportions (load carried by each individual bolts). The load-displacement and the
elongation data were recorded using the load cell and an extensometer placed at each
bolt-hole. The bolt-hole elongation for each hole was significantly different with
nonlinear behavior. The relative displacement between the bolt-hole was converted into
ratio of loading proportion. The damage analysis using SEM and the X-ray radiography
showed that the compressive damage state around each hole differed due to the difference
between the loading proportions.
Hong, Chang and Fu-Kuo [51] experimentally investigated the effect of clamping
pressure on the bearing response and bearing failure mechanism of composite bolted
29
joints. The bearing damage was characterized either as a pure bearing failure, which had
no lateral support, or as a bolt bearing failure which contained lateral supports with
various levels of clamping pressure. Specially designed semi-circular notched specimens
were used to characterize the pure bearing damage* while a load cell was used to monitor
the clamping pressure in the bolted joint. Three different bolt-hole diameters and two
different laminate thicknesses were considered for the study. The failed specimens were
inspected using the microscope and Xray-radiography. The shear cracks induced by the
compression failure were the main cause for the bearing failure. The bearing failure
without lateral constraint was catastrophic. The critical bearing distance (5C) was
identified beyond which the catastrophic failure occurred, and this was proportional to
the laminate thickness and independent of ply-orientation. Lateral support prevented the
catastrophic failure and increased the bearing strength.
Liyong [52] studied the effect of two extreme positions of the loose fit fasteners
on the bearing failure in double-lap bolted composite joints. When the washers were
placed to their extreme positions in the loading direction, an unconstrained gap between
the bolt shank and the washers were observed, whereas, when the washers were placed in
the extreme positions in the opposite loading direction no unconstrained gap existed. The
results showed that the bolted joints with an unconstrained gap had lower initial failure
load than those joints having no unconstrained gap. However, there was no difference in
the ultimate failure loads.
Different strategies for improving the bearing strength were examined by
A.Crosky et al. [53]. Fiber steering (directed placement of fibers), matrix stiffening by
nano-reinforcement and the through thickness reinforcement using z-pins were the
30
different strategies analyzed in the study. The bearing strength was improved by 36%
using two sets of steered fibers in tensile and compressive principle stress direction, as
obtained by the FEA analysis. The addition of clay nano-particles to the matrix resin
stiffened the matrix but induced a different premature failure mode, which reduced the
joint bearing strength. However it was found that the bearing behavior would improve by
avoiding the premature failure. Through thickness reinforcement using z-pins increased
the ultimate bearing load by 7%, while the bearing strength remained the same
1.4.4 Finite Element Analysis of Composite Bolted Joints
Ireman [54] was one of the earliest researchers to develop a three dimensional
finite element model of a single lap composite bolted joint to determine the non-uniform
stress distribution through the thickness of the composite laminate in the vicinity of a
bolt-hole. Number of significant joint parameters including the laminate lay-up, the bolt
diameter, the bolt type, the bolt pre-tension and the lateral support conditions were
investigated. The commercially available finite element code IDEAS for pre and post
processing and ABAQUS ® were used in the study. The experiments were carried out to
verify the strains, the displacements and the bending effects obtained from the finite
element analysis. A good agreement for the measured strains was obtained and the
primary differences were attributed to the difference between the frictional coefficients in
the experimental and the finite element analysis. For the displacements, the agreement
between experimental results and analytical results were not as good as the strains. This
difference was attributed to the misalignment between the joint coupons and the friction
between them. It was clear from this study that the finite element method was able to
31
predict the through thickness stresses, strains at the vicinity of the bolt hole and many
such complex design parameters in a composite bolted joint.
Finite Element Analysis was carried out by Johan and Joakim [55] to study the
effect of secondary bending on the damage behavior and strength of composite bolted
joints. The commercial finite element software ABAQUS was used to model the
composite joint assembly. An orthotropic linear material property was considered for the
composite plates. Both the tensile and the compressive loading were used to study the
bolt bearing behavior. For tensile loading, the secondary bending increased the bearing
strength and reduced the ultimate joint strength. The bearing strength was much lower
for compressive loading, this was due to the reduced bolt to bolt-hole contact. The joint
stiffness also reduced due to secondary bending. The secondary bending influenced
various macroscopic failure modes and in the process changed the ultimate failure mode.
It was recommended to reduce the secondary bending in the bolted joints which resulted
in an eccentric load path.
Tserpes et al. [56] conducted a finite element analysis to investigate the effect of
failure criteria and material property degradation rules on the tensile behavior and
strength of graphite/epoxy laminate bolted joints. The analysis was based on three
dimensional progressive damage model (PDM) developed earlier by the authors. The
PDM comprises the components of the stress analysis, the failure analysis and the
material property degradation. The experiments were conducted to compare the finite
element results. The effect of various joint geometries and stacking sequence on the load-
displacement behavior were investigated. The failure load predicted was influenced by
32
the combination of failure criteria and material property degradation rules considered in
this study, while the stiffness of the joint was relatively accurate.
Dano et al. [57] developed a two-dimensional finite element model to predict the
response of the pin-loaded composite plates. The model was developed taking into
account the contact at the pin-hole interface, the progressive damage, the large
deformation theory, and the non-linear shear stress-strain relationship. To predict the
progressive ply failure, the analysis combined Hashin failure criteria and the maximum
stress failure criteria. The influence of the failure criteria and nonlinear shear behavior
on the strength prediction and the load-pin displacement were investigated. Based on the
theoretical and experimental results it was concluded that the maximum stress criteria had
more realistic strength predictions for linear shear stress-strain relationship. Both the
Hashin failure criteria and maximum stress failure criteria showed same predictions for
the non-linear shear stress-strain relationship. The failure strengths predicted from the
developed model was within 1-15% of the experimental results
McCarthy et al. [58] developed a three dimensional finite element model using
MSc. Marc ® (commercially available software) to study the effect of bolt-hole clearance
on the behavior of single-bolted single-lap graphite-epoxy bolted joints. Experiments
were conducted to validate the finite element analysis. Issues in modeling the contacts
between the joint parts were studied. The surface strains and joint stiffness measured in
the experimental study were compared with the finite element study involving the
variations in the mesh density, element order, boundary conditions, material model and
analysis type. Three dimensional affects such as the through thickness stresses and
strains, secondary bending and bolt tightening were represented in this study.
33
It is evident from the literature that the bearing behavior in composite joints is
dependent on laminate lay-up, joint geometry, bolt preload and clamping pressure. The
initial bolt-load in a joint exerts pressure perpendicular to the plane of the material, and
most of the composites haVe their fibers oriented along the plane of the material. The
composite bolted joint experiences a biaxial loading condition when subjected to both in-
planes loading and bolt preload; hence the bolt preload and joint clamping pressure is a
critical component in a composite bolted joint design. Figure 1.7 shows a typical joint
subjected to in-plane loading and bolt preload. Very few research works focus on the
effect of bolt preload on thick composite bolted joints. Thick composite structures do not
necessarily behave in the same manner as thin structures with the same laminate
orientation. The strength and failure modes of thick composite joints cannot be scaled,
nor predicted based on the results of thin composite joints [33]. The influence of bolt
preload level investigated in the literature, according to this author's knowledge, does not
simulate the performance of heavily loaded composite structures. The study on behavior
of multi-bolted composite joint is also limited. The effect of tight and loose fastener
combination on the behavior of multi-bolted composite joints is hardly available in the
literature. This has been the main motive for studying the effect of bolt preload on
bearing behavior in composite bolted joints.
1.5 Objective of the Dissertation
In the first part of this dissertation, an analytical model based on continuum
mixture theories is developed to study the bi-axial interfacial shear stresses in adhesive
bonded joints due to thermo-mechanical loading. The model predicts the effect of
34
adhesive thickness and properties on the bi-axial interfacial shear stresses. The
interfacial shear stresses between the adhesive and each adherend is determined using the
constitutive equations. Numerical results show that both the adhesive thickness and the
material properties have a significant effect on the thermo-mechanically induced
interfacial shear stresses between the adherends and the adhesive. The developed model
inherently has the capacity for optimizing the selection of the adhesive thickness and
material properties that would yield a more reliable bonded joint.
In the second part, experimental and numerical investigations are carried out to
study the affect of bolt-load level, washer geometry and bolt tightness on the bearing
behavior of composite joints. A double lap shear joint is considered to study the effect of
bolt-load levels and washer geometry, while a double bolted single lap shear joint is
considered to study the effect of bolt tightness and joint material on the bearing behavior
of composite bolted joints. Finite element analysis using a commercially available code
ABAQUS ® is carried out to validate the experimental results. Failure analysis using
optical microscope and digital photography is conducted to analyze the bearing failure
mode in composite laminates.
35
Figure 1.1 Example of an adhesively bonded joint
• |
Adhesive shear stresses •Adhesive Direct (peel) stress
(a) (b)
Figure 1.2 Shear stresses and peel stresses in an adhesive bonded joint: (a) Shear stresses; (b) Peel stresses. (Modified from [3])
36
Tension
Adherend I
Adherent! 2
CTEi> CTE2 Compression
Figure 1.3 Shear stress due to difference in coefficient of thermal expansion (Modified from [3])
. „ • •
Adherend
Adhesive
m m Failure ^ Location
- Adherend
(a) (b) (c) (d)
Figure 1.4 Failure modes in adhesive bonded joints: (a) Cohesive failure; (b) Interfacial failure; (c) mixed failure mode; (d) Adherend failure. (Modified from [5])
37
N
^
x
>-" j 'X Thickness =t
Width = W \ ^jw Bolt hole diameter = D
Edge distance =E
Figure 1.5 Joint parameters in a typical composite bolted joint.
38
(a) -(b) (c)
P
(d) (e) (f)
Figure 1.6 Failure modes in composite bolted joints: (a) Tension failure; (b) Shear failure; (c) Cleavage failure; (d) Bearing failure; (e) Fastener pull through failure; (f) Bolt failure. (Modified from [48])
Bolt
1 earing Test
fixture
Composite Laminate
• Loading Direction
Figure 1.7 Single bolted double lap shear joint subjected to in-plane loading.
40
CHAPTER TWO
EFFECT OF ADHESIVE THICKNESS AND PROPERTIES ON THE BI-AXIAL INTERFACIAL SHEAR STRESSES IN BONDED JOINTS USING A CONTINUUM
MIXTURE MODEL
In this chapter, an analytical model is developed to study the interfacial shear
stresses which accounts for effects of bidirectional mechanical loading, uniform thermal
loading, thickness of the adhesive and the adherends, and the mechanical properties of
the adhesive and adherend materials. A continuum mixture theory developed by Nayfeh
et al. [10, 14] is extended to analyze the statically induced bi-directional interfacial shear
stresses in adhesive bonded joints subjected to various mechanical and thermal loadings.
Two sets of governing partial differential equations are solved for the displacement field
in each layer of the joint. The interfacial shear stresses between the adhesive and each
adherend is determined using the constitutive equations that are developed for the model.
Numerical results show, both thickness and the material properties of the adhesive have a
significant effect on the thermo-mechanically induced interfacial shear stresses between
the adherends and the adhesive. The proposed model inherently has the capacity for
optimizing the selection of the adhesive thickness and material properties that would
yield a more reliable bonded joint.
2.1 Formulation of the Problem
A linearly elastic model is considered for isotropic adherends that are perfectly
bonded by a layer of isotropic adhesive as shown in Figure 2.1a. All layers are assumed
41
to have the same length Lx and width Lz; layers are stacked normal to the y-axis. Because
of symmetry, a one quarter model is used, as shown in Figure 2.1b. The thickness of the
adhesive is 2ho and the thicknesses of the adherends are considered to by h a where a
represents materials 1 and 2.
The displacement vector at any point is described in terms of its components u(x,
y, z), v(x, y, z), w(x, y, z) in the x, y, and z directions, respectively. Figure 2.1a shows
the model of a mechanically loaded bonded joint that is composed of two plates
(adherends) and the sandwiched bonding agent (adhesive); the thermal loading is a
uniform temperature change from the ambient temperature. In light of the described
thermo-mechanical loading, the y-displacement v is assumed to be independent of x and z
/• dvq _ dvq _Qx
dx dz
2.1.1 Equilibrium and Constitutive Equations
If body forces are neglected, the equilibrium equations within each material a (a =
1,0,2) are respectively given by [59]
3o-xa | daXya | 3qXza = Q ~ „
dx 3y dz
— — + — + —3-— = 0 (2.2) (fy dx dz
dz dx dy
The constitutive relations are given by
derm , dojun | ^gyza _ Q ,-„
42
dx
Oya = (2 M-a + ^a) "T^ + la
dy dz - Y a T
3ua + 3w_a
8x 3z
dza = (2 ^ a + ^a)—-^ + la
dz dUg 3vg
dx dy
Y T 'a
Y T 'a
(2.4)
(2.5)
(2.6)
tfxya _ M^a dug , dvg
dy 9x
Oyzg - Ma
0"zxg — M*a
3vg + 3wg dz dy
dWg | dUg
dx 3z
(2.7)
(2.8)
(2.9)
where A,a and jxa are the Lame' constant and shear modulus, respectively, while ax, cy ,
az> °xy> °yz, CTxz a r e the components of the stress tensor. In equations (2.4-2.6), T
represents the temperature change from the ambient value, y is related to the coefficient
of linear thermal expansion p, the Bulk Modulus K, Young's Modulus E, and the
Poisson's ratio u as follows
Yg = 3PgKg EPg
( l -2u a )
2.1.2 Continuity Conditions
At the interface surfaces between the adherends and the adhesive, the
displacement field must be continuous. Additionally, the normal stresses oy
43
perpendicular to the laminate thickness, as well as the in-plane shear stresses o"yx, o"yz,
and ozx are continuous.
With reference to Figure 2.1a, the following continuity conditions are used ui=uo>
vi=vo> wi=wo, o-yi= Oyo, cjXyi= cxyo, oZyi = GjyQ at the interface between materials 1 and
0 (y = hi). Similarly with reference to Figure 2.1a, the following continuity conditions
are used ui=uo, V2=vo> W2=wo> ay2= oyo, oxy2 = oxyo, ozy2 = Ozyo at the interface
between material 2 and 0 (y = h).
2.1.3 Continuum Mixture Equations
In the following formulation the aim is to use the above equations to obtain two
sets of partial differential equations for x and z displacements that will ultimately yield
the solution for the interfacial shear stresses. In arriving at such equations, it is
guaranteed that the continuity conditions are satisfied. Hence, the behavior of this
adhesively bonded model is described as that of an equivalent higher order interacting
continuum.
This analysis is carried out in a continuum mixture format by eliminating the y-
dependence and defining some average values for the displacement and stresses over
their respective laminate thickness in y-direction. To this end, equations (2.1) and (2.4)
are averaged over the respective laminate thickness (for a =1, 0 and 2) according to
, v l hi (quantity), = — /(quantity \ dy (2.1 Oa)
hi o
44
. v 1 hl+2ho (quantity )0 = —— J (quantity )0 dy
2h0 h l
(2.10b)
h +h2
(quantity )2 = — / (quantity )2 dy h2 h
(2.10c)
Applying the continuity conditions on aXy« ,va and averaging according to equation
(2.10a-2.10c), the following set of equations are obtained
hi 3ojd + 3oxzi 9x 3z
•XxylO (2.11a)
2ho da xO j 3o~xz0 3x 3z
TxylO_TXy02 (2.11b)
h 2 3a x2 [ 3o~xz2 3x 3z
TXy02 (2.11c)
hi a x l - ( 2 u 1 + M ) ^ -dx
/ zr— 'N 3wi
v dz J
U + YiT = vio (2.12a)
2h0
h2
X2
CJXO""(2^O + ^ O ) T — " ^o
Ox2'
3x
dx A.2
dz
3w2 az
+ Y0T
y2T
vo2~vio (2.12b)
- V 0 2 (2.12c)
where, Txyl0 = a x y l (hj = axyo (hi), xxy02» x z y io , a n d Tzy02 a r e t h e equilibrium interaction
terms that represent the interfacial shear stresses on both sides of the adhesive, while
vio = vi (hi) = vo (hi) and vo2 a r e m e constitutive relation interaction terms.
45
Similarly, if equations (2.3) and (2.6) are averaged (for a =1, 0 and 2) along y
direction according to equations (2.10a), (2.10b) and (2.10c), equations similar to (2.11 a,
b, c) and (2.12 a, b, c) in terms of oz a r e obtained as follows
hi dCTzl + dCxzl dz dx
"TyzlO (2.13a)
2ho dCzQ ! d a xzO
dz dx Tyzl0_tyz02 (2.13b)
h 2 dgz2 [ dO~xz2
3z 9x Xyz02 (2.13c)
Ozl" •foi + A-i) 3wi
dz
z' ^ \ 9u_i
v d x y M + YlT V10 (2.14a)
2h0
Xo OzO~V^o (2li0 + ^o)
dwo dz
Xo 3uo dx
+ Y0T = vo2_vio (2.14b)
h2 Oz2" dz
. 3u2 3x , + y2T -VQ2 (2.14c)
2.1.4 Evaluation of the Interaction Terms
If the constitutive relation (2.5) is averaged according to equations (2.10a, b, c)
and the continuity conditions oyi = GyO = ay2 = a y are imposed, the following
equations are obtained
hi
Ul + 2Ri) Oy-A,l
dui dwi
dx dz + YiT vio (2.15a)
46
2ho (Xo + 2n0)
h 2
ta + 2n2)
A.0
O v_ ^ 2
8UQ 3wp 8x 9z + ToT V20~v io
3u2 3w2
3x 3z + Y2T V02
(2.15b)
(2.15c)
2.1.5 Relationship Between Shear Stresses and Average Displacements
The following linear distribution (across each laminate thickness) is assumed for
the shear stresses 0"xva (a = 1, 0, 2).
G x y l - A i y 0 < y < h i
OxyO-XxylO" 2h 0
lTxylO-TXy02j h i < y < h
axy2 = A 2 ( y - ( h + h2) ) - - h < y < h + h 2
(2.16a)
(2.16b)
(2.16c)
Similarly, an assumed linear distribution of the shear stress Gv z a in each laminate a (a =
1,0,2) is given by
o - z y l - B i y 0 < y < h j (2.17a)
ry - h i ^ CzyO-TzylO"
2h 0 f
azy2 = B2(y - ( h + h2))
,TzylO-Tzy02) " hi ^ y ^ h (2.17b)
-- h < y < h + h i (2.17c)
where the arbitrary constants Ai , A2, B j , B2 are defined as follows
TxylO TzylO A i = — — B i ~
hl hi
47
TXy02 Tzy02 A 2 = ; B2 = ~
h 2 h 2
It can be seen that the assumed shear stress distribution across the laminate thickness, in
equations (2.16a-2.17c), is dictated by the continuity conditions on axyand c z yas listed
in continuity conditions and illustrated in Figure 2.2.
Substituting for axyi from equation (2.16a) into equation (2.7), multiplying the
resulting equation by y, and then integrating according to equation (2.10a) by parts gives
TxylO 1 L = ui(hi)- ui (2.18a)
for material 0, equations (2.16b), (2.7), and (2.10b) are used to obtain
2h0
Ho
TxylO XXy02 - u o ( n ) - u ( (2.18b)
for materials 2, equation (2.16c), (2.7), and (2.10c) are used to obtain
•TXy02 Jl2_ 3u2
h) U2\n )~U2 (2.18c)
Following a similar procedure for ozycx (a = 1, 0, 2), equations (2.17a, b, c) and (2.10a, b,
c) yield
TzylO" ~ W l ( h l ) ~ w i 3Hi
(2.19a)
2ho
Ho
tzylO TZy02 wo (h)-wo (2.19b)
•Tzy02^ = W 2 ( n ) ~ W 2 3^2
48
(2.19c)
Finally, two relations similar to equation (2.19b) are derived as follows, for relating the
interfacial shear stress values TXylO a nd TXy02 to the difference between the
interfacial displacement UQ (hi) and the average displacement u 0 . From Figure 2.2, the
shear stress oxyo may be expressed in the alternate form
OxyO-X X y02" y - (h i + 2h0)
2ho llxylO-Txy02J (2.20)
J
Substituting for axyo from equation (2.20) into equation (2.7) with cc=0 and then
multiplying the resulting equation by [y-(hi+2ho)], and following the same procedure
which lead to equation (2.19a, b, c), gives
2h0
Ho
Txy02 TxylO -Uo(hl) -uo (2.21)
Following a similar procedure, the second relationship relates the interfacial shear
stresses Tyzio and xyZ02 to the difference between the interfacial displacement wo (hi) and
the average displacement WQ anc* is derived in a similar fashion by expressing the shear
stress Gyzo in the following alternate form
O"zy0-Tzy02" y - (h i + 2h0y
2h0 (xzylO -Tzy02) (2.22)
2h0
n Tzy02 TzylO
- w o ( h i ) - W0 (2.23)
49
2.1.6 Expression for Shear Stress in Terms of Displacements
Using the displacement continuity conditions, together with the symmetry
relations, equations (2.18 a, b, c) and (2.21) are combined and solved for the interfacial
shear stresses Txyio and xXy02 as follows
TxylO = Di(u2-uo)+D2(uo-ui) (2.24a)
TXy02 = D3(u2-uo)+D4(uo-ui) (2.24b)
In a similar way, expressions for the interfacial shear stresses xzyio and TZV02 are given
by
TzylO - Dl \W2 - W0J+ D2 (wo ~ Wl)
Tzy02 = D3 (w2 - Woj+ D4\WQ _ Wlj
(2.25a)
(2.25b)
where
Di = a 22 , D 2 = -ai2
ana22 _ ai2a2i ana22 _ai2a2i D3 = -a21
ana22 _ ai2a2i
D 4 = an
ana22~ai2a2i
a n - a 2 2 : 2hp 6u0
•> a i 2 2ho + h2 3u0 3u2
•> a 2 i -2 h o + hi
3^o 3 ^ 1 .
2.1.7 Governing Differential Equations
In this section, the governing partial differential equations are derived for the
layered model. Substituting equations (2.15 a, b, c) into equations (2.12 a, b, c), and
50
differentiating with respect to x and substituting the resultant equations in to equations
(2.11 a, b, c), the following expressions are obtained.
9 9
Mi + M2 dx< dxdz
- T xylO (2.26a)
32u(i , ^ 2 w p M3 + M4 dx' dxdz
TXylO_Xxy02 (2.26b)
d 2 u 2 w - ^ 2 w 2 A , M5 + M6 dx' dxdi
Txy02 (2.26c)
Mi through Mg reflect the material properties and layer thicknesses as follows
_ 2 u 1 + Xi Xi x . M i - 7- \— , M 2 :
Xlhi ( 2 ^ + A.iJhi Xi
2H! + A.i_
1
hi
M3 = 7- ^ - \ , M 4 :
X,o2ho v2^i0 + X,oj2ho 1 — ^0
2^0 + ^0. 2h 0
M 5 = 2^2 + ^2 7,2
^2h2 (2^2 + ^2) h2
M 6 = 1 — X2
2u 2 + ^2
1
h 2
In light of the model symmetry and the anticipated loading (Figure 2.1a), the shear stress
°zxa given by equation (2.9) is negligible; the equation may be manipulated to yield
9 2 w a _ 3 2 u a „ . 9 2 w a _ 3 2 u a
dxdz az2 and-
dx' dxdz . Substituting the expressions for xXyio an(*
Txyo2 from equations (2.24 a, b) into equations (2.26 a, b, c), yields the following set of
governing partial differential equations in terms of the average x-displacement u a m
each layer (a = 1, 0, 2)
51
= -b l (u 2 -uo)+D2(uo-ui )J (2.27a)
= [(^2-^o)(Di-D3)+(uo-m)(D2-D4)] (2.27b)
= D3(u2-uo)+D4(uo-ui) (2.27c)
The second set of governing partial differential equations in terms of the average z-
displacement is obtained by using equations (2.15 a, b, c) and following the same
procedure that lead to equations (2.27 a, b, c), which yields
= - [ D I ( W ^ - W O ) + D 2 ( W ^ - W ^ ) ] (2.28a)
= [(w2~wo)(Di-D3)+(wo-wi)(D2-D4)] (2-28b)
= D3iw2 - wo) + D4lwo _ wij (2.28c)
2.1.8 General Solutions for the Governing Partial Differential Equations
The general solution for the two sets of governing differential equations (2.27 a,
b, c) and (2.28 a, b, c) is given by
u > a a e P x (2.29)
w > a a e P z (2.30)
Where aa are constants (a= 1, 0 and 2), and p is the eigen value. Substituting the general
solutions given by equations (2.29) and (2.30) into the governing differential equations
52
a2m ax2 M r
a2
3z y M 2
a2uo 3x2 M 3 - uo
dz' M4
a2 U2
ax2 M 5 -a 2 u 2
az2 M 6
a wi az2 M r wi
3x' M 2
a wo. , a wp„ M3 T-M4
a^ 3x'
a W 2 W a W 2 W
az2 a x
2
(2.27a, b, c) and (2.28a, b, c) gives the eigen values for p, by solving a third order
2 polynomial in p . The roots of the polynomial equation are properties of the model that
are solely determined by the material properties and thickness of the layers.
The non-trivial solution for the average x-displacement u a (a = 1, 0,2) in each layer is
given by
Ua = ciasinh(p1x)+c2aSinh(p2x) (2.31)
where c i a and C2a are arbitrary constants to be determined from the boundary conditions.
In a similar fashion, the non-trivial solution for the average z-displacement w a is
given by
w a = diasinh(p1z)+d2a smh(p2z) (2-32)
where d i a and d2a are to be determined from the boundary conditions.
The normal strains exa and £va (a = 1, 0, 2) are obtained by differentiating equations
(2.31) and (2.32) with respect to x and z, respectively.
2.1.9 Boundary Conditions
For the layered model shown in Figure 2.1b, a uniform tensile stress oo is applied
only to the faces perpendicular to the x and z directions. Additionally, the model
temperature is changed by T from the ambient temperature. These loading conditions are
considered to be the generalized case in the study. The model can be used to analyze
other types of adhesive joints by modifying the boundary conditions. For example, a
single-lap joint may be simulated by limiting the non-zero surface loading (boundary
53
conditions) to the positive and negative x-directions on materials 1 and 2, respectively as
shown in Figure 2.1c. Using normal strains and equations (2.16-2.21), (2.12 a, b, c) and
(2.15 a, b, c) and assuming that the average stress <yya is negligible yields
o"xa: 2jXa + X,a Xa
[ c i a p 1 cosh (p 1 x)+c 2 aP2 c o s h (P2 x ) ] +
2 ^ a
2u a + )ia
Xa ^M'a ^a .
[diaPiCOsh(p 1z)+d 2aP2 c o s h(P2 z)]-YaT 2 ^ a
Oza
2 ^ a
2u a + A,a ^ a [dlaPi c o s h(Pl z)+d2aP2 c o s h(P2 z)]+
2^ a + ^a
Xa 2jia + /,a_
[c i a p 1 cosh(p 1 x)+c2aP2 c o s h (P2 x ) ] -YaT 2 ^ a
(2.33)
(2.34)
where the constants cia , C2a, dla> a n ( i ^2a ( a = 1> 0» 2) in equations (2.33) and (2.34) are
determined from the following boundary conditions
°xa x=±Lx /2=°0 and c z a | z = ± L 7 / 2 - C O (2.35)
where OQ is the applied uniform stress.
2.1.10 Interfacial Shear Stresses
After the boundary conditions have been implemented, the average displacements
u a and w a given by equations (2.31) and (2.32) are substituted into equations (2.24 a, b)
and (2.25a, b) to obtain the following expressions for the shear stresses at the interfaces
between the adhesive and the two layered materials
54
TXyio = Di[(ci2sinh(p1x)+c22sinh(p2x))-(ci0sinh(p1x)+c2osinh(p2x))J
(2.36)
+ D2[(ciosinh(pj x)+ C2osinh(p2x))- (C11 sinh(pjx)+ C2isinh(p2x))]
Txy02 = D3Kci2sinh(p1x)+ C22sinh(p2x))- (ciosinh(pjx)+ C2osinh(p2x))J
+ D4 [(cio sinh (pj x)+C20 sinh (p2 x)) - (C1! sinh (pj x)+c2i sinh (p2 x))]
TzylO = Di [(di2 sinh(pj z)+ d22 sinh(p2 z))- (dio sinh(pj z)+ d20 sinh(p2 z))J
+ D2 [(dio sinh(pj z) + d2o sinhfpj z))- (di 1 sinh(pj z)+d2i sinh(p2 z))]
Tzy02 = D3 l(di2 sinh(pj z) + d22 sinh(p2 z)) - (dio sinh (pjz) + d20 sinh(p2 z
D4 [(dio sinh (pjz) + d20 sinh(p2 z)) - (di 1 sinh(pj z)+ d2l sinh(p2 z))]
(2.37)
(2.38)
(2.39)
+
2.2 Numerical Results and Discussions
The solution for the interfacial shear stresses xXyio, TXy02, TzylO a n ( i Tzy02> given
by equations (2.36-2.39), demonstrate their dependence on the geometry and properties
of the adherend (material 1 and material 2), the adhesive (material 0) and on the
mechanical and thermal loadings, 00 and T, respectively.
In the numerical results, two main issues are investigated; namely, the influence
of the adhesive thickness and mechanical properties on the interfacial shear stresses. A
boron laminate (material 1) and a carbon phenolic laminate (material 2) are used as
adherends. Table 2.1 shows the properties of the adherend materials. For the adhesive,
various arbitrary sets of elastic properties (Xo, \IQ) and thickness are used. The Lame'
constant XQ; and shear modulus uo, for the bonding material were assigned as percentages
55
of the boron laminate properties X\ and \i\. Four cases are considered for the numerical
investigations; namely, 5%, 10%, 20% and 30% of the boron laminate properties.
2.2.1 Finite Element Verification
The finite element code ABAQUS ® is used for the comparison of shear stresses
at the adherend adhesive interface. Due to symmetry, one quarter model is analyzed
using 3-dimensional continuum 8 node reduced integrated elements (C3D8R) [60].
Isotropic material properties for the adherends and the adhesive are considered. Tie
constraints are imposed at the adhesive interface with the adherends. A finer mesh,
32000 solid continuum elements, is used for the complete model to analyze the interfacial
shear stresses. Uniform tensile stress of 10 MPa was applied to the faces of the joint
along with a uniform temperature field of 10°C.
Figures 2.3-2.10 show the results from both the theoretical and FEM models for
interfacial shear stresses, TXY and Tzy on the lower and upper interfaces between the
adhesive and the adherends. A tensile stress of 10 MPa is applied to the external
boundaries of the joint as shown in Figure 2.1a. The interfacial shear stresses increase in
a nonlinear fashion as the distance is increased from the origin towards the edge of the
model. The distributions of the 3D interfacial shear stresses from both the theoretical and
FEM have similar trends, but there is a difference in the magnitude of the shear stresses.
This difference may be attributed to the assumptions in the model and the limitations in
the FEM procedure. The through thickness averaging procedure for the displacement in
the continuum model, as well as the linear approximation of the shear stresses are one of
56
the reasons. The change in normal stresses c y is considered to be negligible in the
theoretical model, which cannot be simulated in the FEM analysis. Further in the FEM
model the stresses at the individual nodes are the average between the adjacent nodes and
this does not necessarily produce absolute stress free boundary condition. Where as in the
theoretical model stress free boundary conditions are maintained when required for
equilibrium conditions. All these along with the mesh size of the FEM model of 8-node
brick elements contributes to the difference in the shear stresses [9, 60].
Figure 2.3 and Figure 2.4 show the shear stress xXy distribution on the upper
interface from the theoretical and FEM analysis respectively. Similar distribution of
shear stresses, maximum at the edge of the joint and zero at the center of the joint is
observed in both the cases. Figures 2.5 and 2.6 show the shear stresses xzy, distribution
on the upper interface and these are rotated version of the shear stresses xxy, about the y
axis. Figure 2.7 and 2.8 show the interfacial shear stresses at the lower interface. The
theoretical results closely match the FEM results in both the magnitude and the trend of
interfacial shear stresses except near the edges. The theoretical and FEM interfacial shear
stresses xzy, at the lower interface is shown in Figure 2.9 and 2.10 respectively. For
simplification, all the numerical analyses were carried out assuming the geometric model
to be symmetric, that is Lx and Lz were considered equal.
57
2.2.2 Effect of Elastic Properties of Adhesive
Due to model symmetry, the numerical results for the effect of adhesive
L - L properties are shown for the one quarter model — < x < 0, < z < 0. Figures 2.11 and
Figure 2.12 demonstrate the effect of adhesive material properties on the interfacial shear
stresses at the upper interface (xZy02, Txy02) a n ^ lower interface (xXyio, tzyloX
respectively. The thickness of the adhesive is maintained at 0.09 m and the applied stress
oo at the boundaries (x = , z = ) were maintained at 10 MPa. The properties XQ
and (io of the adhesive material are considered to be 5%, 10%, 20% and 30% of the boron
laminate and are referred to as case 1, 2, 3 and 4 respectively. Figure 2.11 shows that the
shear stresses on the upper interface increased, as the properties no and 1Q of the adhesive
are increased from 5% to 30% of those of material 1. However, the corresponding shear
stresses on the lower interface (Figure 2.12) decreased. The reason for reduced shear
stresses on the lower interface and increased shear stress on the upper interface is due to
the increase in the difference in material properties at the upper interface and reduction at
the lower interface as the adhesive properties are increased from 5% to 30% of those for
the boron laminate (material 1).
2.2.3 Effect of the Adhesive Thickness
Figures 2.13 demonstrate the effect of adhesive thickness on the shear stresses
xXyi 0, xZyio at the lower interface. The adhesive thickness is described by using a non-
58
dimensional volume fractions n which is the ratio of the adhesive thickness 2ho to the
overall thickness h of the model, as shown by equation (2.40)
n = ^ (2.40) h
In this section, the elastic properties no and XQ of the adhesive are maintained at 10% of
those for the boron laminate (material 1). The applied surface traction at the boundaries is
10 MPa. The volume fraction of the adhesive is varied from 0.03 to 0.1 which
corresponds to an adhesive thickness between 0.03m to 0.1m.
Numerical results in Figures 2.13 show that the magnitude of the maximum shear
stress at (x = z = ), is increased on both interfaces as the volume fraction of the 2
adhesive is increased.
2.3 Summary
New formulas are derived for the bi-axial interfacial shear stresses that develop in
an adhesively bonded joint due to static thermo-mechanical loading. The analysis is
carried out along the lines of continuum mixture theories of wave propagation.
Numerical results that show the effect of both the elastic properties and the thickness of
the adhesive on the interfacial shear stresses are investigated. Numerical results show
that both the material properties and the thickness of the adhesive have a pronounced
effect on the developed interfacial shear stresses due to the thermo-mechanical loading.
For the present model, it has been found that increasing the thickness of the adhesive
causes a significant increase of the interfacial shear stresses. The larger difference in the
59
elastic and thermal properties between the adhesive and the layered adherends the higher
the corresponding interfacial shear stress is. The proposed model inherently has the
capacity for optimizing the selection of the adhesive thickness and material properties
that would yield a more reliable bonded joint.
Table 2.1
Material properties of Boron and Carbon Phenolic Laminate
Property
-3
Density p (kg/m )
Shear Modulus, u ( MPa)
Lam'e constant, X (MPa)
y (MPa °C)
Boron laminate (Material 1)
2370
95100
80600
6.48
Carbon Phenolic Laminate (Material 2)
1420
6620
11400
9.48
60
Material 2 (Adherend)
Material 0 (Adhesive)
^Material 1 (Adherend)
(a)
Figure 2.1 Geometric model (a) Complete model of the adhesive bonded joint
61
Y
Material-2
Materta!-0
(Adhesive) Material-1
Lx/2
h2
h+h2
(b)
Figure 2.1 (b) One quarter model of adhesive bonded joint
62
Material 2 (Adherend)
Material 0 (Adhesive)
Material 1 (Adherend)
Figure 2.1 (c) Model representing an adhesive bonded single lap joint.
63
h+h0
• x
Figure 2.2 Shear stress distribution
64
CO CL
CO CO
2 CO
co a) sz CO
Distribution of Shear Stresses (XY) along the Upper interface
(Theoretical)
1 Y
/ J 2 J
— ,..j— —
A I
*• z
1.6 -0.05
(Z-axis) Width of the Joint (m)
(X-axis) Length of the Joint (m)
Figure 2.3 Theoretical shear stress, (xxy), at the upper interface
65
Distribution of Shea along the Uppei
(FEM)
I l
1.8 Hf^*"" ' (Z-axis) Width of
the Joint (m)
o e l - 0 . 6 ^
V _ - --1.9 -- „ o °
i
r Stresses (XY) r interface
""IN 1 "v
HH^T0'3
JHHHo.2 •HH0'1
\ M.1 \ [-0.2 ^^f-0.3
io T •
ci T-
(X-axis) Length Joint (m)
(0 Q.
(0
s> CO
to
<D
CO
of the
Figure 2.4 FEM shear stress, (xXy), at the upper interface
66
CO CL
!/) . fi
CO i_ CO (1)
. c CO
Distribution of Shear Stresses (ZY) along the Upper Interface
(Theoretical)
0.30
(X-axis) Length of the Joint (m)
(Ml (Z-axis) Width of the Joint (m)
Figure 2.5 Theoretical shear stress, (xZy), at the upper interface
67
Distribution of Shear Stresses (ZY) along the Upper Interface
(FEM)
(X-axis) LengtH ° of the Joint (m)
<^e> r(Z-axis) Width of the Joint (m)
Figure 2.6 FEM shear stress, (izy), at the upper interface
68
Distribution of Shear Stresses (XY) along the Lower Interface
(Theoretical)
CD EL
s
to CO CD w co i _
CD CO
CO
2 1.5
1
0.5
0 -0.5
-1 -1.5
-2
X - •
* z
(Z-axis) width of
the joint (m)
(X-axis) length of the joint(m)
Figure 2.7 Theoretical shear stress, (xXy), at the lower interface.
69
CD Q .
CO CO
8>
CD CD
. c CO
Distribution of Shear Stresses (XY) along the Lower Interface
(FEM)
2.5-r ~^^ririDffiflM9&
2]mmmm. 1.5-
1-0.5
0 r ^^^^H
-0.5 j '"""HI
-1-1 "1-51 / -zlkl
-1.8
5 -1
.35
-0.8
5 -0
.35
/ 0.
15
/
0.65
/
(X-axis) Length of the Joint (m)
-S|
1.15
/
X
• ' z
0.9 -0.55 (Z-axis) Width of
the Joint (m)
m CO
Figure 2.8 FEM shear stress, (Txy), at the lower interface.
70
Distribution of Shear Stresses (ZY) along the Lower Interface
(Theoretical)
(X-axis) length of joint(m)
(Z-axis) width of joint (m)
*< z
Figure 2.9 Theoretical shear stress, (xzy), at the lower interface.
71
Distribution of Shear Stresses (ZY) along the Lower Interface
(FEM) , _ . — . — • • - — " " " ™ T \
i "—• " *
^
\
> 2 . 5
iX ! ^ ..
>H^ | \ ^ ^ ^ ^
:~"~~r " J ^ ^ ^ ^
•^r^"^%
"2 -ro -1.5 9: -1 1 0.5 $ 0 2>
+-< -0.5 « . 1 CD
1 0 -1.5 -?
(X-axis) Length 0% ^ f of the Joint (m) 1 \ ^ " 2 5
2 ^ rt w ™ « d ^ & " ^ 9 d> T— '
(Z-axis) Width of the Joint (m)
Figure 2.10 FEM shear stress, (xzy), at the lower interface.
72
-3.50
Effect Of Adhesive Properties on the Shear Stress at the Upper Interface
-3.00
-2.50
-2.00
-1.50
-1.00
-0.50
0.00
a=10 Mpa
AT=10"C
*—case 1
2000 1750 1500 1250 1000 750 500 250
Distance from the center (mm)
2.11 Effect of adhesive properties on the shear stress at the upper interface.
73
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
2000
Effect of Adhesive Properties on the Shear Stress at the Lower Interface
\
A - \
• S i ^
2
•™Jr™
T
7 i
< *
X
a=10 Mpa AT=10"C
m case 1
--*—• case 2
2/ '" —»— case 3 z —#— case 4
1500 1000 500
Distance from the center (mm)
ure 2.12 Effect of adhesive properties on the shear stress at the lower interface.
74
Effect of Adhesi\e Volume Fractions "n" on the Shear Stress at the Lower Interface
Volume fraction " n " ^ d h e s i v e
Total Thickness
1500 1000
Distance from the center (mm)
Figure 2.13 Effect of adhesive thickness on the shear stresses at the lower interface
75
CHAPTER THREE
EFFECT OF WASHERS AND BOLT TENSION ON THE BEHAVIOR OF THICK COMPOSITE JOINTS
In this chapter, experimental characterization of thick composite bolted joints is
performed to study the effect of washer size and bolt preload on bearing properties. S2-
glass fabric-epoxy composite coupons [0/90; +45/-45 @ 10 sets] of 12.5 mm thickness
were tested under double shear tensile loading. Two different washer sizes and
thicknesses were used in this investigation. A force washer is used to monitor the clamp
load variation during the test. It has been found that the initial bolt tension (preload) and
washer size have a significant effect on bearing stiffness and bearing strength of thick
composite joints. For a low bolt preload, test data shows a significant clamp load
increase with the joint displacement. However, the percentage increase in clamp load is
reduced as the preload is increased to 50kN. The outward buckling and delamination of
the laminate in the composite coupons were found to be the main cause for clamp load
increase.
3.1 Experimental Setup and Procedure
Extensive experiments were conducted to investigate the effect of bolt preload,
washer area and washer thickness on the bearing strength, bearing stiffness and ultimate
strength of glass-mat epoxy laminated composite bolted joints. ASTM standard D
5961/D 5961-05 [33] was followed to study the bearing response of single bolted double-
shear tensile loaded joints.
76
3.1.1 Material
Multi-directional 20-ply fiber-reinforced polymeric matrix laminated composite
coupons were supplied by Sherwood Advanced Composite Technologies. The composite
coupons of SO 15 toughened epoxy resin/S-2 fiberglass-mat with [0/90; +45/-45 @ 10
sets] orientation was manufactured by Vacuum Assisted Resin Transfer injection
Molding (VARTM) process. The nominal thickness of tested coupons is around
12.5mm; they were designed for bearing failure. Figure 3.1 shows the geometry of the
test coupon used in the study. The test coupon was designed for bearing failure. The
width to diameter (W/D) ratio of 4 and edge distance to diameter ratio (E/D) of 3.5 was
maintained through out the experiments.
3.1.2 Test Fixture and Instrumentation
Figure 3.2 shows the double shear test fixture used in this study. The fixture is
designed to mount the extensometer for monitoring the coupon displacement relative to
the fixture. An MTS hydraulic testing machine is used to apply the tensile loading to the
specimen at a rate of 5mm/min. A force washer and a data acquisition system are used to
monitor the bolt preload, joint clamp load and as well as the joint displacement during the
tests. Figure 3.3 shows the experimental set used in the study.
Five levels of bolt preload, two different washer sizes and two washer thicknesses
are used in this study. Bolt preload levels are 0, 25, 50, 75 and 100% of the proof
strength of 1/2"-20 SAE Grade 5 fasteners. Large washers (USS) with an effective area of
796 mm2 and small washers (SAE) with an effective area of 430 mm2 are used. Single
and double washers are used to simulate two different washer thicknesses. Fasteners
77
were tightened to the desired preload level as indicated by the force washer. Table 3.1
presents the actual bolt load and corresponding clamping pressures for different washer
configurations.
Load control method was used to tighten the fasteners in-order to produce the
required reliable initial bolt load. Torque control method for tightening the fasteners does
not necessarily produce the required bolt load [61, 62]. T = KdF is the basic equation
used to calculate the initial bolt load [61]. Where K is the nut-factor, T is the applied
torque, d is the bolt diameter and F is the initial bolt-load. Here, K the nut-factor is
generally selected from published tables [62] for various combinations of materials,
surface finish, plating, coatings and lubricants. However, the literature [63, 64] has
showed that this is highly unreliable and the nut-factor depends on thread friction and
washer under head frictional coefficients. Equation 1 [61] gives the relation for the nut-
factor, considering various frictional coefficients.
T = F — + J-L7r + M,nrn 271 COS p
(3.1)
where T = torque applied to the fasteners (lb-in, N-mm), F= bolt preload (lb, N),
P=thread pitch (in, mm), Ut= thread friction coefficient, rt= effective contact radius of the
threads (in, mm), p= half-angle of the threads, |i„ = washer under head frictional
coefficient, rn = effective radius of contact between the nut and washer or joint surface
(in, mm).
In the present study, instead of selecting the nut-factor from published source, a
load control method of bolt tightening is followed, in which a force washer is used to
monitor the initial bolt load in real time. This procedure ensured that the required (0%,
78
25%, 50%, 75% and 100% of bolt proof load) initial bolt load was achieved in all tested
joint configurations.
3.1.2.1 Bearing Properties
The effect of various joint parameters, discussed in the previous section, on the
bearing stiffness, the bearing strength and the ultimate joint strength and strain is
investigated in the study.
Figure 3.4 shows the typical bearing stress distribution in a bolt loaded joint [65]. Radial
bearing stress p due to a bolt in a hole is generally considered to be distributed around the
loaded half of the pin-hole circumference [65] as follows,
p = pmcose [ - ^ < 0 < ^ ] (3.2)
v 2 2)
where pm is the maximum radial stress on the bearing region due to bolt load L. The bolt
load L can be expressed as
L = J pcosOh^dO (3.3) -71/2 2
where d is the bolt-hole diameter and h is the laminate thickness. Substituting equation
(3.2) into equation (3.3) gives a relation for the bearing stress
L = ^ p JCOs20de (3.4) 2 -nil
L = | p m h d (3.5)
In this study, the bearing stress a is considered as the average stress acting uniformly
over the projected cross-sectional area of the hole given by [33] as follows
79
c = i - (3.6) hd
The corresponding average bearing strain 8 for each displacement 8 is e = — , where 8 is
d
the extension of the composite coupon at the bolt hole region measured using an
extensometer. The maximum load prior to failure was used for the ultimate bearing
stress.
The slope of the initial linear bearing stress- strain curve is used to determine the
bearing joint stiffness (Figures 3.5 and 3.6). An effective origin is defined at the
intersection of the bearing stress-strain line with the strain axis. The stiffness line is then
translated from the effective origin by the offset 2% strain to obtain the 2% offset bearing
strength (Figure 3.6).
3.2 Results and Discussion
Figure 3.5 and Figure 3.6 show the bearing stress-strain plots for the zero bolt
preload and for bolt preload of 50% of its proof load, respectively. The bearing stress-
strain data for the zero bolt preload joint shows different behavior when compared to the
joints with non-zero bolt preload. The initial portion of the bearing stress - strain curve
in Figure 3.6 (strain correction zone) shows a nonlinear response due to combination of
joint straightening, overcoming of joint friction, and joint slippage [33]. This initial
nonlinear response is observed for the non-zero bolt preloads. Beyond this initial
response, the bearing stress-strain curves show a linear increase in stress until the bearing
failure in initiated. The slope of the initial bearing stress- strain curve is used to determine
the bearing stiffness of the joint (Figures 3.5 and 3.6). A slight stress plateau is observed
80
at point A indicating initial bearing failure for joint with zero bolt preload (Figure 3.5).
Beyond this point the joint continues to carry the load until the bearing stress drops
significantly, indicating the final rupture at the bolt hole boundary in the composite
coupon. A similar stress plateau has not been observed for a joint with a preloaded bolt
(Figure 3.6); the change from linear to non-linear behavior was gradual. For this reason,
2% offset bearing strength is considered in this study for comparison purpose. For both
preload levels, the joint continues to carry the load after the initial bearing failure until
the ultimate bearing strength has been reached. The strain measured at this maximum
bearing stress from the effective origin is called as the ultimate joint strain. This joint
strain or the joint elongation is due to the combination of increase in the bolt-hole
diameter and joint material elongation. In the present study the joint material elongation
was negligible.
3.2.1 Effect of Bolt Preload
As described earlier, five different bolt preload levels ranging from 0% to 100%
of the bolt proof load is considered in the study. Figure 3.7 - Figure 3.10 show the effect
of initial bolt load on the bearing joint stiffness, offset bearing strength, ultimate joint
strength and joint strain for various joint configurations, respectively. Table 3.2 - Table
3.5 show the average values of the bearing properties for single large washer, single small
washer, double large washer and double small washer composite joints, respectively.
3.2.1.1 Effect of Bolt Preload on Joint Bearing Stiffness
Figure 3.7 shows the bearing stiffness at various levels of bolt preload for various
washer configurations. The bearing stiffness is largest for the untightened joint (zero bolt
81
preload). The stiffness reduces by 15-20% for the joints in which the bolt preload is 25%
of the proof load. The axial load transfer in the tightened joint coupons is by the
combination of bearing contact on the cylindrical surface of the hole and the frictional
contact between the flat coupon surfaces [62]; whereas, in a zero preloaded bolted joints
the load transfer is only due the bearing contact. Because the composite coupon used in
this study is thick, relatively stronger through the thickness for the bearing load transfer,
the joint behavior was stiffer for the untightened joints where the frictional force is
negligible. The joints with 25% bolt preload displayed a lower stiffness as their initial
behavior was dominated by the frictional force between the washers and the surface of
the composite coupon. The frictional effect was reduced as the bolt preload increased to
100% of proof load.
3.2.1.2 Effect of Bolt Preload on Offset Bearing Strength
The offset bearing strength increases progressively with increasing the bolt
preload. As the bolt preload is increased from 0% to 25%, 50%, 75% and 100% of its
proof load, the bearing strength of the clamped composite coupon increased by about
28%, 37%, 37% and 40%, respectively (Figure 3.8). Higher initial bolt load created
enough lateral constraint on the composite coupons to delay the initiation of bearing
failure on the contact surface between the bolt shank and the hole surface [29, 30, and
32].
3.2.1.3 Effect of Bolt Preload on Ultimate Joint Strength and Strain
Figure 3.9 shows that for the small washer configuration the ultimate joint
strength was unaffected by the increase in bolt preload, which is consistent with [31] and
82
[66]. The ultimate joint strain (elongation) was about 15% more for the untightened joint
as compared to other bolt preloads (Figure 3.10). The clamping pressure created by the
initial bolt load reduced the bolt-hole elongation resulting in lower joint strain. For large
washer composite joints, the ultimate failure load exceeded the load cell capacity (MTS
100 kN).
3.2.2 Effect of Washer Size and Thickness on Bearing Behavior
Figure 3.11 shows that joints with smaller diameter washers had higher bearing
stiffness than those with larger washers for bolt preloads up to 50% of the proof load.
The bearing stiffness was unaffected by the washer size for higher bolt preloads. This
increase in bearing stiffness for small washer joints was mainly due to the high clamping
pressure. For the same bolt preload, smaller washers exerted higher clamping pressure
on the composite coupons than the large washers. Figure 3.11 and Figure 3.12 show the
effect of washer size on the bearing stiffness for single washer and double washer joints,
respectively, with various levels of bolt preload. Table 3.1 presents the lateral clamping
pressure exerted by the small and large washers for different initial bolt loads.
Figure 3.13 and Figure 3.14 show the results for the effect of washer area on the
offset bearing strength. It is observed that joints with smaller washers have a slight higher
bearing strength (5%) than those joints with large washers. This suggests that the higher
lateral clamping pressure exerted by the smaller washers delays the initiation of bearing
failure which translates to an increase in the offset bearing strength.
After the initiation of bearing failure, both small washer joints and large washer
joints, continue to carry the load as the bearing damage progresses to ultimate failure.
83
The joints with smaller washers fail at about 550 MPa; whereas, the joints with larger
washers had its ultimate strength beyond 585 MPa (load cell limit). The larger clamping
area of the large washers suppressed the delamination in the bearing zone, resulting in
increased ultimate joint strength and strain. The higher lateral clamping pressure by
small washers induced additional surface damage, resulting in lower ultimate joint
strength
Figure 3.16 and Figure 3.17 show the effect of washer thickness on the bearing
stiffness for larger and smaller size washers at various preloads levels. It is observed that
using single washer causes a slight increase in bearing stiffness (5%), as compared to
joints with double washers (thick washer). Figure 3.18 and Figure 3.19 show the
corresponding effect on the offset bearing strength. The use of single washer produced a
slight increase (5%) in bearing strength. By using a two washer stack in the joint, one
introduced an additional frictional surface which induces relative instability in the joint
behavior. This unstable joint behavior is likely the reason for the slight decrease in the
corresponding bearing stiffness and bearing strength. The washer thickness had no
significant effect on the ultimate joint strength and strain. This behavior was expected as
friction has a minimal influence on the joint behavior after the bearing failure has been
initiated.
3.2.4 Clamp-Load Variation
Figure 3.20 and Figure 13.21 show the measured joint clamp-load verses joint
displacement/applied load for zero and 50% bolt preload (of proof load) joints,
respectively. For the zero bolt preload joints, the clamp load increased linearly with joint
84
displacement. This linear increase continued until the initial bearing failure, beyond
which clamp load increased significantly in a nonlinear manner. At the point of ultimate
failure the clamp load further increased with a larger slope. For the non-zero bolt preload
joints, the clamp load remained almost constant until the joint overcame the friction
between the parts (points F on Figure 3.21). At this point the clamp load slightly
dropped, and then increased linearly with lower slope until the initial bearing failure
initiated (point A). Beyond the initial bearing failure the clamp load variation was
similar to that of the zero bolt preload. The clamp load variation for joints with 25, 75
and 100% bolt preload followed the same trend as that of the 50% bolt preload joints
(Figure 3.21). This increase in clamp load after the initial bearing failure is mainly due
the progressive increase in through thickness of the composite coupon due to the
delamination and fiber-matrix outward buckling in composite coupons [66].
Figure 22 shows the variation of joint clamp load with applied load for joints with
small washers. The increase in joint clamp load for zero bolt preload, was significantly
higher than that for the tightened joint. The lateral clamping pressure induced by the
washers increased with the bolt preload, and reduced the delamination failure in the
bearing zone. This explains the reduction in clamp load change with increasing the bolt
preload. Test data shows the sudden increase in clamp load at ultimate joint failure. This
failure load remained almost the same regardless of the level of bolt preload. Figure 23
shows the joint clamp-load variation with the applied axial load when large washers are
used. The clamp load variation for large washer joints was similar to the small washer
joints, except in the ultimate failure region. The sudden increase in clamp load at the end
85
of each curve was absent, showing that the large washer joints carried load beyond 95kN
(load cell capacity).
3.2.5 Failure Analysis
Bearing failure in composite coupon was the prominent failure mode observed in
all tested joint configurations. The area and the extent of bearing damage varied with
washer size and initial bolt load. Figures 3.24 a, b show the bearing damage in small
washer and large washer joint coupons with zero bolt preload, respectively. The extent of
bearing damage and the bolt-hole elongation in the small diameter washer joints were
more sever compared to the large diameter washer joints. For the coupons with large
washers the bearing damage was more uniform and was only seen under the washer
contact surface. However, the bearing damage for coupons with smaller washers spread
over a larger area beyond the washer contact. The delamination was more severe just
outside the washer contact region; this was responsible for the significant load drop at the
ultimate failure region. The increase in coupon thickness on the loaded side of the bolt-
hole was observed for joints with smaller and larger washers. This was mainly due to the
delamination and outward bucking of laminate in the localized bearing regions. As the
outward buckling and delamination increased, the laminate were pressed against the
washers creating the increase in clamp load observed in Figures 3.22 and 3.23 for
untightened joints [32].
Figure 3.25 shows the extent of bearing damage for coupons with large washers.
It can be observed that the bearing damage was more significant for joints with zero bolt
preload; the damage extent reduced with the increase in bolt preload. The bearing
86
damage was primarily under the washer surface; washer imprint was also observed for all
joint coupons. For the joints with higher initial bolt load, the lateral restraint of the
washers reduced the delamination and outward bucking of the laminates. This behavior
reduced the increase in clamp load as observed in Figure 3.22 and 3.23 for joints with
higher bolt preload.
3.3 Summary
Experimental data is presented on the affect of initial bolt preload, as well as the
washer size and thickness on the behavior of heavily loaded thick composite joints.
Friction between the joint parts played a significant role in defining joint stiffness. The
joint bearing stiffness was higher for the untightened bolted joint than that with much
higher bolt preload (100% of proof load). The bearing stiffness was smallest for the joint
with a preload equal to 25% of bolt proof load, and it increased with bolt preload. The
offset bearing strength increased progressively with bolt preload. The ultimate joint
strength was unaffected by increasing the bolt preload. Joint with small washers had
higher bearing stiffness than those with large washers for initial bolt preload of 0%, 25%
and 50%. Joints with small washers had higher offset bearing strength than the joints
with large washers. The washer thickness had an insignificant effect on the ultimate joint
strength and strain.
As the axial test load is increased, an untightened bolted joint showed a
significant increase in the clamp load (from its zero initial value). This increase in the
clamp load was progressively reduced by the increase in initial bolt-load. Bearing
damage was the prominent failure mode in all tested joint configurations. The extent of
87
bearing damage was more severe in smaller washer joints, where the damage extended
beyond the washer contact. Out-of-plane buckling of laminates exerted lateral pressure
on the washers resulting in an increase in clamp load during the experiments. These
experimental results help in the selection of an optimum initial bolt preload and washer
size and thickness in order to enhance composite joint performance and reliability.
Table 3.1
Initial bolt-load and corresponding clamping pressure for small and large washer joints
Bolt Clamp-Load
% of Proof Load
0%
25%
50%
75%
100%
Actual Clamp Load (kN)
0.2
13.34
26.68
40.03
53.37
Clamping
Large washer (USS)
0.28
16.74
33.48
50.22
66.97
Pressure
Small washer (SAE)
0.52
31.05
62.55
93.16
124.22
88
Table 3.2
Bearing properties of single large washer composite joints
Single Large (USS) washer composite joint
Clamp Load (% of bolt proof
strength)
Bearing 2% bearing Ultimate Stiffness strength strength Joint (MPa) (MPa) (MPa) strain (%)
0 %
2 5 %
50%
7 5 %
100 %
50.54
41.37
41.50
44.50
49.83
364.00
455.38
495.24
496.45
497.08
>585
>585
>585
>585
>585
>30
>27
>23
>23
>17
89
Table 3.3
Bearing properties of single small washer composite joints
Single Small (SAE) washer composite joint
Clamp Load 2% bearing Ultimate (% of bolt proof Bearing Stiffness strength strength Joint
strength) (MPa) (MPa) (MPa) strain (%)
0%
2 5 %
50%
75%
100%
56.46
47.09
46.00
45.40
50.94
372.44
489.64
518.90
512.22
535.46
535.00
551.36
569.63
570.68
572.74
22.10
18.65
18.00
18.50
19.30
90
Table 3.4
Bearing properties of double large washer composite joints
Double Large (USS) washer composite joint
Clamp Load (% of bolt proof
strength)
0 %
2 5 %
50%
7 5 %
100%
Bearing Stiffness (MPa)
48.37
37.89
39.70
41.90
46.90
2% bearing strength (MPa)
361.07
424.88
462.01
485.70
491.20
Ultimate strength (MPa)
>585
>585
>585
>585
>585
Joint strain (%)
>27
>25
>26
>22
>18
91
Table 3.5
Bearing properties of double small washer composite joints
Double Small (SAE) washer composite joint
Clamp Load (% of bolt proof
strength)
0%
25%
50%
75%
100%
Bearing Stiffness (MPa)
54.43
46.92
45.39
44.67
49.90
2% bearing strength (MPa)
368.00
440.49
470.10
494.10
523.53
Ultimate strength (MPa)
524.34
540.56
545.14
548.86
573.22
Joint strain (%)
24.47
19.70
20.33
19.44
20.94
92
D=Bolt Hole diameter 12.5mm
25.4 mm X *t
W=50.8mm
Figure 3.1 Geometry of the test coupon
93
Force washer
I vtensometer mounting plate
Composite coupon
Figure 3.2 Experimental double lap-shear test fixture
94
xtensometer
Figure 3.3 Bearing test experimental set-up.
95
Bolt hole
Cross section of Bolt
Figure 3.4 Schematic representation of bearing stress distribution in a pin loaded joint (modified from [65])
96
^
aing
Str
ess
(MI
m
600 550 500 450 400 -350 300 250 200 -150 100 50 0 1
Initial Bearing Failure
Bearing Stiffness
~T^ Ultimate Strength
0 5 10 15 20 25
Beaing Strain (%)
Figure 3.5 Bearing stress Vs bearing strain curve for a small washer finger tightened bolted joint
1/3 00 C
•a u ffl
10 15 20 25 30
Beaing Strain (%)
35
Figure 3.6 Bearing Stress Vs. strain curve for joints with 50% bolt preload
97
OH
VI 60
<a ffl
50
40
30
20
10
-is— single large washer
-•— double large washer
-•— single small washer
-•— double small washer
25 50 75
Bolt preload (% of Proof Load)
100 125
Figure 3.7 Effect of bolt preload on joint bearing stiffness
00
s h s 'S o
600
500
400
300
200
100
-A— single large washer
-•— double large washer
-•—single small washer
-•— double small washer
25 50 75 100
Bolt preload (% of Proof Load)
125
Figure 3.8 Effect of bolt preload on offset bearing strength
98
g a S/3 U
a
400
300
200
100
Hi— Single small washer
-•— double small washer
25 50 75 100
Bolt Preload (% of Proof Load)
125
Figure 3.9 Effect of bolt preload on ultimate joint strength
c
'i 1/3
30
25
20
15
J 10 -•—Small single washer
-•— Small double washer
25 50 75
Bolt Preload (% of Proof Load)
100 125
Figure 3.10 Effect of bolt preload on j oint strain
99
60
1? 50 PH
¥40 u
I 30-
.B 20 -
« 10 -1 I
0 -
-jk— Small single washer
-•— Large single washer
25% 50% 75%
Bolt-preload (% of Proof)
100%
Figure 3.11 Effect of washer size on bearing stiffness of joints: single washer
60
1? 50 pu
r 40
| 30
oo c 20
• c o « 10
-A—Small double washers
-•— Large double washers
0% 25% 50% 75%
Bolt-preload (% of Proof)
100%
Figure 3.12 Effect of washer size on bearing stiffness: double washers.
100
00
600
500
400
§ 300
00
.S 200 S
m loo
TA— Small single washers
-•— Large single washers
0% 25% 50% 75%
Bolt-preload (% of Proof)
100%
Figure 3.13 Effect of washer size on offset bearing strength: single washer
600
^ 500 a
& 400
| 300 -4-» (/}
60
•g 200 a pa
100
-AT— Small double washers
-•— Large double washers
0% 25% 50% 75%
Bolt-preload (% of Proof)
100%
Figure 3.14 Effect of washer size on offset bearing strength: double washers
101
700
600
TO PL, a e +*
OQ 60 e
•c
CO
500
400
300
200
100
0
single small washer joints with.100% Ultimate Strength
Joint Continue^ to Carry the Lo id
single large washer joints with 100% bok-
10 Bearing Strain (%)
15 20
Figure 3.15 Effect of washer area on bearing stress-strain behavior
60
B Single large washers
H Double large washers
60 a •c 03 U
PQ
50
40
30
20
10
0% 25% 50%
Bolt clamp load
75% 100%
Figure 3.16 Effect of washer thickness on joint bearing stiffness: large washers
102
60
^-v e3
OH
s 00 Cfi <U
iffii
•*-»
tzi 00
•c
50
40
30
20
ffl 10 -t
0 —-
B Single small washers ,
B Double small washers
50%
Bolt clamp load
100%
Figure 3.17 Effect of small washer thickness on joint bearing stiffness.
C3 O H
SO
a
so a i m
600
500
400
300
200
100
0 —
0%
H Single large washers
H Double large washers
25% 50%
Bolt clamp load
75% 100%
Figure 3.18 Effect of washer thickness on bearing strength: large washers.
103
M Single small washers
II Double small washers
1?
Str
engt
h (M
B
eari
ng
600
500
400
300
200
100
0
0% 25% 50% 75%
Bolt clamp load
100%
Figure 3.19 Effect of washer thickness on bearing strength: small washers.
Ultimate Strength
Initial bearing
\ Joint clamp load curve
100
80
60
40
20
0
O
.2
1 2 3
Joint Displacement (mm)
Figure 3.20 Joint clamp-load Vs. with joint displacement: zero bolt preload
104
o
1 'S
Applied Load curve
A.
0 1 2 3 4 Joint Displacement (mm)
Figure 3.21 Joint clamp load Vs. displacement: 50% bolt preload.
20 40 60 80
Applied Load (kN)
100 120
Figure 3.22 Joint clamp load Vs. applied axial load: small washers.
105
O hJ
to
U
0
'S
60
50
40
30
20
10
0
Bolt preload =100% of Proof
20 40 60 80
Applied Load (kN)
100 120
Figure 3.23 Joint clamp load Vs. applied axial load: large washers.
Single Small washer with 0% Clamp Load
#
(a)
Single Large washer with 0% Clamp Load
•
(b)
Figure 3.24 Bearing damage in finger tightened joint coupons: (a) Coupons with small washers; (b) Coupons with large washers.
106
•
Large washer with 0% bolt-load
(a)
•
Large washer with 25% bolt-load
(b)
PK
•
^arge washer with 30% bolt-load
•
i.L net\/ u_ix
(c)
Large washer witn / :>"/<> ooit-load
(d)
Figure 3.25 Bearing damage in various joint coupons with large washers: (a) Coupons with 0% bolt-load; (b) Coupons with 25% bolt-load; (c) Coupons with 50% bolt-load; (d) Coupons with 75% bolt-load.
107
Large washer with 100% bolt-load
(e)
Figure 3.25 Bearing damage in various joint coupons with large washers: (e) Coupons with 100% bolt-load.
108
CHAPTER FOUR
EFFECT OF BOLT TIGHTNESS ON THE BEHAVIOR OF COMPOSITE JOINTS
In this chapter, experimental and numerical investigations have been carried out
to study the affect of bolt tightness and joint material on behavior of double bolted single
lap shear composite joints. Various scenarios of bolt tightness were considered for
composite-to-composite and composite-to-aluminum bolted joints. Progressive damage
analysis of glass mat-epoxy composite coupons was carried out to understand the bearing
failure mechanism. Optical microscope was used to study the damage under the bolt
head region, and as well as at the region of contact of bolt shank with the hole boundary.
Four tightening configurations were used in testing of each double bolted joint. These
configurations permit each of the two bolts to be either tight or loose. The numerical part
of the study utilizes a 3-D finite element model that simulates the bolt tightness and the
multilayered composite coupons. The experimental and finite element results are
correlated.
4.1 Experimental Set-up and Procedure
Figure 4.1 shows the joint geometry considered in the experimental study. The
joint geometry was based on ASTM D5961/D5961M-96 [67] standard. The glass-epoxy
woven composite coupons were cut from 6mm thick plaques. The coupons were
machined at Oakland University machine shop. The bolt holes were carefully drilled with
sacrificial plates on either side of the test coupons to avoid edge delamination at bolt-hole
109
boundary. The aluminum coupons were machined from sheets supplied by McMaster-
Carr ®. The non-dimensional geometric variables w/d (joint width to hole diameter
ratio), e/d (edge distance to hole diameter ratio), p/d (bolt pitch to hole diameter ratio),
and d/t (hole diameter to coupon thickness ratio) were kept constant through out the
experiments. The values used for the non-dimensional variables were w/d=6, e/d=3,
p/d=4.5, and d/t=2.5. Table 4.1 lists the material properties for the various components
of tested joints. Metric M8 x 1.25 Class 8.8 fasteners were used for the experiments.
4.1.1 Experiments
A screw driven 50kN capacity MTS tensile machine was used for joint testing.
Test Works4 ® material test software from MTS was used to record the load and
displacement data. Four tightening combinations were used for the tightness of the top
and bottom bolts. The combinations included Loose Top -Loose Bottom (LT-LB), where
both the bolts were loose, Tight Top-Loose Bottom (TT-LB), where the top bolt was tight
and the bottom bolt was loose, Loose Top-Tight Bottom (LT-TB), where the top bolt was
loose and the bottom bolt was tight, Tight Top-Tight Bottom (TT-TB) bolts, where both
the bolts were tight. The tight bolt condition is achieved by using 16 Nm torque to
tighten the bolt using a digital torque wrench. The loose bolt condition corresponds to
finger tightening that produce negligible bolt load in the joint. Joint material
combinations included either composite-to-composite or composite-to-aluminum
coupons. 10 Nm torque produced a clamp load of approximately 9000 N, which is about
40% of the proof load of the M8 x 1.25 Class 8.8 fasteners. This level of clamp load was
carefully selected so that the composite coupons would not be damaged during bolt
110
tightening. The bearing friction variation was minimized by using a new, cleaned high
quality washer under the turning nut in each test [62]. Preliminary testing showed that a
16 Nm torque produced a clamp load that ranged from 8950 N to 9046 N in the
composite-to-aluminum joints and from 8850 N to 8900 N in composite-to-composite
joints.
The load-displacement data was used to evaluate the effect of different bolt
tightness condition and joint materials on the strength and stiffness of the double bolted
composite joint. The composite joint shown in Figure 4.1 was clamped between the
upper and lower grips of an MTS tensile machine. The movement of the upper crosshead
applied the tensile load to the specimen, while the lower crosshead remained stationary.
The crosshead speed was maintained at 1.5 mm/min throughout the experiments, and the
test was continued until the final rupture of the composite coupons. The joint stiffness
was determined by the slope of the load-displacement curve.
4.1.2 Progressive Damage Analysis
The damage assessment of composite coupons at different intermediate loads
before the final rupture was carried out using an optical microscope. The damage
inspection at two different regions; namely, the surface under bolt heads and at the
contact of the bolt shank with the composite hole boundary was carried out to understand
the bearing failure mechanism. The examined damage regions are schematically
represented in Figure 4.2.
I l l
4.2 Experimental Results and Discussion
In this section, test data is presented and analyzed. The affect of various bolt
tightness conditions on the stiffness, strength, and damage is discussed for the composite-
to-composite and composite-to-aluminum double bolted joints.
4.2.1 Effect of Fastener Tightness Condition
For the double bolted joint shown in Figure 4.1, four scenarios of bolt tightness
were investigated; namely, Loose Top-Loose Bottom (LT-LB), Tight Top-Loose Bottom
(TT-LB), Loose Top-Tight Bottom (LT-TB), and Tight Top-Tight Bottom (TT-TB) bolts.
Figures 4.3a - Figure 4.3d show the load-displacement curves for the composite-to-
aluminum joints, which correspond to the four scenarios of bolt tightness. Point D
represents the ultimate failure load of the composite joint.
Figures 4.4a - Figure 4.4d represent an enlarged portion of the load-displacement
curves for each of the four tightening scenarios. At point B, the shank of the bolt comes
in contact with the curved surface of the bolt hole. Point C represents the beginning of
the bearing failure at the contact surface. The slope of the line segment BC represents the
joint stiffness. The static friction between the components of the joint dominates the
behavior of the joint below point B; which is consistent with [48].
The affect of the four bolt tightness scenarios on the joint stiffness is shown in
Figures 4.4. The three scenarios of composite-to-aluminum joints with at least one loose
bolt had the same stiffness of 4 kN/mm, as determined from the slope of the load-
displacement curve BC in Figures 4.4 a, b, and c, for LT-LB, LT-TB and TT-LB,
respectively. For the fourth configuration, where both the bolts were significantly tight
112
(i.e. TT-TB), the joint stiffness was increased by 31% to 5.25 kN/mm as determined by
the slope of line segment BC in Figure 4.4d.
Bearing failure was initiated by fiber - matrix cracking and interlaminar shear
delamination of the laminate. This corresponds to point C in Figures 4.4 a, b, c, and d.
The failure load at this point was about 3.5 kN for joints that had at least one tightened
bolt, This includes the three tightness scenarios of LT-TB, TT-LB, and TT-TB that are
shown by Figures 4.4 b, c, and d, respectively. One may observe that an additional line
segment AB appeared in the load-displacement curve of the three tightening scenarios,
with at least one tight bolt; this includes TT-TB, TT-LB, and LT-TB bolts. For the
remaining scenario (LT-LB), where both bolts were loose, the bearing failure load
dropped by 29% to 2.5 kN as shown in Figure 4.4a.
The ultimate failure in composite coupons for all test configurations was at the net
cross section. Figure 4.5 a - Figure 4.5 b show that the ultimate strength of the
composite joint, which ranges from 15kN to 16kN. This value remained almost constant
for all the tightening configurations, showing no obvious effect on the ultimate strength
of both composite-to-aluminum and composite-to-composite joints. Post failure damage
inspection was carried out to analyze the micro-failure behavior. Figures 4.6 to Figure
4.9 show the surface damage at the bolt holes for various tightening configurations of the
top and bottom bolts in, composite-to-aluminum joints. Figure 4.6a, Figure 4.7b, Figure
4.9a and Figure 4.9b, show that there is no significant delamination near the bolt-hole
boundary. This was mainly due to the compressive stress created by the bolt load in the
vicinity of the tightened bolt. By contrast, Figure 4.6b, Figure4.7a, and 4.8a and Figure
113
4.8b show significant delamination near the holes where the corresponding bolt was
loose.
4.2.2 Effect of Joint Materials
Figure 4.10 and Figure 4.11 show the load-displacement data for composite-to-
aluminum and composite-to-composite bolted joints in which the two bolts are either
loose or both tight (i.e. LT-LB or TT-TB), respectively. Test data show that the ultimate
strength was almost same for both composite-to-aluminum and composite-to-composite
joints. However, the joint material had a significant effect on the joint displacement
characteristics. Figure 4.10 shows that the total displacement at failure was 33% more
for the composite-to-composite joint when compared to the composite-to-aluminum joint,
when both the bolts were tightened. For the scenario where both the bolts were loose, the
total displacement at the ultimate failure was 38% higher for the composite-to-composite
joint when compared t o composite-to-aluminum joint, as shown in Figure 4.11. The
significant increase in the total displacement at failure for the composite-to-composite
joints may be attributed to the cumulative damage and delamination in each of the two
composite coupons. This also shows that composite-to-composite coupons observed
more energy compared to composite-to-aluminum joints. Figures 4.12 and Figure 4.13
show an enlarged portion of the initial load-displacement curve for the composite-to-
composite and composite-to-aluminum joints with loose bolts (LT-LB) and tightened
bolts (TT-TB), respectively. It can be observed that the joint material had no significant
effect on the joint stiffness or the value of the tensile load that would initiate bearing
failure (point C).
114
4.2.3 Failure Mode Progression
A bearing failure mode is desired over other modes because of its progressive
non-catastrophic nature. The fiber orientation, clearance of the bolt hole and clamping
pressure are the factors, which affect the bearing failure mechanism. In this section,
damage and failure mode analysis are provided for the composite regions that are near the
contact with the shank of the bolt. The affect of bolt tightness on failure modes in double
bolted composite joints is investigated. Figure 4.2 illustrates the two regions that are
inspected for progressive damage analysis; namely, Region 1 for the damage due to
under-head contact surface and Region 2 for the damage due to bolt shank contact.
Figure 4.14 - Figure 4.16 show the micrographs of the internal damage through the
composite thickness near the bearing contact with the bolt shank (Region 2-Figure 4.2).
Figure 4.14a and Figure 4.14b show the damage caused by a tensile load level that is just
above point C on Figure 4.4a and Figure 4.4d, respectively, where the bearing failure
begins. This corresponds to 3kN for the LT-LB joint and 4kN for the TT-TB tightness
conditions. Initiation of matrix cracking and interlaminar delamination was observed in
the case of loose bolts (LT-LB), whereas in the case of tightened bolts (TT-TB), the
compressive stress from both washers and the bolt shank was responsible for fiber
breakage and matrix compression. Figures 4.15a and Figure 4.15b show the micrographs
of the damage that corresponds to 12 kN tensile load (70% of the ultimate load), when
the bolts are either both loose or both tightened, respectively. Interlaminar delamination
was more prominent in the case of LT-LB than TT-TB bolts. In the case of TT-TB bolts,
the matrix and fiber cracking was more obvious at the edge of the hole. This is due to the
eccentric placing of the washer. Figure 4.16a and Figure 4.16b show the final damage
115
inspection that corresponds to about 15kN tensile load, which is just before the ultimate
failure, point D in Figure 4.3a and Figure 4.3d. At this load, the interlaminar
delamination and fiber-matrix shear failures increased and resulted in an out-of plane
deformation when both bolts were loose (LT-LB), as shown in Figure 4.16a. However,
when both bolts were tightened the lateral support from the washers inhibited the out of
plane deformation; as a result, fiber compressive failure was observed as shown in Figure
4.16b.
The progressive damage was carried out on the flat composite surface in contact
with loose bolt heads (LT-LB) for various levels of tensile loads. It was observed that the
surface delamination increased by increasing the tensile load. The surface delamination
was significantly less for tightened bolt holes. The clamped washers significantly
reduced the surface delamination. In some cases the surface delamination was partially
caused by unintended eccentric positioning of the washers.
4.3 Finite Element Modeling
The commercial finite element code ABAQUS ® [60] was used for the 3-
dimensional analysis of the tested composite-to-aluminum double bolted lap joint. Figure
4.17 show the finite element model of the single lap shear composite-to-aluminum joint.
A refined mesh was built around the bolt holes and the contact region between the bolt
head/shank and the composite coupons. The washer thickness was added to the modeled
bolt head/nut in order to create a single entity with the outer diameter of the bolt head
being equal to the outer diameter of the washer. A 3-dimensional, 8 nodes, reduced
integration brick elements (C3D8R) were used for meshing the joint materials. An
116
orthotopic material model was used for the composite plate with 16 elements through-
thickness layers that were stacked at 0° and 90° orientations. Isotropic material properties
were used to model the steel fasteners and the aluminum plate. The material properties
considered in the analysis are tabulated in Table 4.1 for the composite plates, aluminum
plates, steel bolts, washers and nuts.
The contact pair option in ABAQUS®, which is based on a master-slave
approach, was used to model the contact between the two plates, bolt shank and the
plates, bolt bearing surfaces and the upper composite plate, and between nut bearing
surfaces and the lower aluminum plate. Typical contact pair definitions in the finite
element model are shown in the Figure 4.18. The coefficient of friction is different for
various contact interfaces, and is generally lower for metal-to-composite contact as
compared to that for a metal-to-metal contact [54]. A factional co-efficient value of 0.2
was used for all metal-to-composite interfaces and a value of 0.3 was used for metal-to-
metal contact. A "small sliding" option in ABAQUS® was used in the analyses, which
meant that the contact between the master and slave nodes was defined in the initial stage
and were not redefined in the later stages of the analysis.
The FEA loading was applied in two steps. First, the bolt preload was applied to
its middle section; second, a tensile load was applied to the upper composite plate while
fixed end boundary conditions were applied to the lower aluminum plate. The tensile
load was applied as a concentrated nodal force; the rest of the nodes on the loaded edge
are forced to have the same displacement as the loaded node by using the multi-point
constraint (MPC) option in ABAQUS®. Light springs were used in ABAQUS to
compensate for the rigid body motion, as the bolt head sled to cause the shank to contact
117
with the joint, after the clearance in the bolt hole had been consumed. A bolt load of
approximately 9000 N for a tight bolt condition and about 800 N for a loose bolt
condition were used.
The four scenarios of bolt tightness used in the experimental study (TT-TB, TT-
LB, LT-TB and LT-LB) were considered in a linear finite element model. Figure 4.19
shows the load-displacement results for the TT-TB and LT-LB scenarios using various
values of the coefficient of friction at the metal-to-metal interface. It appears that
increasing coefficient of friction does not seem to significantly affect the stiffness of the
joint (slope of the load-displacement curve). Figure 4.20 shows the load-displacement
curves for the four tightness scenarios; namely TT-TB, LT-LB, LT-TB and TT-LB
bolts. The coefficients of friction were chosen to be 0.3 and 0.2 for the metal-on-metal
and metal-on-composite contact, respectively. The load-displacement data show that the
FEA results are in close agreement with the experimental results presented in this study.
4.4 Summary
The study provides an experimental procedure and an FEA model for
investigating the mechanical behavior and the failure modes of a composite single-lap
double bolted joint. It has been demonstrated that sufficiently increasing the bolt
tightness (without exceeding the joint strength), would significantly reduce the potential
for delamination around the bolt hole when a tensile load is applied to the joint. The
opposite has been found to be true as well. The tightening of at least one bolt has
increased the tensile load that would just initiate the bearing failure in the composite
plate. Joint stiffness is increased only when both bolts are sufficiently tightened. Both
118
the bolt tightening configuration and joint materials are found to have an insignificant
effect on the ultimate strength of the single-lap double bolted composite joint. When the
bolts were loose, the progressive damage analysis showed interlaminar delamination and
fiber-matrix shear failure that is subsequently followed by an out-of-plane deformation at
higher tensile loads. However, when both bolts are sufficiently tightened, a fiber
compressive failure mode is observed. The linear part of the load-displacement curves
obtained from the 3-D FEA show good correlation with the experimental results for all
four scenarios of bolt tightness.
119
Table 4.1
Material properties of joint components
E-GlassEpoxy Alloy 6061 Steel Woven Aluminum Bolt-Washer-Nut
AISI1035
Young's Modulus (E)
Young's Modulus (En)
Young's Modulus (E22)
Young's Modulus (E33)
Poisson's ratio (y)
Poisson's ratio (712)
Poisson's ratio (Yl3= Y13)
Shear Modulus (Gi2=Gi3=G23)
30.678 GPa
29.782 GPa
7.583 GPa
0.114
0.27
4.756 GPa
68.9 GPa
0.33
200 GPa
0.29
120
48 mm
24 mm
191 mm
36 mm
24 mm
* *
32 mm
3.18 mm
•*• Upper coupon
, Bolts 0 8 mm
"Top bolt
298 mm
Bottom bolt
- • Lower coupon
Figure 4.1 Geometry of single lap, double-bolted joint
121
Region 1 (Damage on the under head contact surface)
Bolt shank contact line
Region 2 (Damage at the bolt shank contact)
Loa&is; Difeciion
Figure 4.2 Schematic representation of inspected damage regions.
122
IO
16
14 -
^ 12
i . 10
o ~" 6
4
2 n
C / ^
y f t B
LT-LB
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
Cross Head Displacement (mm)
(a)
16 14
~ 12 1 10
Load
4 2 n
B ^
/ A
LT-TB D
| I
j
|
I 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Cross Head Displacement (mm)
(b)
Figure 4.3 Load displacement curves for aluminum-composite joints: (a) LT-LB; (b) LT-TB
123
CO O
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Cross Head Displacement (mm)
5.5
(c)
T3 CD O
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Cross Head Displacement (mm)
5.5
(d)
Figure 4.3 Load displacement curves for aluminum-composite joints :(c) TT-LB; (d) TT-TB.
124
LT-LB
0 0.2 0.4 0.6 0.8 1 1.2 1.4
displacement in mm
(a)
LT-TB
0 0.2 0.4 0.6 Oi 1 1.2 1.4
displacement in mm
(b)
Figure 4.4 Initial portion of the aluminum-composite load-displacement curve: (a) LT-LB; (b) LT-TB.
125
TT-LB
0 0.2 0.4 0.6 0.8 1 1.2 1.4
displacement in mm
(c)
TT-TB
o
0 0.2 0.4 0.6 0.8 1 1.2 1.4
displacement in mm
(d)
Figure 4.4 Initial portion of the aluminum-composite load-displacement curve: (c) TT-LB; (d) TT-TB
126
Composite-Aluminum joints
•a S3 o
T3
o • J
Ultimate
1 2 3 4 5 6 7
Cross Head displacement (mm)
(a)
Composite-Compoiste joints
Ultimate failure
1 2 3 4 5 6 7
Cross Head displacement (mm)
(b)
Figure 4.5 Load-displacement curves showing the ultimate failure load: (a) Composite-aluminum joints; (b) Composite-composite joints
127
Top Hole
(a)
Figure 4.6 Bearing surface delamination for TT-LB joints: (a) Top Hole; (b) Bottom Hole.
Top Hole |••: Bottom Hole
(a) (b)
Figure 4.7 Bearing surface delamination for LT-TB joints: (a) Top Hole; (b) Bottom Hole
128
Too Hole
HaBgaBBgaHWgmmBBimflflgHgBBm
Bottom Hole
(a) (b)
Figure 4.8 Bearing surface delamination for LT-LB joints: (a) Top Hole; (b)Bottom Hole.
^ v *
* ^ % l
* *. ^ fc
^ i
Rotioni Hole
• • • * & . . . - » » • _ « ;
,' ' ' ^ , ' « ' fi . *
"l*>It'»i'i
•\***' • '•'?;>
- - • . ' , ' ? . . J^-K-
« i, \* - ? « * ; * ,
' .. A.V# 'S» '
(a) (b)
Figure 4.9 Bearing surface delamination for TT-TB joints: (a) Top Hole; (b) Bottom Hole.
129
Aluminum/Composite VS Composite/Composite for TT-TB joints
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5
Displacement (mm)
Figure 4.10 Strength comparison of aluminum-composite and composite-composite TT-TB joints.
Aluminum/Composite VS Composite/Composite for LT-LB joints
Al/Comp
Comp/Comp
o
17 16 15 14 13 12 11 10 9 8 7 H 6 5 4 3 2 1 0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
Displacement (mm)
Figure 4.11 Strength comparison of aluminum-composite and composite-composite LT-LB joints.
130
(0 O
8
7
6
5
4
3
2
1
0
0.5 1 1.5
Displacement in mm
(a)
LTLB
Bearing failure load
0.5 1 1.5
Displacement in mm
(b)
Figure 4.12 Initial portion of the load-displacement data for LT-LB joints: (a) Composite -composite joint; (b) Aluminum-composite joints.
131
c T5 CO O
0.5 1 1.5
Displacement in mm
(a)
0.5 1 1.5
Displacement in mm
(b)
Figure 4.13 Initial portion of the load-displacement data for LT-TB joints: (a) Composite -composite joint; (b) Aluminum-composite joints
132
(a) (b)
Figure 4.14 Initiation of bearing failure: (a) LT-LB joints; (b) TT-TB joints.
*•?* •J
• ' s i r ^ ) 8 ' -- -' .
(a) (b)
Figure 4.15 Bearing failure at 70% of ultimate failure load: (a) LT-LB joints; (b) TT-TB joints.
133
3V3Mg3fn|
(a) (b)
Figure 4.16 Bearing damage just before the ultimate failure: (a) LT-LB joints; (b) TT-TB joints.
134
Composite plate through-thickness section showing the layers
Top Bolt
Bottom Bolt
Composite Plate
Aluminum Plate
Figure4.17 Finite element model of double bolted composite to aluminum joint.
Contact friction between bolt shank and plates
Contact friction between two plates 3
Contact friction between bolt underhead and composite plate
ontact friction between nut and aluminum plate
Figure 4.18 Contact surfaces in the finite element model.
135
Load Displacement Curve (TT-TB)
3500 -
3000 -
2500
& 2000
o
0.2 0.4
Displacement (mm)
Friction Coefficient
•0.2
•0.2/0.25
•0.2/0.3
• Experimental
0.6
(a)
Load Displacemet Curve (LT-LB)
0.2 0.4
Displacement (mm)
Friction Coefficient
—•-0 .2
-0.2/0.25
•0.2/0.3
• Experimental
0.6
(b)
Figure 4.19 Frictional effect on the load displacement curves: (a) TT-TB; (b) LT-LB.
136
TT-TB
0.1 0.2 0.3 Displacement (mm)
0.4 0.5
(a)
LT-LB
0.2 0.4 0.6 0.8
Displacement (mm)
(b)
Figure 4.20: Comparison of FEA and experimental results: (a) TT-TB; (b) LT-LB
137
3500
3000
2500
& 2000
1 1500-
1000
500
0 *
0
TT-LB
3500
3000
2500
2000
1500
1000
500
0
(d)
Figure 4.20: Comparison of FEA and experimental results :( c) LT-TB; (d) TT-LB.
LT-TB
0.2 0.4
Displacement (mm)
0.6
(C)
0.2 0.4 0.6 0.8
138
CHAPTER FIVE
CONCLUSIONS AND FUTURE STUDY
5.1 Conclusions
5.1.1 Effect of Adhesive Thickness and Properties on the Bi-axial Interfacial Shear Stresses in Bonded Joints Using a Continuum Mixture Model
New formulas are derived for the bi-axial interfacial shear stresses that develop in
an adhesively bonded joint due to static thermo-mechanical loading. The analysis is
carried out along the lines of continuum mixture theories of wave propagation.
Numerical results that show the effect of both the elastic properties and the thickness of
the adhesive on the interfacial shear stresses are investigated. Numerical results show
that both the material properties and the thickness of the adhesive have a pronounced
effect on the developed interfacial shear stresses due to the thermo-mechanical loading.
For the present model, it has been found that increasing the thickness of the adhesive
causes a significant increase of the interfacial shear stresses. The larger difference in the
elastic and thermal properties between the adhesive and the layered adherends the higher
the corresponding interfacial shear stress is. The proposed model inherently has the
capacity for optimizing the selection of the adhesive thickness and material properties
that would yield a more reliable bonded joint.
5.1.2 Effect of Washers and Bolt Tension on the Behavior of Thick Composite Joints
Experimental data is presented on the affect of initial bolt preload, as well as the
washer size and thickness on the behavior of heavily loaded thick composite joints.
139
Friction between the joint parts played a significant role in defining joint stiffness. The
joint bearing stiffness was higher for the untightened bolted joint than that with much
higher bolt preload (100% of proof load). The bearing stiffness was smallest for the joint
with a preload equal to 25% of bolt proof load, and it increased with bolt preload. The
offset bearing strength increased progressively with bolt preload. The ultimate joint
strength was unaffected by increasing the bolt preload. Joint with small washers had
higher bearing stiffness than those with large washers for initial bolt preload of 0%, 25%
and 50%. Joints with small washers had higher offset bearing strength than the joints
with large washers. The washer thickness had an insignificant effect on the ultimate joint
strength and strain.
As the axial test load is increased, an untightened bolted joint showed a
significant increase in the clamp load (from its zero initial value). This increase in the
clamp load was progressively reduced by the increase in initial bolt-load. Bearing
damage was the prominent failure mode in all tested joint configurations. The extent of
bearing damage was more severe in smaller washer joints, where the damage extended
beyond the washer contact. Out-of-plane buckling of laminates exerted lateral pressure
on the washers resulting in an increase in clamp load during the experiments. These
experimental results help in the selection of an optimum initial bolt preload and washer
size and thickness in order to enhance composite joint performance and reliability.
5.1.3 Effect of Bolt Tightness on the Behavior of Composite Joints
The study provides an experimental procedure and an FEA model for
investigating the mechanical behavior and the failure modes of a composite single-lap
140
double bolted joint. It has been demonstrated that sufficiently increasing the bolt
tightness (without exceeding the joint strength), would significantly reduce the potential
for delamination around the bolt hole when a tensile load is applied to the joint. The
opposite has been found to be true as well. The tightening of at least one bolt has
increased the tensile load that would just initiate the bearing failure in the composite
plate. Joint stiffness is increased only when both bolts are sufficiently tightened. Both
the bolt tightening configuration and joint materials are found to have an insignificant
effect on the ultimate strength of the single-lap double bolted composite joint. When the
bolts were loose, the progressive damage analysis showed interlaminar delamination and
fiber-matrix shear failure that is subsequently followed by an out-of-plane deformation at
higher tensile loads. However, when both bolts are sufficiently tightened, a fiber
compressive failure mode is observed. The linear part of the load-displacement curves
obtained from the 3-D FEA show good correlation with the experimental results for all
four scenarios of bolt tightness.
5.2 Future Study
Based on the developed model, one can further extend the model to predict the
interfacial peel stresses which are critical in brittle adhesive applications. An
experimental methodology using optical techniques can also be developed to analyze the
interfacial stresses under thermomechanical loading.
141
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