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

INFORMATION TO USERS

The quality of this reproduction is dependent upon the quality of the copy

submitted. Broken or indistinct print, colored or poor quality illustrations and

photographs, print bleed-through, substandard margins, and improper

alignment can adversely affect reproduction.

In the unlikely event that the author did not send a complete manuscript

and there are missing pages, these will be noted. Also, if unauthorized

copyright material had to be removed, a note will indicate the deletion.

®

UMI UMI Microform 3333081

Copyright 2008 by ProQuest LLC.

All rights reserved. This microform edition is protected against

unauthorized copying under Title 17, United States Code.

ProQuest LLC 789 E. Eisenhower Parkway

PO Box 1346 Ann Arbor, Ml 48106-1346

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


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


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


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


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 + â) "T^ + la

dy dz - Y a T

3ua + 3w_a

8x 3z

dza = (2 ^ a + â)—-^ + la

dz dUg 3vg

dx dy

Y T 'a

Y T 'a

(2.4)

(2.5)

(2.6)

tfxya _ Mâ 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 0 (Adhesive)


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


(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

/


-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


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


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


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


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


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


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%


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%


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%


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)

•


(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


(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


(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


5.5

(c)

T3 CD O

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5


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

REFERENCES

1. Robert M. Jones, 1999, Mechanics of composite materials, second edition, Brunner-Routledge, New York and London.

2. A.Baldan, 2004, Adhesively-bonded joints and repairs in metallic alloys, polymers and composite materials: adhesives, adhesion theories and surface pretreatment, Journal of Material Science, 39, 1-49.

3. R.D. Adams, 2005, Adhesive bonding science, technology and applications, Woodhead Publishing Limited, Cambridge England.

4. Weijian Ma, Rajesh Gomatam, Rick D. Fong and Erol Sancaktar, 2001, A Novel Mathematical Procedure to Evaluate the Effect of Surface Topography on the Interfacial State of Stress: Part I: Verification of the Method for Flat Surfaces, Journal of Adhesion Science and Technology, 15,13, 1533-1558.

5. Jin-Hwe Kweon, Jae-Woo Jung, Tae-Hwan Kim, Jin-Ho Choi, Dong-Hyun Kim, 2006, Failure of carbon composite-to-aluminum joints with combined mechanical fastening and adhesive bonding, Composite Structures, 75, 192-198.

6. Christina Helene Ficarra, 2001, Analysis of adhesive bonded fiber-reinforced composite joints, Masters Thesis, North Carolina state university.

7. A Baldan, 2004, Review- Adhesively-bonded joints in metallic alloys, polymers and composite materials: Mechanical and environmental durability performance, Journal of Materials Science, 39, 4729-4797.

8. Timoshenko S. P, 1925, Analysis of bi-metal thermostats, J. Opt. Amer., Vol. 11, pp.233-255.

9. E. Suhir, 1998, Interfacial stresses in bimetal thermostats, Journal of Applied Mechanics, Paper No. 90-WA/APM-l.

10. Adnan H. Nayfeh, 1977, Thermomechanically Induced Interfacial Stresses in Fibrous Composites, Fiber Science and Technology, 10, 195-209.

11. G.A. Hegemier, G.A. Gurtam and A.H. Nayfeeh, 1973, A Continuum Theory for Wave Propagation in Laminated and Fibrous Composites, International Journal of Solids and Structures, 9.

142

12. Adnan H. Nayfeh, Elsayed Abdel-Ati M. Nassar, 1978, Simulation of the Influence of Bonding Materials on the Dynamic Behavior of Laminated Composites, Journal of Applied Mechanics, 78-WA/APM-15.

13. A.H. Nayfeh, 1978, Dynamically Induced Interfacial Stresses in Fibrous Composites, Journal of Applied Mechanics, 45.

14. A.H. Nayfeh and E.A. Nassar, 1982, The Influence of Bonding Agents on the Thermomechanically Induced Interfacial Stresses in laminated Composites, Fiber Science and Technology, 16,157-174.

15. Yi-Hsin Pao, Ellen Eisele, 1991, Interfacial shear and peel stresses in multilayered thin stacks subjected to uniform thermal loading, Journal of Electronic Packaging, 113,164-172.

16. Hui-Shen Shen, J.G. Teng, J.Yang, 2001, Interfacial stresses in beams and slabs bonded with thin plate, Journal of Engineering Mechanics, 127, 4.

17. C.Q.Ru, 2002, Interfacial Thermal stresses in biomaterial Elastic Beams: Modified Beam Models Revisited, Journal of Electronic Packaging, 124.

18. Hyonny Kim, Keith Kedward, 2001, Stress analysis of in-plane, shear-loaded, adhesively bonded composite joints and assemblies, National Technical Information Service (NTIS), Springfield, Virginia 22161, April.

19. Chihdar Yang, Hai Huang, John S. Tomblin and Wenjun Sun, 2004, Elastic-plastic model of adhesive-bonded single-lap composite joints, Journal of Composite Materials, Vol. 38, No. 4.

20. John N. Rossettos, 2003, Thermal peel, warpage and interfacial shear stresses in adhesive joints, Journal of Adhesion science Technology, 17, 115-128.

21. Do Won Seo, Ho Chel Yoon, yang Bae Jeon, Hyo Jin Kim and Jae Kyoo Lim, 2004, Effect of overlap length and adhesive thickness on stress distribution in adhesive bonded single-lap joints, Key Engineering Materials, 270-273, 64-69.

22. Gang Li, Pearl lee-Sullivan, Ronald W. Thring, 1999, Nonlinear finite element analysis of stress and strain distributions across the adhesive thickness in composite single-lap joints, Composite Structures, 46, 395-403.

23. Toshiyuki Sawa, Izumi Higuchi and Hidekazu Suga, 2003, Three-dimensional finite element stress analysis of single-lap adhesive joints of dissimilar adherends subjected to impact tensile loads, Journal of Adhesion Science and Technology, 17, 16, 2157-2174.

143

24. Q.S. Yang, X.R. Peng, A.K.H.Kwan, 2004, Finite element analysis of interfacial stresses in FRP-RC hybrid beams, Mechanics Research Communications, 31, 331-340.

25. J.P.M. Goncalves, M.F.S.F. de moura, P.M.S.T. de castro, 2002, A three-dimensional finite element model for stress analysis of adhesive joints, International Journal of Adhesion and Adhesives, 22, 357-365.

26. J.D.Mathias, M.Grediac, X. Balandraud, 2006, On the bidirectional stress distribution in rectangular bonded composite patches, International Journal of Solids and Structures, 43, 6921-6947.

27. Weijian Ma, Rajesh Gomatam, and Erol Sancaktar, 2003, A Novel Mathematical Procedure to Evaluate the Effect of Surface Topography on the Interfacial State of Stress Part II: Verification of the Method for scarf interfaces, Journal of Adhesion Science and Technology, 17,6,831 -846.

28. V.Kradinov, E.Madenci, D.R. Ambur, 2004, Combined in-plane and through the thickness analysis for failure prediction of bolted composite joints", AIAA 2004-1703, 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 19-22, April, Palm Springs, California.

29. P. P. Camanho and F. L. Matthews, 1999, A progressive damage model for mechanically fastened joints in composite laminates, Journal of Composite Materials, 33(24), 2248 - 2280.

30. P. P. Camanho, S. Bowron, and F. L. Matthews, 1998, Failure Mechanisms in Bolted CFRP, Journal of Reinforced Plastics and Composites, 17,205-233.

31. Hsien-Tang Sun, Fu-Kuo Chang and Xinlin Qing, 2002, The response of composite joints with bolt-clamping Loads, Part I: Model Development, Journal of Composite Materials, Vol. 36, No. 01.

32. Cooper C and Turvey, G.J., 1995, Effects of joint geometry and bolt torque on the structural performance of single bolt tension joints in pultruded GRP sheet material, Composite Structures, Vol. 32, pp 217-226.

33. ASTM standard D 5961/D 5961M, 2005, Standard test method for bearing response of polymer matrix composite laminates, ASTM international, west Conshohocken, PA 19428-2959, United States.

34. Sandra Polesky Walker, 2001, Thermal effects on the bearing behavior of composite joints, Ph.D Dissertation, University of Virginia, May.

144

35. A.R Hutchinson, Advanced materials engineering and joining-mechanical connections in polymer composite materials, Oxford Brookes University.

36. B. Vangrimde, R. Boukhili, 2002, Bearing Stiffness of Glass fiber-reinforced Polyester: Influence of Coupon Geometry and Laminate Properties, Composite Structures 58,57-73.

37. Li Hou and Dahsin Liu, 2003, Size Effects and Thickness Constraints in Composite Joints, Journal of Composite Materials, Vol. 37, No. 21.

38. Je Hoon Oh, Young Goo Kim & Dai Gil Lee, 1997, Optimum Bolted Joints for Hybrid Composite Materials, Composite Structures, Vol. 38, No. 1-4, pp. 329-341.

39. Alaattin Aktas, M. Husnu Dirikolu, 2004, An experimental and numerical investigation of strength characteristics of carbon-epoxy pinned-joint plates, Composites Science and Technology 64,1605-1611.

40. Alaattin Aktas, 2005, Bearing strength of carbon epoxy laminates under static and dynamic loading, Composite Structures 67,485^489.

41. M.A. McCarthy, V.P. Lawlor, W.F. Stanley, C.T. McCarthy, 2002, Bolt-hole clearance effects and strength criteria in single-bolt, single-lap, composite bolted joints, Composite Science and Technology 62,1415-1431.

42. V.P. lawlor, M.A. McCarthy, W.F.Stanley, 2002, Experimental Study on the Effect of Clearance on Single-Bolt, single-Shear, Composite Bolted Joints, Journal of Plastic, Rubber and Composites, Vol.31, No. 9, pp. 405-411.

43. Claire Girard, Marie-Laure Dano, Andre Picard, Guy Gendron, 2003, Bearing Behavior of Mechanically Fastened Joints in Composite laminates-Part I: Strength and Local Strains, Mechanics of Advanced Materials and Structures, 10:1-21.

44. Heung-Joon Park, 2001, Effect of Stacking Sequence and Clamping Force on the Bearing Strengths of Mechanical Fastened Joints in Composite Laminates, Composite Structures, 53, 213-221.

45. Hsien-Tang Sun, Fu-Kuo Chang, and Xinlin Qing, 2002, The Response of Composite Joints with Bolt-Clamping Loads, Part II: Model Verification, Journal of Composite Materials, Vol. 36, No 01.

46. Y.Yan, W.D.Wen, F.K.Chang, P.Shyprykevich, 1999, Experimental Study on Clamping Effect on the Tensile Strength of Composite Plates with a Bolt-Filled Hole", Composites Part A: Applied Science and Manufacturing, 30, 1215-1229.

145

47. U.A. Khashaba, H.E.M. Sallam, A.E. Al-Shorbagy, M.A.Seif, 2005, Effect of washer size and tightening torque on the performance of bolted joints in composite structures", Composite Structures.

48. V.P.Lawlor, W.F.Stanley, M.A.McCarthy, 2002, Characterization of damage Development in single-shear bolted composite joints, Journal of Plastics, Rubber and Composites, The Institute of Materials, London, UK, Vol. 31, No. 3, pp. 126-133.

49. Claire Girard, Marie-Laure Dano, Andre Picard and Guy Gendron, 2003, Bearing Behavior of Mechanically Fastened Joints in Composite Laminates-Part II: Failure Mechanisms", Mechanics of Advanced Materials and Structures, 10:23-42.

50. Yi Xiao, 2003, Bearing Deformation Behavor of Carbon/Bismaleimide Composites Containing One and Two Bolted Joints, Journal of Reinforced Plastics and Composites, Vol.22, No. 2.

51. Hong-Sheng Wang, Chang-Li Hung and Fu-Kuo Chang, 1996, Bearing Failure of Bolted Composite Joints. Part I: Experimental Characterization, Journal of Composite Materials, Vol. 30, No. 12.

52. Liyong Tong, 2000, Bearing failure of composite bolted joints with non-uniform bolt-to-washer clearance, Composites: Part A 31, 609-615.

53. A. Crosky, D.Kelly, R.Li, X.Legrand, N.Huong, R.Ujjin, 2006, "Improvement of Bearing Strength of Laminated Composites", Composite Structures 76, 260-271.

54. Tomas Ireman, 1998, Three-dimensional stress analysis of bolted single-lap composite joints, Composite Structures, 43,195-216.

55. Johan Ekh, Joakim Schon, 2005, Effect of Secondary Bending on Strength Prediction of Composite, Single shear lap Joints, Composite Science and Technology 65, 953-965.

56. K.I. Tserpes, G.Labeas, P.Papanikos, Th. Kermanidis, 2002, Strength Prediction of Bolted Joints in Graphite/epoxy Composite Laminates, Composites: Part B 33, 521-529.

57. Marie-Laure Dano, Guy Gendron, Andre Picard, 2000, Stress and Failure Analysis of Mechanically Fastened Joints in Composite Laminates, Composite Structures 50, 287-296.

58. McCarthy, C.T. McCarthy, V.P. Lawlor, W.F. Stanley, 2004, Three-dimensional finite element analysis of single-bolt, single-lap composite bolted joints: part I-model development and validation, Composite Structures.

146

59. Arthur P. Boresi, Richard J. Schmidt, Omar M. Sidebottom, 1992, Advanced Mechanics of Materials, Fifth edition, John Wiley and Sons, Inc., USA

60. ABAQUS Documentation, 2004, Analysis User's Manual, Version 6.5, ABAQUS Inc., Rhode Island - 02909, USA, www.hks.com.

61. John H. Bickford, 1995, An introduction to the design and behavior of bolted joints, third edition, Marcel Dekker, New York.

62. John H. Bickford, Sayed Nassar, 1998, Handbook of bolts and bolted joints, Hand book of bolts and bolted joints, Marcel Dekker, New York.

63. Nassar, S.A. and Matin, P. H., and G. C. Barber, 2005, Thread friction in bolted joints, journal of pressure vessels technology- ASME Transactions, 127, pp. 387-393

64. Nassar, S.A., Barber, G.C., and Zuo, D., 2005, Bearing friction torque in bolted joints, STLE Tribology Transactions, 48, pp 69-75.

65. T.A. Collings and M.J. Beauchamp, 1984, Bearing deflection behavior of a loaded hole in CFRP, Composites, 15, 1.

66. Nassar, S.A. and Virupaksha, V.L., Ganeshmurthy, S., 2007, Effect of Bolt Tightening and Joint Material on the Strength and Behavior of Composite Joints, ASME Journal of Pressure Vessels Technology, Vol. 129, pp. 43-51.

67. ASTM Standard D5961/D 5961M-96, 1996, Standard Test Method for Bearing Response of Polymer Matrix Composite Laminates, ASTM international, west Conshohocken, PA 19428-2959, United States.

147

http://www.hks.com

behavior of fastened and adhesively bonded composites under mechanical and thermomechanical loads

Documents

behavior of composite

adhesive bonded joints

bearing behavior

mechanical engineering

father virupaksha

bonded composites

abstract behavior

vijayshankar virupaksha