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SOME THREE-DIMENSIONAL ISSUES IN COMPOSITE PIN JOINTS
By

Li Hou

A DISSERTATION

Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of

DOCTOR OF PHYLOSOPHY
Department of Mechanical Engineering

2004

ABSTRACT
SOME THREE-DIMENSIONAL ISSUES IN COMPOSITE PIN JOINTS
By
Li Hou

Demands for thick composite plates in mechanical joint structures are booming. Yet
still lacking are mechanical joint associated studies related to size scaling effects,
especially three-dimensional scaling effects involving thickness scaling. In current
research, an original three-dimensional size scaling study was carried out in order to
reveal joint load-capacity variation as well as various damage mechanisms caused by size
scaling, especially thickness scaling. Woven glass-fabric/phenolic and glass/epoxy
composite were included in a double-lap-single-pin joint structure for expenmental
studies. A previous study was first extended into three-dimensional scaling effect study
by combining and comparing thickness scaling effect and in-plane, or two-dimensional,
scaling effect. An important geometric ratio H/D, i.e. composite laminate thickness H to
fastener hole diameter D, was found to be influential to size scaling effects in many
aspects. Later, three technical approaches in meeting out-of-plane constraint
requirements, or thickness constraint requirements, of a mechanical joint structure -
thickness scaling, bonding technique and bolting technique were compared. Their key
roles in local and global damage process were discussed. Finally, a three-dimensional
finite element analysis was carried out in order to reveal stress distribution through the
thickness direction and its sensitivity to thickness scaling effect. Several commonly-used
failure criteria were investigated for suitability on glass/epoxy case. A broadened two-

parameter failure theory was also included for discussion.

ACKNOWLEDGMENTS

My sincere gratitude goes to Professor Dahsin Liu (Mechanical Engineering
Department, Michigan State University) for constantly guiding and supporting this
research. Professor Liu and his previous students’ research work initiated this study. And
this study could not possibly reach current level without his continuous contribution.

I would like to thank John F. Whalen (Vice President, Fisher Dynamics at ST. Clair
Shores, MI) and Peter Rizk (Program Manager, Hydro Automotive Structures at Holland,
M1) for encouraging continuous pursue of this study.

I thank my wife, Aijun and my daughter, Aili for their support during this six-year-
long project. Aili, now a two-year-old, has in her own way taught me how to be persistent
and patient in my research. I would like to acknowledge my parents, Naiwen and Yiai
who gave me the opportunities to reach my goals and did that at a great personal

sacrifice.

Table of Contents

List of Tables ............................................................................
List of Figures ............................................................................
Chapter 1 Introduction
Statement of Problem and Literature Review ......................
Objectives and Scopes of Current Study ..............................
Organization of Following Chapters ..................................
Chapter 2 Three-dimensional Size Effects in Composite Pin Joints

Chapter 3

Introduction ..............................................................
Experimental Methods ...................................................
Experimental Results ...................................................
Various Effects ..........................................................
Size Effects ...............................................................
Conclusions ...............................................................
Scaling Effects and Thickness Constraints in Composite Joints
Introduction ...............................................................
Experimental Methods ...................................................
Joint Properties ..........................................................
Experimental Results ....................................................
Assembled and Laminated Composites ................................
Difference Between Pinned and Bolted Joints .....................

Conclusions .................................................................

Chapter 4

Chapter 5

References

Three-dimensional Finite Element Analysis of Composite Pin Joints

Introduction ............................................................... 64
Finite Element Modeling ............................................... 68
Finite Element Results ................................................... 80
Failure Analysis .......................................................... 87
Conclusions ............................................................... 1 00

Conclusions and Recommendations

Conclusions ............................................................... l 02
Recommendations ........................................................ 1 05
................................................................................. l 06

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Table 7

Table 8

Table 9

Table 10

Table 1 1

List of Tables

Geometrical elements and geometrical ratios of glass-fabric/phenolic
composite central laps .......................................................

Types of load-displacement curves, maximum loads, and offset
displacement percentage of all joints based on W-l pins ................

Types of load-displacement curves, maximum loads, and offset
displacement percentage of some joints based on various pins .........

Geometrical elements and ratios of glass/epoxy central laps ............

Types of load-displacement curves, maximum loads and percentage
of offset of displacement of various glass/epoxy joints ..................

Comparison between laminated and assembled glass/epoxy joints
Material properties of glass/epoxy laminate ...............................
Geometrical elements and ratios of three simulation models ............
Failure indicators at Bo-Bs line ..............................................
Failure indicators at No-Ns line ..............................................

Joint load capacity prediction ................................................

vi

14

20

29

42

47

56

69

71

94

96

98

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13

Figure 14

List of Figures

Schematic diagram of a double-lap-single-pin joint ......................
Load-displacement curves, glass-fabric/phenolic composite joints
Details of the shaded zone in Figure 1 ......................................
Microscopic damage patterns of glass-fabric/phenolic composite

laminates in joint/compression loading ....................................

Comparisons of bearing strengths between composite-composite
assemblies and steel-composite assemblies ...............................
Bearing strengths due to three-dimensional scaling ......................
Bearing strength ratios due to in-plane scaling ............................
Bearing strength ratios due to thickness scaling ...........................
Load-displacement curves, glass/epoxy composite joints ...............
Microscopic damage in an H17D6.35 glass/epoxy joint ................
Glass/Epoxy joint strengths of different sizes and analysis based on

Weibull theory ..............................................................

Load-displacement curves of assembled (bonded) and laminated
glass/epoxy joints .............................................................

The coordinate system established for problem modeling ..............

The model in the finite element analysis (quarter of components in
Figure 1) ........................................................................

vii

16

19

21

24

27

33

34

34

45

49

52

59

72

73

Figure 15
Figure 16
Figure 17

Figure 18

Figure 19
Figure 20
Figure 21

Figure 22

A Schematic diagram of hole area on the composite plate ............. 74

Details of composite hole area in the finite element model ............ 76

Comparison of stress results between [32] and current model ......... 79

ABAQUS result of radial displacement on the hole periphery of

[04/9045 cross-ply ............................................................ 81
H/D=1 stress state through the thickness at 80-85 line .................. 82
H/D=l stress state through the thickness at No-N5 line .................. 83
Stress comparison of H/D=1/2, 1 and 2 cases at 80-85 line ............ 85

Two-parameter failure mode] triangle and Front, Top view of a failed
sample ......................................................................... 97

viii

Chapter 1
Introduction
1.1 Statement of Problem and Literature Review
A. Thick Composite Plate

What we today call composites, or more specifically fiber-reinforced plastics, were
first produced five decades ago. Fibers, primarily glass, were first converted into different
forms, such as woven-fiber or unidirectional-fiber, which were then impregnated with a
plastic matrix resin, e.g. epoxy, into a composite ply. Multiple numbers of composite
plies, each possibly at a different orientation, were then stacked together into a composite
laminate plate.

Due to their high strength and light weight but high cost, composite materials were
initially developed for, yet limited to, aerospace structural applications. Since most
composite plates back then were of a much smaller dimension in thickness as compared
to other two in-plane dimensions, i.e. length and width, they were generally viewed as
thin plates. Accordingly, in-plane mechanical behaviors of composite plates have drawn
much more attention than out-of-plane mechanical behaviors, associated with thickness
direction, over the past several decades.

Ever since their birth, however, composites have gradually worked their way into a
seemingly endless number of applications beyond aerospace industry. Meanwhile,
demands for thick-section composite plates, generally defined as thicker than one half
inch, are quickly booming. Submarine hull and armored vehicle bodies, for example,
demand rigorous mechanical performance requirements in the thickness only thick

composite plates could possibly meet. The extension from thin composite plates to thick

ones, however, is not trivial. In fact, it requires careful modifications in many aspects of
composite technologies, e.g. manufacturing, testing, analysis and design [1 -7].
B. Mechanical Joining Technique

Joining is a secondary process in structure manufacturing. In manufacturing
conventional metallic structures, small components are fabricated individually and then
assembled to form large sections. Although complex composite structures can be molded
in single pieces to simplify manufacturing processes and to reduce assembly cost, they
cannot be completely exempted from the joining process. The joining process is
especially needed when composite components are to be assembled with components
made of dissimilar materials, such as metals.

Both mechanical fastening and adhesive bonding are commonly used in structure
assemblies. Each technique has its own advantages and disadvantages in terms of
function, cost, etc. Adhesive bonding is privileged for being free from structural
discontinuity. In terms of structural strength, however, adhesive bonding is primarily
relying on shearing strengths of adherent, adhesion and the bonding between them [8,9].
Also well recognized, shearing strengths are not as promising as the in-plane strengths
and shear stress related failures are often catastrophic [10]. Moreover, as components to
be assembled in a joined structure become thicker, substantially increasing bonding areas
two-dimensionally and applying complex joining techniques [1 1-13], such as scarf joints,
prove to be only available options. On the other hand, thicker components could be
straightforwardly incorporated in a mechanical fastening by increasing fastener size
accordingly. As a result, high in-plane strengths of composite materials could be fully

taken advantage of and high stress concentrations due to structural discontinuity could be

released. Therefore, in joining thick composite laminates, mechanical fastening technique
is superior to the adhesive bonding technique thanks to its three-dimensional nature.

Generally, the parameters affecting the performance of a mechanical joint could be
categorized into three groups: (1) Material parameters: fiber type and form (woven fabric,
unidirectional, etc.), resin type, fibre orientation, laminate stacking sequence, etc.; (2)
Fastener parameters: fastener type (screw, bolt, rivet etc.), fastener size, hole size,
tolerance, washer size, clamping force, side lap material and geometry; (3) Design
parameters: joint type (single lap, double lap, multiple/single fastener), in-plane geometry
(width, length, end distance, hole pattern, etc.), laminate thickness, load direction,
loading rate, etc.

C. Size Scaling

Small coupons are usually used in laboratories for material characterizations. Results .
from small coupon tests are then- used for design of large structures. However, small
coupons do not always behave the same as large structures made of an identical material
[14-18]. The difference of behaviors due to size’variation is usually called “size scaling
effects”. Some investigations regarding the performance of composite materials at
different scales have been reported [16-18]. It has been concluded that scaling effect
should be carefully examined in material characterization and structural designs.

In an adequate design of mechanical joint structure, moreover, size scaling effect is
complicated and can be categorized into in-plane scaling, thickness scaling and three-
dimensional scaling. As a matter of fact, in-plane scaling is based on the presumption of
uniform material properties and stress distribution in the thickness direction and has been

more thoroughly studied; thickness scaling did not draw much attention until recently

when broad thick composite plate application became reality. Research on three-
dimensional scaling is even more scarce.

In studying in-plane scaling, thin composite laminates without notches [18] and with
notches [16] were investigated. The strengths of composite laminates were found to
decrease monotonically with the increase of in-plane dimensions. In a two-dimensional
study on mechanical fastening, Wang et al [19] reported that the bearing strength had a
first-decrease-then-increase change as the in-plane dimensions increased.

Thickness also plays an important role in composite size scaling [1, 3, 6, 17]. In fact,
there are some unique concerns in scaling the thickness of composite laminates. Unlike
scaling the thickness of conventional metals, there exist at least two different approaches
in scaling thicknesses of composite laminates, so-called sub-laminate scaling and ply-
thickness scaling, each meeting different design purposes. Various stacking sequences
also result into different failure phenomena and mechanisms [21]. Also, limited by the
immaturity of manufacture technology, thick composites unavoidably contain residual
stresses to some extent [21-24]. As a result, material property variation would become
noticeable not only between thin and thick composite plates, but also within a thick
composite plate itself, through the thickness direction between inner and outer plies.
Moreover, geometry-induced variations including non-uniform stress distributions
through laminate thickness, specifically as in mechanical joining structure [25-27], render
the study very complicated.

In a previous study [28] regarding to thickness scaling involved in mechanical joint,
the thickness effect in composite pin joints was found to be dependent on the ratio of

laminate thickness H to hole diameter D, i.e. H/D. If the H/D ratio is smaller than 1.0,

the pin joint has a relatively small thickness but a relatively large hole. On the contrary, if
the H/D ratio is greater than 1.0, the pin joint has a relatively large thickness but a
relatively small hole. As the H/D ratio changes from smaller than 1.0 to greater than 1.0,
both the types of the load-displacement curve and the strengths of the composite joints
change significantly due to the change of the contact condition between the pins and the
composites. Joint configurations with ratios of WI) close to one were found to be more
efficient in joint performance.
D. Investigation Techniques

Many analytical studies concerning mechanical fastening were presented and most of
them were based on two-dimensional assumptions. However, as mentioned by Oplinger
[25], two-dimensional studies unavoidably ignored the details of the stress distribution
. through the thickness of the fasteners. Nelson, Bunin and Hart-Smith [26] also presented
some important insights into the effects of thickness on fastener bending. The importance
of using three-dimensional techniques in studying mechanical fastening was also
recognized by other researchers [27, 29-31]. According to Chen, Lee and Yeh [28], the
bolt elasticity had a tendency to change the stress distribution through the laminate
thickness. Ireman [27] found that bending of the bolt created a non-uniform contact stress
distribution between the bolt and the hole. An investigation based on a three-dimensional
spline variational technique was conducted by Iarve and Schaff [31] to analyze the
interlaminar stresses in a composite fastener.

Among the very few studies based on three-dimensional analysis, the interlaminar
stresses between different layers were often not examined thoroughly. Shokrieh and

Lessard [32] studied a pin-joint structure with radial displacement boundary conditions.

Stress singularities were reported at the interface between layers with different ply
orientations on the free edges. However, the contact stress and friction between the pin
and the plate were not considered in their study.

Many studies [33-36] were focused on predicting the strength of joint structures
solely based on the stress distribution on the hole surface. Their studies belonged to the
category of so-called “one-parameter failure theory”. Stresses, strain or distortional
energy results right on the hole surface were input into a failure criterion, e.g. maximum
stress criterion, to predict the failure of entire joint structure. The one-parameter failure
theory was simple to apply but did not account for the localized material response near
the hole. Hart-Smith [37] experimentally reported that prior to the entire structure failure
localized damage could occur near the hole, instead of right on the hole surface. As a
result, one-parameter failure theory generally underestimated the strength of composite
. joints.

The idea of two-parameter failure theory was taken from Whitney-Nuismer’s work
[38], which was originally focused on hole size effects. A characteristic dimension,
which was normally a certain distance away from the hole in the laminate plane, was
required in both point stress and average stress failure theory. The characteristic
dimension was considered as a material property in early studies. Later investigations
[39.40], however, proved that it was dependent upon laminate quality and type of load.
Furthermore, it was concluded that the predicted failure loads were quite sensitive to the
value of the characteristic dimension [39-41] or the shape of the characteristic curve [42].
Thus, the two-parameter failure theory was problem dependant and could not be used

straightforwardly.

With the assumption that damage took place in the zones where a failure criterion was
satisfied, progressive damage theories were proposed to simulate damage initiation.
Besides, with the use of elastic property degradation as a function of the degree of
damage, progressive damage theories were fiirther used to simulate damage growth [43-
47]. The predicted failure loads were in good agreement with experimental results for
open holes subjected to compression and tension, by Chang and Lessard [48] and by
Chang, Liu and Chang [49], respectively. However, the good experimental correlation
can be partially due to the fact that the authors used the value of 5, fibre failure
interaction zone introduced by Tsai [50],which best fit with the test data for CFRP;
Furthermore, the damage growth used in the compression case [48] was sensitive to the
finite element mesh used, so the authors adopted meshes in order to obtain expected
damage propagation for each lay-up. This procedure also disabled the generalization of
the model for lay-ups and geometries in which damage propagation was difficult to
predict. For loaded holes [51], no improvement in accuracy was found in predicting joint
strengths with or without the progressive damage models [42, 52].

Also as an open hole study [53], Tan’s approach neglected the different effects of
different micro-mechanical failure types on the stiffness degradation of a lamina as used
by Chang [44]. The stiffness degradation was represented by factors assumed and lamina
material properties, En, E22 and G12, were reduced by the product of their initial values
with the corresponding factor. Close correlation with experimental data was achieved for
several lay-ups in terms of strengths. However, it should be noticed that the results were

very sensitive to the values of the degradation factors assumed.

1.2 Objectives and Scopes of Current Study

Studies devoted to size scaling effect in a mechanical joint structure are scarce yet
very crucial to an adequate design. Especially, while more and more thick composite
plates have been widely practiced in joint systems, scaling effects involving thickness
scaling have not drawn as much research attention as they actually deserve. This could be
attributed to many factors: thick composite plates are generally expensive; scaling effect
theories in composite fields are still lacking; a large variety of failure phenomena
compete with each other in a composite material at the same time and their underlying
mechanisms have not yet been fully understood; computational simulation of joint
' structure through thickness is very costly, etc. Nevertheless, research in this area could be
rewarding and this study was primarily devoted to size scaling effect, particularly
thickness scaling effect, in composite joint system. As regarding to research approaches,
experimental study and computational study were both explored intending to provide
different perspectives.

As stated before, many parameters affect the performance of a mechanical joint. As a
matter of fact, bolt-joint is more commonly practiced in the industry and attracts more
research [19, 25, 27, 30, 54-56], as compared with pin-joint. Bolt-joint practice, however,
introduces clamping force, another important parameter in the thickness direction other
than thickness dimension parameter, and results in a state of intertwining between these
two key parameters. A pin joint structure, on the other hand, could single out thickness
parameter by simply eliminating the clamping force parameter in a mechanical joint.
Since this study was mainly devoted to thickness parameter, pin joint was focused

accordingly. Through the entire research, therefore, the joint structure studied was a so-

called “double-lap-single-pin” joint - double side laps and one single pin, assembled with
one central composite material lap. For generalization purpose [57-59], woven glass-
fabric/phenolic composite and cross-ply glass/epoxy composite were both included in the
study.

1.3 Organization of Following Chapters

Firstly, a previous study [28] was extended into a three-dimensional scaling effect
study by combining and comparing thickness scaling effect and in—plane scaling effect. A
woven glass-fabric/phenolic composite was first selected for study. Based on four
different thicknesses and seven different hole diameters, total nine composite joining
configurations were prepared. The nine configurations were organized into three groups
with different H/D ratios (thickness vs. hole diameter). Strength results as well as damage
modes within these groups were compared in order to reveal size scaling effects. Effects
due to variation of outer-lap stiffness and pin hardness were also discussed. Experimental
results were included in Chapter 2.

Later in Chapter 3, three-dimensional scaling effect study was extended to
Glass/epoxy composite laminates. In addition, this part of the study also explored three
different technical approaches in meeting out-of-plane requirements of a mechanical joint
structure — thickness scaling, bonding technique and bolting technique. Key factors
related to constraints in the thickness direction, namely composite thickness, bonding
strength through laminate thickness and clamping force from bolting, were compared and
their key roles in damage process were discussed. Beyond that, effects due to variation

of pin-hole clearances and loading rates were also studied.

Chapter 4 was aimed at gaining more insights into thickness-involved effects in a
joint structure by using the aid of finite element analysis method - a computational
analysis method. When a glass/epoxy composite joint was subjected to a load comparable
to its load capacity, stress distributions around damage susceptible areas were presented
in detail attributed to a fine three-dimensional meshing. Stress variation through the
thickness direction was studied and its sensitivity to thickness scaling effect was also
studied. Suitability of several commonly-used failure criteria was investigated in this
special case. A broadened two-parameter failure theory was also included for discussion.

Chapter 5 drew several conclusions of this study and laid out some recommendations

for future studies.

10

Chapter 2

Three-dimensional Size Effects in Composite Pin Joints
2. 1 Introduction

Joining is a secondary process for structure manufacturing. For conventional metallic
structures, small components are fabricated individually first and then assembled to form
large sections. Although many polymer matrix composite structures can be molded in
single pieces to simplify manufacturing process and to reduce assembly cost, they cannot
be completely exempted from joining process. The joining process is especially necessary
when a polymer composite component is to be joined with a component made of a
dissimilar material such as metal.

Both mechanical fastening and adhesive bonding are commonly used in structure
assemblies. Each technique has its own advantages and disadvantages in .terms of
functiOn and cost. In terms of strength, different techniques also lead to different damage
modes and failure strengths. Based on the high in-plane strengths of composite materials,
mechanical fastening is commonly performed in assembling composite laminates.
However, mechanical fastening can cause high stress concentration due to structural
discontinuity. Adhesive bonding, although free from structural discontinuity, is primarily
based on the shearing strengths of the adherent, the adhesion and the bonding between
them. These shearing strengths are no greater than the in-plane strengths and are limited
to the bonding surface, instead of through the thickness. As the joining components
become thicker, a much larger bonding area is required, not only to achieve a higher
joining strength but also to reduce the high stress concentration around the bonding ends.
Since mechanical fastening is actually a three-dimensional technique, it is superior to

two-dimensional adhesive bonding in joining thick composite laminates.

11

Thickness is an important parameter in composite structure analysis and many studies
concerning thickness effects have been reported in the literature [1, 3-6]. Although
studies of composite mechanical fastening commonly focus on effects due to in-plane
configuration, the effects due to thickness should also be adequately considered. As
mentioned by Oplinger [25], two-dimensional studies unavoidably ignore the details of
the stress distribution through the thickness of the joint. Nelson et a1. [26] have provided
some important insights into the effect of thickness on fastener bending. The importance
of using a three-dimensional technique in the analysis of mechanical fastening has also
been recognized by other researchers [27, 29, 30]. According to Chen et a1. [30], the bolt
elasticity has a tendency to change the stress distribution through the laminate thickness.
Ireman [27] has found out that bending of the bolt creates a non-uniform contact stress
distribution between the bolt and the hole.

In a previous study by Liu et al. [28], the effects of thickness on composite pin joints
have been identified as associated with the ratio of laminate thickness to hole diameter,
i.e. H/D. Wehn H/D < 1, it implies that the pin joint has a small thickness but a large
hole. When H/D > 1, it implies that the pin joint has a large thickness but a small hole. As
the H/D ratio changes from less than one to greater than one, both the type of the load-
displacement curves and the joining strengths change significantly due to the change of
contact between the pins and the composites. The objective of the present study is to
identify the effects of three-dimensional scaling (thickness scaling as well as in—plane

scaling) on the behavior of composite pin joints.

12

2. 2 Experimental Methods
A. Composite Material

The composite material used in the study was made of S-2 glass fabrics and a
phenolic matrix, namely a glass-fabric/phenolic composite. Since the glass fabrics were
of plane weave, each piece of fabric could be viewed as a (0/90) cross-ply unit. In
preparing composite laminates, an angle of 45° was imposed in laying up consecutive

plies of fabric, resulting in quasi-isotropic laminates [(0/90)/(45/-45)]ns. This stacking

sequence could be considered as a sublaminate mode of scaling in laminate thickness as
the building block [(O/90)/(45/-45)]. Composite laminates of 8-ply (n=2), 24-ply (n=6),
40-ply (n=10) and 80-ply (n=20) were prepared in the study. Thus all laminates tested
were quasi-isotropic.
B. Joint Configurations

The 8-ply, 24-ply, 40-ply and 80-p1y composite laminates ‘had thicknesses of 1.96,
5.97, 9.40 and 20.42mm, respectively. In order to investigate the effects due to three-
dimensional scaling, seven hole sizes were chosen to match the four thicknesses,
resulting in nine different joint configurations. The geometric elements of the joints, such
as width W, hole diameter D, thickness H and the distance between hole center and
specimen end E, and the associated geometric ratios, such as W/D, 13/1) and H/D, were
important parameters in studying mechanical fastening. The geometric elements and
ratios of the nine joints were summarized in Table 1. To ensure bearing failure, instead of
a net-section or a shear-out failure, all laminates had W/D= 4 and E/D 2 2.66.

For identification purpose, a special notation system based on HXDY has been used

where H and D, as defined earlier, represent the thickness and the hole diameter of the

13

Table 1 -— Geometrical elements and geometrical ratios of glass-fabric/phenolic

composite central laps.

 

 

 

 

 

unit: mm 8-ply 24-ply 80-ply
H 1.96 5.97 20.42

ID H8D2.77 H24D3.96

D 2.77 3.96

w 11.08 15.85

E 7.48 10.62

H/D 0.71 1.51

W/D 4.00 4.00 ,

E/D 2.70 2.68

ID H8D5.16 H24D7.54 H4OD6.35

D 5.16 7.54

w 20.33 30.46

E 13.73 20.51

H/D 0.38 - 0.79

W/D 3.94 ‘ 4.04 ‘

E/D 2.66 2.72

ID H24D15.1 H40D12.7 ‘~,H80D12.7
D ‘~ 15.09 ‘ ‘~ 12.7
w 60.96 50.80
E - 41.20 34.04
H/D 0.40 1.61
W/D - 4.04 4.00
E/D 2.73 _‘ 2.68 9.
II)D H4OD25.4 ‘ W105
w 1016 HID==0.75

E

H/D

W/D

E/D

H: laminate thickness

W: laminate width

D: hole diameter

E: distance from hole center to laminate end

14

HID=0A

joints, respectively, while X and Y are the ply number of the composite laminate and the
hole diameter in millimeters (mm), respectively. For example, a composite joint having a
thickness of 8-ply (1.96mm) and a hole diameter of 2.77mm is designated as H8D2.77.
C. Three-Dimensional Scaling

Although all composite joints investigated in the study have identical W/D (equal to
4) and similar E/D (greater than 2.66), their H/D ratios are different. Based on the ratio of
mu the nine joints listed in Table 1 could be divided into three groups. Each group
consists of three joints along a diagonal line of Table l. The three groups had H/D ratios
of 0.4, 0.75 and 1.5. The joints with H/D=0.4 and H/D=0.75 have relatively small
thicknesses but large hole diameters. The joints with H/D=l.5 have relatively large
thicknesses but small hole diameters. Since the joints in each group have identical
. geometric ratios of W/D, E/D and H/D but different values of geometric elements W, D,
H and E, they are of three-dimensional scaling.
D. Dissimilar-Material Assembly

Some experimental results of double-lap-single-pin joints have been reported in a
previous study [28]. Both the central laps and the outer laps of the composite joints were
made of glass-fabric/phenolic composite, resulting in composite-composite similar-
material assemblies. In the present study, a similar double-lap-single-pin joint, as shown
in Figure l, was taken as the experimental model due to the simplicity of this
arrangement. However, the central laps were made of the glass-fabric/phenolic composite
whereas the outer laps were made of steel, resulting in composite-steel dissimilar-
material assemblies. Since various joint configurations with different geometric elements

and ratios were investigated, different thicknesses of steel outer laps were required. In the

15

       
  
 

  
       

    

  
      
     
   
  
     
   
  
 

 
 
 
 

  
   
    
   
   
 
 
        
  
   
      

   
  
  
  
   

   
    
  
  
 
    
 

  
   
   
      
   

    
  

      

   
  

   
   
  
  
 
    
   
    
    

   
    

   
   
   
 
    
 
  
    

   
     

  

  

 

     

        
 

 

 

 

 

   
      
          
   
 

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.00... 0... 0..
0000. 0.0. .0.
.00... ..0 .0.
0.0 .000 .000
...0 00 .00
-0.. . .0
0... 0 . .00
-0.0 0 00 0. ____
0... 0 .0. .0.
-0.0.00.0.00 .0
0....00000. .0.
-0.0.00.000. ..
00.......00.0 0.0
~..0.0.0.0.0. .0
..0..0.0..... 0..
~00..0...0.00 ..
..’......... .“
-.....0000.... ..
0.000.000... ..0
-...0. 0.0. 00
.0..00 ..0 .0.
-....0 0. .0
.00... .0.
'...‘. 0..
OO .‘ .
~....0.
00.. .00.
- 0... .0.
.0... 0...
~..... 00.
fiflffiflfi ”p0. .
0.... 0.. 0
'0 0.0. °.’0‘0'0
.000
.0.0
O...
0.00
..0.
.mp0. . .
—.--0- 6"”. ..—..—..—-.---—-- --:—--—- _
.0. .
0..
q;
0

  

 

Central
C ross-section

07 Outer Laps

 

 

 

 

 

—— Testing Grips

 

 

Figure l — Schematic diagram of a double-lap-single-pin joint.

study, the thicknesses of the steel outer laps were chosen to be half those of the
corresponding composite central laps to ensure the failure of the composite-steel
assemblies be dominated by damage to composite central laps. Since steel was stiffer
than the composite, the effect of the rigidity of the outer laps on the bearing failure of the
composite joints was also a primary concern in the study.
E. Pins with Various Hardnesses

Steel pins were used in the assembly of composite joints. Since the interaction
between the pins and the composite central laps played an important role in the failure
processes of the composite joints, the effect of pin hardness on the bearing strength of
composite joints was also a primary concern in this study of mechanical fastening. Three
types of steel pin based on different heat treatment processes were used. They were W--1,
O-l and M-2, based on the A181 classification system. The W-l pins and O-l pins were
in soft states while the M42 pins were hardened before applications. The hardening
process boosted the hardness of the pins significantly. The hardness indices of the pins
were 6.0-13.4 for W-l pins, 8.5-13.4 for O-l pins and 63-65 for M-2 pins, based on
Rockwell Hardness. The yielding stresses of the pins were proportional to their
hardnesses [62, 63]. Consequently, M-2 had the highest yielding stress, followed by O-l,
and W-l had the lowest yielding stress.
2. 3 Experimental Results
A. Load-Displacement Curves

All composite joints were loaded with a constant crosshead rate of 1.27mm/min until
bearing failure took place. The obtained load-displacement curves could be divided into

two different types: brittle and ductile. If a load-displacement curve had an almost linear

l7

relation until an abrupt loss in load of at least 10%, it was called a brittle-type curve. If,
however, the displacement of a curve increased smoothly, not necessarily linearly, with
the load and there was no sudden load loss in the curve, the load-displacement curve was
called a ductile-type curve. Figure 2(a) shows an example of a brittle-type curve for an
H8D2.77 joint while Figure 2(b) shows an example of a ductile-type curve for an
H80D12.7 joint. Table 2 summarizes the types of load-displacement curves of all joints
based on W-l pins. The type of the load-displacement curve of a joint was dependent on
the H/D ratio of the joint. According to the table, all the joints in the groups with
H/D=O.4 and H/D=0.75 had brittle-type curves while all the joints in the group of
H/D=1.5 had ductile-type curves.

As hypothesized in a previous study [28], the ductile-type curves were mainly
attributed to pin bending. The joints in the group of H/D=l.5 had relatively small hole
diameters but large laminate thicknesses. The combination of a small-diameter pin and a
large-thickness composite resulted in a non-uniform pin-hole contact through the
laminate thickness. A similar result was also reported by Ireman [27] based on three—
dimensional finite element analysis. More specifically, the contact between the pin and
the composite laminate of the central lap was tighter at the vicinity near the laminate
surfaces whereas it was looser at the vicinity near the laminate mid-plane, as shown in
Figure 3. In contrast, the joints of the groups with H/D=O.4 and H/D=O.75 had relatively
large hole diameters but small laminate thicknesses. The combination of a large-diameter
pin and a small-thickness composite resulted in a relatively uniform pin-hole contact

through the laminate thickness.

18

Load (N)

 

 

 

 

 

 

 

 

 

 

Fmax _ ........................ ..’..,:#:.6 ..............
.x"? O," sudden load loss
I’o’o .I.’ 2, OG ._ ..............
700 .4»
43””!
3" .’.1°
.0, .’.’
0 .9' ."
f f
0 0.4 0.8 1.2
' Displacement (mm)
0.65% of D
(a) brittle type (H8D2.77)
60000
Fmax ..._.._.._.._.._.._.._..,:
I
30000
0 in?
0" 2‘— 2 4 6

1% 0f Displacement (mm)

off-set
displacement

(b) ductile type (H80D12.7)

Figure 2 - Load-displacement curves, glass-fabric/phenolic composite joints

l9

Table 2 - Types of load-displacement curves, maximum loads, and offset displacement
percentage of all joints based on W-l pins.

 

 

 

 

 

 

 

 

 

T.lMax.2 Off.3 T.1Max.2 Off.3 T.TMax.2 Off.3 T.IMax.zOff.3
H8D2.77 H24D3.96
B 1.30 1.7 D 5.23 1.0
B 1.21 1.0 D 5.12 1.0
B 1.22 1.8 D 4.94 1.0
B 1.15 2.6 D 4.76 1.0
B 1.20 2.8 D 4.62 1.0
B 1.24 0.65 D 4.57 1.0
Avg,(sd)4 1.22(0.05) 4.87(0.27)
Average5 0.2248 0.2060
H8D5.16 H24D7.54 H4OD6.35
B 2.00 1.16 B 11.11 0.45 D 14.00 1.0
B 2.01 0.76 B 11.39 0.37 D 12.13 1.0
B 2.12 0.67 B 12.05 0.40 D 12.62 1.0
B 2.17 0.61 B 12.22 0.49
B 2.13 0.53 B 11.37 0.90
B 2.01 0.38 B 11.48 0.93
Avg,(sd)4 2.06(0.‘08) ll.60(0.43) 12.92(0.97)
AveragCS 0.2034 0.2578 0.2165
H24D15.1 H40D12.7 H80D12.7
B 17.10 0.46 B 26.72 0.78 D 43391.0
B 15.61 0.59 B 24.01 1.8 D30.501.0
B 16.90 0.64 B 25.85 0.71 D 37091.0
Avg,(sd)4 16.54(0.81) 25.44(1.38) 36-99(645)
Average5 0.1836 0.2131 (“428
H4OD25.4
B 37.99 0.15
B 41.91 0.42
B 42.63 0.44
Avg,(sd)4 40.84(2.50)
Average5 0. 1 71 l

 

1
Type of load-displacement curve; B for brittle and D for ductile

2 Maximum load (Unit: kN)
3

Offset displacement percentage (with respect to hole diameter)

A

Average maximum load (standard deviation) with a unit of kN
Average bearing strength (Unit: GPa)

5

20

P/2H PIZH

 

 

 

 

 

 

 

 

 

Steel Pin

 

 

 

 

Laminate Surf. Laminate Surface

 

 

 

 

Laminate E
Mid-plane E ‘ Composite
’ 3’ . Central Lap
~————~¢ T :4 a?

H . H H

Figure 3 — Details of the shaded zone in Figure 1.

21

The correlation between the type of load-displacement curve and the geometric ratio
H/D could be established by the following analysis. Figure 3 shows the core section of a
double-lap-single-pin joint, which is the shaded zone given in Figure 1. Based on a
strength-of-materials analysis, the maximum bending stress in the steel pin can be

identified as

 

 

3PH a
0. = My ___ 8 2 : .9_PH
bending 1 1-D3 4 D 2
12

Similarly, the averaged bearing stress in the composite central lap can be identified as

—.£_—_P —L
Obearing _ A _ H-l _ H

Again, unit depth was used in the two-dimensional analysis. The ratio between the
bending stress and the bearing stress can be found as

Ubending : .9_.(fl_)2
0' bearing 4 D

Thus, the type of load-displacement curve of a composite joint is dependent on the
geometric ratio H/D of the joint. The failure of a composite joint with a large H/D ratio
would be dominated by pin bending and have a ductile-type load-displacement curve.
However, the failure of a composite joint with a small H/D ratio would be dominated by
bearing failure of composite laminate and have a brittle-type load-displacement curve.

B. Damage Modes

To further understand the effect of the IUD ratio on the joint damage, some composite

joints unloaded shortly beyond the occurrence of bearing failure were examined

microscopically. All joint damage was identified to be fiber buckling. Both surface and

22

cross-sectional damage patterns were examined. In the surface investigation, the damage
pattern below the holes was of primary concern. In the cross-sectional investigation, the
damage pattern at the central cross-sections of composite laminate, shown in Figure l,
was of primary interest.

Except for those joints made of 8-ply laminates, two kinky bands could be clearly
identified from the central cross-sections of the joints having brittle-type load-
displacement curves. Each kink band ran from the laminate mid-plane to the laminate
surfaces with an angle of 45° from the laminate mid-plane. The kink bands were formed ,
by buckled fibers in every layer. Figure 4(a) shows the two kinky bands outlined by
dotted lines in an H40D12.7 joint. The ends of the kink bands on the laminate surface at
various cross-sections cumulatively formed an arch-shaped benchmark at a distance from
the hole edge approximately equal to half the laminate thickness. Figure 4(b) shows the
arch-shaped benchmark on the surface of an H24D7.54 joint.

Although the joints made of 8-ply laminates also had brittle-type load—displacement
curves and fiber buckling damage, they did not have kink bands. The fibers buckled
outward, namely outward buckling, as shown in Figure 4(c) with enhanced lines for an
H8D5 .16 joint. It was believed that the lesser constraint in the thickness direction due to
the smaller laminate thickness was responsible for the outward buckling, instead of kink
bands. A similar view has also been presented in a study concerning the compressive
strength of composites by Zhang and Robert [64]. As a result of the outward buckling,
there was no arch-shaped benchmark on the laminate surfaces.

The composite joints with ductile-type load-displacement curves had relatively

complex damage patterns. Due to the large thicknesses, the damage patterns in these

23

. l-a

   

(c) central cross-section of (d) central cross-section of H80D12.7
H8D5.16

Figure 4 — Microscopic damage patterns of glass-
fabric/phenolic composite laminates in
joint/compression loading.

   

   

" 35;; ‘i‘fi Dig ”1 1-‘3‘

(e) edge of 24- 1y specimen

24

joints were expected to be non-uniform through the laminate thicknesses. The
compressive damage in the plies close to laminate surfaces had kink bands although they
were not necessarily at 45° from the laminate mid-plane. The damage in the plies close to
laminate mid-planes was also attributed to kink bands but the kink bands were relatively
irregular. Figure 4(d) shows the damage pattern of an H80D12.7 joint at the central cross-
section. The associated surface damage pattern of the thick composite joint also had an
arch-shaped benchmark. The non-uniform damage pattern through the laminate thickness
revealed the non-uniform stress distribution through the laminate thickness, probably due
to the non-uniform pin-hole contact in the joints with large H/D ratios. The pin-hole
contact was apparently tighter in the plies close to the laminate surfaces than in the plies
close to the laminate mid-plane. A tight contact resulted in a high compressive stress and
45° kink bands. A loose contact, however, resulted in a low compressive stress and non-
45° fiber kinks.
C. Maximum Loads and Bearing Strengths

The composite joints investigated in the study all failed due to bearing damage. The
joints with brittle-type curves had clear maximum loads. However, the joints with
ductile-type curves had no clear maximum loads. The determination of the maximum
loads for the joints with the ductile-type curves then required extra care. Since most of
the joints with brittle-type curves reached their maximum loads at offset displacement
levels around or less than 1% of the corresponding hole diameters, see Figure 2(a), a 1%
hole diameter was chosen as the “yielding displacement” for determining the maximum
loads of the joints exhibiting ductile-type curves. Once the maximum load of a joint was

determined, it was normalized by the bearing area DH to give the average bearing

25

strength, i.e., Pmax/DH. Both the maximum loads and bearing strengths of all composite

joints are shown in Table 2.
2. 4 Various Effects
A. Effect Due to Stiffness of Outer-laps

In the present study, the outer laps of joints were made of steel, resulting in
composite-steel dissimilar-material assemblies. Results from the present study were
shown in Figure 5 along with those from the previous study [28], based on composite-
composite similar-material assemblies, for comparison. The results of the dissimilar-
- material assemblies were represented by open symbols while those of the similar-material
assemblies were represented by closed symbols. Although the geometric elements of the
dissimilar-material assemblies and the similar—material assemblies are not exactly the
same, they are very close. For example, the open circles are for H24D7.54 with steel
outer laps while the solid circles are for H24D6.35 with composite outer laps. According
to Figure 5, the bearing strengths of all the dissimilar-material assemblies are consistently
higher than those of similar-material assemblies. For example, the difference between
H24D7.54 and H24D6.35 is about 45%. This is more than what might be expected to be
caused by the geometrical difference.

The difference in bearing strength between the two types of assemblies was believed
to be due to the different contact conditions in the two types. Since the steel was more
rigid than the glass-fabric/phenolic composite, the pin bending in the steel outer laps was
smaller than in the composite outer laps. For example, H24D7.54 experienced an average
of 0.59% offset displacement at failure while H24D6.35 experienced an average of

0.98%. Consequently, the pin-hole contact through the thickness of the composite central

26

0.3

c:bearing strength (GPa)<3
‘ .O to
N 0'!

_s
0'!

0.1

 

 

0 11805.16 (S) . 11806.25 (C)

 

I; 4 14802.77 (S) ‘ H8D3.13(C)

8 ‘ 0 11240161 (8) e H24D12.7 (C)

3 ‘ A H24D7.54 (S) A H24D6.35 (C)
° C] D H24D3.96 (S) - H24D3.13 (C)
3 El A ‘ 0 14400254 (S) 0 H40D25.4 (C)
3 c1 6 l A H40D12.7 (S) A H40D12.7 (C)
9 E Q (:1 H4ODG.35 (S) - H40D6.35 (C)

. g .DHQQQI-2-Zi§l,!t'30912-7(DC)
. Q Cl
3 ' A
. ’ 8 I
O l D
8 24 40 80

laminate ply number

Figure 5 — Comparisons of bearing strengths between
composite-composite assemblies and steel-composite
assemblies (S for steel and C for composite central laps)

27

 

laps was more uniform in the steel-composite assemblies than in the composite-
composite assemblies. A more uniform contact could avoid premature high stress
concentrations at laminate surfaces and result in higher maximum loads, and
subsequently higher bearing strengths, of composite joints.
B. Effects due to Pin Hardness

As mentioned earlier, the load-displacement curves of the joint groups with H/D=O.4
and H/D=0.75 were all of brittle type while those of H/D=1.5 were all of ductile type.
When comparing the bearing strengths of composite joints in the different groups, a
similar type of force-displacement curve, i.e. brittle-type, was preferred. Some efforts
were made to change the type of load-displacement curves from ductile to brittle by using
pins with higher hardnesses. Table 3 shows the results based on W-l, O-l and M-2 pins
for the joints having the smallest size in each group, i.e. H8D2.77, H8D5.l6 and
H24D3.96. As could be seen from Table 3, the change in bearing strength is not
significant for the joints already having brittle-type curves, i.e. H8D2.77 and H8D5.l6.
However, there are noticeable changes in maximum loads for H24D3.96 joints. The
average bearing strength increased by 22.6% when the M--2 pins were used to replace W-
1 and O-l pins. It was also found that M-2 pins could not change the type of load-

displacement curves for joints made of 40-ply and 80-ply laminates.

28

Table 3 - Types of load-displacement curves, maximum loads, and offset
displacement percentage of some joints based on various pins

 

 

 

 

 

H8D2.77 H8D5.l6 H24D3.96
TypeI Max. Offset2 Typel Max. Offset2 TypeI Max. Offset?
Load (%) Load (%) Load (%)
(kN) (kN) (kN)
W-l B 1.30 1.7 B 2.00 1.2 D 5.23 1.0
pin B 1.21 1.0 B 2.01 0.8 D 5.12 1.0
B 1.22 1.8 B 2.12 0.7 D 4.94 1.0
B 1.15 3.2 B 2.17 0.6 D 4.76 1.0
B 1.20 2.2 B 2.13 0.5 D 4.62 1.0
B 1.24 0.7 B 2.01 0.4 D 4.57 1.0
Avg.(sd)3 1.22(0.05) 2.06(0.08) 4.87(0.27)
Average“ 0.2248 0.2034 0.2060
0.1 B ’ 1.27 2.8 B 2.07 0.6 D 5.03 1.0
Pin B 1.19 3.1 B 2.16 0.4 D 4.98 1.0
B 1.19 1.0 B 2.03 0.5 D 4.82 1.0
B 1.25 0.7 B 2.08 0.6 D 4.75 1.0
B 1.18 1.4 B 2.08 0.4
Avg.(sd)3 1.21(0.04) 2.09(0.05) 4.90(0.13)
Average4 0.2236 0.2062 0.2072
M-2 B 1.28 0.9 B 2.06 0.5 D 6.14 1.0
Pin B 1.26 1.1 B 2.18 0.7 D 5.86 1.0
B 1.30 2.0 B 2.03 0.5 D 6.02 1.0
B 1.16 1.4 B 2.15 0.6
B 1.17 2.4 B 2.17 0.6
Avg.(sd)3 1.23(0.06) 2.12(0.07) 6.01(0.14)
Average“ 0.2271 0.2092 0.2541

 

I Type of load-displacement curve; B for brittle and D for ductile
2Offset displacement percentage (with respect to hole diameter)
3 Average maximum load (standard deviation) with a unit of kN
4Average bearing strength (Unit: GPa)

29

The advantage of using high-hardness pins over low-hardness pins was essentially
due to higher yielding stresses of the harder pins. The higher yielding stresses were
associated with higher elastic limits, which reduced the pin bending to some extent.
Accordingly, the non-uniform pin-hole contact through the laminate thickness could be
improved and thus a higher bearing strength achieved.

C. Effect Due to Compressive Strength

No matter whether outward buckling or kink bands occurred, the damage of the pin
joints investigated in the study was due to compressive fiber buckling. Compressive
strength is, therefore, an important parameter in the damage analysis. To firrther
understand the damage processes in compression, some compressive tests have been
performed. Specimens based on 24-ply and 40-ply laminates were prepared and their
dimensions were three-dimensionally scaled. In performing the compressive tests, anti-
buckling devices similar to those suggested by ASTM D695 standard were built and used
in the tests.

The damage mode of the specimens subjected to compressive loading was different
from those subjected to pin loading. Instead of fiber buckling, such as outward buckling
and kink bands, two shearing fractures were found in each damaged specimen, shown by
the enhanced lines in Figure 4(e). In addition, rather than initiating from the mid-plane as
the kink bands did in the pin joining cases, each shearing fracture started from a contact
location close to a laminate surface. The shearing fractures extended with an average
angle of about 20° to the laminate mid-plane of a 24-ply specimen and eventually merged
together. The average angle of the shearing fractures in the 40-ply specimens was around

30°.

30

The differences in damage mode and strength were significant between the cases
subjected to pin joining and compressive loading. The average compressive strength of
the 24-ply specimens was 0.136 GPa while that of 40-ply specimens was 0.118 GPa.
Apparently, the compressive strengths were much lower than the bearing strengths given
in Table 2. A similar result has also been reported by Collings [65]. Besides the
difference of loading mode, another possible interpretation of the discrepancy could be
based on the outward bulging of the central laps due to compression. The outward
bulging beneath the pin-hole contact could create some sort of interlocking and clamping
between the central laps and the outer laps. In fact, it has been shown by some
researchers [56, 66, 67] that a small clamping force could improve joining strength by 30-
100%. A large bolting force has even been found to produce a 300% increase in joint
strength [68].

2. 5 Size Effects

All the pin joints investigated in the study were based on three-dimensional scaling.
The three cases of the group with H/D=0.4 were scaled from 8 to 24 and to 40, i.e. a 1:315
scaling ratio. The three cases of the group with H/D=0.75 had an identical scaling ratio as
the cases of the group with H/D=0.4. The three cases of the group with H/D=l.5 were
scaled from 24 to 40 and to 80, i.e. a 1:1.67:3.33 scaling ratio.

The bearing strengths of the group with H/D=0.4 decreased by 9.2 and 15.4% as the
size increased by three times and five times, respectively, resulting in a monotonic
decrease of bearing strength with the increase of joint size. The bearing strengths of the
groups with H/D=0.75 increased by 14.7% then decreased by 5.6% as the size increased

to three times and five times. Similarly, the bearing strengths of the group with HfD=1.5

31

increased by 5.1% then decreased by 30.7% as the size increased to 1.67 times and then
3.33 times. Both the groups with H/D=l.5 and H/D=1.5 had non-monotonic changes of
bearing strength with the increase of joint size. The non-monotonic changes in the groups
with H/D=O.75 and 1.5 were believed to be associated with higher thickness effects than
the monotonic decrease in the group with H/D=0.4. That is, the higher the H/D ratio, the
higher the thickness effect. The bearing strengths of all the joints are listed in Table 2.
They are also shown graphically in Figure 6.

The changes of bearing strength with the increase of joint size were not monotonic in
the groups with H/D=0.75 and 1.5. They actually increased then decreased. Thus, the
three-dimensional size effect in the pin joints was not Weibull type, which states that the
strength of materials always decreases with the increase of size. This discrepancy might
be associated with the difference of damage mode. As mentioned earlier, the smallest
cases (made of 8-ply laminates) of the groups with H/D=0.4 and H/D=0.75 had a damage
mode of outward buckling while the medium and the largest cases (made of 24-ply and
40-ply laminates) had a damage mode of kink bands. Both the differences in bearing
strength (monotonic and non-monotonic) and damage mode (outward buckling versus
kink bands) implied that both material properties and geometrical parameters should be
considered in the three-dimensional size effect.

In an effort to understand why the three-dimensional size effect was not Weibull-
type, the three-dimensional sealing was divided into in-plane scaling and thickness
scaling. The in-plane scaling and the thickness scaling were investigated individually and
the results are presented in Figure 7 and Figure 8 (based on Liu et al. [28]), respectively.

In the studies of in-plane size effect and thickness size effect, only joints with brittle-type

32

 

 

 

 

750.25 S
9 i i
., 02 a
5 0
cc” 0 Cl
9 0.15 Cl
a
I:
_g’ 0.1
8
n 0.05
0 I l I I
8 24 40 80

laminate ply number

0 H/D=0.4
A HID=0.7
El HID=1.5

Figure 6 — Bearing strengths due to three-dimensional scaling.

33

1.6 ~

9
.Is

:-‘
N

Bearing Strength Ratio
9
m .1.

.0
a:

0.4 4

08-90
A24-ply
D40-ply
A
A
i a
8 a 4
A Q
C]
”2‘ 4 4 4

h—plane Scaling Factor

10

Figure 7 -- Bearing strength ratios (bearing strengths normalized by

1.6 ‘
1.4

1.2 4

Bearing Strength Ratio

Figure 8 — Bearing strength ratios (bearing strengths normalized by

that of H8D2.77) due to in-plane scaling.

O
Q A A D=12.5mm
A El D=25mm
o 3 a
o E Q
o

1 2 3 4 5 6 7 8 9
Thickness Scaling Factor

that of H8D6.25) due to thickness scaling.

34

O D=6.25mm .

10

damage were included since brittle-type damage was better defined than ductile-type
damage.

In the study of the in-plane size effect, the bearing strength of the H8D2.77 joint was
used to normalize the strengths of all joints. As shown in Figure 7, there were three
groups, designated as 8-ply, 24-ply and 40-ply. In each group, the thickness is kept
constant while the in-plane dimensions are scaled. It could be seen from Figure 7 that the
bearing strength in each group decreases as the in-plane scale increases. Similar results
for the in-plane size effect have also been reported in the literature for specimens without
crack [18] and with cracks [16]. Apparently, the Weibull theory [17, 18] is capable of
interpreting the in-plane size effect because the Weibull theory is essentially based on the
argument that larger specimens have larger defects and hence have lower strengths. In
addition, it is interesting to point out that the theory of Bazant et al. [16] is also capable of -
interpreting the in-plane size effect because the Bazant theory, based on fracture
mechanics, predicts that the reduction rate of strength with the increase of size is
approximately equal to 1/2 for large isotropic, brittle specimens.

In the study of the thickness size effect, the bearing strength of H8D6.25 was used to
normalize the strengths of all the joints. There were three groups in the study [28],
designated as D625, D125 and D25. In each group, the in-plane dimensions were kept
constant while the thickness was scaled. It could be seen from Figure 8 that the bearing
strengths in each group increase as the thickness scale increases. A similar result based
on the thickness study has also been reported by Wang et a1 [19]. The interpretation of
the change in bearing strength due to the thickness scaling was more complicated than

that due to in-plane scaling. In addition to the negative influence based on the Weibull

35

theory for specimens subjected to pin loading (also true for specimens subjected to
compressive loading reported in the section “Effect Due to Compressive Strength”), there
was apparently a positive contribution due to the thickness scaling. The damage of pin
joints was essentially due to fiber buckling, and hence the increase of thickness constraint
was expected to greatly increase the buckling resistance of fibers. However, as the
thickness increased, the risk to pin bending also increased. Thus, the increase of bearing
strength due to increase in thickness was a combined result of the positive contribution
from the increase in buckling resistance and the negative influences from the Weibull-
type size effect and pin bending.

Based on the negative influence from the in-plane scaling and the resultant positive
contribution from the thickness scaling, the three-dimensional size effect of the pin joints
could be postulated as follows. The resultant three-dimensional size effect in pin joints
was not monotonic because of a negative influence and a positive contribution. The three-
dimensional size effect was not Weibull-type, which is essentially based on material
defects. Although the non-monotonic effect was based on pin joints with brittle-type
damage, i.e. H/D=0.4 and 0.7, this conclusion could be extended to the pin joints with
ductile-type load-displacement curves, i.e. H/D=1.5.

Geometrical scaling, such as in-plane sealing and thickness scaling, are directly
responsible for size effects. They can also affect the material properties of composite
laminates to some extent. For example, the size of material defects such as microcracks,
voids, resin-rich pockets, etc., can be affected by the thickness scaling of composite
laminates. Since composite laminates are constructed by plies, the properties of

composite laminates are usually not constant through the laminate thickness because non-

36

uniform curing temperature histories are experienced in individual plies [24, 69] even if
the plies have an identical fiber orientation. This phenomenon can become significant as
composite thickness increases. Besides, the associated thermal residual stresses are also
likely to increase as the thickness and hence the geometrical constraint in the thickness
direction increases. Thus, as a material defect, the thermal residual stress due to
composite curing may impose a size effect in the composite laminates.

2. 6 Conclusions

Based on experimental results and discussions, the following conclusions can be
drawn from the investigations of pin joints:

1. The steel-composite joints had higher bearing strengths than the composite-
.composite joints because the higher constraint imposed by the stiffer steel outer laps,
which renders a more uniform pin-hole contact.

2.1 Steel pins with higher hardnesses seem to give more uniform contacts through the
laminate thicknesses, resulting in higher bearing strengths.

3. Composite laminates subjected to compressive loading had different damage
modes and lower strengths than those subjected to pin loading.

4. For in-plane scaling, the bearing strength decreases as the size increases. For
thickness scaling, the bearing strength increases as the size increases. For three-
dimensional scaling, the bearing strengths change non-monotonically as the size

increases for the groups with H/D=0.75 and 1.5.

37

Chapter 3
Scaling Effects and Thickness Constraints in Composite Joints
3. 1 Introduction

Joining is a secondary process in structure manufacturing. In manufacturing
conventional metallic structures, small components are fabricated individually and then
assembled to form large sections. Although complex polymer composite structures can be
molded in single pieces to simplify manufacturing processes and to reduce assembly cost,
they cannot be completely exempted from the joining process. The joining process is
especially needed when polymer composite components are to be assembled with
components made of dissimilar materials such as metals.

Both mechanical fastening and adhesive bonding are commonly used in Structure
assembling. As structure components to be assembled become thicker, both the diameter
and length of mechanical fasteners should be increased proportionally. Similarly, the
bonding areas in the plane and through the thickness [1 l] of the structure components
should be increased in adhesive bonding. The increase in the diameter and length of
mechanical fasteners and the increase in the bonding areas of adhesive bonding, however,
are not purely geometrical scaling issues. Material properties should also be considered
as the size increase.

The studies of scaling for composite structures can be divided into in-plane scaling,
thickness scaling and three-dimensional scaling. In studying in-plane scaling, thin
composite laminates with notches [16] and without notches [18] were investigated. The
strengths of composite laminates were found to decrease monotonically with the increase

of in-plane dimensions. In a two-dimensional study on mechanical fastening, Wang et a1.

38

[19] reported that the bearing strength had a first-decrease-then-increase Change as the in-
plane dimensions increased.

Thickness also plays an important role in composite size scaling [1, 3-6]. In fact,
there is a special concern in scaling the thickness of composite laminates. Being different
from simply increasing or decreasing the thickness in scaling the thickness of
conventional metals, there exists at least two different ways in scaling the thickness of
composite laminates, so-called sub-laminate scaling and ply—thickness scaling. The
thickness scaling is actually more complicated than in-plane dimension scaling since both
material properties and geometrical parameters are involved in the thickness scaling.
More specifically, the non-turiform material properties induced by thickness scaling and
the non-uniform stresses through laminate thickness caused by fastener bending due to
large thickness [25-27] render the study very complicated. In a previous study [28], .the
. thickness effect in composite pin joints was found to be dependent on the ratio of
laminate thickness H to hole diar'neter D, i.e. H/D. Joint configurations with ratios of
H/D around one were found to have more adequate performance than those with ratios of
H/D greater than one.

Combining the in-plane dimension scaling and the thickness scaling, the three-
dimensional size scaling needs to be understood before designers could predict the
performance of large composite assemblies based on the properties of small models,
especially when thick composite laminates are of primary concern. The objective of this
study is to investigate the effects of three-dimensional size scaling on the performance of

composite mechanical fasteners.

39

3. 2 Experimental Methods
A. Joint Configurations
Composite laminates made from glass/epoxy prepreg tapes were investigated in the

study. Cross-ply laminates were of interest. They were made with alternate 0° and 90°

plies and their stacking sequences can be expressed by [0/90/0/90. . .]n where n is the total

number of plies. Three composite laminates having 9 plies (n=9), 17 plies (n=1 7) and 34
plies (n=34) were prepared. Their thicknesses were 3.30mm, 6.48mm and 12.95mm,
respectively.

The double-lap-single-pin joint shown in Figure l was used as the experimental
model. The glass/epoxy composite laminates were used as central laps of joints while
[steel plates were used as outer laps, resulting in steel-composite dissimilar-material
joints. The steel outer plates had thicknesses half those of composite central laps,
warranting that the damage of jornts was dominated by the damage of composite central
laps. For mechanical fastening, steel pins designated as M-2 according to AISI
classification system were used. The hardness of the steel pins was in the range of 63-65
based on the Rockwell C Hardness standards.

Figure 1 shows the geometrical elements of composite joints. These elements include
the joint width W, the hole diameter D, the laminate thickness H, the distance between
the hole center and the joint end B, and the distance between the hole center and the
gripping end L, also called joint length. The associated geometrical ratios W/D, E/D, H/D
and L/W are also important parameters in studying mechanical fastening. In order to have
bearing damage, at least initially, instead of net-section damage or shear-out damage, W

and B were chosen to be four times the hole diameter, resulting in W/D=4 and E/D=4.

40

For identification purposes, each composite joint was assigned with a notation of HXDY,
where H and D were laminate thickness and hole diameter, respectively, while X and Y
were the ply number of the composite laminate and the hole diameter in millimeter (mm),
respectively.

In investigating three-dimensional size effects, three composite joints were prepared
based on three-dimensional scaling. Since the composite laminates used in the study had
a thickness scaling ratio of l:l.97:3.92, i.e. 3.30mm:6.48mm:12.95mm, the closest
integer ratio of 1:2:4 was used for sealing all other dimensions D, W and E. Since H/D
was an important parameter in the thickness study and H/D=1 was found to be the critical
value for composite joints to have load-displacement relations with distinct maximum
loads in Chapter 2, the hole diameter was chosen to be as close to the laminate thickness
as possible. Based on the availability of drill bits and M2 pins, hole diameters of 3.181nm
(1/8”), 6.35mm (l/ ”) and 12.7mm (0.5”) were used in the study, resulting in H9D3.18,
H17D6.35 and H34D12.7. joints. Details of the geometrical elements and geometrical
ratios of the three composite joints are given in Table 4.

B. Joint Lengths

As mentioned earlier, the distance between the hole center and the gripping end, i.e.
the joint length, was designated as L. Although this distance is the key parameter
associated with Saint Venant’s end effect, it was not exercised in the three-dimensional
scaling due to the limited sizes of the composite laminates available and the length
confinement of the testing machine used. In fact, the joint length L for the joints
H9D3.18, H17D6.35 and H34D12.7 were 241.3mm, 228.6mm and 203.2mm,

respectively, resulting in L/W =19, 9 and 4, respectively. In order to verify that the joint

41

Table 4 - Geometrical elements and ratios of glass/epoxy central laps.

 

 

 

Unit: mm H9D3.18 H17D6.35 H34D12.7
H 3.30 6.48 12.95
D 3.18 6.35 12.70
W 12.70 25.40 50.80
E 12.70 25.40 50.80
L 241.3 228.6 203.2
H/D 1.04 1.02 1.02
W/D 4.00 4.00 4.00
E/D 4.00 4.00 4.00
L/W 19.00 9.00 4.00
H: thickness

D: hole diameter

W: width

E: distance from hole center to specimen end
L: distance between hole center and gripping end

42

length had insignificant effect on joint performance when L/W had a minimum value of
4, H9D3.18 joints with L/W=9, 4, and 1.5 were investigated. These specimens were
designated as H9D3.18-L/W9, H9D3.18-L/W4, and H9D3.18-L/W1.5.

C. Pin-Hole Clearances

Pin-hole Clearance has significant effects on joint performance [54]. Studies
concerning the effects of bolt-hole clearance on bearing stress distributions are also
available in the literature, e.g. References [70-73]. These studies were focused more on
joint performance prior to final failure than on ultimate joint strength. Pierron et al. [74]
investigated the effects of pin-hole clearance on bearing strength. The clearances used in
their study were higher than 0.1mm. It was concluded from their study that minimum
Clearance was optimum for joint designs.

In the present study, pins having the same sizes as hole diameters, i.e. so-called snug
fitting between pins and holes, were initially used in H9D3.18, H17D6.35 and H34D12.7
joints. In order to assess the effects of pin-hole clearance on joint performance, additional
efforts were exercised for H9D3.18 joints. Besides the standard pins that had a diameter
of 3.18mrn, pins with diameters of 3.15mm, 3.11mm and 3.09mm, i.e. with pin-hole
clearances of 0.03, 0.07 and 0.09mm, respectively, were also prepared. The composite
joints having large pin-hole clearances were designated as H9D3.18-pc0.03, H9D3.18-
pc0.07 and H9DB.18-pc0.09.

D. Loading Rates

The epoxy matrix of the composite material used in the study was of a viscoelastic

material. The behavior of the composite material was thus expected to be sensitive to

loading rate [75-77]. Studies concerning the effects of loading rate on composite

43

performance were reviewed by Sierakowski [78]. Ger et a1. [79] and Li et a1. [80] even
studied the performance of composite joints under various impacting rates. Although the
investigation of composite joints was usually performed at a quasi-static loading rate,
there was no consensus on the definition of quasi-static loading rate in the material
testing community. In an experimental report on mechanical fasteners [81], the loading
rate was set to be lmnr/min. In a second experimental report on pin-joint structures [19],
the relative speed between the loading beads was 1.27mm/min. In a third report [80], the
loading rate of static tensile tests was set to be 0.5mm/min.

In engineering practice, the quasi-static loading rates could vary from a very small
level up to 5mm/min as recommended by ASTM D638 for tensile testing of composite
laminates. In the present study, the effects of loading rates on joint performance were of .
interest. The loading rate of 1.27mm/n1in was considered to be the basic loading rate 1 .
because it was commonly used in material testing. This loading rate was applied to all
.three types of composite joints..In order to investigate the effects of loading rate. on joint
performance, loading rates of 0.16mm/min (1/8 of 1.27mm/min), 0.64mm/min (1/2 of
1.27mm/mirr) and 5.08mm/min (four times 1.27mm/min) were also applied to H9D3.18
joints. They were designated as H9D3.18-lr0.16, H9D3.18-lr0.64 and H9D3.18-lr5.08.

3. 3 Joint Properties
A. Load-Displacement Relations

Load-displacement relations bore important information concerning properties of
joints. Beyond the initial linear ranges, all load-displacement curves seemed to exhibit
two different types of profiles that could be categorized as ductile type and brittle type.

Figure 9 gives an example for each type. The ductile-type curve shown in Figure 9(a) was

 

7000
6000
qu
5000
4000
3000
2000

1 000

v sudden load loss

-00-..—

 

 

0

 

_>

180000
qu
70000
60000
50000
40000
30000
20000
10000

0

 

1:4—
5.0% ofD

 

41

J

 

4

 

 

 

.N
5

:04 0.5 :61 1.5 2 2.5 3
' 5.6% ofD
(b)
Figure 9 — Load-displacement (N -m) curves, glass/epoxy
composite joints. (a) ductile type (H9D3.18) and (b)
brittle type (H34D12.7).

45

3.5

obtained from an H9D3.18 joint. It featured a small but noticeable loss in load right after
a local maximum load. This loss in load was found to be associated with bearing damage.
The value of load usually recovered as loading process continued before another load loss
occurred. This second load loss, however, was drastic and non-recoverable and was
found to be associated with the net-section damage. The brittle-type curve shown in
Figure 9(b) was based on an H34D12.7 joint. It showed a continuously smooth relation
until a catastrophic drop of load, which was found to be associated with net-section
damage, occurred.
B. Maximum Loads and Joint Strengths

Based on Figures 9(a) and 9(b), the strengths of composite joints may be defined by
the maximum loads. An “offset of displacement” associated with the maximum load was
also presented for further evaluations. The “offset of displacement” was defined as the
distance between the initial linear segment of a load-displacement curve and a line
passing through the maximum load and parallel to the linear segment. A term named
"percentage of offset of displacement" was firrther defined as the percentage of the ratio
of the “offset of displacement” to the hole diameter. The presentation of the “percentage
of offset of displacement” was aimed at justifications of maximum loads. According to
Table 5, the percentages of offsets of displacement of all joints ranged from 4 to 7%. The
identifications of maximum loads for joints with different types of load-displacement
relations, i.e. the ductile type and the brittle type, were thus justified. Once the maximum
loads of joints were identified, they were divided by corresponding bearing-contact areas,

i.e. DH, to determine the bearing strengths. The maximum loads, percentages of offset of

46

Table 5 — Types of load-displacement curves, maximum loads and percentage of offset of
displacement of various glass/epoxy joints.

 

2

 

 

 

 

 

 

T.‘ Max. on? T.‘ Max? 06? T.‘ Max? on? T.‘ Max? oer?
H9D3.18 H9D3.18-L/W9 H9D3.18-L/W4 H9D3.18-L/W1.5
D 5.18 5.0 D 5.29 6.2 D 5.37 5.2 D 4.48 6.2
D 5.89 6.8 D 4.78 6.8 D 5.50 6.0 D 5.08 6.2
D 4.54 5.8 D 5.46 5.2 D 5.78 7.0 D 5.83 6.8
D 5.27 7.7 D 5.50 5.9 D 5.34 4.5 D 5.30 5.3
D 4.86 5.4 D 5.87 6.7 D 4.97 6.6 D 5.67 5.5
D 5.70 6.2 D 5.01 4.8
D 5.47 7.0 D 5.69 5.7
D 5.49 6.7 D 5.41 6.3
D 5.52 6.2 D 4.67 5.1
D 5.32 7.1 D 5.00 6.5
D 5.85 5.2 D 5.85 8.2
D 5.23 6.8
Avg.(sd)4 5.37(0.41) 5.38(0.40) 5.39(0.29) 5.25(0.44)
Avg. Strengths 512.66 513.30 515.32 501.09
H9D3.18-pc0.03 H9D3.18-pc0.05 H9D3.18-pc0.09 H9D3.18-lr0.16
D 4.32 4.4 D 4.52 4.2 D 4.23 5.2 D 4.89 3.1
D 5.27 5.0 D 5.24 4.2 D 4.80 4.3 D 4.89 5.8
D 5.60 5.9 D 4.64 4.8 D 4.76 4.4 D 5.00 5.1
D 5.25' 6.2 D 4.84 5.1 D 4.65 5.0 D 4.47 4.5
D 4.85 5.7 D 4.91 4.2 D 4.38 3.8 D 4.26 4.9
' D 4.77 4.7
. D 5.01 5.3
Avg.(sd)4 5.06(0.49) 4.83(0.28) 4.56(0.25) 4.76(0.29)
Avg. Strengths 482.46 461.06 435.36 453 .80
H9D3.18-lr0.64 H9D3.18-1r5.18 H17D6.35 H34D12.7
D 4.95 5.7 D 5.48 4.5 D 17.66 5.3 B 70.07 4.8
D 4.58 6.4 D 5.85 4.3 D 18.19 3.8 B 71.80 5.6
D 5.15 6.4 D 5.19 4.6 D 16914.4 B 71.90 5.3
D 5.07 6.4 D 6.15 5.7 D 17.15 5.0
D 5.08 5.2 D 4.97 5.1 D 19.19 6.0
D 5.33 6.3 D 5.21 4.9
D 5.01 5.2 D 6.21 5.2
D 4.68 5.2 D 5.66 6.0
D 5.24 4.4 D 5.60 4.9
D 5.38 5.2 D 5.30 4.5
D 5.62 5.0
D 6.04 6.4
Avg.(sd)4 5.05(0.26) 5.6I(0.40) 17.82(0.91) 71.25(1.03)
Avg. Strengths 481.62 535.15 433.14 431.85

 

1 Type of load-deforrnation curve: B for brittle and D for ductile;
2 Maximum load (Unit: kN); 3 Percentage of offset of displacement at maximum load;
4 Average load (standard deviation) with a unit of kN; 5 Average strength (Unit: MPa).

47

displacement and average joint strengths of all composite joints were given in Table 5
along with the types of load-displacement curves.
C. Macroscopic and Microscopic Damage Modes

Because it was less catastrophic than net-section damage and shear-out damage,
bearing damage was preferred in the failure of mechanical fasteners. Accordingly,
W/D=4 and E/D=4 were imposed to all joints in order to have bearing damage, at least
initially. However, not all composite joints investigated in the study started failure with
initial. bearing damage. Composite joints of H9D3.18 and H17D6.35 had initial bearing
damage prior to ultimate net-section failure. However, the dominant damage mode of
H34D12.7 joints was the direct catastrophic net-section failure. In an effort to further
understand the process of damage, microscopic damage modes in the neighborhood of '
bearing-contact zones were also examined.

Figure 10 shows the microscopic damage of an H17D6.35 joint. As shown in Figure
10(a), there are matrix cracks along the net-section lines and delamination underneath the
’ bearing-contact zone. On the cross-section along the laminate centerline, zig-zag kinks
U can be found in the 0° plies as shown Figure 10(b). The fiber kinks were the results of
fiber buckling due to the high compressive stress around the contact-bearing zone. The
microscopic damage of H9D3.18 was similar to that of H17D6.35. However, the
microscopic damage around the bearing zones of H34D12.7 joints was relatively
insignificant; only very few fiber kinks were found in the 0°-plies close to the laminate
surfaces. It seemed a correlation between macroscopic damage and microscopic damage

could be established.

48

 

(a) Front View

 

(b) Cross-sectional view

Figure 10 - Microscopic damage in an
H17D6.35 glass/epoxy joint.

49

3. 4 Experimental Results
A. Effect of Joint Lengths

From experiments, the average joint strengths of H9D3.18-L/W9, H9D3.18-L/W4
and H9D3.18-L/W1.5 were 513.3, 515.3 and 501.1MPa, respectively. Both H9D3.18-
L/W9 and H9D3.18-L/W4 had average strengths very close to 512.7MPa of the H9D3.18
joints, whose L/W=19. In other words, the joint strengths seemed to remain constant as
the ratio of L/W surpassed 4. Accordingly, the uses of different ratios of UW for
H9D3.18, H17D6.35 and H34D12.7, i.e. l9, 9 and 4, respectively, were considered to
have no significant effect on the joint performance.
B. Three-dimensional Size Effects

In the experimental study, the joint length L between the hole center and the gripping
end were chosen to be at least four times the joint width W. The joint width W and the
distance between the hole center and the joint end B were chosen to be exactly four times
the hole diameter D. The hole diameter D was chosen to be close to the laminate
thickness H. Hence, the laminate thickness H can be considered as the most fundamental
scaling parameter. Based on the laminate thickness of the three composite joints
H9D3.18, H17D6.35 and H34D12.7, the thickness scaling 3.30mm:6.48mm:12.95mm,
i.e. l:l.96:3.92 or approximately 1:2:4, was used in the study of three-dimensional
scaling.

As shown in Table 5, the average joint strengths of H9D3.18, H17D6.35 and
H34D12.7 were 512.7, 433.1 and 431.9MPa, respectively. The joint strength decreased
by 15.5% and 15.8% as the joint size doubled and quadrupled, respectively, from

H9D3.18. The average joint strength had a monotonic decrease as the joint size increased.

50

This result seemed to be comparable with that based on Weibull’s theory. The
experimental results and Weibull analysis were also presented in Figure 11 for
comparisons. In fact, the feasibility of using Weibull’s theory in three-dimensional size
scaling is an important issue in mechanical fastening designs.

Weibull theory was a statistical analysis. It stated that the larger the size of a material,
the larger the size of defect in the material, and hence the lower the strength of the
material. In order to examine the feasibility of using Weibull’s theory in three-
dimensional size scaling of composite joints, the two-parameter Weibull theory [82] was
used in strength analysis. According to the two-parameter Weibull theory, the probability
of failure Pf can be expressed as

__v_(_<:-_)m

v0 0'0
Pf = exp

(1)

where m is the Weibull modulus and 0'0 is the normalizing strength. They are the two

parameters of the Weibull’s theory. Besides, v is the volume and v, is the normalizing
volume. The above equation can be rewritten as follows by taking nature log twice on

both side of the equation, i.e.

ln(ln(7:—)) = 1n —V— + m In 0' — m In 0'0

(2)
f Va
The first term on the right-hand side of the equation vanishes when the concerned
specimens have constant dimensions. The reduced equation is usually assumed to be of a

straight line. The Weibull modulus and the normalizing strength can then be found from

curve fitting such as the least-squares method.

51

 

Joint Strength (MPa)

200 Z

100 7

. Experiment

7 "“ Weibull’s prediction with various m

1'12 '3 ‘4

Scaling Factor

Figure 11-- Glass/Epoxy joint strengths of different
sizes and analysis based on Weibull theory.

52

The Weibull moduli for the three joints H9D3.18, H17D6.35 and H34D12.7 were
found to be 13, 25, and 161, respectively. The higher the Weibull modulus, the smaller
the variation of strength. However, it was noted that the small joint H9D3.18, having the
largest number of testing specimens, seemed to have much larger variation than the larger
joints H17D6.35 and H34D12.7 which had smaller number of testing specimens (five for
H17D6.35 and three for H34D12.7). If the lowest modulus, i.e. m=13, along with the

volume v1 and the strength of H9D3.18, i.e. 0',=512.7MPa, were used for three-

dimensional scaling analysis, the scaled strengths of H17D6.35 and H34D12.7 could be

calculated from the following equation

(1)“ = 31
0'] v (3)

where 0' and v are the corresponding strength and volume of H17D6.35 and H34D12.7
joints. As can be seen in Figure 4, the Weibull’s theory, based on m=13, seems to predict
a clearer size effect than that obtained from limited tests. Weibull’s predictions based on
m=25 and m=161 are also presented in Figure 4 for comparison. It seems Weibull’s
theory agrees with the experimental results up to some extent.
C. Effect of Pin-Hole Clearances

From experiments, the average joint strengths of H9/D3.18-pc0.03, H9/D3.l8-pc0.07
and H9/D3.l8-pc0.09 were found to be 482.5, 461.1 and 435.4MPa, respectively. These
strengths were lower than the average strength of H9D3.18, i.e. 512.7MPa, which had a

snug fit between the pin and the hole. Based on these experimental data, it was clear that

the joint strength decreased as the pin-hole clearance increased. An explanation for this

53

 

result could be based on the change of contact area between the pin and the hole. As the
pin-hole clearance increased, the contact surface between them decreased, as verified by
Eriksson [70] based on a numerical simulation. The decrease in contact area increased the
contact-bearing stress and subsequently decreased the joint strength.
D. Effect of Loading Rates

The average joint strength of H9D3.18 under a loading rate of 1.27mm/rnin was
512.7MPa. The average joint strengths of H9D3.18 at different loading rates, e.g.
0.1'6mm/min (H9D3.18-lr0.16), 0.64mm/min (H9D3.18-lr0.64) and 5.08mm/min
(H9D3.18-lr5.08), were 453.8, 481.6 and 535.2MPa, respectively. When compared all
four cases together, it was found that the joint strength increased with the increase of
loading rate. This result was consistent with some reports in the literature. For instance, -
waas et al. [76] had found that the dynamic strength of a glass/epoxy composite could be
' as "high as 1.7 times the 'static values. The result that the higher the loading rate, the
higher the joint strength could also be applied to joint stiffness.
3. 5 Assembled and Laminated Composites
A. Assembling Techniques

Thick composite larrrinates have many applications in heavy-duty structures suCh as
armored vehicles. However, their costs are high and their properties are not uniform due
to uneven curing cycles, especially in the thickness direction [24, 69]. Assembling thin
composite laminates together to form thick composite structures was found to be feasible
in reducing cost and achieving property uniformity. Techniques such as adhesive
bonding, riveting and clamping were presented in previous studies on assembled

composites [83, 84]. It was found that the impact resistance of assembled composites was

54

 

very comparable with that of laminated counterparts. The present study investigated
mechanical fasteners in both assembled and laminated composites. The comparisons of
joining strengths and damage processes were of primary interests.

In studying assembled composites, two 9-ply laminates were bonded together with a
room-curing epoxy to form an assembled composite. Because the total thickness of the
1 assembled composite was close to that of H17D6.35 laminated composite, for
~ comparison purpose, a resembling 6.35mm-diameter hole was prepared in the assembled
- composite for mechanical fastening. For identification purpose, the assembled composite
. was designated as H9x2D6.35-B where B stands for bonded. If the two 9-ply laminates
were simply put together and contacted each other without any form of bonding, a
: notation of H9x2D6.35-C (C for contacted) was used for the assembled composite. The
- geometric elements and ratios cf the mechanical fasteners made of the assembled
composites were similar to those of the laminated counterpart, i.e. H17D6.35, so were the
experimental parameters.

In a similar investigation, four 9-ply laminates were bonded together to form an
assembled composite. Since it had a total thickness close to that of the 34-ply laminates,
i.e. H34D12.7, a hole of 12.7mm in diameter was prepared in the assembled composite
for mechanical fastening. A notation of H9x4D12.7-B was used to identify the assembled
composite. Similarly, a notation of Hl7x2D12.7-B was used for an assembled composite
bonding two l7-ply laminates together.

B. Normalized Strengths
Table 6 gives experimental results of the joints. Besides the averaged strengths,

normalized strengths are also presented in the table. The normalized strengths were

55

Table 6 — Comparison between laminated and assembled glass/epoxy joints.

 

r.‘ Max.2 orf.3 Mode“ r.‘ Max.2 orr.3 Mode4 r.‘ Max.2 Off?Mode4

 

 

 

 

 

 

Pinned H9x4D12.7-B Hl7x2D12.7-B H34D12.7
D 73.99 4.2 BR D 67.19 5.7 BR 370.07 4.8 NS
D 76.32 3.8 BR D 64.91 5.2 BR 871.80 5.6 NS
D 73.53 5.8 BR D 69.67 7.0 BR B71.90 5.3 NS
Avg.(sd)° 74.61(1.50) 67.25(2.38) 71.25(1.03)
Avg. Strength° 421.31 410.09 431.85
Norm. Strength7 21.06 22.79 25.48
Pinned H9x2D6.35-C H9x2D6.35-B H17D6.35
D 19.20 2.7 BR D2038 5.1 BR D1766 5.3 BR
D 19.32 3.6 BR 'D 19.90 6.6 BR D1819 3.8 BR
D 18.76 4.1 BR D 19.55 4.3 BR D16.91 4.4 BR
D 19.82 5.4 BR D17.15 5.0 BR
D 19.19 6.0 BR
Avg.(sd)5 I9.10(0.29) 19.91(0.35) l7.82(0.91)
Avg. Strength° 435.16 453.80 433.14
Norm. Strength7 43.52 45.38 48.13 .-
' Bolted H9x2D6.35-C H9x2D6.35-B Hl7D6.35.
B 20.65 7.4 NS ,B 21.23 5.4 NS B1987 5.8 NS
B 20.46 7.0 NS B 21.45 7.4 NS B 19.35 3.8 NS
B 20.44 6.9 NS B 21.35 7.1 Ns B2031 4.2 Ns
Avg.(sd)5 20.52(012) 21.34(0.1 1) 19.84(0.48)
Avg. Strength° 467.56 486.44 482.34
Norm. Strength7 46.76 48.64 53.59

 

I Type of load-deformation curve: B for brittle and D for ductile

2 Maximum load (Unit: kN)

\lO‘M-bw

Percentage of offset of displacement at maximum load

Average maximum load (standard deviation) with a unit of kN

Average maximum load per contact area --- DH (Unit: MPa)

Failure mode at maximum load: BR for bearing and NS for net-section

Average strength normalized by the number of 0° plies (Unit: MPa)

56

 

obtained from dividing averaged joint strengths by corresponding numbers of layers that
had fibers oriented in the loading directions. The normalized strengths were presented
due to the fact that the laminated composites and the assembled counterparts did not have
the same numbers of total layers, nor did they had the same numbers of layers with fibers
oriented in the loading directions, i.e. 0°-direction in the present study. For example, the
laminated composite H34D12.7 had a total number of 34 plies; and only 17 out of the 34
plies were in the 0°-direction. The assembled counterpart H9x4D12.7-B had a total
number of 36 plies; and only 20 out of the 36 plies were in the 0°-direction.

Experimental results of the joints based on assembled composites and laminated
counterparts are given in Table 6. The normalized strengths of the two assembled
composites H9x4D12.7-B: and Hl7x2D12.7-B were 10% lower than that of the laminated
counterpart, i.e. H34D12.7. However, the normalized strengths of the bonded composite
l I H9x2D6.35-B and unbonded composite H9x2D6.35-C were about the same as that of the
laminated counterpart, i.e. H17D6.35. It seemed the assembled composites could
resemble the laminated composites up to some extent, at least, as far as mechanical
fastening was concerned.

C. Ultimate Failure

Besides the joint strength, another important experimental result was associated with
the damage process. All specimens investigated in the study seemed to fail with initial
bearing damage except H34D12.7, which experienced direct catastrophic net-section
damage. The interpretation of this phenomenon is stated as follows. Being compared with
H9x2D6.35-B, H9x2D6.35-C and H17D6.35, H34D12.7 was more constrained in the

thickness direction due to its larger thickness. Being compared with H9x4D12.7-B and

57

Hl7x2D12.7-B, H34D12.7 was more constrained in the thickness direction due to its
better bonding through the laminate thickness. Accordingly, the constraint in the
thickness direction played a key role in the damage process. A composite with more
constraint in the thickness direction had higher resistance to fiber buckling and
delamination, resulting in direct catastrophic net-section damage. In contrast, a composite
with less constraint in the thickness direction was more prone to fiber buckling and
delamination. For example, the H17D6.35 joint shown in Figure 10(a) resulted in initial
bearing damage prior to final net-section damage.

Although their geometrical elements and ratios were about the same, H9x4D12.7-B,
Hl7x2D12.7-B and H34D12.7 joints had different damage processes. The former two
types had initial bearing damageprior to finial net-section damage while‘the latter one
. had direct catastrophic net-section damage. Initial bearing damage was an important
damage mode in composite fasteners as shown in Chapter 2, at least in thin composites.
. The primary mechanism of the bearing damage was fiber buckling and delamination.
They rendered composite joints more ductile. Shown in Figure 12 are the load-
displacement curves of the aforementioned three joints. Although H34D12.7 had the
highest normalized strength, it had the lowest displacement to failure. The total energy
absorbed by H34D12.7 due to damage formation, which was equal to the area under the
load-displacement curve, was also smaller than those absorbed by the assembled
counterparts, i.e. H9x4D12.7-B and Hl7x2D12.7-B. In fact, it was easier to have
delamination on the assembled interfaces than on the laminated interface because the

adhesive bonding strength on the assembly interfaces was lower than the matrix bonding

58

 

80000

70000 *3

60000

. 2 50000 -«

:1; 40000
30000

Lo

20000 —

10000

 

 

 

    

o H34D12.7
A H17)QD12.7-B
D H9x4D12.7-B

 

 

 

0 1 ' 2 3 4 5

. Displacement (mm)

Figure 12 — Load-displacement curves of assembled
(bonded) and laminated glass/epoxy joints.

59

 

strength on the laminated interfaces. Once delaminated, the disassembled thin laminates
were prone to fiber buckling and delamintion, i.e. the bearing damage. In contrast, the
laminated counterpart H34D12.7 was not vulnerable to delamination, except those
interfaces very close to the laminate surfaces. As a result, the bearing damage was
insignificant in H34D12.7 joints. They failed by direct catastrophic net-section damage.
3. 6 Difference Between Pinned and Bolted Joints
A. Constraints in Thickness Direction

As mentioned earlier, the constraint in the thickness direction played a key role in the
damage process of composite fasteners. The higher the constraint in the thickness
direction, the higher the resistance of composite to fiber buckling and delamination.
Hence, a composite joint with high constraint in the thickness direction, such as
H34D12.7, would result in direct catastrophic net-section damage, i.e. a relatively brittle-
type failure. However, a composite joint with low constraint in the thickness direction;
such as H9x4D12.7-B, would result in initial hearing damage prior to final failure, i.e. a
relatively ductile-type failure. Another way to verify the shift of failure mode from a
ductile type to a brittle type as the constraint in the thickness direction increased was to
compare pinned joints with bolted counterparts since the latter had additional constraints,
i.e. clamping forces, in the thickness directions.
B. Bolted Joints

Although pinned joints were commonly used in research studies, bolted joints were
more practical in structure assembly. In fact, the clamping force used in bolted joints

seemed to enhance the joining strength [85, 86]. Matthews et al. [87] had shown that a

60

 

pinned joint had the lowest strength, a fully bolted joint had the highest strength, while a
riveted joint had a strength between the two extremes.

In comparing the pinned and the bolted joints, H17D6.35, H9x2D6.35-B and
H9x2D6.35-C joints were used. The clamping force for the bolted joints was 20 Nm. The
experimental results were given in Table 6. The normalized strengths of the bolted joints
were slightly higher than those of the pinned counterparts. This result was consistent with
that obtained from the comparisons among H9x4DlZ.7-B, Hl7x2D12.7-B and H34D12.7
cases.

There was also a shift in damage mode due to the increase of constraint in the
thickness direction. For pinned joints, i.e. H9x2D6.35-B and H9x2D6.35-C, the damage
modes showed initial bearing damage prior to final net-section damage; for bolted
counterparts, however, direct catastrophic net-section damage dominated.zSince the only
variation introduced was the clamping force in the thickness direction, this result further
verified the important role of the through-the-thickness constraint in the behavior of
joints. Apparently, the high constraint due to clamping force rendered the composite
joints higher resistance to delamination. Accordingly, direct catastrophic net-section
damage, instead of initial bearing damage followed by final net-section damage, took
place in the bolted joints.

In summary. the constraint in the thickness direction played a key role in both joining
strength and damage process. A composite with a higher constraint based on larger
thickness, better bonding through the thickness or clamping force in the thickness
direction could increase the joining strength slightly. However, the higher constraint in

the thickness direction rendered the composite more brittle, i.e. smaller displacement to

61

 

failure and smaller energy absorption during failure process, and resulted in direct

catastrophic net-section damage, instead of initial bearing damage followed by final net-

section damage.

3. 7 Conclusions

1.

The load-displacement curves of the mechanical fasteners investigated in the .

study can be categorized as ductile type and brittle type. Both H9D3.18 and
H17D6.35 joints had ductile-type load-displacement curves while H34D12.7
joints had brittle-type curves. The “percentage of offset of displacement” was

presented to determine the maximum loads and the subsequent joint strengths.

There was a monotonic decrease in joint strength as the three-dimensional size ;

increased. The reduction of joint strengths seemed to agree with the Weibull’s
theory up to some extent; Although the final failure of all joints was due to net-
section damage, the joints with the ductile-type load-displacement curves

experienced initial bearing damage prior to final net-section damage while the

joints with the brittle-type load-displacement curves failed by direct catastrophic - '

net-section damage.

The constraint in the thickness direction played a key role in the damage process
of composite fasteners. In addition to large thickness, good bonding through the
thickness and adequate clamping force from bolting also contributed to the
constraint in the thickness direction.

High constraint in thickness direction prevented fibers from bucking and
composites from delamination. Composite joints with high constraints in the

thickness direction failed in direct catastrophic net-section damage while those

62

 

with low constraint in the thickness direction failed with initial bearing damage
prior to final net-section damage.

. Composite joints that failed with initial bearing damage had higher displacement
to failure and higher energy absorption during failure process than those that

failed with direct catastrophic net-section damage.

63

 

I I P“ Inn" "7'-

Chapter 4

Three-dimensional Finite Element Analysis of Composite Pin Joints

4. 1 Introduction

Composite materials are originally developed for use as aerospace structures. They
are thus of thin plates. The in-plane behavior of composite plates has been the focus of
composite research in the past few decades. As more composite materials are used for
non-aerospace applications, there are more thick-section composites structures, e.g.
submarine hull and armored vehicle bodies. The extension from thin composite plates to
thick-section composites, however, is not a trivial practice. In fact, it requires careful
modifications in many aspects of composite technologies, e.g. manufacturing, testing,
analysis and design [1-7].

Taking composite joining as an example, both adhesive bonding and mechanical
fastening are commonly used in joining composite plates. Adhesive bonding is in fact a
two-dimensional joining technique as it takes effect only at the contact areas between the
structural components being joined. Mechanical fastening, on the contrary, is a three-
dimensional joining technique. Both diameters and lengths of mechanical fasteners
should increase as the thickness of the structure components increase. Hence, adhesive
bonding is more adequate for joining thin composite plates while mechanical fastening
can be used for joining thick-section composites [11].

The three-dimensional nature of mechanical fastening in composite joining was
experimentally recognized by some researchers [28, 88]. The significant effect of
composite thickness on the efficiency of pin joint was reported [28], so was the key role
of thickness constraints in the damage process as discussed in Chapter 3. The effects of

thickness on composite pin joints were found to be associated with the ratio of composite

64

 

thickness (H) to hole diameter (D), i.e. H/D, as in literature [28] and Chapter 2. If H/D is
smaller than 1.0, it refers to a composite joint consisting of relatively thin plates and a
relatively large pin. On the contrary, if H/D is greater than 1.0, it refers to a composite
joint is consisting of relatively thick sections and a relatively small pin. As the H/D ratio
changes from smaller than 1.0 to greater than 1.0, both the type of the load-displacement
curve and the strength of the composite joint change significantly due to the change of
the contact condition between the composite and the pin

Many analytical studies concerning mechanical fastening were presented and most of
them were based on two-dimensional assumptions. As mentioned by Oplinger [25], all
two-dimensional studies ignored the details of stress distribution through the thickness of
the fasteners. Nelson, Bunin and Hart-Smith [26] also presented important insights of the
thickness effects on fastener bending. The importance of using three-dimensional
techniques in studying mechanical fastening was. also recognized by other researchers
[27, 29-31]. Ireman [27] found that the bending of a bolt created a non-uniform contact
stress distribution between the bolt and the hole. According to Chen, Lee and Yeh [30],
the bolt elasticity had a tendency to change the stress distribution through the laminate
thickness.

3 Besides the nonuniform contact through the length of the bolt, the nonuniform
properties of composites through their thickness posed more challenges to the
investigations of composite joints. Among the very few studies based on three-
dimensional analysis, the interlaminar stresses between different layers were often not
examined thoroughly. An investigation based on a three-dimensional spline variational

technique was conducted by Iarve and Schaff [31] to analyze the interlaminar stresses in

65

 

a composite fastener. Shokrieh and Lessard [32] studied a pin-joint structure with radial
displacement boundary conditions. Stress singularities were reported at the interface
between layers with different ply orientations on the free edges. However, the contact
stress and friction between the pin and the plate were not considered in their study.

Some studies, including References [33-36], were focused on predicting the strength
of joint structures solely based on the stress distribution on the hole surface. Their studies
belonged to the category of so-called one-parameter failure analysis in which the
maximum stress, maximum strain or distortional energy on the hole surface was input
into a failure criterion to assess the status of the joint structure. The one-parameter failure
analysis was simple to use but did not account for the composite response near the hole.
- Hart-Smith [37] reported that the ultimate joint failure could be attributed to the damage
. near the hole, instead of right at the hole surface. The one-parameter failure analysis
based on the large stress on the hole surface could underestimate the strength of the
composite joints.

The idea of two-parameter failure analysis was similar to Whitney-Nuismer’s work,
which was focused on hole size effects in composite plates. A Characteristic dimension
[38], which was normally a certain distance away from the hole in the laminate plane,
was required in a two-parameter failure theory. Two failure theories were proposed by
‘ them; one was the so-called point stress failure theory and the other was the average
stress failure theory. The Characteristic dimension was considered as a material property
in early studies for two-parameter failure analysis. Later investigations [39, 40], however,
proved that it was dependent upon laminate quality and type of load. Furthermore, it was

concluded that the predicted failure loads were quite sensitive to the value of

66

characteristic dimension [39, 41] or the shape of characteristic curve [42]. Thus, the two-
parameter failure theories were problem dependant and could not be used
straightforward.

With the assumption that damage took place in the zones where a failure criterion was
satisfied, some progressive damage models were proposed to simulate the damage
initiation. Besides, with the use of elastic property degradation as a fimction of the degree
of composite damage, the progressive damage models were further used to simulate the
. damage growth [43-47]. The predicted failure loads were in good agreement with
‘ experimental results for open holes subjected to compression and tension by Chang and
Lessard [48] and by Chang, Liu and Chang [49], respectively. However, it seemed that

. the good experimental correlation could be partially attributed to the fact that the authors
. 4 used the best fitted fiber failure interaction zone introduced by Tsai [50]. Furtherrnore,4it
was noted that the damage growth‘in the compression case [48] was sensitive to the finite
element mesh and the authors adopted a specific mesh to obtain the known damage
propagation for each composite lay-up. This manipulation disabled the generalization of »
the computational modeling for various lay-ups and geometries. For loaded holes [51], no
improvement in accuracy was found in predicting the joint strengths with the use of a
progressive damage model [42, 52].

Instead of accounting for the many microscopic damage modes in the failure analysis
as Chang [44], Tan [53] modeled the stiffness degradation of composite laminate in a
more global sense. No specific damage modes were considered in his failure analysis.
Once damage took place, the degradation of a composite property was represented by the

product of its initial value and a corresponding factor. The predicted strengths were in

67

 

close agreement with experimental results for several types of lay-up. However, it was
found that the results were very sensitive to the degradation factors used.

Aiming at understanding more insights of the damage process of composite joints,
this study was to analyze the stress distributions around the critical area of a composite
joint and to investigate the suitability of existing failure criteria. Several stress-based
failure criteria under the one-parameter failure theory were compared. A two-parameter
failure theory was also included for discussions.

4. 2 Finite Element Modeling
A. Composite Materials and Mechanical Fasteners

As investigated in two previous chapters, a double-lap-single-pin joint, as shown in
Figure l, was of primary interest. The central lap was made of a glass/epoxy laminate
with a stacking sequence of [0/90/0/90.. .]9 while the outer laps were made of steel. Each
ply of the composite laminate was considered as a transversely isotropic material. Details-
of the material properties are given in Table 7. A steel pin designated as M-2 according to
AISI classification system was used to assemble the composite lap and steel laps
together, resulting in a dissimilar-material joint.

In investigating a mechanical joint, some geometrical parameters are essentially
important. Their definitions are shown in Figure 1. That is, the width of the joint W, the
diameter of the hole D, the thickness of the laminate H, the distance between the center of
the hole and the free end of the laminate E, and the distance between the center of the
hole and the gripping end of the laminate L, also called the joint length. In this particular
study, a model with H= 3.30mm, D= 3.18mm, W= E= 12.70mm and L =50.8mm was

identified as a basic model, resulting in the following geometrical ratios: H/D= 1.04,

68

 

Table 7 — Material properties of glass/epoxy laminate (3M Aerospace Systems Lab).

 

 

Notation Value
Exx Longitudinal moduli 39.3GPa
Eyy=Ezz Transverse/Normal moduli 8.3GPa
ny=ze x-y/x-z shear moduli 3.1GPa
Gyz y-z shear moduli 2.9GPa
vxy=vzx x-y/z-x Poisson’s ratio 0.26
vyz y-z Poisson’s ratio 0.30
Strength data
Xt Longitudinal tensile 965MPa
Xc Longitudinal compression 880MPa
Yt Matrix tensile 31MPa
Yc Matrix compression 118MPa
Sxy=Szx x-y/z-x shear 72MPa
Syz y-z shear 26MPa

Microscopic properties

7y
$0

Longitudinal shear yield strain
Initial fiber misalignment

69

0.024 (1.40)
20

 

W/D= 4, E/D= 4 and L/W=4. For identification purpose, this model was named as
H/D=l. Two other models, H/D= 0.5 and H/D= 2 were also investigated. The complete
geometrical parameters and geometrical ratios of all three models are given in Table 8.

B. Finite Element Model

A coordinate system XYZ, as depicted in Figure 13, originated at the center of the
hole and the mid-plane of the composite laminate was established. An angular coordinate
0 measured from X axis was also established in the X-Y plane. The joint geometry and
loading condition were symmetric with respect tothe X-Y and X-Z planes. Hence, only
one quarter of the joint model needed to be. examined. The quarter composite lap is '
denoted by ACDEIFGH and symmetric boundary conditions are applied on both ACDE
plane and ACGF plane. The ‘nodes on CDHG plane were deprived of all degrees of
translational freedom, simulating the fixed boundary conditions imposed by the grip-
fixture depicted in Figure 1. In addition, quarter the joining and loading pins and quarter
the central loading plate as well as half one outer steel lap were included in the model.
Figure 14 shows the model in the finite element analysis. With regard to loading, normal
tensile forces were applied to the bottom plane of the central loading plate.

Key locations on composite plate around the hole were specifically denoted for
studying the stress distributions and the damage process of the mechanical joints. As
shown in Figure 15, B0 (bearing) is located at Z= 0 and 0= 0° while N0 (net-section) at Z=
O and 0= 90°. It is worth noting that both Bo and N0 are located in the mid-plane of the
most inner 0°-ply of the [0/90/0/90. . .]9 composite laminate, i.e. right at the mid-plane of
the composite laminate. The Z/H ratios for both Bo and No are zero as the X-Y plane, i.e.

the plane of Z= O, coincides with the mid-plane of the composite laminate.

70

 

Table 8 — Geometrical elements and ratios of three simulation models.

 

 

 

H/D=l H/D=1/2 H/D=2
H (mm) 3.30 3.30 3.30
D (m) 3.18 6.36 1.59
W (m) 12.70 . 25.40 6.35
E (m) 12.70 25.40 6.35
L (m) 50.8 101.6 25.4
H/D 1.04 0.52 2.08
W/D 4.00 4.00 4.00
E/D 4.00 4.00 4.00
L/W 4.00 4.00 4.00
H: thickness

D: hole diameter

W: width

E: distance from hole center to specimen end
L: distance between hole center and gripping end

71

 

\,
/N

 

 

Figure 13 -4 The coordinate system established
for problem modeling.

72

I; Lust-Int: 41.11 I I!

 

 

Figure 14 - The model in the finite element
analysis (quarter of components in
Figure 1).

73

/
Bo, le=0l18

r 4 Bl,z/H=1I18

\ ‘ B2, z/H=3/18

‘ ~ B3, z/H=5/18

 

 

\

wBS, zIH=9/18

   

Figure 15 - A Schematic diagram of hole area
on the composite plate.

74

The points B5 and N5 are located on the surface of the composite laminate. Hence, the
Z/H ratios for both 85 and N5 are 0.5. Similarly, B1, B2, B3, and B4 are located at 0= 00 but

different Z positions while N1, N2, N3, and N; are located at 0: 900 with Z positions

identical to the corresponding 13,, points.

The composite laps investigated in this study were considered to behave linearly up to
catastrophic failure. For the case H/D= 1, an ultimate force of 5.23 kN was used in the
finite element simulation. This force was based on the testing results of Chapter 3. Since
only one quarter of the mechanical fastener was modeled in the study, only 1.308 kN was
required in the finite element simulation. Proportionally, 2,616N was required for the
case H/D= 0.5 and 654N was required for the case H/D= 2.

The finite element analySis was based on the commercial code ABAQUS 6.3. Eight-
noded brick elements were used as the building brick of the finite element model. Since
the stress states on the hole surface and its vicinity were of primary interest, very fine
meshes were used in these areas. Figure 16 shows the details of composite hole area in

the finite element model. In the X-Y plane, there were 60 elements around the

circumference of the half hole from Bn to N". In the thickness direction, 27 layers of

element were modeled, resulting in six layers of element for each composite ply.

The contact between the composite laminate and the elastic pin and between the
composite laminate and the steel lap were modeled using the contact pair approach in
ABAQUS. The contact pair approach was selected for its simplicity. It was based on a
master-slave concept, and the contact problem was solved with the Lagrange multiplier

method. Since the movement between joint components was expected to be small, the

75

WT'"

 

 

 

Figure 16 - Details of composrte hole

area in the finite element

model.

76

‘small sliding’ option given by ABAQUS was selected. The ‘small sliding’ option
defined the possible contact pair between the master and the slave nodes in the beginning
of each simulation and was not redefined afterwards. Besides, a friction coefficient of 0.2
was assumed at the contact surfaces between the composite laminate and the steel lap.
This value was selected based on the measurements by Blom [89]. On the contact surface
between the composite laminate and the elastic pin, the friction coefficient was lower due
to the relatively smooth surface of the pin and the hole surface. Hence, a friction
coefficient of 0.1 was used.

C. Validation of Finite Element Analysis

Finite element modeling must be validated before being applied to general analyses.
Experimental investigations based on strain gages were performed by Thomas [27] and
Hung et al [55] for finite element validations. Hung et al [55] used a progressive damage
model to predict the response 'of the pinned and clamped joints. Although the nearest
strain gauge was only one hole radius from the hole edge, it was too far from where the
failure took place, i.e. the hole edge. In his study, Tomas [27] mounted strain gauges
2.5mm from the edge of a hole with a diameter of 6mm. The comparisons between the
measured and the calculated strains were inconclusive. The difficulties in both studies
were believed to be attributed to the high gradients of strain around the hole edges.

In addition to experiments, validated computational results available in literatures
were often used for justifications of new finite element modeling. Mahmood, Shokrieh
and Lessard [32] studied the stress states of pin-joined composite structures with a finite
element code developed by them. Radial displacement boundary conditions were applied

to the nodes on the hole surfaces in their study rather than the aforementioned contact

77

pair approach, which was more computationally demanding. No friction between the pin
and the hole was included in their study. In the present study, Lessard and Mahmood’s
studies were repeated with the use of ABAQUS and the contact pair approach to justify

the proposed finite element model.

Cross-ply composite laminates with stacking sequences of [04/90415 and [904/0413

were investigated by both finite element codes, the Mahmood-Shokrieh-Lessard’s and
ABAQUS. The finite element mesh used by Mahmood, Shokrieh and Lessard was also

adopted. Figure 17 shows the comparisons along the interface between the top two layers

of the [04/90415 laminate, i.e. the interface between lamina 04 and lamina 904, at the hole

edge. It is clear that the stress values from both studies agree with each other well at e=0°
and e=90°, where the stress values were believed to be most influential to the joint

failures due to the potential bearing and net-section damage modes, respectively. Another

study on [904/04]s laminate also concluded‘the good agreement at e=0° and e=90° based

on the two approaches.

For the areas between o=0° and 90°, Mahmood-Shokrieh-Lessard’s study and the
present approach predicted similar trends. The present approach, however, gave higher
values of longitudinal compression cxx while lower values of other stress components
than those given in Reference [32]. The discrepancies were believed to be attributed to
the difference of boundary conditions used in simulations. In Mahmood-Shokrieh-
Lassard’s study, the assigned radial displacement around a section of the hole periphery
without friction implied a rigid, frictionless pin. In the present study, however, contact

condition was established between the hole surface and a rigid pin. The validation of the

78

oxx (MPa)

oyy (MPa)

022 (MPa)

400

200 -

-200
-400

 

-10 3

-15

-20 4.
-25 .4

-30

 

 

 

 

oxy (MPa)

 

 

 

 

 

 

 

 

45 90 135 180 0 45 90 135 180
6 (Deg) 9 (Des)

 

ozx (MPa)

 

 

 

45 90 135 180 0 45 90 135 180
0 (Deg) 6 (Deg)

 

oyz (MPa)

 

 

 

 

 

45 90 135 180 0 45 90 135 180
0 (Deg) 9 (Des)

Figure 17 - Comparison of stress results between [32]
and current model: Bolt line, [32]; ‘+’ 0°
ply results; ‘-’ 900 ply results.

79

displacement distribution around the hole surface was also made. The result is shown in
Figure 18.
4. 3 Finite Element Results
A. Three-dimensional Effect

The six stress components along line 80-85 and line No-N5, i.e. the bearing points and
the net-section points through the half thickness of the composite laminate as depicted in
Figure 15, respectively, are presented in Figure 19 and Figure 20, respectively. They are
expressed in terms of the global XYZ coordinate system as shown in Figure 13 instead of
the local material system of individual plies.

From Figure 19, it was Clear that thestress distribution was non-uniform through the

laminate thickness. It seemed most stress components reached the highest values at the

laminate surface, i.e. B5. For example, the longitudinal compressive stress Gxx increased

from 672MPa at 130 to 962MPa at B5 in the mid-plane of the innermost 0°-ply Bo, i.e. the

mid-plane of the composite laminate. That was an increase of 43%. The increase was

290% for oyy, transverse tensile stress from 52MPa at B0 to lSlMPa at B5. The largest

non-uniformity, however, was obviously seen in on, where it Changed from -45MPa

(compression) at B0 to 75MPa (tension) at B5. Among the three shear stress components,

rxy , sz and ryz, sz took the highest value, around 60MPa, as well as highest level of

non-uniformity, ranging from 0 at B0 to -37MPa at B5.

There were two 90° plies in the half thickness. The stress distributions in these two

90° plies were not uniform either. Figure 19 shows that Uxx ranged from -152 to

80

Radial displacement (mm)

 

0.018
0.013 . _____ - _

0.003 W-__ _

 

 

 

 

 

--0002 0 45 96 "t35——t80
6(deg)
Figure 18 - ABAQUS result of radial displacement on
the hole periphery of [04/904]s cross-ply

81

 

oxx (MPa)

oyy (MPa)

022 (MPa)

 

 

1600 5 160

 

 

 

 

 

 

 

 

 

 

     

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1200 -~--—---—-—--—- ~— . ~ 80 . . -3, -
iii " ' a “W " “i "
0 -~ L — - - >.
_400 . g -160
-800 , 1 -240
-1200 ‘ ~320
0 0.5 O 0.5
(Bo BI 32 Ba B4 35) (Bo B1 32 Ba B4 Bs)
Thickness (z/H) Thickness (z/H)
750 f ( - I 80 I [ I
i . 1 y 7 g |
500 - , ~ 40 i
250 - — . E 0 4
. ; g
0 -—~~~~ e -40
D . .
-250 A- ._ . - -» -80 -~ - a
'°°° Em“ ’ 0.5 42° 0 ' w 0.5
(Bo B1 32 Ba B4 B5) (Bo B1 Bz B3 B4 Bs)
Thickness (z/H) Thickness (le)
100 ---~--—-— 80 ----—--—---~~-~--——~————--——-——-—-
75 ’ 40
50 A . -
m 0 W
25 $3 ,
0 g -40
-25 °
_50 5 430
-75 -120
0 0.5 0 0.5
(B0 B1 Bz Ba B4 B5) (Bo BI 32 B3 B4 Bs)
Thickness (z/H) Thickness (z/H)

Figure 19 - HID=1 stress state through the thickness
at 80-85 line.

82

 

cxx (MPa)

oyy (MPa)

022 (MPa)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1600 160
1200 j 80 1-4---- -____-
:21 :r . W
é 804-»5-4 4 - . ~ - . 4
o - :- —. g .
.400 . . . . 3,257,, b 460
.300 4 . . . . . .-,,-,, -240 4 . . . . - . ..
-1200 -320
0 0.5 0 0.5 1”
(MM N2 N3 N4 N5) (N0N1 N2 N3 N4 N5) 5
Thickness (z/H) Thickness (z/H) i
750 . j 30 i
500 ‘ - ~ . ~ .. 4o - g
256....,..... 350-...-.“
0 WW g .40
D
-500 ----~ -120 _4 _..__-..
0 0.5 0 0.5
(N0 N1 N2 N3 N4 N5) (N0 N1 N2 N3 N4 N5)
Thickness (z/H) Thickness (le)
100 , I so —— .
75 W . 40
50 .3... - . - - - a
25 y E .
-25+ 0 -80 - . . -,.
-75 ‘ -120
0 0.5 0 0.5
(N0 N1 N2 N3 N4 N5) (N0 N1 N2 N3 N4 N5)
Thickness (z/H) Thickness (le)

Figure 20 - H/D=1 stress state through the thickness
at No-Ns line.

83

 

-180MPa, oyy ranged from 522 to 662MPa, 022 ranged from -50 to 25MPa and sz

ranged from -11 to -4OMPa.
Comparisons between Figure 19 and Figure 20 revealed that the stress distribution

along line No-N5 was much more uniformly distributed through the thickness than along

line Bo-Bs. The longitudinal tensile stress Oxx valued 1231MPa at B0 and 1177MPa at BS.
That was a variation less than 5%. The variation of the transverse normal stress oyy was

only 3%, from 18.8MPa at B0 to 18.3MPa at 85. However, on remained positive

(tension) throughout the thickness and valued almost equally from No to N5,
B. Size Effect

Figure 21 shows the stress distributions at the bearing point through the half thickness

of the laminates for cases H/D= 0.5 (cross line), HID: 1 (solid line), and HID: 2 (dash

:line). They had similar trends and were all non-uniform through the laminate thickness.
Comparisons of the three cases also revealed that case H/D= 0.5 bore the least non-

uniformity whereas case H/D= 2 the highest non-uniformity. The increase in longitudinal

compressive stress Oxx from B0 to 85 for case H/D= 0.5 was 17%, i.e. from —713 to
-835MPa. It was 43% for case H/D= 1, from -672 to -962MPa, and 343% for case H/D=

2, from -476 to -1632MPa. The increase in the transverse tensile stress Uyy from Bo to B5

for case H/D= 0.5 was 68%, i.e. from 56 to 94MPa. It was 290% for case H/D= 1, from

52MPa at Bo to 151MPa, and 536% for case HID: 2, from 61 to 327MPa. The through-

Til

 

 

oxx (MPa)

oyy (MPa)

022 (MPa)

 

 

 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 i 160 w
i 80 ~- : 77—77 1 --—~
400 -4 ~ + A _ I . , . 7 .
g 0 W ‘ - 7 few
-800 7 g 30 -72 .— 77—
‘ a ‘ 9 5-160 77 '7 77
-1200 7M 7
. . § -240 l 7
-1600 4320 ‘
O 0.5 0 0.5
(30 B1 32 33 B4 35) (30 B1 32 Ba 84 35)
Thickness (le) Thickness (le)
1000 '
800 ~- I § A , ~—
600 7+7 277—.
400 18‘7"; ;
200 j 3 -
0 I } gm: : i I . 7 A 1
0 0.5 O 0.5
(Bo B1 32 Ba B4 35) (30 B1 32 33 B4 35)
Thickness (z/H) Thickness (z/H)
100- - 80 ~— g .
75 2 ~ ' g x '

25 i ‘ I E 0 "mi-WM
0 - ,. g, . ‘ 1 T l I ,1
_25 '. " r; -40 7 7- 71 ~71 77—» -

, o f
'50 " -80 ‘i .,,. + A a"- . .7
-75 , 1 .
-100 * * l 5 -120 L - E
0 0.5 O 0.5
(30 B1 32 B3 B4 35) (30 B1 82 83 B4 35)
Thickness (z/H) Thickness (le)

Figure 21 -— Stress comparison of H/D=1/2 (cross
line), 1 (solid line) and 2 (dash line) cases
at Bo-Bs line.

85

 

(WT

the-thickness normal stress all changed from -17MPa at B0 to 62MPa at B5 for case

H/D= 0.5. It changed from -45MPa at Bo to 75MPa at B5 H/D= 1 and from -78MPa at B0

to 91MPa at B5 for case H/D= 2. The variation of transverse shear stress sz from B0 to

B5 was from O to -21MPa for case H/D= 0.5, from O to -37MPa for case H/D= l, and
from 0 to ~95MPa for case HID: 2.
Similarly, as the ratio H/D became larger, i.e. from 0.5 to l and to 2, the non-

uniformity of stress distributions in 90° plies became higher. Along line Bo-Bs, the

variation of “XX was from 1260MPa at Bo to 1201MPa at B5 for case H/D= 0.5. It was

from 1231MPa at B0 to 1177MPa at B5 for case H/D= l and from 1,093MPa atBo to

1267MPa at B5 for case H/D=' 2. The variation range in oyy from B0 to 35 was from 21.9

to 18.4MPa for case H/D= 0.5, from 18.8 to 18.4MPa for H/D=l model. and from 17.4 to

19.8MPa for H/D== 2, The variations of all fi'om B0 to B5 for cases HID: 0:5, 1 and 2 are

from 58.7 to 58.5MPa, from 73.5 to 73.4MPa, and from 74.1 to 62.9MPa, respectively.
C. Comparisons with Experiments

As discussed in section A in this Chapter, the stress state around the hole not only
varied along the hole periphery in the X-Y plane, but also varied through the laminate
thickness. Only a three-dimensional study, as opposed to two-dimensional plane-strain or
plane-stress study, could possibly reveal these responses. The finite element analysis
revealed that the bearing line, from B0 to B5, had the highest non-uniformity along the
hole periphery. The surface point B5, in most cases, had the highest stress along the

laminate thickness. This result seemed to indicate that the non-uniform stress distribution

86

"I“- “um-.1

m

 

through the laminate thickness was caused by the bending of pin. which and associated
indentations had been observed in experiments.

The three-dimensional stress study could also provide out-of-plane stress

components. In the case H/D= l, the out-of-plane normal stress oll amounted up to
75MPa, which was about 7.8% of the longitudinal compressive stress oxx, i.e. 962MPa,
at B5. Moreover, oll switched its sign from negative in the inner plies to positive in the

outer plies. Since positive all could cause matrix cracking and delamination, it indicated

that the outer plies were more vulnerable to these types of failure than the inner plies.

Experimental results verified this argument. Besides, the out-of-plane shear Stress sz

also valued 37MPa, which was about 51% of the shear strength (Szx was equals to

72MPa for the composite studied), at the outer ply of the composite laminate. Hence, it
seemed that the out-of-plane stresses should be involved in all composite failure analysis.
The previous section concluded that when the geometric ratio H/D increased from 0.5
to 1 and to 2, the level of non-uniformity also increased. As observed in experiments in
Chapter 2, a larger H/D ratio would resuit in a “tighter” contact and more localized
damage in the area close to laminate surface, such as B 5.
4. 4 Failure Analysis
A. One-Parameter Failure theory
Once the stress distributions were obtained, they could be substituted into a failure

criterion to evaluate the status of a composite joint. This process was especially useful for

87

’ _m mafia”

 

failure criteria based on material strengths and the point with the most critical stress.The
many failure criteria available in the literature could be divided into the following three
categories: global failure criteria, fiber-buckling failure criteria, and micro-mechanical
failure criteria.
A. 1 Global Failure Criteria

The maximum stress failure criterion for composite materials is similar to those used
for isotropic materials which were based on maximum normal stress or maximum shear
stress proposed by Rankine and Tresca, respectively. Based on the maximum stress
criterion, the composite failure is predicted in the lamina level. If any of the normal or
shear stress of a composite lamina reaches the corresponding ultimate strength, the
composite lamina, and hence the composite joint, is considered to fail. Instead of using
the stress components individually in the maximum stress criterion, Tsai-Hill [90]
proposed a failure theory which was based on) the combination of individual stress
~* components. In their theory, a lamina will fail when the distortion energy of it is greater
than the allowable level. Tsai-Wu [91] refined the Tsai-Hill theory by distinguishing the
compressive stress from the tensile stress in a lamina. Maximum stress, Tsai-Hill and

Tsai-Wu failure theories could be represented by equation (1-3) respectively.

88

-" ‘1 .-.‘m

 

Maximum Stress F ailureCriterion

 

MGXI m um (emax_xx’ emax_yy’ emax_zz ’ emax_xy’ emu}: ’ emax_zx) : emax
Where,
0'
_ xx
fora“ > 0, emx xx —
.. XT
0'
_ xx
foro'xx < 0, emx xx -— ——-
_ XC
fora > 0 e = &
Y)’ ’ max_)y Y
T
fora' < 0 e - fl_
yy ’ max)? — Y
C
0:-
fordzz > 0, emax x = —'—
_ YT
0.-
forazz < O, emax :2 = —7
..- )fcv
! .
__ l 0.17 __ l0- : _ 0:: I
emax_xy—|S ’e'naXJ'Z—IS ’emax_xy- S . ()
xy y: 3'

..Tsai- Hill Failure Criterion

 

 

 

 

 

 

0'”, 0' 2 O»,-
(—;)z + (l) + (__:)2 — ZGn'Tl-laxxo-yy _ ZszTHa 220-10: _ 2(;szH()-){yO-zz
X 1 Yr Yr
0' an 0' .
+(—"’)2 +672 +(-—”)2 = em:
SW 5,, 5,,
Where,
1 : XT
nyTH + Ga”!
1 2 Yr
szTH + GszH
1 - Y (2)
GszH + nyTH T

89

Tsai - Wu Failure Criterion
0' 0' 0' 0' U 0'
xx + yy + z: +( xx )2+(__yy__)2+(__zz_)2+
XxTW YyTW YzTW XxxTW YnyW YzzTW

20mg» 20.22030: zawazz

 

 

 

 

 

 

2
+ + X H; ”CT—W ”250)+( Ml=erw
X xyTW X szW szW xyTW SszW SszW
Where,
XxTW’ YyTW’ YzTW a XxxTW’ YnyW a Yzzrw ’ SxyTW ’ SJyTW and vaTW
could be solved by theoretical single stress cases, and by assuming
2
X xyrw : 2(Xr)
2

XszW : 2(YT)2

' A. 2 Fiber-buckling Failure Criteria.
In a micromechanical study concerning the compressive failure of fiber composites,

Argon [92] identified that the shear yielding stress of a composite x, which was equal to

the multiplication of shear modulus ny and yielding shear strain 7’}, . and an initial fiber

misalignment angle ¢0 as the main parameters controlling the compressive strength of

the composite. Equation (4) shows the Argon theory,

0'

XX

for Gxx < 0 ny o yy 26%” (4)

9150

90

 

where ny is shear modulus and 7), is yielding shear strain The composite is considered

to have failed when cargo" reaches 1. In the Argon theory, the material was considered to

be rigid perfectly plastic. Budiansky [93] extended Argon’s formula by assuming the
material to be elastic perfectly plastic. His prediction of critical compressive stress is

shown in Equation (5).

0'

xx _ e
— b d-
foroxx<0 ny 07y I” (5)

¢0+7y

 

Both the Argon theory and the Budiansky theory accounted for fiber micro-buckling or
fiber kinking failure typically seen in polymer-matrix composite under compression.
A. 3 Micro-mechanical Failure Criteria

Yamada and Sun [94] proposed a failure criterion accounting for lamination effect.
The shear strength in their criterion was proposed to be measured from a symmetric
cross-ply laminate instead of a unidirectional specimen. The Yamada-Sun theory is given
in Equations (6a) and (6b) accounting for the failure mode combining fiber tension
(breakage) and shear and the failure mode combining fiber compression (buckling) and

shear, respectively,

 

0' 2 Txv 2 2
(—n) +( ' ) = 9
for oxx > O X, Sxy ft (6a)
0.x: 2 Txy 2 2
__ + __ = e
for 0., < 0 ( Xe) ( SW) f. (6b)

91

 

where X, and Xc are tensile and compressive strengths of unidirectional composite lamina

along the fiber direction and 8,0, is the in-plane shear strength of a symmetric cross-ply

laminate. Hashin [43] included matrix tension and compression in his failure criterion.
His matrix related failure theory is given in Equations (7a) and (7b) to differentiate the
failure mode combining matrix tension and shear and the failure mode combining matrix

compression and shear, respectively,

 

0' .
yy 2 xy 2_ 2
forayy>0 (Y, ) +(Sxy) —eml (7a)
0' 2' -
_fl 2 -1 2: 2
forayy<0 (Ye) +(Sxy,) . emc - (7b)

where Y, and Yc are tensile and compressive strengths of unidirectional composite lamina

along the matrix direction. Puck [95] put a major emphasis on matrix failure in three--
dimensional cases by including interlaminar composite failure, such as delamintation, in

his failure criterion shown in Equations (8a) and (8b),

 

far 2 T? .. .2 0:: 2 2
for 622 > 0 (F) + (Ev-i.) + (7-) = epuck (83)
:x y: t
73 2 ,2 2 0'3: 2 2
for all < 0 (3") + (S‘ ) + (T) = epuck (8b)
zx yz c

where Szx and Syz are interlaminar strengths.

92

B. Comparisons of One-Parameter Failure Criteria

As given in Table 9 are the effective status values, or failure indicators, based on all
failure criteria presented in the previous section for point B5 of case H/D= 1. When an
effective value is equal to or greater than 1, it implies that failure will take place at the

point according to the damage mode specified by the equation; otherwise the point

remains intact. Hashin’s tensile matrix failure emt took a value of 4.87, comparing to

0.18 for emc , 0.18 for efi and 1.1 for BfC. It could be inferred from these values that

tensile matrix failure beneath the pin occurred at a much earlier stage than the ultimate
failure of the composite joint. In other words, the composite joint could still withstand a

higher load beyond the occurrence of tensile matrix failure.

The out-of-plane failure indicator epuck had a value of 2.47. It also indicated that the .

local out-of-plane failure beneath the pin would not dictate the load capacity of the
composite joint. Nevertheless, the matrix cracking and out-of-plane buldging could be

easily identified in the damaged specimens. 0n the contrary, the values of the indicators,

Cfc= 1.11, Cargon= 1.10 and ebudi= 1.41, seemed to indicate that a compressive fiber

failure was the primary failure mode of the composite joint. Taken into account that both
Argon’s and Budiansky’s theories were aimed at fiber micro-buckling or fiber kinking
failure typically seen in polymer-matrix composites under compression, it would be
logical to predict that these types of failure mode would take place in failed specimens. In
fact, in Chapter 3, zig-zag kinks were reported in the bearing area of failed composite

joints.

93

Table 9 — Failure indicators at Bo-B5 line.

I emax I CTHZ I eTWZ I eargon I ebudi I efl I efc I emt I ernc I epuck

 

 

 

Bo(0°) [1.80 [2.03 [3.55 [0.81 [1.05 [0.03 [0.81 [1.80 [0.03 [0.15
° 2.24 3.93 4.58 0.88 1.13 0.07 0.88 2.24 0.07 0.31

 

 

 

 

 

B1

32 0° 2.23 3.38 4.94 0.87 1.12 0.08 0.87 2.29 0.08 0.23
B3 0° 2.56 7.22 4.71 0.89 1.15 0.09 0.89 2.56 0.09 0.56
B“ 0 2.74 5.43 6.25 0.87 1.13 0.11 0.88 2.74 011 0.45

 

135(0") [3.02 [1.74 [2.25 [0.95 [1.23 [0.05 [0.95 [3.02 [0.05 [2.04
HID=1

130(0") [1.67 [0.46 [4.49 [0.77 [0W 0.03 [0.76 [1.67 [0.03 [0.38
1.10 0.07

 

 

 

   
 

 

 

 

B“ ' " .52 .17 . . 0.70
B,(0°) F871717 [3.15 [1.10 [1.41 [0.18 [1.11 [4.87 |0.18[2.47
HID=2

Bo(0°) [1.97 [0.47 [7.51 70.54T0707 0.0 [0.54 [1.97 L00 [0.66

 

 

 

 

 

 

 

 

0° 5.32 11.14 25.12 1.07 1.38 0.33 1.12 5.33 0.33 1.09

 

 

B5(0°) T10.54[62.47 J 16.83 [1.86 [2.39 [0.53 [1.93 [10.56 [ 0.53 [3.24 [

 

94

In Table 10, epuck at N0, N1 and N5 also revealed that out-of-plane failure would

not dictate the load capability. However, Cfi at N0, N1 and N5 were all higher than 1.

This fact indicates that at net-section plane, net-section failure is also a potential failure
model competing against bearing failure.
C. Two-Parameter Failure Analysis

As discussed earlier, a two-parameter failure model is useful because it does not
underestimate the joint strength as the one-parameter counterparts and is simpler than the
progressive counterparts in failure prediction. Based on the foregoing detailed
computations for both in-plane stresses and through-the-thickness stresses, it is possible
to develop a two-parameterrfailure model by introducing a characteristic dimension in the
thickness direction, i.e. away from the laminate outer surface.

Based on the previous studies in both Chapters 2 and 3, the stresses along laminate
surface, i.e. along line B5-S5 as depicted in Figure 22(a), and along the 45° line from the
mid-plane of the composite laminate to the laminate surface, i.e. line Bo-Ss, were also of
interest. More finite element simulations were carried out for the points along these lines,
each focusing on one point along the three edges of the triangle zone given in Figure

22(a). The failure criteria presented earlier were also used for calculating the load

capacity of the composite joint. The results are given in Table 11. For example, Cfi

stands for the load capability based on the Yamada-Sun fiber tension failure criterion.

95

Table 10 — Failure indicators at No-Ns line.

 

e 2 2 e e - e e e e e
I max IeTH IeTW I argonI budr I R I fc I mt I mc Lpuck

HID=1/2

N0(0°) [1.89 [3.03 [3.31 [0 [0 [1.31 [0.15 [0.72 [0.15 [1.89

N1 0° 1.89 1.87 2.93 0 0 1.28 0.08 1.47 0.08 1.94

 

 

 

0° 1.88 1.86 2.92 0 0 1.28 0.08 1.47 0.08 1.93
0° 1.88 1.85 2.91 0 0 1.28 0.08 146

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

0° 2.09 2.29 3.20 0 0 1.39 0.08 1.45 0.08 2.12
N5(0°) [2.03 [3.61 [3.58 [0 [0 [1.33 [0.22 I0.68 [0.22 [2.03 [

 

 

96

 

 

 

    

S 5 BS 85
22(0). 22(0)-
Figure 22 7 TWO~parameter failure model triangle
22 a ront 22 b
failed sample '

, op 22(c) View of a
111 Chapter 3
97

Table 11 — Joint load capacity prediction .

 

98

The lowest value in Table 11 takes 1.03kN. It is for point B5 with the use of Hashin’s

matrix tension failure criterion, i.e. Cmt- This value is well below the load capacity of

5.37kN from the experiment. Also, the predictions based on Cpucka Cbudia and Cfc at B5

are all below 5.37KN, indicating that the composite joint at B5 would fail before the true
load capacity is reached if Puck’s, Budiansky’s and Yamada-Sun’s failure theories are
used. In other words, if B5 is selected as the location to predict the load capacity for the
composite joint, the joint strength would be underestimated no matter what failure theory
is implemented. With the introduction of a characteristic dimension as suggested by the
two-parameter failure criterion, it is possible to look for a neighboring point along line
Bs-Ss that may predict load capacity close to the true one. Following this approach and
using 5.37kN as the benchmark, different failure theories would provide different
.charactcristic dimensions. In fact, Puck’s delamination theory and Yamada-Sun’s fiber
compression theory both yield a characteristic dimension below 0.32mm whereas
Budiansky’s fiber buckling theory and Hashin’s matrix tensile theory give 0.48mm and
0.80mm as the characteristic dimension, respectively.

The characteristic dimension can also be obtained from the line B5-Bo. Puck’s
delamination theory and Yamada-Sun’s fiber compression theory both yield a
characteristic dimension lower than 0.35mm while Hashin’s matrix tensile theory does
not yield a reasonable characteristic dimension lower than 1.65mm, i.e. half thickness of
the composite laminate. Besides, Budiansky’s theory gives a characteristic dimension of

1.62mm, fairly close to the half thickness of the laminate.

99

 

l-

In identifying the characteristic length, the approach based on line Bo-Bs, i.e. along
the laminate thickness, seems to indicate that the failure of the composite joint will not
take place until the stress at point Bo reaches the allowable level. On the contrary, the
approach based on line B5-Ss, i.e. along the laminate surface, seems to indicate that the
failure of the composite joint will not take place until the stress at a point between B6 and
B7 reaches the allowable level. Both approaches seem to be supported by the
experimental results as shown in Figure 22(b) and 22(c), respectively. Another interesting
correlation between computation and experiment can also be found from comparing
Table 11 and Figure 22(b) and 22(c). In Table 11, the predicted values of load capacity
below 5.37KN seem to be located around the left-lower corner while the damage in
Figure 22(b) seems to be also primarily located around the left-lower area bounded by the
triangle vertices B0, B5 and S5,

4. 5 Conclusions
The following conclusions can be drawn from the foregoing investigations.

1. Three-dimensional stress analysis is critically important to the failure analysis of
composite joints because the stress distribution around the composite joint is not only
dependent on the in-plane (X-Y plane) dimensions but also dependent on the
composite thickness. In addition, the out-of-plane stresses are not negligible when
compared with the joint strength.

2. The geometrical ratio of composite joint H/D can greatly influence the stress non-
uniforrnity through the composite thickness. The higher the ratio of H/D, the higher

the non-uniformity.

100

3. The comparison of various failure theories can help to justify the suitability of the
failure theories in predicting the strengths and failure modes of composite joints. It
seems that Argon’s theory, Budiansky’s theory and Yamada—Sun’s theories are the
best ones to predict the strength and failure mode of the composite joint investigated.

4. Conventional two-parameter failure theories accounting for an in-plane characteristic
dimension can be extended to account for a characteristic dimension in the thickness

direction.

101

Chapter 5
Conclusions and Recommendations

5.1 Conclusions
A. Thickness, constraint and damage mechanisms

Thickness of composite plates plays an important role in the damage mechanism of
single-pin-double-lap composite joints. As observed in Chapter 2 for woven glass-
fabric/phenolic composite material as well as in Chapter 3 for glass/epoxy laminated
composite materials, thickness variation would change local microscopic damage modes
of joint structures. As shown in Chapter 2, for 1.96mm-thick (8-ply) composite plate,
outward buckling of plies in composite plates accounts for the local bearing damage; for
5.97mm and 9.40mm-thick (24-ply and 40-ply) cases, however, kinky bands through the
composite plate cross-section accounts for the local damage; for 20.42mm-thick (SO-ply)
case, local damage occurs when non-uniform kink bands develops through composite
thickness with a concentration in outer plies. As shown in Chapter 3 about glass/epoxy
composite joints, meanwhile, for 3.30mm and 6.48mm-thick (9-ply and 17-p1y)
composite plates, zig-zag kink bands account for the local bearing damage; whereas for
12.95mm-thick (34-ply) composite plate, net-section is the main damage when only few
fiber kinks were found in the 0°-plies close to the laminate surfaces in the bearing plane.

As shown in Chapter 2 and Chapter 3, large thickness, along with two other factors -
adequate bonding between ply-interfaces and clamping force from bolting technique,
provides a constraint in the thickness direction for the joint structure. In a local area
beneath the pin where bearing damage usually occurs, this very constraint prevents fibers

from buckling and composites fiom delamination at early stages of loading process.

102

Hence, increase in the first peak load capability is tangible, though limited, for joint
structure with adequate constraint in the thickness direction.

With regard to ultimate damage load, or second peak load, and energy absorption
during the damage process, however, constraint in the thickness direction, including large
thickness, does not necessarily contribute positively. In fact, as observed in Chapter 3 for
glass/fiber composite joint, higher constraints in the thickness direction result in more
brittleness of joint load-displacement relationship, lowering the energy absorption in the
damage process.

B. H/D ratio, load-displacement curve and stress distribution

As an important contribution initially recognized by Liu [13], H/D, i.e. geometric
ratio of laminate thick to hole diameter, H/D, is found to be influential to joint
mechanical performance in many respects. In fact, this concept was further explored in
Chapter 2 and Chapter 4. In Chapter 2, the type of load-displacement curve of a joint was
found to be dependent on the H/D ratio. Specifically, all the joints in the groups with
H/D=0.4 and H/D=0.75 had brittle-type curves while all the joints in the group of
H/D=1.5 had ductile-type curves. Meanwhile, pin-bending associated failure mechanism
occurred in high H/D groups while composite bearing associated failure mechanism
occurred in low H/D groups. Moreover, the group featuring H/D=0.75, being more close
to 1 than other two groups with H/D=0.4 and H/D=1.5 respectively, seems to have more
efficient load capability in terms of strength after comparison. These findings further
reinforce the statement that H/D ratio is an important parameter in an efficient joint

design.

103

As numerically discussed in Chapter 4, higher H/D would ensure higher stress
concentration in plies close to composite outer surface. Based on failure criteria as
included in Chapter 4, for high H/D joints, localized damage would occur at outer plies
by local kink bands or outward buckling demonstrated in Chapter 2 and 3, coupling with
pin bending as demonstrated in Chapter 2, and lead into a ductile-type load-displacement

curve.

C. Size scaling

As explored in Chapter 2 and Chapter 3, three-dimensional size scaling in a
composite joint structure is complicated. With respect to load capability, size scaling
effect seems able to be separated into in-plane scaling effect and thickness scaling effect,
as discussed in Chapter 2. For in-plane scaling, the bearing strength decreased as size
increased; for thickness scaling, however, the bearing strength increased as thickness
increased. Three-dimensional size scaling seems to be a complicated combination of in-
plane scaling and thickness scaling, where bearing strengths either decreased
monotonically or non-monotonically in different groups categorized by H/D ratio.
Discussion in Chapter 3 further revealed that not only strength capability decreased
monotonically, but also major failure mechanism shified from bearing failure into net-
section failure as joint size three-dimensionally scaled two and four times. All these
findings demonstrated that three-dimensional size scaling needs to be carefully studied
before results from small coupons could be used in order to predict joint performance in

real application.

104

D. Investigation technique

As an important tool in understanding failure mechanisms, a finite element simulation
of joint loading phenomenon, as demonstrated in Chapter 4, is crucial yet challenging
task. Detailed three-dimensional stress study is time-consuming, even for modern
computers and FEA programs. Nevertheless, study results included in Chapter 4 are
much needed in a fiiture failure investigation. The proposed two-parameter failure theory
using thickness as characteristic dimension is inspiring and seems to make more physical
sense. However, it needed to be tested and justified in a wider application.

5.2 Recommendations

In summary, the current study, using both experimental and analytical methods,
demonstrated the complexity triggered by the thickness variation involved in a composite
joint structure. Nevertheless, there are still many related areas uncovered by the scope of '
the current study. As a matter of fact, extensive further research would be needed in order
to expand our knowledge and lead into an optimum composite joint design involving
thickness requirement.

Possible recommendations for future study:

1. Material property variation caused by three-dimensional size scaling should be
quantified by extensive material testing and the results should be integrated in a FEA
model to correlate the strength variation observed in experimental studies.

2. Interface interaction from bonding technique as well as clamping force from
bolting technique should be adequately integrated in a three-dimensional FEA in order to
compare various thickness scaling techniques and guide an optimum composite joint

design involving thickness requirement.

105

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