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SCALING EFFECT OF MECHANICAL FASTENING ON
THICK COMPOSITE STRUCTURES

By

Junling You

A THESIS

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

MASTER OF SCIENCE
Department of Materials Science and Mechanics

1998

ABSTRACT

SCALING EFFECT OF MECHANICAL FASTENING ON
TI-HCK COMPOSITE STRUCTURES

By

Junling You

Mechanical joints are suitable for joining composite laminates, especially thick-
section composites. In most studies on mechanical joints, the interactions between pin
diameter (D) and composite dimensions such as width (“0 and distance from hole center
to composite end (e), i.e. W/D and e/D ratios, were the primary concerns. However, as
composite thickness increases, the contact interaction between the pin and composite
becomes more complicated. This study investigated the mechanical joint efficiency of a
composite material made of woven glass fabric and phenolic matrix. Sixteen joint conﬁg-
urations based on four composite thicknesses and four pin diameters were examined. Both
experimental method and ﬁnite element analysis were performed in this study. Results
showed that thick composites with small pins and thin composites with large pins had
lower efﬁciencies of joint stiffness and joint strength than those having similar dimensions

between pin diameter and composite thickness.

ACKNOWLEDGEMENTS

The author wishes to express her sincere thanks to Professor Dahsin Liu in the
Department of Materials Science and Mechanics, and also thanks to U. S. Army -

TARDEC for ﬁnancial support.

iii

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................. vi

LIST OF FIGURES ........................................................................................................... vii

CHAPTER 1

INTRODUCTION .............................................................................................................. 1
Literature Review .................................................................................................... 1
Statement of the Problem and Objective ............................................................... 11
Organization of Thesis .......................................................................................... 12

CHAPTER 2

EXPERIMENTAL METHOD .......................................................................................... 14
Composite Material ............................................................................................... 14
Composite Thickness ............................................................................................ 14
Pin Diameter .......................................................................................................... 16
Composite Mechanical Joint ................................................................................. 26
Experimental Results ............................................................................................ 31

CHAPTER 3

COMPUTATIONAL METHOD ...................................................................................... 36
Finite Element Method .......................................................................................... 36
Finite Element Model ............................................................................................ 38
Finite Element Analysis ........................................................................................ 53
Computational Results .......................................................................................... 57

CHAPTER 4

CONCLUSIONS AND RECOMMENDATIONS ............................................................ 87
Conclusions ........................................................................................................... 87
Recommendations ................................................................................................. 89

REFFERENCES ............................................................................................................... 91

iv

LIST OF TABLES

Table 1: Linear orthotropic material properties determined from experiments and

assumed (underlined) for computer simulations ................................................. 15
_ . W e H 2
Table 2. Ratios of D , D . and (.5) ........................................................................ 18
Table 3: Specimen nomenclature for various combinations of pin diameter and
plate thickness .................................................................................................... 21

Table 4: Experimental results of joint stiffness and joint stiffness per unit bearing area . 22

Table 5: Experimental results of the type of load-deformation relation, joint strength,

and offset deformation percentage from linear range .......................................... 29
Table 6: Numbers of elements used around the hole edge ............................................... 42
Table 7: Numbers of layers used in the thickness directions .......................................... 43
Table 8: Loading used in ﬁnite element linear analysis ................................................... 51
Table 9: Bending behavior of the pin after deformation from linear analysis ................. 60

Table 10: Computed results of the node numbers and locations in polar coordinates for

the maximum bearing stresses .......................................................................... 67
Table 11: Joint stiffnesses from both experiments and computations ........................... 73
Table 12: Joint strengths from both experiments and computations ............................. 76
Table 13: Joint strengths from experiments and nonlinear computations ...................... 81
Table 14: Joint stiffnesses from experiments and nonlinear computations .................... 85

LIST OF FIGURES

Figure l - Schematic diagram for double-lap, single-pin joint ......................................... 17
Figure 2 - Progressive hole drilling in composite joint system ....................................... 20
Figure 3 - Load-deformation relation for D2H2, a type A joint ..................................... 23
Figure 4 - Load-deformation relation for D4H4, a type B joint ..................................... 24
Figure 5 - Load-deformation relation for D8H8, a type C joint ..................................... 25
Figure 6 -Pin subjected to bearing forces ........................................................................ 33

Figure 7o-Schematic diagram for double-lap, single-pin joint in computational method . 39

Figure 8 -Symmetric boundary conditions for computer simulation model .................... 41
Figure 9 -The finite element mesh of joint DIH l ............................................................ 45
Figure 10 -The finite element mesh around the contact area of joint DlHl ................... 46
Figure 1] -Nonlinear stress-strain relation of composite material ................................... 47
Figure 12 -Nonlinear analysis computer simulation process ........................................... 58
Figure 13 -Bending behavior of the pin in joint D8H1 ..................................................... 61
Figure 14 -The contact normal stresses on the pin contact surface for joint DlHl ........ 64
Figure 15 -The contact shear 1 stresses on the pin contact surface for joint D1 H1 ........ 65
Figure 16 ~The contact shear 2 stresses on the pin contact surface for joint DlHl ........ 66

Figure 17 -The in-plane tensile stresses of the central composite plate for joint DlHl .. 69
Figure 18 -The in-plane shear stresses of the central composite plate for joint DlHl 70

Figure 19 -The in-plane compressive stresses of the central composite plate for joint

DlHl ............................................................................................................... 71
Figure 20 -Comparison of joint stiffnesses ...................................................................... 75
Figure 21 -Comparison of joint strengths ........................................................................ 78

vi

Figure 22 -Load-deformation relation of joint D1 H1 from computational results ........... 79

Figure 23 -Comparison of joint strengths ........................................................................ 82
Figure 24 -Extended damage of D8H1 joint ..................................................................... 83
Figure 25 -Comparison of joint stiffnesses ..................................................................... 86

vii

CHAPTER 1 INTRODUCTION

1. Literature Review

Composite materials are commonly used in recent years in structures which demand a
high level of mechanical performance. The success of composite materials in replacing
conventional metals is primarily due to their high speciﬁc strengths and stiffnesses cou-
pled with cost effectiveness. Improvements in understanding of the mechanics of compos-
ite materials, and advances in the technology of making and using them, are greatly
extending the range of potential applications of these materials. Examples of the use of
composite materials which can be found in the automotive, aerospace and defense indus-
tries were once reported by Harris and Morris [1]. However, studies of composite materi-
als have tended to be limited to thin shell structures such as aircraft fuselages or pressure
vessels due to the ease in making and designing them.

As the technologies of composite manufacturing advance and the applications of com-
posites to non-aerospace industries are identiﬁed, more and more thick-section composites
are used for structure applications. For example, thick-section composites used for the
submarine hull and armor vehicle bodies have been proved to be feasible. It is believed
that thick-section composites have many advantages that thin-section composites cannot
provide. Bogetti and Gillespie [2] reported the growing interest in thick-section compos-
ites.

The extension from thin plates applications to thick-section composites applications,

however, is not trivial. In fact, it requires careful modiﬁcations in almost every aspect of

composite technologies, e.g., manufacturing, testing, analysis, and design. Taking com-
posite joining as an example, the design of an adhesive joint may turn out to be impractical
if the composite become very thick. Since thick-section composites behave differently
from their thin-section counterparts, investigations on thick composites should be per-
formed carefully [3]. Increasing application of thick-section composites has prompted
increasing research activities, both analytical and experimental.

Investigations on thick composites can be found in the literature. Twardowski [4]
obtained thick part (>5 cm) temperature proﬁles from a one dimensional experiment, and
compared the experimental results with the predictions of a computer simulation contain-
ing improved and existing models for extent of reaction, viscosity and other composite
properties of the same resin/ﬁber system. The following results were found: the initial
extent of reaction was relatively unimportant; the viscosity never reached low values
simultaneously through the thickness in laminates which were in excess of 10 cm thick-
ness. Based on strain energy approaches and ﬁnite element techniques, an effective prop-
erty model was developed by Alexander and Tzeng [5] to compute the properties for an
arbitrarily shaped element with multiple anisotropic material regions. The effective mate-
rial stiffness calculated by the model was compared to those by other models, results
showed that this model was especially suitable for thick composites. An analytical model
for the buckling of thick wall orthotropic composite pipe under external pressure has been
developed by Yang et a1 [6]. F irst-order laminated anisotropic plate theory was used to
construct models of the kinematic and constitutive behavior of the composite cylinders.
The Ritz Method was then applied to determine the buckling load under external pressure.

Results obtained from the developed model were compared with the theory derived by

F lugge and experimental results, good agreement was found. Avva et a1 [7] measured the
through-the-thickness strength of three-dimensional triaxially braided graphite/epoxy
composites and compared it with an equal thickness and ﬁber orientation laminated graph-
ite/epoxy composite. Laminated specimens were made from AS4/3501-6 graphite/epoxy
prepreg using hand lay—up molding and autoclave curing and tested in a uniaxial tension
machine. A simple curved beam equation was used to calculate the through-the-thickness
strength of composites from the measured failure load. Results showed that the strengths
of braided and equivalent laminated composites were nearly equal within the data scatter.
Through-the -thickness strength of both braided and laminated composites was found to
be a matrix dependent pr0perty.

Studies of thick composites focused on failure analysis were also performed by some
researchers. Nguyen [8] extended the Renard et 31’s [9] transverse matrix cracking model
to the three-dimensional analysis of laminated composite structures. The generalized
model was implemented in the general ﬁnite element system. It was based on the contin-
uum damage mechnics and used with the composite three-dimensional multilayer ﬁnite
elements to determine the development of transverse matrix cracking in complex compos-
ite structures under quasi-static loadings where the three-dimensional stress state has to be
considered. The results from the presented approach were compared with the classical
approaches of damage, which generally use phenomenological failure criteria to predict
the strength of composites and impose arbitrarily small components of the stiffness matrix
when the failure occurs. The former was more precise since the last on describes more
realistically the behavior of composites until their ultimate failure. Camponeschi et al [10]

described an analysis of 6.4-25.4 mm thick composite laminates subjected to uniaxial

compressive loading that experimentally showed a decrease in strength with increasing
thickness. The analysis was based on closed form solutions for the formation of kink-band
failures in the presence of ﬁbers misaligned with the principal axis of compression load-
ing. The ﬁber misalignment was determined by a ﬁnite element analysis that accounted
for the displacement of the laminated outer plied where the laminate exited the compres-
sion test ﬁxture. The correlation between the experimental results and the theoretical anal-
ysis showed that the compression strength of the AS4/3501-6 and 82/3501-6 laminates to
be independent of the thickness and directly proportional to the through-the-thickness ﬁx-
ture restraint on the through-the-thickness Poisson expansion. A practical computational
procedure based on global/local ﬁnite element method was developed by Woo and Whit-
comb [1 1] for detailed failure analysis of thick textile composites. The procedure utilizes
two problem levels: global and local levels. An initial global solution was obtained using a
coarse global mesh, and a small portion of the textile composite was modeled with a
reﬁned local mesh. lnfmitely repeating plain weave unit cell and ﬁnite thickness plain
weave conﬁgurations under tension load were considered to study the stress and failure
behavior. Results indicated that the failure behavior of plain weave textile composites was
sensitive to the ﬁber bundle waviness. The initial failure mode was the ﬁber bundle sepa-
ration when the waviness ratio was large while it was the ﬁber bundle fracture when the
waviness ratio was small. It was also found that the stress distributions near the free sur-
face were different from those inside. The stress level was much higher inside than near
the free surface while the boundary region was shallow and was limited to the outer-most

layer.

Composite joining is a study of assembling technique in composite structural

components together. Both mechanical fastening and adhesive bonding are commonly
used in composite joining. In mechanical fastening, a pin is inserted through holes of sev- ,
eral composite laps. The composite laps are usually thin shells. As the applications of the
composite structure expand, more and more thick composite sections are used in indus-
tries. However, the change from two-dimensional thin shells to three-dimensional thick
sections can greatly alter the contact mechanisms between the fastener and the composite.
Subsequently the stress distributions in thick composites will be different from those
expected on the bases of conventional thin composite designs. Certainly, the failure mech-
anism may change, and unexpected failures or expensive over-design might result. That is
to say, unwise extension of thin-wall design procedures to thick sections can cause the
design process to lose its major signiﬁcant assets, those can be predictable and controled.
On the contrary, adhesive bonding is impractical if composite thicknesses become very
large. Hence, mechanical fastening has been an important assembling technique for join-
ing composite structures.

Many articles regarding the study of mechanical fastening for thin-shell composite
structures can be found in the literature. For example, Hamada et a1 [12] presented a study
on predicting the joint strength of mechanical fasteners. Two joint geometries that exhibit
net-section failure and bearing failure were chosen to examine the prediction method in
consideration with bearing failure. The idea of combining the Yamada-Sun failure crite-
rion and the characteristic length appears in the formulation of the point stress criterion
reported by Whitney and Nuismer [13] was used in the prediction method, the deﬁnition
method of the characteristic length for compression was most important for predicting the

bearing strength. Good agreement was found between the experimental and predicted

results. Dattaguru and Rao [14] studied the contact problems of fastener joints in compos-
ite plates, the contact constraint methods, friction laws, contact searching algorithms and
possible solution techniques were presented. de Jong [15] dealt with stresses in inﬁnite
plates, the loading force being in equilibrium with inﬁnitely small, unifonnly distributed
forces at inﬁnity. A solution was presented for the stress distribution around an unrein-
forced hole in an orthotropic plate, loaded on only a part of its edge by an inﬁnitely rigid
pin of material, there was assumed to be no friction. It was concluded that in the pin-
loaded inﬁnite plate there was a clearance, resulting from elastic deformations of the plate
material, not only between the pin and the lower half of the hole, but also between the pin
and a small part of the upper half. Waszcac & Cruse [16] studied the stresses in inﬁnite
plates, the loading force being in equilibrium with inﬁnitely small, uniformly distributed
forces at inﬁnity. The solutions are applicable to joints with large interferes between the
pin and the hole. de Jong [17] investigated the stress distribution around a pin-loaded hole
in an elastically isotropic or orthotropic plates. The hole was loaded frictionless on only a
part of its edge by an inﬁnitely rigid pin of the same diameter. The loading force was car-
ried over on the edge by normal stresses, represented by a sine series. The numerical
results showed that the stress distribution depended strongly on the material properties.
Lessard et a1 [18] studied the modeling of damage in a laminated composite pinned-joint
using ﬁnite element method. A laminated composite plate with a circular hole ﬁlled with a
rigid pin where the load was applied at one end of the plate and this load was resisted by
the rigid pin. Results indicated that two-dimensional linear and non-linear modeling could
predict ﬁnal failure load, and three-dimensional modeling methods could be extended

from these two-dimensional methods required further work.

It is well known [19, 20] that fasteners can severely reduce the load-carrying capabil-
ity of the components by more than ﬁfty percent. Due to anisotropy and inhomogeneity of
composites, the failure and strength of bolted composite joins can be considerably differ-
ent from the failure and strength of metallic joints. Damage in bolted composite joins can
initiate at an early loading stage and accumulate inside the laminates as the load increases.
The accumulation of damage and the mode of failure strongly depend upon the material,
ply orientation, laminate thickness, joint geometry, and loading condition, etc. As a conse-
quence, the strength and failure of bolted composite joints are signiﬁcantly inﬂuenced by
the damage accumulated inside the composites. Hence, failure analysis is very important
in composite joints studies. Wang et al [21, 22] performed an investigation to study the
bearing failure and response of a mechanically fastened laminated composite joint. The
results of the study were presented in two parts: experimental characterization and analyt-
ical prediction. Only double-lap metal/composite/metal bolted joints were considered. In
experiments, a load cell was designed and manufactured which was mounted on the fas-
tener to monitor the bolt clamping pressure as a function of the applied load. An accumu-
lative damage model based on the damage mechanisms observed from the experimental
study was developed to simulate the bearing failure in the laminated composite joints. The
prediction was in good agreement with the data. Based on the experimental results, it
could be concluded that the lateral support was crucial for bolted laminated composite
joints. Bearing damage could be catastrophic if there was no lateral support. Shear cracks
induced by accumulated compression failure appeared to be the primary failure mode of
the bearing damage. Lateral supports could suppress the shear crack propagation and

change failure from a catastrophic to a progressive failure mode. Clamping pressure could

increase bearing strength. It was believed that the model could be extended to three
dimensions in order to simulate accurately the bearing response of bolted composite joints
in real structures.

Mechanical joints for thin composites are usually investigated in laboratories for joint
characterizations. Results from the thin composite joints studies are then used for thick
composite joint designs. However, thin composite joints do not always behave the same as
the thick composite joints made of identical material, that is to say, if mechanical joints
are to be used in composite assembly, the differences betweentwo-dimensional thin shells
and three-dimensional thick sections will greatly alter the contact mechanisms between
the pins and the composites; subsequently the stress distributions in the thick-section com-
posites will be different from those in the thin shells, so will be the failure mechanisms.

There has been some achievements regarding the study of stress analysis of mechani-
cal fastening for thick-section composite structures. Sperling [23] computed the three-
dimensional stress distribution around pin-loaded holes in composite laminates using
ﬁnite element method. A rigid pin and an elastic bolt were both considered. The results
showed that stresses around the pin-loaded holes varied not only with the angles along the
hole surface, but did also vary through the laminate thickness. By replacing the rigid pin
by an elastic bolt it was found that the stress distribution around the hole changed signiﬁ-
cantly and depended on the bolt stiffness. Sundarrai and Dataguru [24] presented a study
of stress distribution in a double-shear lap joint with an interference-ﬁt pin subjected to in-
plane loading by using three-dimension ﬁnite element analysis. The results graphically
showed the through-the-thickness stress distribution and the beneﬁcial effects of interfer-

ence on fatigue life of the joint. Hwang and Stallings [25] reported a two-dimensional

unsymmetrical ﬁnite element model and a three-dimensional solid ﬁnite element model
generated to investigate the stress behaviors in high pressure bolted ﬂange joint. Compari-
sons between the experimental results and the computer simulation results from these two
models showed the feasibility of these models. Grifﬁn et a1 [26] gave a numerical proce-
dure for determining loading proportioning in composite joints. The joints in this paper
were of single pin, double lap fashion and loaded in tension. The commercial ﬁnite ele-
ment program ABAQUS was used to predict the loading proportioning among fasteners
through two plane-stress ﬁnite element models, one model represented for the composite
inner lap and the other for the two steel outer laps. The results indicated the accuracy of
this numerical procedure. Ireman et al [27] discussed problems related to the determina-
tion of the load distribution in a multi-fastener joint using the ﬁnite element method, such
as the stress singularities at the interface. Results showed that the mesh reﬁnement must
be applied to obtain more accurate results. Madenci and Ileri [28] focused on the assess—
ment of the contact stresses in mechanical joints with single fastener, with two fasteners,
and with a row of fasteners perpendicular to loading in ﬁnite composite laminates. The
solution was obtained by solving the governing equations of elasticity under plane-stress
assumptions and modiﬁed mapping-collocation method. The load exerted by the fastener
through the contact region, which consists of no-slip and slip zones due to the presence of
ﬁiction, was modeled with appropriate mixed boundary conditions. The importance of the
study of the contact stresses in mechanical joints was indicated through the results.

Since test specimens and computing cost is an important factor, two-dimensional ﬁnite
element techniques has been used to analyze the pin-loaded case. However, by consider-

ing out-of-plane behavior of pin-loaded cases, such as edge effects, delamination, etc., the

failure behavior of composite plates becomes a three-dimensional problem, and the two-
dimensional assumption may not be accurate or sufﬁcient. Therefore, three-dimensional
studies is unavoidable for failure analysis of mechanical fastening. Shokrieh and Lessard
[29] established a three-dimensional nonlinear ﬁnite element code to analyze the effects of
material nonlinearity on the state of stress and failure prediction near the stress concentra-
tions of a pin-loaded laminated composite plate. A composite plate with a pin-loaded hole
was considered, the pin was ﬁxed and the load was applied on the other end of the com-
posite plate. The results of prediction of failure initiation load by considering the material
nonlinearity was in excellent agreement with experimental results. The results obtained
from failure analysis emphasize that considering the material nonlinearity, especially for

highly shear induced cases like [+454/-454]s was important in failure analysis of compos-

ite laminates using stress based failure criteria.

Small coupons are usually used in laboratories for material characterizations. Results
from small coupon tests are then used for large structural designs. However, small cou-
pons do not always behave the same as the large structures made of identical materials.
The difference of behaviors due to size difference is usually called scaling effects. Scaling
effects include both in-plane scaling effect and thickness scaling effect. The former has
gained more attention than the latter possibly due to the fact that most conventional com-
posite material are thin plates. Some investigations on the performance of composite
materials and structures at different sizes have been presented by Rajapakse [30]. It has
been concluded that scaling effects should be carefully examined in material characteriza-
tions and structural designs.

Scaling effects in two-dimensional problems, that is, in-plane scaling effect, has been

10

discussed by some researchers. The interactions between pin diameter (D) and composite
dimensions such as width (W) and distance from hole center to composite end (e), i.e. W/
D and e/D ratios, were of the primary concerns. Waszcac and Cruse [16] reported that the
stress distribution around the pin-loaded hole depends on the ratios of width of plate to
hole diameter. The results from Sperling [23], Marshall et a1 [31], Hamada et a1 [32], and
Lassard [29] gave the relation between the ratios of the plate width to the pin diameter (W/
D) and the net-section failure, the relations between the ratio of the distance to plate end to
the pin diameter (e/D) and the shear-out failure. In order to avoid the net-section failure
and the shear-out failure taking place before bearing failure, the W/D and e/D ratios
should be at least 4 or greater.

To the best knowledge of the author, no literature has ever discussed the scaling effect
in the thickness direction, that is, thickness scaling effect. The design of mechanical fas-
tening for composites has tended to be done on a case-by-case basis. Studies of mechani-
cal fastenings for composites with various thicknesses would be very tedious if no
“uniﬁed rule” is included or developed. Alternatively, the study may be very efﬁcient if
some fundamental knowledge for thin composite mechanical fastening can be
“transformed into” that for thick composite mechanical fastening. In other words, it will
prove to be very useful if fundamentals of thickness scaling effects can be extracted from
the existing information for thin composite fastening and some extra, but limited, studies

on thick composite fastening.

2. Statement of the Problem and Objective

ll

 

There are obvious advantages, in utilizing very thick composites for bodies and hulls
of combat vehicles. The joining of these components to substructure or other components
must be, to a large degree, by mechanical fastening in order to gain high load-carrying
capability and ease of structural disassembly. In the analysis of composite joints, contact
mechanisms between the pins and the composites are strongly affected by the thickness of
the composites. The contact condition along the pin is not uniform. Accordingly, three-
dirnensional composite joints need to be studied. In other words, the study to identify the
interaction between the pin diameter and the composite thickness becomes the primary
concern in composite joint analysis. Since both pin diameter and composite thickness are
subjected to change, different combinations will result in different stress distributions, and
subsequently strengths. In fact, there exist scaling effects in composite joint analysis.

Although the mechanical test can give both the stiffnesses and the strengths of the
composite joints, it cannot give the detail stress information in the structure. Besides, it is
very costly to perform a great amount of experiments. Hence, numerical analysis becomes
very important since it is more efﬁcient. Various scales composite joint can be examined
from computer simulations. Accordingly, in this study, the objective is to investigate the

composite joints with various thicknesses and pin sizes.

3. Organization of Thesis

Four chapters were given in the thesis. Chapter 1, Introduction, includes the literature

review, the statement of the problem, the objective of the study, and the organization of

the thesis. Chapter 2, Experiment Method, brieﬂy reports the testing methods involved in

12

the investigation. Chapter 3, Computational Method, gives the general idea of the impor-
tant role of the computer simulation in this study and the techniques of the numerical
method. Chapter 4, Conclusions and Recommendations, summarizes the ﬁnding from the

investigations and gives suggestions for future work.

13

CHAPTER 2 EXPERIMENTAL METHOD

1. Composite Material

The composite material investigated in this study was made of 5-2 glass fabric and

phenolic matrix. Since the fabric was of the plane weave, each piece of fabric could be

viewed as unit of [M] cross-ply. In making the composite laminate, an angle of 45° was
imposed in laying up consecutive pieces of fabric, resulting in quasi-isotropic laminates
[DIE/Mm. Mechanical tests were performed to determine the engineering constants.
Experimental results are given in Table 1 along with some assumed values (underlined)

for computational analysis.

2. Composite Thickness

For a given pin diameter, the composite joint strengths due to bearing failure
should be linearly proportional to composite thickness, if the contact conditions between
the pin and composites are identical for various composite thicknesses. If not, the stress
distributions in the composite laminates will be different, so will be the damage processes.
Since contact mechanisms were the primary interests in this study, four composite thick-
nesses, namely 8-ply, 24-ply, 40-ply, and 80-ply with average thicknesses (H) of 1.93
mm, 5.89 mm, 9.5 mm, and 20.37 mm, respectively, were investigated. In addition, it
should be noted that the stacking sequence [DIE/Ml“; used in laminating composites

qualiﬁed the thickness increase in a sublirnate mode instead of a ply-level mode. The

14

Table 1: Linear orthotropic material properties determined from experiments

and assumed (underlined) for computer simulations.

 

 

 

 

 

 

 

 

 

 

 

 

 

Young’s moduli Ell, = 22’ £116 = 22c E33
GPa l 1.65 13.17 5.65
Poisson’s ratios v t = v t v C = v C v
13 23 13 23 12
0.3 0.3 0.3
Shear moduli 013 = 623 612
GP“ 2.07 5.03
Strengths Xt = y! X6 = Yc
MPa 18% 134.18
Bolt bearing strength obu(strength) aby(yielding)
MPa 218.23 153.14

 

15

 

sublaminate mode was deﬁned as repeating the quasi-isotropic unit [gm/M] until the
desired thickness was reached in composite lamination while the ply-level mode repeated
the cross-ply unit [9M] ﬁrst then [M], resulting in [(0/90)n/(45/-45)n]s. Reports, such
as Ref. [3], showed that thick section composites based on sublaminate mode gave better

properties than their ply-level counterparts.

3. Pin Diameter

Another important parameter for studying contact mechanisms was the pin diame-
ter. The effects of pin diameter on composite joint strength are available for thin compos-
ite plates. Those studies were primarily aimed at two-dimensional analysis, i.e. in-plane
scaling effect. Very few studies based on three-dimensional analysis are reported. To the
authors’ best knowledge, thickness scaling effect had not been mentioned. Since the pin
diameter was believed to have signiﬁcant effects on the contact mechanism and stress dis-
tribution around hole edge, four different steel pin diameters (D) of 3.125 mm (0.125 in),
6.25 mm (0.25 in), 12.5 mm (0.5 in), and 25 mm (1.0 in) were considered in the present

investigation.

4. Composite Mechanical Joint

In this study, a double-lap, single-steel-pin joint as shown in Figure l was consid-

ered for experimental and ﬁnite element model. Since the contact mechanisms between

the steel pin and composite and the interaction between the steel pin diameter and

 

 

 

0%///// ///w//%_

 

 

 

 

 

 

 

 

 

 

//////a

 

Figurel - Schematic diagram for double-lap, single-pin joint.

 

 

 

 

 

 

 

 

 

 

 

. W e H 2
‘7- _ _
Table -. Ratios of D 'D ,and (D) .
8~ply 24-ply 40-ply 80-ply
W e H 2 H 2 H 2 H 2
"°“ 5 23 5) 5 5 5
diameter

(mm)

3.125 32 24 0.370 3.445 8.952 41.165
6.25 16 1 l .75 0.092 0.861 2.238 10.291
12.5 8 5.625 0.023 0.215 0.560 2.573

25 4 2.5625 0.006 0.054 0.140 0.643

 

 

 

 

 

 

 

 

l8

 

composite thickness were the primary focuses for this study, only damage due to bearing
failure was of primary interest. Hence, in order to avoid net-section failure from taking
place before bearing failure, a relatively large ratio for plate width to pin diameter, i.e. W/
D, was required. Regardless of the composite thickness (H), the width (W) for all speci-
mens was ﬁxed as 100 mm (4 in), which was the largest size the tensile grips of the testing
machine could accommodate. Accordingly, the W/D ratio were at least 4 or greater for all
cases as shown in Table 2.

Similarly, in order to avoid shear-out failure from taking place before bearing fail-
ure, the distance from the hole center to the specimen end (e) should be as large as possi-
ble. However, it should be pointed out that another important consideration in this study
was to minimize the number of composite specimens through using each specimen for all
four hole diameters. To begin with, the composite specimens were prepared with 3.125
mm holes by using a carbide drill. The joints were then tested until bearing failure took
place. Holes of next size, i.e. 6.25 mm, were then introduced in the failed specimens with
the top edges tangent to the existing holes, as shown in Figure 2, to remove the bearing
damage around the 3.125 mm hole. The specimens were inspected by X-ray radiography
to conﬁrm their integrity before being tested again until bearing failure. If an X-ray radio-
graph showed extended damage beyond a hole edge, a hole of next size (12.5 mm) was
prepared. This process was repeated for holes of 12.5 mm and 25 mm in diameter.
Accordingly, the distance from the hole center to the specimen end varied with the hole
diameters. The W/D and e/D ratios are summarized in Table 2. For identiﬁcation purpose,
the 16 types of joints made from four thicknesses and four hole diameters, were also given

names and are listed in Table 3. The four hole diameters 3.125 mm, 6.25 mm, 12.5 mm,

19

 

 

 

 

 

 

W= 100mm
6 $
206 mm
D/8 = 3. 2
l 5 mm D/4 = 6.25 mm
D/2 = 12.5 mm
75 mm

 

 

 

 

 

 

Figure 2 - Progressive hole drilling in composite joint specimen.

20

Table 3: Specimen nomenclautue for various combinations of pin diameter and

 

 

 

 

 

 

 

 

 

 

plate thickness.
dirrfrﬁer 8-ply 24-ply 40-ply 80-ply
3. 125 D8118 DSH4 D8H2 D8Hl
6.25 D41-l8 D4H4 D4112 041-11
12.5 D2H8 D2H4 D2H2 D2Hl
25 D1118 D1114 DIHZ DIHl

 

21

 

 

Table 4: Experimental results of joint stiffness and joint stiffness per unit bearing area.

 

 

 

 

 

 

 

 

 

 

8-ply 24-ply 40-ply 80-ply

3.125 mm 0.316 0.336 0.216 0.021
Diameter 0.273 0.252 0.220 0.030
0.440 - 0.097 0.040

Average“ 0.343 0.294 0.178 0.030

Efﬁciency 1 .00 0.86 0.52 0.09
Average" 2.069 5.41 1 5.284 1 .910
6.25 mm 0.376 0.267 0.241 0.118
Diameter 0.259 0.284 0.247 0.097
0.202 0.275 0.218 0.126

- 0.288 - -

Average“ 0.279 0.279 0.235 0.1 14

Efﬁciency 0.81 0.81 0.69 0.33
Average” 3.365 10.271 13.953 14.514
12.5mm 0.130 0.196 0.184 0.110
Diameter 0.1 15 0.169 0.179 0.1 10
0.1 19 0.156 0.170 0.096

- 0.211 0.169 -

Average“I 0.121 0.183 0.176 0.105

Efﬁciency 0.35 0.53 0.51 0.31
Average" 2.919 13.473 20.900 26.736
25 mm 0.102 0.104 0.095 0.057
Diameter 0.103 0.098 0.087 0.059
0.107 0.100 0.084 0.059

Average‘ 0.104 0.101 0.089 0.058

Eﬂiciency 0.30 0.29 0.26 0. 1 7
Average“ 5.018 14.872 21.138 29.537

 

 

"' Average joint stiffness per unit bearing area in GPa/mm
” Average joint stiffness in kN/mm

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and 25 mm are designated by D8, D4, D2, and D1, respectively, while the four thicknesses
8-ply, 24-ply, 40-ply, and 80-ply are designated as H8, H4, H2, and H1, respectively. As
an example, the composite joint with a hole diameter of 12.5 mm and a laminated thick-
ness of 24-ply is named D2H4.

In addition to W/D and e/D, parameters such as the integrity of hole surface and
the clearance between pin and hole also play important roles in composite joining. Since
the composite material under investigation was made out of laminates, micro-delamina-
tion was likely to take place during hole drilling. Extra care was exercised in hole prepara-
tion. X-ray radiographs taken after drilling showed insigniﬁcant micro-delamination. In
addition, because the pins and composite holes were designed to be snug-ﬁtting, extra care

was required in assembling the composite joints.

5. Experimental Results

5.1 Joint Stiffness

Experimental results of joints stiffnesses for all tests are given in Table 4 along
with average values. The joints load-deformation curves were determined from the loads
measured by Instron testing machine load cell and deformations measured by the LVDT
mounted on the hydraulic actuator of the testing machine. The loads and deformations
were scanned at every one-tenth of a second. The stiffness of a joint was determined from

the slope of the linear portion of the load-deformation curve and is a measure of the rigid-

ity of the joint.

26

The stiffness were then divided by the corresponding bearing area, i.e. DH, to
determine the joint stiffnesses per unit bearing area. Both average values for stiffnesses
and stiffnesses per unit bearing area are given in Table 4 for comparisons. Apparently, the
stiffness increases as the pin diameter and composite thickness increase except for the
cases of D8H2, D8H1, and D2H8. It should be pointed out that these cases are located on
the upper right and lower left corners of Table 3.

Another signiﬁcant result was the efﬁciency of joint stiffness. also given in Table
4. The efﬁciencies of joint stiffnesses were obtained by normalizing the average stiff-
nesses per unit bearing area of all 16 cases with respect to the average stiﬁness per unit
bearing area of D8H8. The D8H8 joint represents a typical thin section joint with match-
ing pin diameter size whose structure behavior is well understood by the researchers. The
joint properities of D8H8 were used to normalize the properties of other joints to obtain
the efﬁciencies of the joints. It is noted that all cases have efﬁciencies lower that D8H8. In
fact, the efﬁciency of joint stiffness seems to decrease as the pin diameter or the composite
thickness increases. Besides, it was also found that among the four cases which have rela-
tively similar dimensions between pin diameter and composite thickness, i.e. D8H8,
D4H4, D2H2, and DlHl, the efﬁciency of joint stiffness reduces from 100% for D8H8 to
75% for D4H4, to 47% for D2H2, and to only 15% for DlHl. This result indicates the

important role of joint conﬁguration in mechanical joint designs.

5.2 Joint Strength and Bearing Strength

In this study, every composite joint was loaded until bearing failure took place.

27

The load—deformation relations for all 16 cases can be divided into three categories: type
A, type B, and type C. Type A represents load-deformation curve for composite joints
having an almost linear load-deformation relation until an abrupt (A for abrupt) loss of
load due to bearing failure. The load then picks up again until the ultimate load level is
reached. In type C, the linear load-deformation relation continuously (C for continuously)
changes into a smooth nonlinear relation without a local maximum or minimum. The third
type of load-deformation relation is named type B, which is an intermediate type between
(B for between) A and C. Figs. 3-5 show the three types of load-deformation relations, A,
B, and C, respectively. The types of load-deformation relation for individual joints are
identiﬁed and summarized in Table 5.

As mentioned above, every type A joint underwent an abrupt loss of load very
close to the end of linear load-deformation relation, and thus had a distinct local peak
force. This peak force was considered as the joint strength for type A joints since it
matched with bearing failure. Figure 3 shows the load-deformation relation for a D2H2
joint and the peak force. In addition, the offset deformation from the linear range at the
peak force could also be identiﬁed from the diagram. The offset deformation was then
divided by the pin diameter to determine the offset deformation percentage. Results for all
type A joints were given in Table 5. It can be seen that the offset deformation percentages
for type A joints are all smaller than 1%.

The typical load-deformation relation for type C joints can be found in Figure 4,
which is for a D4Hl joint. Apparently, it was difﬁcult to identify the joint strength due to
bearing failure since there was no local peak force in the load-deformation relation.

Although there were local peak forces for type B joints, e.g. the load-deformation relation

28

Table 5: Experimental results of the type of load-deformation relation. joint

*

strength. and offset deformation percentage from linear range.

 

 

 

 

 

 

 

 

 

 

 

8-ply 24-ply 40-p1y 80-ply
typelkN2%3 typckN% typekN‘7o typekN%
D/8 A 0.91 0.00 C 2.65 1.00 C 3.56 1.00 C 2.531.00
A 0.99 0.00 C 2.17 1.00 C 3.12 1.00 C 3.35 1.00
- - C 4.00 1.00 C 2.691.00
average“ 0.95 2.41 3.56 . 2.86
average“ 0. 1553 0.1286 0.1 180 0.0442
efﬁciency 1.00 0.83 0.76 0.28
D/4 A 1.74 0.16 A 6.89 0.69 C 10.90 1.00 C 10.681.00
A 1.54 0.34 A 6.55 0.95 C 9.910 1.00 C 10.96 1.00
A 1.33 0.00 A 6.38 1.07 C 9.163 1.00 C 10.17 1.00
- A 6.85 1.20 C 8.006 1.00 -
average“ 1.54 6.67 9.497 10.60
average“ 0.1256 0.1782 0. 1574 0.0819
efficiency 0.81 1.15 1.01 0.53
D/2 C 1.94 1.00 A 11.12 0.15 A 20.27 0.12 C 35.42 1.00
A 1.78 0.33 A 10.66 0.27‘ A 18.55 0.36 B 35.24 1.00
A 1.92 0.60 A 10.05 0.33 A 17.57 0.24 B 33.53 1.00
- A 10.78 0.90 A 19.91 0.40 -
average‘“ 1 .88 10.66 19.07 34.73
average“ 0.0768 0.1424 0. 158 1 0. 1343
efficiency 0.50 0.92 1.02 0.86
D B 3.42 1.00 A 19.57 0.12 A 30.69 0.25 B 58.84 1.00
B 3.08 1.00 A 19.26 0.12 A 32.43 0.13 B 51.55 1.00
A 3.34 0.50 A 18.73 0.17 A 31.14 0.13 B 51.58 1.00
B 3.72 1.00 - - B 58.94 1.00
average* 3.39 19.18 31.42 55.23
average“ 0.0691 0.1282 0. 1302 0. 1067
efﬁciency 0.45 0.83 0.84 0.69

 

type of load-deformation relation

joint strength in kN
offset deformation percentage from linear range

average joint suengths in kN

** average joint strengths per unit bearing area in GPa

29

 

for a D1H8 joint shown in Figure 5, they were far away from linear ranges. Accordingly, it
required a uniﬁed deﬁnition for determining the joint strength due to bearing failure for all
types of joints. Since the offset deformation percentages to bearing failure for type A
joints were all smaller than 1%, 1% offset deformation percentage was then used in deter-
mining the joint strengths for type B and type C joints. The joint strengths for all cases
were identiﬁed and are summarized in Table 5. It can be concluded that the joint strength
increases as the pin diameter and composite thickness increase except the D8Hl case.
The joint strengths given in Table 5 were also divided by the corresponding bear-

ing area to determine the joint strengths per unit area, i.e.

“3:171

where P is the joint strength. Since this actually represents the average stress around the
bearing area, it is also called bearing strength. The bearing strengths for all 16 cases are
also given in Table 5 along with the efﬁciencies of bearing strength. The efﬁciency of
bearing strength is deﬁned as ratio determined by normalizing the bearing strength of each
case with respect to the bearing strength of D8H8. As can be seen from Table 5, the efﬁ-
ciency of bearing strength remains high for cases close to the diagonal line formed by
D8H8, D4H4, and D2H2. However, the efﬁciency of bearing strength decreases for cases
located away from the diagonal line. This result seems to be similar to that observed for
the efﬁciency of joint stifﬁress to some extent.

The diagonal cases seem to have relatively higher efﬁciencies of bearing strength
than the non-diagonal cases except the DlHl case which has efﬁciency of bearing

strength of 69%. All joints of DlHl case have the type B load-deformation relation.

30

However, by closely examining these curves, they are found to have peak forces corre-
sponding 3% of deformation offset. If the 3% peak forces, instead of those based on 1%
deformation offset, are used as joint strengths, the average joint strengths will become
63,949 N rather than 55,226 N, and the efﬁciency of bearing strength will rise to 80%.

This result indicates the critical role of strength deﬁnition in mechanical joint analysis.
6. Discussions

6.1 Joint Type

Although there are a few exceptions, the type of load—deformation relations for all
16 cases given in Table 5 can be divided into two zones separated by the D8H8-D1H1
diagonal line. Most of the cases located above the diagonal line are of type C while those
located on and below the diagnoal line are primarily of type A. The sharp difference of the
load-deformation types between the zones is believed to be dependent on the bending
rigidity of pins. The upper right zone are joints with thick composites and small pins while
the lower left zone are joints with thin composites and large pins. As the loading level
increases, the small pins of the upper right zone bend and create highly local contacts with
the composites. These contact areas increase and become more uniform through the com-
posite thicknesses as the loading level increases. Accordingly, the type C cases in upper
right zone have a smooth nonlinear load-deformation relation following the initial linear
relation. In order to identify the type of a composite joints, the following calculation based

on strength of materials analysis is proposed.

31

Consider a pin with a length of 3H (double-lap joint) as shown in Figure 6. The

maximum bending stress in the pin can represented by:

OPP/)2
o _ My = 8 2 = 3PH
b 1 n04 41:03

4
which stands for bending stress in the steel pin. A ratio for bending stress t bearing stress

can then be deﬁned as

2
91: = 3H
03 41tD2

Table 2 gives the ratio of HZ/D2 for all 16 cases. The values of mm2 ratio can be divided

into two categories: smaller than unity and greater than unity. In comparison with Table 5,
it can be concluded that type A joints have H2/D2 ratios smaller than unity while type C

joints have HZ/D2 ratios greater than unity. The type A joints are deﬁned as bearing-mode
joints while the type C joints area called bending-mode joints. Since type B is an interme-

diate type between type A and type C, its failure mode can be either bearing mode or

bending mode.
6.2 Bending-Mode Joints (Type C Joints)
In the comparison of joint efﬁciencies, different considerations should be made to

different types of joint. For the joints dominated by pin bending mode, the comparison of

joint efﬁciencies should be based on a constant pin diameter. In this case, the joint

32

 

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strengths are expected to increase in proportion to thickness according to

P = 0301']

However, the joint strength actually ﬁrst increases then decreases. In fact, the efﬁciency of
bearing strength decreases as thickness increases. It is believed that the load-deformation
curve moves away from linear range as the steel pin indents composite material and
causes local bearing failure in composite. Since the strengths of bending-mode joints are
deﬁned at 1% deformation offset, the joint strengths are lower for thick composites with
small pins due to the premature local bearing failure. In other words, the loading level to
cause the local failure does not reﬂect the total capability of type C joints. As a summary,
the efﬁciency of joint strength is attributed to the two sources: (1) the positive contribution
from the increase of bearing area of DH, and (2) the negative contribution due to prema-
ture local bearing failure resulting from pin bending. This behavior can be expected for the

joint stiffness also.

6.3 Bearing-Mode Joints (Type A Joints)

The comparison of joint efﬁciencies for bearing-mode joints should be made based
on a constant composite thickness. In this case, the joint strengthsare expected to increase

in proportion to pin diameter according to

P = O'BDH

34

The joint strength does increase as pin diameter increases; however, the efﬁciency of joint
strength decreases. It is believed that the increase of pin diameter not only provides a
larger foundation for supporting a higher joint load but also weakens the integrity of the
composite laminates with the associated larger hole. The loss of composite integrity due to
the hole size increase has been known as the hole size effect [1 3]. As a summary, the efﬁ-
ciency of joint strength is attributed to the two sources: (1) the positive contribution due to
the pin diameter increase, and (2) the negative contribution due to the loss of joint strength
arising from the hole size effect. Similar arguments also hold good for the efﬁciency of

joint stiffness.

35

CHAPTER 3 COMPUTATIONAL METHOD

1. Finite Element Method

Although mechanical testing can give both stiffness and strength of a composite joint,
it cannot offer any information regarding details of joining characteristics such as the
interaction between the pin and the composite and the behaviors of individual elements. In
order to gain insight into the behavior of composite joints, e.g. the stress distribution
around the hole and the deformed shape of the pin, numerical method is required. In the
present study, a very common numerical method, namely ﬁnite element method, was used
for composite joint investigations. This method is not only useful for studying composite
structures with complex geometry, it is also suitable for exploring composite joints with
various conﬁgurations.

The ﬁnite element method is a numerical technique which provides an approximate
solution for boundary value problems. It has been used for solving a wide range of engi-
neering and physics problems. Because of its power in solving problems with complex
geometry, the ﬁnite element method has become a very common technique for computer
simulation in solid mechanics. For example, it is a process which is capable of predicting
deﬂections and stresses for a structure subjected to both static and dynamic. In the earliest
developments of ﬁnite element analysis, quite naturally almost all emphasis was directed
toward the development of effective ﬁnite elements for the solution of speciﬁc problems.
However, the potential of the method when used effectively on a digital computer was

rapidly realized, and increasingly larger and more complex ﬁnite element systems were

36

considered. This, in turn, enhanced the development of efﬁcient data-handling procedures
and effective techniques for the solution of the governing ﬁnite element equilibrium equa-
tions.

At present, computer programs are in use that can handle at reasonable cost very large
ﬁnite element systems, because the algorithms employed have been developed speciﬁ-
cally for ﬁnite element analysis. As a result of this development, when referring to ﬁnite
element analysis, a complete numerical process implemented on the digital computer is
implied.

Three steps should be performed in ﬁnite element method of analysis. First, ﬁnite ele-
ment pre-process designs the ﬁnite element mesh for the structures or problem investi-
gated, it is called ﬁnite element modeling. Finite element modeling is not just a way to
make pictures of structure parts and assemblies, it divides the problem geometry into a
mesh of elements which are used to calculate the stiffness of the structure and solve for
deﬂections, given the loads and boundary conditions. Second, ﬁnite element process per-
forms the ﬁnite element analysis to get the solutions for the problem studied. Finite ele-
ment program development is necessary in this step. Third, ﬁnite element post-process
analyzes the results from the ﬁnite element process, detail stress distribution diagrams,
deformation diagram, and single values can be obtained from this post-process, i.e. com-
plex simulation can be readily visualized and understood through post-process.

In this thesis, two commercial codes named F EMB and ABAQUS were involved in
the study. The former is a model generator to build ﬁnite element mesh while the latter is
a numerical solver for ﬁnding numerical solutions. That is, in the computer simulation

investigation, the ﬁnite element modeling software package FEMB was used in the

37

pre-process work, the ﬁnite element analysis software package ABAQUS was used in the
ﬁnite element process work and post-process work.

In the ﬁnite element method analysis study, both linear analysis and nonlinear analysis
were performed. Since the load-deformation relations were almost linear until bearing
failure took place, linear analysis was studied to obtain the detail stress information in the
joint structures. In the linear analysis, the composite material was linear orthotropic, and
the loading for each case was linearly proportional to the contact area in order to gain
identical contact mechanisms for all the cases. Nonlinear analysis was studied to obtain
the maximum loading before the bearing failure took place. In the nonlinear analysis, the

composite material was nonlinear, and the damage process was performed.

2. Finite Element Model

The composite join investigated in computer simulations was modeled as a double-lap,
single-steel-pin joint as shown in Figure 7. It is slightly simpliﬁed from the real experi-
mental joint conﬁguration as shown in Figure 1. In order to study the scaling effect of pin
diameter, four different pin diameters were investigated. In order to study the scaling
effect of composite thickness, four different composite thicknesses were investigated.
Accordingly, totally 16 cases were investigated in the study of scaling effect. The 16 cases
of composite joint, four composite thicknesses and four pin diameters, were assigned
names according to these two parameters for identiﬁcation purpose. Table 3 summarizes

the 16 names.

Different combinations of pin diameter and composite thickness will result in different

38

 

 

 

 

 

 

/////////// ////////////. ///

 

 

 

 

 

 

 

 

 

////////

 

 

 

 

Figure 7 - Schematic diagram for double-la
method.

contact conditions. Depending on the contact condition, the deformations and stress distri-
butions of the pin and the composite will be different and result in different stiffnesses and
strengths for composite joints. For example, a pin with small diameter used in a thick
composite material will not have the same uniform stress distribution along the pin as a
pin with large diameter used in a thin composite. Accordingly, the scaling effects - both
pin diameter and composite thickness - are important issues in composite joining and they
are the primary concern of the study.

The composite joint of concern is shown in Figure 7 where three composite plates hav-
ing the same width, thickness, and material properties are joined together by a steel pin.
The middle piece of the three composite plates is called central layer in this study, while
the remaining two plates are named outer layers. Due to the symmetry of composite mate-
rial, joint geometry, loading condition, and boundary condition, only one quarter part of
the composite joint needs to be considered in the ﬁnite element analysis. Figure 8 gives
the symmetric boundary condition and the coordinate system used in the computer simula-
tion. The l-direction (x-direction) is positive when pointing toward the right side of the
composite plate, the 2-direction (y-direction) is positive when pointing toward the top end
of the composite plate, and the 3-direction (z-direction) is positive when pointing from the
center layer to the outer layer. Also shown in the diagram are the loading direction and
ﬁxed boundary condition.

A ﬁnite element model generator named F EMB was used to build the ﬁnite element
mesh of all composite joints. In the process of mesh generation, a structure was divided
into a grids of “elements”. Each of the elements is a simple shape (in this study, the best

design should be cubic), for which the ﬁnite element program has information to write the

40

 

 

ﬁx y-direction

 

 

yz
symmetry

 

 

b———--——q

 

 

 

 

 

77

P

/'

__ y(2 W)

Ewe” v i i
P

Figure 8 - Symmetric boundary conditions for computer simulation model.

41

Table 6: Numbers of elements used around the hole edge.

 

 

 

 

 

 

 

 

 

 

8-ply 24-ply 40-ply 80-P1Y
DIS 8 8 8 3
DI4 18 18 18 13
D12 20 20 20 20
D 30 3o 30 30

 

42

 

Table 7: Numbers of layers used in the thickness directions.

 

 

 

 

 

 

8-p1y 24-p1y 40-p1y 80-ply
DIS 4 4 4 3
D/4 4 4 4 3
D/2 4 4 4 4
D 4 4 4 4

 

 

 

 

 

43

 

governing equations in the form of a stiffness matrix. The unknowns for each element are
the displacements at the “node” points, which are the points at which the‘elements are con-
nected. The ﬁnite element program will assemble the stiffness matrix for these simple ele-
ments together to form the global stiffness matrix for the entire model. This stiffness
matrix is solved for the unknown displacements, given the known forces and boundary
conditions. From the displacements at the nodes, the stresses in each element can be calcu-
lated. In F EMB ﬁnite element modeling, the basic geometry for the model was built ﬁrst,
then the created “curves”, “lines”, and “points” were transferred to form the “elements”
and “nodes”, where the “elements” were connected by “nodes”, and the structure mesh
was constructed by the “elements” and “nodes”.

In light of the three-dimensional models involved in the computer simulations of this
study, 8-node solid continuum ﬁnite elements were used. There were as many as 16,000
ﬁnite elements for most cases. Figure 9 shows the ﬁnite element mesh of DlHl case.
Since contact mechanism was the primary study in this computer simulation, the area
around the contact surface between the pin and the composite plate needed to be well
designed. Shown in Figure 10, the l, 2, and 3 directions are deﬁned in Figure 7 and Figure
8. The red lines in the Figures indicate the original mesh, and the black ones show the
mesh after deformation. Table 6 shows the number of elements around the hole and Table

7 shows the number of layers in the thickness direction for all the 16 cases.

2.1 . Material

The composite material properties investigated in the computational study was deﬁned

44

 

Figure 9 - The ﬁnite element mesh ofjoint DlHl.

45

 

 

Figure 10 - The ﬁnite element mesh around the contact area of joint DlHl.

46

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47

from the mechanical test. The linear orthotropic material properties obtained from experi-
ments and used in computer simulations are shown in Table 1. The nonlinear composite
material properties investigated was obtained from the mechanical test data as shown in
Figure 11. The material model in this computer simulation includes damage, resulting in
nonlinear behavior. It also includes various modes of failure, resulting in abrupt loss of
stress carrying capacity. The pin material was deﬁned as steel, with Young’s modulus of

206.8 Mpa, and Posson’s ratio of 0.3.

2. 2. Geometry

The composite joint structure in the ﬁnite element simulation is shown in Figure 7.
The symmetric conditions of the composite joint structure are shown in Figure 8.

The purpose of ﬁnite element model is to make a model that behaves mathematically
like the structure modeled, not necessarily one that looks like the real structure. So that the
accuracy of the resulting solution will depend on how well the structure was modeled,
what type of element used and how ﬁne to make the grid in different areas of the model is.
In general, the solution will be more accurate as the structure is subdivided into many ﬁne
elements.

In this study, before the investigation of the 16 cases, initial study was done in order to
verify the appropriate mesh for this mechanical joint structure. Case D1 H1 was performed
for this purpose. The reason for choosing case DlHl is that the area around the hole edge
in the composite plates needs more elements to obtain the ﬁner mesh. Since case D1111

has the largest thickness, it was assumed to be the most difﬁcult one to model. Enough

48

models for the case DlHl were designed, and the ﬁnal solutions from these models were
checked to be sufﬁciently converged, which means the solutions from the computer simu-
lations output were constant. Since the solid brick element used in this composite joint
structure modeling are deﬁned to assume that the strain is constant throughout the ele-
ment, in this study, the ﬁne ﬁnite element mesh requires the solid elements to be almost
cubic. According to the initial study for the case DlHl , for convenience of generating the
16 cases for computer simulations, four primary mesh were designed. The four primary
mesh were based on the same pin diameters, then were sealed in the thickness direction
from 2 mm to the other three sizes, 6 mm, 10 mm, 20 mm. For the D8H1, D8H2, D4Hl
cases, since the pin diameter sizes are much smaller compared with the composite thick-

nesses, the new designs were developed for the ﬁner meshes.

2. 3. Loading

In this computer simulation, the loading was applied to the bottom ends of the out lay-
ers in the downward direction, i.e., along the opposite 2 direction (y direction) in Figure 2,
with the central layer ﬁxed on the top end. The pin was snug-ﬁt into the holes of the com-
posite layers.

The loading-deformation relations were almost linear until bearing failure took place.
Since contact mechanisms were of the primary concerns in this study, in order to give
identical stress distributions in the composite materials and contact conditions, the load-
bearing levels of composite materials should be linearly proportional to the contact area

between the pins and the composite plates. The distributed loading applied in linear

49

analysis for each cases are shown in Table 8. Structural loading can be nodal forces
(forces directly applied at nodes) or pressures on the face or edge of an element (which are
converted to nodal forces internally). In this study, the distributed loading was performed
by nodal forces, that is, forces directly applied at the nodes on the bottom ends of the outer
layers. Each node was applied the same force to form the distributed loading.

Nonlinear analysis loading model was performed by displacement increment of the
cross-head of the outer layer composite plates where the loading was applied. In order to
obtain the distributed loading application, it was assumed that all the nodes on the cross-
head of the outer layer composite plates, where the loading applied, had the same dis-
placement at the same time. The displacement increment stopped after the bearing failure

took place.

2. 4. Boundary Condition

In ﬁnite element analysis, the boundary conditions are used to build analysis cases
containing loads and restraint boundary conditions to apply to the model. An analysis case
is a collection of degrees-of-freedom set, constraints, restraints, structural loads, and heat
transfer load. In this mechanical composite joint structure, only structural loads and
restraints were needed.

In this computer simulation, the nodes on the top end of the central layer were ﬁxed
while those on the bottom end of the outer layers were assigned with distribution loading
in the downward direction. The structural loads applied here are nodal forces. The

restraints were used to restrain the model to match with boundary conditions. Restraints

50

Table8: Loading used in ﬁnite element linear analysis.

 

 

 

 

 

 

unit: kN
8-ply 24-ply 40-ply 80-p1y
D/8 0.356 1.068 1.779 3.558
D/4 0.712 2.135 3.558 7.1 17
D/2 1.423 4.270 7. 1 17 14.234
D 2.847 8.540 14.234 28.468

 

 

 

 

 

51

 

had six values at each node for three translations and three rotations. In ﬁnite element
model, the restrains were deﬁned to have a value for the ﬁxed displacement, i.e. 0.0 gave
the degree fo freedon of no motion. Otherwise, the node was free to move. For example,
the nodes on the top end of the central layer had 0.0 value for the 2 direction (y direction).
Since the ﬁnite element model was of 12 symmetry (xy symmetry), and also 23 symmetry
(yz symmetry), the loading applied was of 12 symmetry (xy symmetry), and also 23 sym-
metry (yz symmetry), it was possible to model only a quarter part of the problem. The
symmetric boundary condition deﬁnitions were given to the central surfaces, i.e., the
nodes on the central surfaces had the restraint deﬁnition. Figure 8 shows the symmetric

boundary conditions of the ﬁnite element model.

2. 5. Contact Surface

In this study, the contact mechanisms of the joint structure were of the most important
concern. The scaling effects including the pin diameter scaling effect and composite thick-
ness scaling effect were studied from this contact mechanisms between the steel pin and
the composite plates. Therefore the contact interaction was deﬁned between the pin and
the composites. Since the loading applied in this composite joint structure was in-plane,
there was no need to deﬁne the contact interation between the composite plates, that is,
between the central layer composite plate and outer layer composite plates.

The motion of a body at any instant of time may be deﬁned by the linear velocity vec-
tor of an arbitrarily chosen point of reference in the body together with the angular veloc-

ity vector of the body. Sliding can be deﬁned as the relative linear velocity between the

52

two surfaces at the chosen point. Since the relative linear velocity between the pin and the
composite layers was small enough, the small-sliding capability can be used to model the
interaction between a deformable body and a rigid body in three dimensions. Small-slid-
ing contact surface was deﬁned between the pin and the composite layers. Figure 8 shows
the contact surfaces in bold line.

With the small-sliding contact approach in this mechanical joint structure, the steel pin
surface was deﬁned as “master” surface and the composites hole surface as “slave” sur-
face. A kinematic constraint that the slave surface nodes do not penetrate the master sur-
face was then enforced. The contacting surfaces need not have matching meshes;
however, the best accuracy was obtained if the meshes are initially matched. Detailed con-

tact stresses information were then obtained from computer simulation.

3. Finite Element Analysis

3. 1. Linear Analysis

Linear analysis was performed in the study since the stress-strain relation of the com-
posite material was almost linear until bearing failure took place, this analysis provided
detail stresses information of the composite joint structure. It should be pointed out that
the stresses information obtained from ABAQUS, the computational analysis were the
Cauchy stresses.

In this linear static analysis, the composite material properties were linear orthotropic,

and the loadings applied were distribution loading. In this structural problem, the initial

53

conﬁguration of the structure and its deformation throughout the history of loading can be
described clearly through this linear analysis. Detail information about the contact stresses
along the contact surface between the steel pin and the composite plates, and in-plane
stresses in the whole composite structure were obtained from this analysis. The joint stiff-
nesses and joint strengths of the composite joint structure were deﬁned through these
information. Then the mechanical composite efﬁciencies for all the 16 cases can be con-

cluded from these results.

3. 2. Nonlinear Analysis

Because of the geometric discontinuity involved in the mechanical joints, the stress
distribution is expected to be highly concentrated around the holes. The high local stress
concentration can cause isolated damage to the composite joint while the majority of the
joint remains intact. Accordingly, damage analysis is necessary for a complete simulation.
The nonlinear analysis which included nonlinear orthotropic material properties and dam-
age process was performed to ﬁnd the allowable loading in individual joint cases.

Failure modes in composites are strongly dependent on geometry, loading direction,
and ply orientation. Failure modes can be divided into in—plane failure modes and trans-
verse failures modes (associated with interlarninar shear and interlarninar normal stresses).
Experimental results showed that the major damage mode was of bearing mode, which
was essentially attributed to delarnination. In order to include delamination modeling lam-
inate analysis, interlaminar stresses need to be calculated. However, this will become

almost impossible since it requires many layers in the thickness direction to represent

54

laminate interfaces. This process can exhaust the computation quickly. Although it is pos-
sible to introduce a reﬁned plate theory for interlarninar stress analysis, it does not exist in
the current version of ABAQUS. As a compromise of taking advantage of the availability
of ABAQUS and honoring the fact of bearing damage, the bearing damage is considered
as compressive damage in computer simulation. Accordingly, in-plane failure modes are
considered. Therefore, ﬁve failure modes can be considered: matrix tensile cracking,
matrix compression, ﬁber breakage, ﬁber matrix shearing and ﬁber buckling. Since the
contact area in the composite plate was loaded in compression, all of the above ﬁve mech-
anisms, with the exception of ﬁber breakage are relevant to compression failure in the
composite joints.

The strength properties for the composite plates were obtained from mechanical test,
and were shown in Table 1. The strength parameters can be combined into Chang-Lessard
failure criteria [33]. The sharp load drop-off in the numerical results later discussed was
due to the lack of residual stress carrying capacity after the failure criterion is exceeded. In
the model analyzed here, four different failure modes are considered.

1. Matrix Tensile Cracking: It can occur due to a combination of transverse tensile
stress, and shear stress. The failure index can be deﬁned in terms of these stresses and the
strength parameters. When the index exceeds 1.0, failure is assumed to occur. The failure

index takes the form

 

20 2
——1¥—+3aoxy4
e 2 = (2)!) + GXJ’.
m Y 25 1
t c +3aSC4
ny

55

2. Matrix Compressive Failure: It can occurs due to a combination of transverse com-
pressive stress and shear stress. The failure criterion has the same form as for matrix ten-

sile cracking:

 

20 2
—xJL+3aoxy4
Y ZS +30tSC.4
xy

The same failure index is used since the above two failure mechanisms cannot occur
simultaneously at the same point. After the failure index exceeds 1.0, both the transverse
and shear stiffness of the ply drop to zero, and stresses can only be carried in the ﬁber
direction.

3. F iber-matrix Shearing Failure: It occurs due to a combination of ﬁber compression
and matrix shearing. The failure criterion has essentially the same from as the other two

criteria:

 

20x 2
-—L+3aox 4
e -
fs X z—C—S 2+301S 4
xy c

This mechanism can occur simultaneously with the other two criteria, and, hence, a sepa-
rate failure index is used. After the failure index exceeds l.0, shear stresses are no longer
supported, but direct stresses in the ﬁber and transverse directions continue to be sup-

ported.

4. Fiber Buckling Failure: It occurs when the maximum compressive stress in the ﬁber

56

direction exceeds the ﬁber buckling strength, independent of the other stress components:

__ 0'
eb_—/—Yx
C

It is obvious that, unless the shear stress vanishes exactly, ﬁber-matrix shearing failure
occurs prior to ﬁber buckling. However, ﬁber buckling may follow subsequent to ﬁber
shearing, because only the shear stiffness degrades after ﬁber-matrix shearing failure.
Fiber buckling in a layer is a catastrophic mode of failure. Hence, after this failure index
exceeds 1.0, it is assumed that the material at this point can no longer support any loads.

In this computer simulation, loading was canied by incremental displacement of the
cross section of the composite plates where the loading was applied. The failure occurred
when anyone of the failure indexes which were mentioned above exceeded 1.0. See Figure
12 for the nonlinear damage computer simulation process.

In this study, it is assumed that once failure occurs, the stresses in the damaged direc-
tions drop to zero immediately. In reality, the load carrying capacity degrades gradually
with increasing strain after failure. Hence, the behavior of the composite after onset of
failure is not likely to be identiﬁed accuratly by this model. Moreover, the instantaneous
loss of stress carrying capacity also makes the post-failure analysis results strongly depen-

dent on the reﬁnement of the ﬁnite element mesh and the ﬁnite element type used.

4. Computational Results

57

 

cm)
1

 

displacement => i

l
/......../

 

 

 

 

 

    
 

anyone of the four

 

i+l=i

 

 

 

 

 

 

 

 

Figure 12 - Nonlinear analysis computer simulation process.

58

1. Deformation

Figure 9 shows the original mesh in red color, and the mesh after the deformation in
black for case DlHl from linear analysis in front view, which is perpendicular to the xy
plane, see Figure 8 for directions. From this diagram, it is seen that the outer composite
layers and the central composite layer except the top surface have been moved downward.
Apparently, it is the reasonable result from this linear static analysis.

Color diagram of Figure 10 gives the original mesh which is around the contact area in
red color, and the mesh after the deformation in black for case DlHl from linear analysis
in front view, which is perpendicular to the xy plane, see Figure 8 for directions. It gives a
clear view on the deformation of the mesh around the contact area.

The contact surfaces of the composite plates which initially match the pin contact sur-
face before and after the deformation for the case DlHl has been shown in color diagram
of Figure 10, also in front view, where the red color shows the original surface and the
black one shows the surface after the deformation. It obviously shows that the contact sur-
faces of the composite plates have been moved downward. The reason of showing DlHl
case here is that it have relatively more elements around the contact surface than other
cases, so it may give better deformation behavior around the contact area of the composite
structure.

Figure 13 shows the deformation of the pin for case D8H1, which gives the clear view
for the bending behavior of the steel pin after the deformation. This case has the largest
thickness and the smallest pin diameter among the 16 cases. The deformation of the pin

after bending can be seen clearly.

59

 

Figure 13 - Bending behavior of the pin in joint D8H1.

60

 

Table 9: Bending behavior of the pin after deformation from linear analysis.

 

 

 

 

 

 

 

8—p1y 24-ply 40-p1y 80-p1y
D/8 598* 54.67 121.80 289.52
D/4 1.00 12.42 39.05 136.67
DIZ 0.00 5.00 8.50 40.25
D 0.00 0.00 1 .50 8.25

 

 

 

* modiﬁed by mutiplying 1o4

61

 

Bending behavior of the pin does exist in this mechanical composite structure. Table 9
shows the information of the bending behavior for all 16 cases. The values in this table are
the sine values of the angles between the very bottom line on the pin contact surface
before the deformation and after the deformation.

The sine values of the angles between the bottom line on the pin surface before the

deformation and after the deformation were obtained from the following equation:

 

displacementZ — displacement 1)
thickness

0 = sin—1(
where the displacement l is the displacement of the node which at the central end of the
bottom line on the pin surface, while displacement 2 is at the outer end in the ﬁnite ele-
ment mesh, and thickness is the thickness of the composite plates in each case.

From Table 9, the results report that the bending behavior of the pin in the composite
plates holes are different with the different pin diameter size and composite thickness. The
angle change is not proportional to the pin diameter and composite thickness change. It

will increase as the pin diameter decreases, while increases as the composite thickness

increases.

2. Contact Stresses

Since the contact mechanisms were of the primary concern in this computer simula-
tion, contact stresses were studied carefully for all 16 cases in the ﬁnite element linear

analysis. See color diagrams Figure 14 for the contact normal stresses (cpress) of case

62

DlHl, Figure 15 for the contact shear stresses in the 1 direction (shearl) of case DlHl,
and Figure 16 for the contact stresses in the 2 direction (shear2). The 1 and 2 directions are
x, y directions and are shown in Figure 8. From the color diagrams, it has obviously shown
that the maximum value of contact normal stresses between the pin and the composite
plate is not right at the central bottom point of the composite hole edge. Since the bottom
sides of the two composite outer layers were under the loadings in the downward direc-
tion, i.e., the y or 2 direction in Figure 8, and the top side of the central composite layer
was ﬁxed in the opposite of the loading direction, it is believed that the maximum contact
normal stress should be approximately at the central bottom point of the hole edge in the
central composite layer. In fact, due to the bending behavior of the pin, which was put
right through the composite holes, the maximum contact stresses locations was different
with the different pin diameter and composite thickness design in this composite joints.
Table 10 shows the locations of the maximum bearing stresses for all 16 cases, which
are indicated by the angles and thickness proportions. The angles here are between the yz
plane and the line which is connected by the center of the pin circle and the location where
the maximum bearing stress happened on the xy plane, see the diagram below the Table
10. The thickness proportions are the z coordination where the maximum bearing stress
happened divided by the thickness of the composite plates for each case. Since the loading
was applied on the bottom ends of the outer composite layers, and the top end of central
composite layer was ﬁxed. The contact surface between the pin and the composite plates
were under compressive loading, and the maximum contact bearing stress would be on the
contact surface between the pin and the central composite plate for sure. So that the

thickness proportion in Table 8 can be considered in another way, that is, 0 means the

63

  
 

  

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8 8 ~ s 8888... mg»...
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2.8%...
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u. a 8%...
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L . 1N.

Figure 14 - The contact normal stresses on the pin contact surface for joint D 1H1.

64

   

Figure 15 - The contact shear] stresses on the pin contact surface for joint DlHl.

65

    

\\\\\\

 

\\\\\\\\\\““\\\\\\\\\$ \ ..
88.888888.
8.888888

....288888
.88 .8888
m8 ....\ \

..x\
a?
aanuﬁgtt
4’96 633;”.
Genus-awn. ’fv”? 9555/04
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o 8 Z 6’ 9???

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H n I I’Iwosoon ”.4st

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Figure 16 - The contact shear2 stresses on the pin contact surface for joint DlH 1.

66

Table 10: Computed results of the node numbers and locations in polar

coordinates for the maximum bearing sresses.

 

 

 

 

 

 

8-ply 24-ply 40-ply 80-ply
22.5118" 22.5118 22.5118 22.5118

D/8 0.5" 0.5 0 .5 0
18.0091 18.0091 35.9989 18.0091

D/4 0.25 0 0 0
20.0101 20.0101 20.0101 20.0101

D/2 0.25 0.25 0 0
30.0152 30.0152 30.0152 30.0152

D 0.25 0.25 0.25 0

 

 

 

 

 

tﬁﬂh

67

 

location is right at the plane of the inner end of the central composite plate in the ﬁnite ele-
ment model, and 0.25 means the location is right at the central plane of the central com-
posite plate in the ﬁnite element model, and 0.5 means the location is right at the plane of
the outer end of the central composite plate in the ﬁnite element model.

From Table 8, it can be seen that the location of the maximum bearing stress has the
tendency to move from outer end of the central composite plate to the inner end of the cen-
tral composite plate as the composite thickness increases. And the location of the maxi-
mum bearing stress has the tendency to move from outer end of the central composite
plate to the inner end of the central composite plate as the pin diameter increases. This

result wil provide a valuable basis on designing thick composite joint structures.

3. In-plane Stresses

The computer simulation also gives the in-plane stress distributions in the whole struc-
ture. Take central composite plate as a example, Figure 17 shows the normal tensile
stresses, which are the stresses along the 1 direction of case DlHl, Figure 18 shows the
S12, which is the shear stress of case DlHl, Figure 19 shows normal compressive
stresses, which are the stresses along the 2 direction of case DlI-Il in different view point.
The 1, 2 and 3 directions are deﬁned in Figure 8.

These diagrams give the detailed information of the in-plane stresses in this composite
joint structure after the deformation. It should be noted that these results of in-plane

stresses distribution can only obtained from the ﬁnite element linear analysis.

68

 

 

Figure 17 - The in-plane tensile stresses of the central composite plate for joint D1H1.

69

       
  
  
  

 

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#:1’QIIIIIIIIIIII
I 0
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lllll
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Figure 18 - The in-plane shear stresses of the central composite plate for joint DlHl.

70

 

 

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71

4. Joint Stiffness

Computational results of joint stiffnesses for all cases are given in Table 11. The joint
stiffnesses were obtained from the loading divided by the displacement of the composite
outer layers ends where the loading applied in the computer simulations, and from divid-
ing the forces output from the load cell by the cross-head movement in experimental
investigations. It obviously shows that the joint stiffness increases as the pin diameter and
composite thickness increase except the cases of D8Hl and D8H2. The change of the joint
stiffness is not linearly pr0portional to the thickness or the pin diameter change. It should
be noted that the cases D8Hl and D8H2 are located on the upper right corner of the Table
11.

Table 11 also gives the results of the efﬁciencies of joint stiffnesses. The efficiencies
were obtained from normalizing the stiffnesses per unit bearing area of all 16 cases by that
of D8H8, where the joint stiffnesses per unit area were obtained from the joint stiffness
divided by the corresponding bearing area-DH. The results show that the efﬁciencies of all
cases are lower than case D8H8, and the efﬁciency of joint stiﬁness decreases as the pin
diameter or the composite thickness increases except D8H8 case. It also shows that the
efﬁciency of joint of the four cases, D8H8, D4H4, D2H2, and D111], which have rela-
tively similar dimensions between pin diameter and composite thickness, reduces from
100% for D8H8 to 57% for D4H4, to 32% for D2H2, and to only 16.9% for DlHl. It indi-
cates that the joint conﬁguration is playing an important role in mechanical joint design.

The computer simulation result of thickness scaling effect, which is based on constant

pin diameters, matches the mechanical test result. But the computer simulation result of

72

Table 11: Joint stiffnesses from both experiments and computations.

 

 

 

 

 

 

 

 

 

 

unit: kN/mm
8-p1y 24-ply 40-ply 80-ply
D/8 2.899 7.661 6.938 4.419
(2.309)* (5.547) (5.398) (1.980)
efﬁciency 1.00 0.88 0.47 0.15
Dl4 3.385 10.02 15.92 20.276
(3.452) (10.52) ( 14.3 1) (14.78)
efﬁciency 0.58 0.576 0.55 0.35
D/2 3.842 11.41 18.53 35.56
(3.002) (13.56) (21.36) (27.40)
efﬁciency 0.33 0.327 0.32 0.31
D 3.983 1 1.83 19.63 38.40
(5.512) (15.32) (21.69) (29.68)
efﬁciency 0. 171 0. 170 0. 169 0. 166

 

* experimental results in parentheses

 

in-plane scaling effect, which is based on constant composite thickness, matches the
mechanical test result except case D2H8. The reason for this mismatch is probably
because that the ﬁnite element mesh is not ﬁne enough. This reason may also be applied to
explain the discrepancy between the computer simulation results and the mechanical test
results. It should be pointed out that more elements used for ﬁner ﬁnite element mesh will
result in more computer memory. Due to the limit of the computer resource, proper ﬁnite
element mesh was designed in this computer simulation study. The comparison of the
joint stiffnesses between the computer simulation and the mechanical test is shown in Fig-

ure 20.

5. Joint Strength

Computational results of j oint strengths for all cases were given in Table 12 along with
the experimental results. The joint strengths in the computer simulations were obtained
from the multiplying of the yielding stress by the loading. The combined value was then

divided by the maximum contact normal stresses, i.e.

strength: w x loading
mcpress

where the yielding stress of 153.14 MPa determined from an independent bearing test was
used as the strength to bearing failure, and mcpress is the maximum contact normal
stresses obtained from the contact stresses output from the computer simulation.

Table 12 also gives the results of the efﬁciencies of the joint strengths. The efﬁcien-

cies were obtained from nomalizing the joint strengths per unit bearing area of all 16 cases

74

STIFFNESS (KN/mm)

 

so ,

 

 

 

 

 

 

 

l l l
O B-ply
A 24—ply
45 b D 40-ply _
0 BO—ply
- experiment
40 h computation ‘
....... 4
35 ,_ o . . . -
30 1—
25 - _
2°” ° ............. 7i
. .[3 ........................
a .
15 L ,,
_ . A ...................................... ,4
10 - , 2 . -
AV:
0
5 F-
: - ’
0 4 1 + i
PIN DIAMETER (mm)

Figure 20 - Comparison of joint stiffnesses.

75

Table 12: Joint strengths from both experiments and computations.

 

 

 

 

 

 

 

 

 

 

unit: kN
8-ply 24-ply 40-ply 80-ply
D/8 0.792 2.678 2.945 3.901
(0.952)* (2.406) (3.558) (2.860)
1 .000 l .170 0.773 0.527
BM 1 .597 4.795 7.909 8.807
(1.539) (6.668) (9.497) (10.600)
1.048 1.050 1.039 1.158
D12 3.145 10.004 17.218 35.264
( 1.882) (10.657) (19.073) (34.730)
1.033 1.095 1.131 1.158
D 6. 196 20.007 34.472 59.283
(3.390) (19.184) (31.416) (55.226)
1 .017 1 .093 1.094 0.794

 

* experimental results in parentheses

76

 

by that of D8H8. The joint strengths per unit bearing area were obtained from dividing the

joint strengths by the corresponding bearing area-DH, i.e.

153.14 x loading

efficiency: mcpress D x H

where D is the pin diameter, and H is the composite thickness of the mechanical compos-
ite joint structure. Figure 21 shows the comparison of joint strengths between the experi-

mental results and computational results.

6. Damage Analysis

Reduced integration element type, which uses a lower order integration method to
form the element stiffness, was applied in the nonlinear damage analysis in order to gain
more accurate results. Load-displacement curve for case D1H1 is shown in Figure 22. It
shows that the load-displacement relation is nonlinear due to the nonlinear stress-strain
relation in composite plates and damage process. The maximum forces for all 16 cases are
shown in Table 13. It is deﬁned that the failure occurs right at the maximum loading and
the peak-force in load-displacement curve is the maximum loading of the composite joint.

The maximum loading can be applied to this double-lap, single-pin mechanical com-
posite joint, which was deﬁned as joining strength increases as the pin diameter and the
composite thickness increase. See Table 13. The joining strengths change with different
pin diameter and composite thickness, but not proportional to the pin diameter and com-

posite thickness.

The efﬁciencies for the joining strength were also shown in Table 13. The efficiencies

77

 

60 1 I I I

 

 

 

 

 

0
O B‘ply
A 24- l
50 - Dy ‘
CI 4o_ply
<> 80—ply
H compmatk)"

40 _ q
2 "I .d
5 _.
E
(D 30 _ -
Z
“J
CK
.-

(D
20 b
.0”
10L ’3 ﬂ
3 ......... c
e/ '. .V ....................
- . .......... . . O ..... ﬂ
0 MI I J J
o 5 10 15 20 25
PIN DIAMETER (mm)

Figure 21 - Comparison of joint strengths.

78

Loading (10)

14000 I

 

12000

I

10000

I

 

2000 ' 1 I

l

l

l

l

l

 

0

0.01

0.02

 

0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Extensometer measurement dE (in)

Figure 22 - Load-deformation relation of joint DlHl from computational results.

79

were obtained from the joining strengths divided by the corresponding contact bearing
area, then normalized by dividing that of the case D8H8. The result shows that the efﬁ-
ciency of all cases are lower than that of the case D8H8, and the efﬁciency of the maxi-
mum load applied decreases as the pin diameter or the composite thickness increases. The
comparison of the joining strengths between the nonlinear computer simulation results
and the experimental results is shown in Figure 23.

The discussions for efficiencies of joining strength in the nonlinear analysis can be
carried out the same way as the linear analysis. That is, the 16 cases investigated here
should be divided into two composite joint mode, one is bearing-mode joint and the other
is bending-mode joint. The bearing-mode joints have relatively large pin diameter and
small composite thickness, and should be discussed based on constant composite thick-
ness. The results give that the efﬁciency of joining strength decreases as the pin diameter
increases. The bending-mode joints should be discussed based on constant pin diameter.
The results give that the efficiency of joining strength decreases as the composite thick-
ness increases.

The load-displacement curve in the computer simulations drops off sharply after the
maximum loading is reached as discussed earlier. This is due to the lack of residual stress
carrying capacity after failure. It should be pointed out that the results from computer sim-
ulation are strongly depended on the ﬁnite element mesh. Figure 24 shows the extended
damage in the central composite plate at the maximum loading for case D8H1. Layer 1, 2,
3 and 4 are the ﬁnite element layers from the inner to outer. Damage initially took place at
the location where the stress concentration located, and then propagated along the contact

area between the pin and the central composite plate. From Figure 24, it can be found that

80

Table 13: Joint strengths from experiments and nonlinear computations.

 

 

 

 

 

 

 

 

 

 

unit: kN
8-ply 24-ply 40-ply 80-ply
D/8 0.832 2.523 3.001 3.459
(0.952)"I (2.406) (3.558) (2.860)
efﬁciency 1.000 1 .01 1 0.721 0.416
D/4 1.594 5.893 8.706 9.358
( 1.539) (6.668) (9.497) ( 10.600)
efﬁciency 0.958 1 . 18 1 1 .046 0.560
D12 2.792 10.187 17.992 35.073
( 1.882) ( 10.657) ( 19.073) (34.730)
efﬁciency 0.834 1.020 1.081 1.054
D 5.617 19.799 33.846 58.384
(3.390) (19.184) (31.416) (55.226)
efﬁciency 0.0844 0.9915 1.017 0.877

 

 

* experimental results in parentheses

81

 

50

 

 

 

 

 

l I I I
A 24-piv
45 _ ‘3 40-ply
° Bil-DIV
"' experiment
40 _ ° °°mPutation
35 p ..............................
o ..........
’5 3° -
E
2 6
2‘.
$3 25 —
1.1.1
2
U.
k H
P . ' a .......................................
"’ 20 -
.5
15 —
10 -
5 —
0
0 1 . I I
0 5 10 15 20
PIN DIAMETER (mm)

Figure 23 - Comparison of joint strengths.

82

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Layer 1 Layer 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 24 - Extended damage of D8Hl joint.

83

 

 

the damage occurs around the hole edge at the outer part of the composite plate. It is
believed that the relatively small pin diameter and the large thickness of this case are
attributed to the bending behavior.

The joining stiffness is actually the slope of the linear part of the load-deformation
curve. Table 14 gives the joining stifﬁiess for all 16 cases. The discussions for the joining
strength are feasible to the joining stiffness, i.e. the 16 cases investigated can be divided
into two composite joint mode. Bearing-mode joints have relatively large pin diameter and
small composite thickness, and should be discussed based on constant composite thick-
ness. The results give that the efﬁciency of joining stiffness decreases as the pin diameter
increases. Bending-mode joints have relatively small pin diameter and large composite
thickness, and should be based on constant pin diameters. The results give that the effi-
ciency of joining stiffness decreases as the composite thickness increases. Figure 25
shows the comparison of the joining stiffness between the experimental results and the

nonlinear computer simulation results.

84

Table 14: Joint stiffnesses from experiments and nonlinear computations.

 

 

 

 

 

 

 

 

unit: kN/mm
8-ply 24—ply 40-ply 80-ply
D/8 2.542 6.983 6.372 3.590
(2.309)* (5.547) (5.398) ( 1.980)
efﬁciency 1 .00 0.91 0.50 0. l4
D/4 3.397 10.31 15.07 18.39
(3.452) (10.52) (14.31) (14.78)
efﬁciency 0.67 0.68 0.60 0.36
D/2 3.539 12.45 20.96 33.83
(3.002) (13.56) (21.36) (27.40)
efﬁciency 0.35 0.409 0.413 0.33
D 4.752 12.97 20.38 35.68
(5.512) ( 15.32) (21.69) (29.68)
efﬁciency 0.23 0.21 0.20 0.17

 

 

 

85

* experimental results in parentheses

 

STRENGTH (kN)

 

60 1 1 T

 

 

 

 

 

l
O 8-ply
A 2
so _ 4-pty _,
0 40-ply
<> BO-piy
— experiment
computation
40 - -
30 ~ _
20 - .
.'D..
10- -
............ 4
./ ' .................
5' ............... 9 ------ ‘1
o M l l l
0 5 10 15 20 25
PIN DIAMETER (mm)

Figure 25 - Comparison of joint stiffnesses.

86

CHAPTER 4 CONCLUSIONS AND RECOMMENDATIONS

1. Conclusions

The following conclusions could be drawn from both experimental and computational

studies:

1. The bending behavior of the pin does exist in mechanical composite joints. The location
of the maximum contact-bearing stress in the composite joints, which is considered as the
starting point of damage process, is strongly affected by the bending behavior of the pin.
The results of the bending behavior of the pins for all 16 cases investigated contribute to

the thick composite joints design.

2. The linear analysis and nonlinear damage process based on the compression failure
model have been used to characterize the mechanical composite joints. The joint stiff-
nesses, the joint strengths, the stress distribution in the joint structure can be obtained from
the investigations. Deﬁnitions for the joint stiffness and joint strength in both experimen-

tal investigation and computer simulation were developed in this thesis.

3. The joint stiffnesses and joint strengths for all 16 cases are not proportional to the bear-
ing area. In other words, both the joint stiffnesses per unit bearing area and the joint
strengths per unit bearing area are different for various cases. These results indicate that

there exist different contact mechanisms for the cases investigated. It is to say that thick-

87

‘ ‘ ' .51

ness scaling effects do exist in mechanical joints.

4. The contact mechanisms for all 16 cases investigated can be divided into two catego-
ries: bending-mode and bearing-mode. Most of the cases located above the diagonal line

formed by D8H8 and DlHl cases belong to bending mode while the remaining cases
belong to bearing mode. The ratio of H2/D2 can be used to distinguish the types of contact

mode. A composite joint with HZ/D2 greater than unity, a bending-mode contact between
the pin and composite is likely to take place. Otherwise, the contact mode will be essen-

tially of the bearing-mode.

5. The comparisons of joint efﬁciencies can be separated into two categories according to
the type of the joint mode. For the cases dominated by bending-mode, the comparisons
should be based on constant pin diameters. Both efﬁciencies of joint stiffness and joint
strength decrease as the composite thickness increases. It is believed that the joint stiffness
and joint strength should increase in proportion to the thickness increase. However, the
increasing rates are hindered by the premature local failure due to the bending of small pin

in thick composite.

6. The comparisons of joint efﬁciencies for bearing-mode joints should be based on con-
stant composite thicknesses. Both efﬁciencies of joint stiffness and joint strength decrease
as pin diameter increases. It is believed that the joint stiffness and strength should increase
in proportional to the pin diameter increase. However, the increasing rates are hindered by

the hole size effect, i.e. the reduction of composite integrity due to the hole diameter

88

increase.

7. From the nonlinear damage process, maximum loading for each case can be found. The
maximum loading was deﬁned as the loading where the damage to occur in the composite
plates, and was studied as joining strength in this thesis. Initially, damage took place at the
location where the stresses are highly concentrated. It then propagated along the bottom

area on the contact surface between the pin and central composite plates.

8. In addition to the low efﬁciencies in stiffness and strength, the ﬁnite element simula-
tions for composite joints made of thick plates with small pins and thin plates with large
pins also experience large numerical discrepancies when compared with experimental
results. It is believed that the larger differences between the pin diameter and composite

thickness in these two cases require much ﬁner mesh for ﬁnite element analysis.

2. Recommendations

From the comparisons between computer simulations and experimental investigations,
it is found that the results from the ﬁnite element simulations bear some degree of error.
The possibility for the discrepancy between computer simulation and experimental inves-
tigations is due to the coarse ﬁnite element meshes used in the study. Finer ﬁnite element
mesh are needed for the future work.

Although experimental technique can give both stiffness and strength of the mechani-

cal fasteners, it is not able to offer the detailed stress distribution around the contact

89

surface. A whole-ﬁeld optical method and a new technique for measuring contact force
should be developed for the experimental analysis.

It must be very valuable if some conclusions drawn from relative thin composites can
be extended to thick composites. This thesis concludes the importance of the thickness
scaling effects in composite joint structures. The investigations on thickness scaling

effects in composites should be carried out in many ﬁelds.

90

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