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CONTENTS
Page
WORD OF WELCOME
LIST OF FIGURES
LIST OF TABLES
xi
vi
ix
STUDY UNIT 1 INTRODUCTION TO COMPOSITES1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
1.15
1.16
1.17
Learning objectives
Introduction
Classification of materials
Advanced materials
Important definitions of composites
Constituents of composites
Importance of composites
General classification of composites
Polymer matrix composites (PMCs)
Metal-matrix composites (MMCs)
Ceramic-matrix composites (CMCs)
Carbon–carbon composites Lamina composites
Sandwich composites
Nanocomposites
Summary
Practice problems
1
1
2
5
5
6
8
10
11
13
14
15
16
18
19
19
20
STUDY UNIT 2: PROCESSING OF COMPOSITES
22
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
22
22
22
23
23
31
33
33
Learning objectives
Introduction
Abbreviations
Guide to processing composites
Fabrication processes
Cost comparison
Summary
Practice problems
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STUDY UNIT 3 PROPERTIES OF COMPOSITES
34
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
34
34
36
47
48
48
49
49
Learning objectives
Geometric and physical definitions
Reinforcement of composite materials
Properties of polymer matrix composites
Properties of metal-matrix composites
Properties of ceramic matrix composites
Summary
Practice problems
STUDY UNIT 4 ELASTIC BEHAVIOUR OF COMPOSITE LAMINA
55
4.1
4.2
4.3
4.4
4.5
55
55
56
62
66
Learning objectives
Introduction
Micromechanical predictions of elastic constants
Stress-strain relations in macromechanics
Problems
STUDY UNIT 5 DAMAGE IN COMPOSITES
70
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
70
70
71
76
77
78
88
90
90
Learning objectives
Introduction
Damage mechanisms
Development of damage in composite laminates
Damage mechanics
Analysis of fracture
Problems
Summary
Activities
STUDY UNIT 6 FATIGUE OF COMPOSITES
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
Learning objectives
Introduction
Fatigue life diagram and the fatigue behaviour of composites
Effects of constituent properties
Unidirectional composites loaded parallel to the fibres
Fatigue of laminates
Failure criterion for a laminate
Summary
Activities
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iv
92
92
92
93
93
94
102
105
106
106
Co nte nt s
STUDY UNIT 7 DESIGN OF COMPOSITES
108
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
108
108
109
111
112
114
120
123
125
133
137
140
Learning objectives
Introduction
Design methodology
Fatigue resistance
Guideline values for predesign
The laminate
Strengths of composite materials
Design example 7.1
Design example 7.2
Design example 7.3
Design problems
Design verification process
STUDY UNIT 8 NON-DESTRUCTIVE TESTING OF COMPOSITES
142
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.14
8.15
8.16
8.17
8.18
8.19
8.20
142
142
143
143
144
144
145
147
148
149
149
149
150
150
150
151
151
152
154
154
Learning objectives
Introduction
Inhomogeneity factors that can affect composite performance
The purpose of non-destructive testing
Visual inspection
Tap test
Ultrasonic methods
X-radiography
Acoustic emission
Acousto-ultrasonics
Eddy current testing
Infrared thermal testing
Laser shearography or holography
Microwave testing
Contact methods and non-contact methods
Physical properties and structural integrity
Inspection type versus NDT method
Conclusion
Activities
Reference list
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CO N T EN T S
LIST OF FIGURES
Figure 1.1
The different constituent forms in composites
7
Figure 1.2
Makeup of the interface between fibre and matrix
8
Figure 1.3Classes of composites based on the form of the structural constituents
11
Figure 1.4Lamina and principal coordinate axes: (a) unidirectional reinforcement and
(b) woven fabric reinforcement
16
Figure 1.5
Multidirectional laminate and reference coordinate system
16
Figure 1.6
Aluminium composite material panel structure
18
Figure 2.1
Steps in moulding process
24
Figure 2.2
Contact moulding
24
Figure 2.3
Compression moulding
26
Figure 2.4
Vacuum moulding
27
Figure 2.5
Resin injection moulding
28
Figure 2.6
Centrifugal moulding
29
Figure 2.7
Filament winding
29
Figure 2.8
The pultrusion process
31
Figure 2.9
Cost comparison for different processes
32
Figure 3.1Macroscopic (A, B) and microscopic (a, b) scales of observation for
unidirectional layers
35
Figure 3.2
Unidirectional discontinuous fibre composite
37
Figure 3.3
Randomly oriented discontinuous fibre composite
37
Figure 3.4
Unidirectional continuous fibre composite
38
Figure 3.5
Cross-ply continuous fibre composite
38
Figure 3.6
Multidirectional continuous fibre composite
39
Figure 3.7Deformation pattern in the matrix surrounding a fibre that is subjected to
an applied tensile load
40
Figure 3.8Stress-position profile when the fibre length l (a) is equal to the critical
length lc, (b) is greater the critical length, (c) is less than the critical length
for a fibre-reinforced composite that is subjected to a tensile stress equal
to the fibre tensile strength σf41
Figure 3.9Longitudinal and transverse directions illustrated on a unidirectional
continuous fibre composite
41
Figure 3.10(a) Schematic stress–strain curves for brittle fibre and ductile materials
(b) Schematic stress–strain curve for an aligned fibre-reinforced composite 42
Figure 4.1Transverse modulus of unidirectional composites as a function of fibre
volume ratio
59
Figure 4.2In-plane shear modulus of unidirectional composites as a function of fibre
ratio61
Figure 4.3
Orthotropic material with transverse isotropy
64
Figure 5.1
Debonds in a fibre-reinforced composite
72
Figure 5.2Matrix crack initiation from: (a) fibre debonds; and (b) void
results
73
Figure 5.3
Extensional and shear modes of fibre microbuckling
74
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Co nte nt s
Figure 5.4
Damage mechanisms in particulate composites
75
Figure 5.5Spacing of cracks in –45° plies of 0/90/±45s graphite/epoxy laminates as a
function of quasi-static and fatigue loading
76
Figure 5.6
Development of damage in composite laminate
77
Figure 5.7Griffith crack: a through-thickness crack in a uniaxially stressed plate of
infinite width
78
Figure 5.8
Stresses at the tip of a crack under plane stress
81
Figure 5.9
Three basic modes of crack deformation
82
Figure 5.10Loaded plate and corresponding load-displacement curve used for strain
energy release rate analysis: (a) plate under uniaxial load and (b) loaddisplacement curve
82
Figure 5.11Single edge crack in a plate under uniaxial stress for example 5.2
85
Figure 5.12Sandwich beam in four-point flexural loading, along with corresponding
shear force and bending moment diagrams
86
Figure 5.13
Mode II shear crack for example 5.3
87
Figure 5.14Thin-walled tubular composite shaft with longitudinal crack
88
Figure 5.15
Variation of specimen compliance with crack length for problem 5.6
89
Figure 6.1Fatigue life diagram of a unidirectional fibre-reinforced composite
subjected to cyclic tension in the fibre direction
93
Figure 6.2
Trends in fatigue life diagrams due to constituent properties
94
Figure 6.3Stress/life data of a unidirectional glass/epoxy composite loaded in tension
parallel to the fibres
95
Figure 6.4Fatigue life diagram of a unidirectional glass/epoxy composite loaded in tension parallel to the fibres
96
Figure 6.5Effect of fibre stiffness and strain to failure on composite stiffness in a
unidirectional composite in longitudinal loading
(a) composite with low stiffness fibres; and (b) composite with high stiffness
fibres96
Figure 6.6Fatigue life diagram of unidirectional composite reinforced by stiff fibres
with low strain to failure 97
Figure 6.7Fatigue life diagram of unidirectional composite reinforced by medium
stiffness fibres, showing a narrow range of strain where fatigue occurs
98
Figure 6.8Fatigue life diagram of a unidirectional composite with low stiffness fibres,
with a relatively wide range of strain where fatigue occurs
98
Figure 6.9Fatigue life of a unidirectional carbon fibre/epoxy composite with a distinct
region I
99
Figure 6.10Fatigue life diagram of a unidirectional Kevlar fibre/epoxy composite
100
Figure 6.11Fatigue life diagram of a unidirectional Kevlar fibre/J2 polymer composite 100
Figure 6.12Multiple matrix cracks in the off-axis ply of a laminate
(left) and subsequent delamination caused by fatigue (right)
103
Figure 6.13Experimental data verifying the anticipated fatigue life
diagram of cross-ply laminates
104
Figure 6.14Fatigue life data for a glass/epoxy 0/±45/90s laminate under
tension–tension loading along 0° direction 105
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CO N T EN T S
Figure 7.1Comparison of the fatigue behaviour of a composite and
aluminium111
Figure 7.2
Comparison of the characteristics of different materials
112
Figure 7.3
Specific characteristics of different fibres
113
Figure 7.4Levels of observation and types of analysis for composite
materials114
Figure 7.5
Effect of ply orientation
116
Figure 7.6
Poor design
117
Figure 7.7
Mediocre design
117
Figure 7.8
Good design
118
Figure 7.9
Common orientations
119
Figure 7.10
Stresses and stress resultants
120
Figure 7.11The specific tensile modulus of various composite materials
121
Figure 7.12
Costs of composite materials
121
Figure 7.13
Example: Trade study of beam with a uniform load
123
Figure 7.14Thin-wall cylindrical pressure vessel under internal
pressure and torque loading
125
Figure 7.15Effect of lamination angle on allowable thickness of [±θ]ns
angle-ply laminate in pressure vessel
126
Figure 7.16Ranking of different material systems and laminate layups
according to weight for pressure vessel design example
133
Figure 7.17
Schematic representation of a tubular composite shaft
134
Figure 7.18A three-point loading scheme for measuring the
stress–strain behaviour and flexural strength of brittle
ceramics134
Figure 7.19
Component verification process
141
Figure 8.1
Tap test with tap hammer
145
Figure 8.2
Ultrasonic testing method
145
Figure 8.3
Pulse-echo test equipment
146
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Co nte nt s
LIST OF TABLES
Table 2.1Advantages and limitations of hand layup and spray-up
processes25
Table 2.2
Advantages and limitations of a filament winding process
30
Table 2.3
Advantages and limitations of a pultrusion process
31
Table 3.1Classes of fibre-reinforced composites according to the matrix used
(polymer, metal, ceramic or carbon matrix composites
39
Table 3.2 Typical longitudinal and transverse strengths for three unidirectional
fibre-reinforced composites
45
Table 3.3 Properties of unreinforced and reinforced polycarbonates with randomly
oriented glass fibres
46
Table 3.4Properties of continuous and aligned glass, carbon and aramid fibrereinforced epoxy-matrix composites in longitudinal and transverse
directions47
Table 3.5 Properties of several metal-matrix composites reinforced with continuous
and aligned fibres
48
Table 3.6Room temperature fracture strengths and fracture toughnesses for various
SiC whisker contents in Al2O3 48
Table 4.1
Independent elastic constants for various types of materials
66
Table 7.1
Design methodology for structural composite materials 110
Table 7.2
Typical materials data for a preliminary design 123
Table 7.3
Results of design trade study of composite beam 124
Table 7.4
Optimum [0m/90n]s layup for three composite materials 127
Table 7.5
Optimum [±θ]ns layup for three composite materials 129
Table 7.6
Optimum [90/±θ]ns layup for three composite materials 130
Table 7.7
Optimum [0/±θ]ns layup for three composite materials 130
Table 7.8
Optimum [0/±45/90]ns layup for three composite materials
131
Table 7.9
Summary of optimum layups for three composite materials 132
Table 7.10Elastic modulus, density and cost data for glass, various
carbon fibres and epoxy resin 135
Table 7.11Fibre and matrix volume fraction for glass and three carbon fibre types as
required to give a composite modulus of 69.3 GPa 136
Table 7.12Fibre and matrix volumes, masses, costs and total material
cost for three carbon fibre epoxy-matrix composites 137
Table 8.1
Contact and non-contact NDT methods
150
Table 8.2
Category of NDT methods based on the detecting factors
151
Table 8.3
Inspection type and NDT methods 152
Table 8.4
Summary of applicability of NDT methods 154
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WO R D O F W ELCO M E
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Wo r d o f we l co m e
WORD OF WELCOME
Welcome to the module Engineering Material Technology II – EMT3701. This study guide presents the course contents and most of the information that you will require for the course. You
are advised to familiarise yourself with the contents of the study guide to facilitate your study
of this module. Information on all assessments, what is expected of you and what you should
expect of the lecturer is provided in the tutorial letters for this module. Each study unit includes
several tutorial questions that you should answer on your own. The answers to these questions
will be made available in due course. The aim of the questions is to promote self-activity and
assist you in achieving success in this module.
The two prescribed texts for this module are the following:
(1)Daniel, IM & Ishai, O. 2006. Engineering mechanics of composite materials. New York:
Oxford University Press.
(2)Peters, ST. 1998. Handbook of composites. 2nd edition. London: Chapman & Hall.
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1
Study unit 1
INTRODUCTION TO COMPOSITES
1.1
LEARNING OBJECTIVES
After students have studied this study unit and chapter 2 of Daniel and Ishai (2006), they
should be able to
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classify conventional materials used in engineering and list their special features
describe advanced materials, and list the types of advanced materials and their special
features
differentiate between matrix and reinforcement
describe the various functions of the matrix
describe the various functions of the reinforcement
explain the importance of composite materials in engineering
define the basic terminology used in the field of composite materials, such as
composite, fibre, matrix, lamina, laminate and monolithic
demonstrate an understanding of the applications of the interface
name and compare the advantages and disadvantages of composites and monolithic
materials
classify composite materials
1.2
INTRODUCTION
In the module Engineering Material Technology 2 we examine how composite materials
are produced, processed and used in engineering for the betterment of society. In this
module we discuss the fundamental structure of composite materials and how this
structure determines the underlying physical properties of a composite. Understanding
these aspects enables you to develop the fundamental knowledge of a composite
material’s behaviour that is necessary for selecting the best material for specific
engineering applications.
A brief overview of the importance of composite materials to aspiring engineers is
presented in this study unit.
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What do we mean by a composite? “Composite materials” are often shortened to
“composites”. The idea of combining chemical or structural elements can be productive
on many different levels of matter, but for engineering purposes, we must limit this
concept so that we can apply it to today’s engineering problems. That two or more
materials thoughtfully combined will perform differently and often more efficiently than
the materials by themselves is obvious and well known. This simple concept offers a
useful and even revolutionary way of thinking about the development and application of
materials.
How are hundreds and thousands of composites classified? After the general structural
characteristics of composites are outlined below, we will show you how this outline can
be used as the basis of a fairly simple scheme for descriptive classification and prediction
of behaviour.
1.3
CLASSIFICATION OF MATERIALS
Materials are often grouped based on their physical properties or functional uses.
Grouping materials based on their chemical character and atomic structure leads to three
basic groups: metals, ceramics and polymers. Composite materials are another important
material group that combine two or more of the basic material groups.
1.3.1 Metals
Metals are materials in which the atoms are arranged in regularly defined and repeating
positions throughout the structure. These regular arrangements are known as crystals (see
chapter 2 in Callister & Rethwisch [2015]). Pure metals can be considered to contain one
element. Metal alloys are materials where one or more metal elements (e.g. copper, gold,
aluminium, magnesium and titanium) or non-metal elements (e.g. carbon, nitrogen and
silicon) are mixed with the base element. Alloys typically have better mechanical
properties than pure metals and thus are more commonly used in engineering
applications.
The typical attributes of metals and alloys include the following:
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relatively good strength
high stiffness
ductile and malleable (capable of plastic deformation)
resistant to fracture or “tough”
excellent thermal and electrical conductors
magnetic (certain metals)
durable
easily deformed or machined into complex shapes
dense
opaque to visible light
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•
generally solid at room temperature (with the exception of bromine and mercury)
relatively high melting points
The common applications of metals materials include the following:
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automotive industry, heavy machinery (body, chassis, engine components, gearing)
aerospace (fuselage, engine components, rocket components)
structures (bridges, buildings)
electronics (wiring, batteries)
machine tools (wrenches, hammers, drill bits, saw blades)
magnets
1.3.2 Ceramics
Ceramics typically contain both metallic and non-metallic elements. Ceramics are most
frequently oxides (e.g. Al2O3, SiO2), nitrides (e.g. Si3Ni3, TiN) and carbides (e.g. SiC, WC).
Ceramics are often crystalline (i.e. the atoms are regularly arranged, as in metals), but
ceramics can also have non-crystalline glassy or amorphous structures where the atoms
are not regularly arranged. The bonding in ceramics is ionic and/or covalent, which are
extremely strong bonding types.
The typical attributes of ceramics include the following:
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high strength
high stiffness
very hard
low ductility and malleability
brittle and susceptible to fracture (low deformability)
typically poor thermal and electrical conductors (good insulators)
lower density than most metals
high resistance to chemical attacks and substance absorption
heat resistant, very high melting point
transparent or opaque to light
The common applications of ceramics materials include the following:
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electrical or thermal insulators
windows, optical fibres, electronic device screens
abrasives (grinding and sanding disks)
corrosion and oxidation resistant applications (chemical containment, furnace linings,
space shuttle heat-shielding)
biomaterials (orthopaedic and dental implants)
transport infrastructure (concrete)
electronic applications (audio and video tapes, hard disks)
household goods (cutlery, pottery)
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1.3.3
Polymers
Polymers are typically organic compounds that consist of long-chain molecules
containing repeating groups of covalently bonded elements. The chains have a carbon
backbone with hydrogen and other non-metal elements (e.g. O, N and Si) covalently
bonded to this backbone. Polymers generally have low strength. However, their low
density means they have very good strength-to-weight ratios.
The typical attributes of polymers are the following:
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low to moderate strength
high ductility, pliability (highly deformable)
low stiffness
soft
largely poor thermal and electrical conductors (insulators)
chemically inert and unreactive in a wide range of environments
low density
low resistance to elevated temperature (low melting point)
either transparent or opaque to light
The common uses of polymer materials include the following:
•
moulded parts (electronic device casings, car instrument panels, airplane interior
components)
electronics (liquid crystal displays [LCDs], compact disks [CDs])
containers
clothing and upholstery
adhesives and sealants
rubbers (gaskets, O-rings, tyres)
biomaterials (orthopaedic implants, drug delivery, wound dressing)
household goods (plastic tableware, Teflon cookware, storage containers)
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1.3.4
Composites
A number of composites occur in nature. Bone is a composite of the strong yet soft protein
collagen and hard, brittle mineral apatite. Wood consists of strong and flexible cellulose
fibres surrounded and held together by a stiffer material called lignin (matrix). Straw and
mud are also composites.
Composites have been used for many centuries, for example to manufacture laminated
iron and steel swords and gun barrels, linoleum, plasterboard and concrete, to name but
a few. One of the first examples of fabricated fibrous composites is the straw-reinforced
clay bricks used by the Israelites as recorded in the book of Exodus in the Bible. Iron rods
were used to reinforce masonry in the 19th century. Phenolic resin reinforced with
asbestos fibres was introduced in the beginning of the 20th century. In 1942, the first
fibreglass boat was made; and reinforced plastics were used in aircrafts and electrical
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components. Much later, structural composites such as steel-reinforced concrete and
polymers reinforced with fibres were developed (Kaw 2006; Gibson 2016).
Composites combine two or more materials (from the above categories) with the main
purpose of producing a new material that incorporates the best properties of each
individual material and has collective properties that would not be possible from the
materials individually. The properties of a composite material depend on both the type
and number of materials included, and the amount and distribution of each material.
Therefore, composite materials can exhibit an incredibly wide range of properties, which
makes it difficult to list general attributes for composites.
Other examples of composite materials include plywood, fibreglass, carbon fibre, steelbelted tires and reinforced concrete.
1.4
ADVANCED MATERIALS
Advanced materials are materials that have been highly processed to exhibit particularly
interesting properties. These interesting properties have led to their use in hightechnology applications. Advanced materials can be materials from any of the first three
basic groups, but these basic materials undergo extensive development for a specific
purpose. Since they are highly processed, they typically have interesting properties and
are generally expensive to produce. Types of advanced materials include semiconductors,
biomaterials, smart materials and nanomaterials.
1.5
IMPORTANT DEFINITIONS OF COMPOSITES
There is no universally accepted definition of composite materials. Definitions in the
literature differ widely. Our main concern is the level of the definition. In everyday usage,
the term composite refers to something made up of various parts or elements. Since we
can state a valid definition in terms of the constituents making up engineering materials
at each of the several structural levels of matter, which materials are to be regarded as
composites and which as monolithic depends upon the level chosen as the basis for
definition.
Elemental or basic level: At this level, the level of single molecules and crystal cells, all
materials composed of two or more different atoms would be regarded as composites.
They would include compounds, alloys, polymers and ceramics. Only the pure elements
would be excluded (Schwartz 1984).
Microstructural level: At this level, the level of crystals, phases and compounds, a
composite would be defined as a material composed of two or more different crystals,
molecular structures or phases. By this definition, many materials traditionally considered
to be monolithic or homogeneous would be classified as composites. Out of all the
metallic materials, only single-phase alloys (e.g. some brasses and bronzes) would be
monolithic by this definition. Steel, a multiple alloy of carbon and iron, would be a
composite (Schwartz 1984).
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Macrostructural level: At this level, which includes the composites that are the focus of
this module, we deal with gross structural forms or constituents, for example matrices,
particles and fibres. We think of a composite as a “material system” composed of different
macroconstituents.
The definition at the macrosectional level encompasses many but not all of the materials
now commonly considered composites. To be more inclusive, we must go beyond the
forms of the constituents and include two other characteristics: (1) the individual
constituents making up a composite, which are almost always different chemically; and
(2) they are essentially insoluble in each other. The following is a working definition of
composite materials that takes into account both the structural form and composition of
the material constituents:
A composite material is a material system composed of a mixture or combination of
two or more macroconstituents that differ in form and/or material composition, and
are essentially insoluble in each other (Schwartz 1984).
Another basic definition would be:
Composite materials are engineered or naturally occurring materials made from two
or more constituent materials with significantly different physical or chemical
properties that remain separate and distinct at the macroscopic or microscopic scale
within the finished structure (Callister & Rethwisch 2015).
1.6
CONSTITUENTS OF COMPOSITES
In principle, composites can be constructed of any combination of two or more materials,
whether metallic, organic or inorganic. Although the possible material combinations are
virtually unlimited, the constituent forms are more restricted. Major constituents used in
composites are fibres, particles, laminae or layers, flakes, fillers and matrices (see
figure 1.1). The properties of composites are a function of the properties of the constituent
phases, their relative amounts and the geometry of the reinforcement phase.
Reinforcement phase geometry refers to the shape of the particles and the particle size,
distribution and orientation.
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Figure 1.1
The different constituent forms in composites (Schwartz 1984)
The matrix is the body constituent, which serves to enclose the composite and give it its
bulk form. The fibres, particles, laminae, flakes and fillers are structural constituents; they
determine the internal structure of the composite. They are generally, but not always, the
additive phase.
The most typical composite is one composed of a structural constituent imbedded in a
matrix, but many composites have no matrix and are composed of one or more
constituent forms consisting of two or more different materials. For example, sandwiches
and laminates are composed exclusively of layers. Taken together, these layers give the
composite its form. Many felts and fabrics have no body matrix but consist exclusively of
fibres of several compositions, with or without the bonding phase (Schwartz 1984).
1.6.1
Application of the interfaces and interphases
There is always an interface between the constituent phases in a composite material. For
the composite to operate effectively, the phases must bond where they join at the
interface. The interface is the surface forming the common boundary of the constituents.
In some cases, this connecting region is a distinct added phase known as an interphase.
Examples are the coating on the glass fibres in reinforced plastics and the adhesive that
bonds the layers of a laminate together. When such an interphase is present, there are
two interfaces – one between each surface on the interphase and its adjoining constituent
(see figure 1.2).
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Figure 1.2
Makeup of the interface between fibre and matrix (Schwartz 1984)
1.7
IMPORTANCE OF COMPOSITES
Materials have a fundamental role in all engineering advances. For example, modern air
travel would not be possible without the development of heat-resistant alloys and
advanced ceramics for turbine engines and high-strength lightweight materials for the
airframe. Smartphones would not be possible without the significant breakthroughs in
semiconductor and battery technology. Hence, the technological advancement of human
civilisation is intimately linked to the field of Materials Science and Engineering.
Engineers continuously confront design constraints relating to materials. Today’s
engineers have tens of thousands of materials already available to them, with new
materials continuously being introduced. While this seemingly infinite number of
materials is a significant advantage to engineers, it also presents them with the conundrum
of how to select the right material for each application.
Engineers typically must consider several criteria when selecting materials, for example:
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the conditions the material will experience during use (e.g. forces)
the durability of the material
the cost of the raw material
the cost of shaping the material into the final component
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It is important to realise that engineers often make compromises between multiple
competing properties (e.g. strength and ductility). Ultimately, engineers can only balance
multiple criteria and select the best material if they have a firm understanding of the
relationship between the processing, structure, properties and cost of materials. The
current module aims to give you this understanding.
Combining two or more materials to make a composite is more work than just
combining traditional monolithic metals such as steel and aluminium. What are the
advantages of using composites instead of metals?
Monolithic metals and their alloys cannot always meet the demands of today’s advanced
technologies. Only by combining several materials can one meet the performance
requirements. For example, trusses and benches used in satellites need to be
dimensionally stable in space during temperature changes from –160 °C to 93,3 °C.
Limitations on the coefficient of thermal expansion are therefore low and may be of the
order of ±1,8 X 10–7 m/m/°C. Monolithic materials cannot meet these requirements,
which leave composites such as graphite/epoxy composites as the only materials to satisfy
this requirement.
In many cases, using composites is more efficient. For example, in the highly competitive
market, one is continuously looking for ways to lower the overall mass of the aircraft
without decreasing the stiffness and strength of its components. This is possible by
replacing conventional metal alloys with composite materials. Even if the composite
material costs may be higher, the reduction in the number of parts in an assembly and
the savings in fuel costs make them more profitable (Kaw 2006).
1.7.1
Advantages of composites
Composites have the following advantages:
•
•
•
•
•
•
•
•
higher specific strength (strength-to-weight ratio)
stiffness
fatigue and impact resistance
thermal conductivity
design flexibility
corrosion resistance
low relative investment
durability
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1.7.2
Disadvantages of composites
Composites also have disadvantages, including the following:
•
•
•
•
High cost of fabrication.
They are heterogeneous.
They are highly anisotropic.
They are difficult to inspect using conventional ultrasonic, eddy current and visual
NDI methods such as radiography.
1.8
GENERAL CLASSIFICATION OF COMPOSITES
Several classification systems are used, including the following:
1.8.1
Classification by production method
Composites are often classified based on the method used to produce them. These
methods include the following:
•
•
•
•
•
lamination methods
compression or compaction
injection
extrusion
pultrusion
1.8.2
Classification by matrix material
Composites can also be classified based on their matrix material:
•
Polymer matrix composites (PMCs) (epoxides, polyesters, nylons, etc.) are widely
used in PMCs and are classified as:
o thermoplastics
o thermosets
•
Metal matrix composites (MMCs) (aluminium alloys, magnesium alloys, titanium, etc.)
are mixtures of ceramics and metals, such as cemented carbides and other cermets.
They offer a higher modulus of elasticity, ductility and resistance to elevated
temperature than PMCs. However, they are heavier and more difficult to process.
Ceramic matrix composites (CMCs) (glass ceramics) include Al2O3 and SiC (i.e. fibre
materials) imbedded with fibres to improve properties, especially in high temperature
applications and where resistance to a corrosive environment is desired. They are
strong and stiff, but they lack toughness (ductility).
Carbon (graphite) matrix composites.
•
•
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1.8.3
Classification based on the form of the structural constituents
When composites are classified based on the form of their structural constituents, the
following classes are used:
•
•
•
•
•
fibre composites (composed of fibres with or without a matrix)
flake composites (composed of flat flakes with or without a matrix)
particulate composites (composed of particles with or without a matrix)
filled or skeletal composites (composed of a continuous skeletal matrix filled by a
second material)
laminar composites (composed of layer or laminar constituents)
Figure 1.3
Classes of composites based on the form of the structural constituents (Schwartz 1984)
1.9
POLYMER MATRIX COMPOSITES (PMCS)
A PMC is a polymer primary phase in which a secondary phase is imbedded as fibres,
particles or flakes.
•
Commercially, PMCs are more important than metal matrix composites (MMCs) or
ceramic matrix composites (CMCs). These composites consist of a polymer (e.g.
epoxy, polyester or urethane) reinforced by thin-diameter fibres (e.g. graphite, aramids
or boron).
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•
Examples of PMCs include most plastic moulding compounds, rubber reinforced with
carbon black and fibre-reinforced polymers (FRPs).
FRPs are most closely identified with the term composite.
•
Classification of polymers
Polymers are classified as follows:
•
thermosetting (thermosets)
o epoxy resin
o epoxide group
o epoxy resin chain
o curing (cross-linking) of epoxy resin
o unsaturated polyesters
o linear polyester
o curing (cross-linking) of polyester
•
thermoplastics (amorphous; partially crystalline)
o commercial thermoplastics:
 polyethylene (PE)
 polyethylene terephthalate (PET)
 polyvinyl chloride (PVC)
 polypropylene (PP)
 polystyrene (PS)
 polyacrylonitrile (PAN)
 polymethyl methacrylate (PMMA)
 acrylonitrile butadiene styrene (ABS)
 polytetrapolyethylene (PTFE)
 polychlorotrifluoroethylene (PCTFE)
 polyamides (Nylons)
 polycarbonate (PC)
 phenylene oxide-based resin
 acetals
 nylon
 thermoplastic polyesters
 polysulfones
 polyphenylene sulphide
 polytherimide
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1.9.1
Typical attributes of PMCs
PMCs typically have the following attributes:
•
•
•
•
•
•
The matrix often determines the maximum service temperature because it normally
softens, melts or degrades at a much lower temperature than the fibre reinforcement.
They are used primarily at relatively low temperatures.
Polymers and metals are generally used as matrix materials because of their ductility.
High strength.
Ease of fabrication.
Low cost.
1.9.2
Typical applications of PMCs
The typical applications of PMCs include the following:
•
•
•
•
•
•
•
aircraft (military aircraft industry, commercial airlines, etc.)
space (remote manipulator arm in space shuttle, high gain antenna for space station,
etc.)
sporting goods (golf club shafts, bicycles, tennis and racquetball rackets, ice hockey
sticks, etc.)
medical devices (face masks, artificial portable lungs, x-ray tables, etc.)
marine (boats, housings, bridges, etc.)
automotive industry (fibreglass body panels, bumpers, doors, etc.)
commercial applications (mops with pultruded fibreglass handles, pressure vessels for
chemical plants, garden tools, etc.)
1.10 METAL-MATRIX COMPOSITES (MMCS)
MMCs are mixtures of ceramics and metals, and include cemented carbides and other
cermets.
Examples of the matrices used for MMCs include aluminium, magnesium and titanium.
The typical fibres found in MMCs include carbon and silicon carbide.
Metals are mainly reinforced to increase or decrease their properties to suit the needs of
the design. For example, elastic stiffness and strength of metals can be increased, while
large coefficients of thermal expansion and the thermal and electric conductivities of
metals can be reduced by the addition of fibres such as silicon carbide.
MMCs are much more expensive than PMCs, hence their use is somewhat restricted.
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1.10.1 Typical attributes of MMCs
The typical attributes of MMCs include the following:
•
•
•
•
•
The matrix is a ductile metal.
Higher operating temperatures.
Non-flammable.
Greater resistance to organic fluids degradation.
High cost.
1.10.2 Typical applications of MMCs
MMCs are typically applied in the following industries and areas:
•
•
Space. The space shuttle uses boron/aluminium tubes to support its fuselage frame.
Military. Precision components of missile guidance systems demand dimensional
stability. MMCs satisfy this requirement.
Transportation. MMCs are used in lighter automotive engines, especially highstrength, low-weight gas turbine engines, because they allow for higher operating
temperatures and better efficiencies.
Mechanical applications. MMCs are used in driveshafts requiring higher rotational
speeds and reduced vibrational noise levels, extruded stabiliser bars, and forged
suspension and transmission components.
•
•
1.11 CERAMIC-MATRIX COMPOSITES (CMCS)
A CMC is a ceramic primary phase (e.g. alumina or calcium aluminosilicate) imbedded
with a secondary phase, which usually consists of fibres (e.g. carbon or silicon carbide).
Examples of CMCs include Al2O3 and SiC imbedded with fibres to improve properties,
especially in high temperature applications. They are the least common composite
matrices.
CMCs represent an attempt to retain the desirable properties of ceramics while
compensating for their weaknesses.
1.11.1 Typical attributes of CMCs
The typical attributes of CMCs are the following:
•
•
They are naturally resilient to oxidation and deterioration at elevated temperatures.
They are resistant to thermal shock.
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1.11.2 Typical applications of CMCs
CMCs are finding increased application in high temperature areas where PMCs and
MMCs cannot be used.
Typical applications include cutting tool inserts in oxidising and high temperature
environments.
1.12 CARBON-CARBON COMPOSITES
Carbon fibre reinforced carbon-matrix composite are termed carbon-carbon composites.
The reinforcement and the matrix are carbon. These types of composite materials are
fairly new and expensive.
1.12.1 Typical attributes of carbon-carbon composites
The typical attributes of carbon-carbon composites are the following:
•
•
•
•
•
•
•
•
•
High-tensile moduli and tensile strengths are retained at temperatures higher than
2000 °C.
Resistant to creep.
Large fracture toughness values.
Low coefficients of thermal expansion.
High thermal conductivities.
High strength.
Low openness to thermal shock.
Require complex processing techniques.
Low density.
1.12.2 Typical applications of carbon-carbon composites
The typical applications of carbon-carbon composites include the following:
•
•
•
•
rocket motors
used as friction materials in aircraft and high-performance automobiles
components for advanced turbine engines
ablative shields (i.e. an aerodynamic heat shield consisting of a protective layer of
special materials to dissipate the heat)
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1.13 LAMINA COMPOSITES
A lamina (or ply) is a plane layer of unidirectional fibres or woven fabric in a matrix (see
figure 1.4).
Figure 1.4
Lamina and principal coordinate axes: (a) unidirectional reinforcement and
(b) woven fabric reinforcement (Daniel & Ishai 2006)
A multilayered structure (a structure made up of two or more layers) such as the one
illustrated in figure 1.4 is called a laminate. In a laminate, unidirectional laminae (or plies)
are bonded together at various orientations (see figure 1.5).
Figure 1.5
Multidirectional laminate and reference coordinate system (Daniel & Ishai 2006)
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1.13.1 Hybrid composites
Composite laminates containing plies of two or more different types of materials are
called hybrid composites and, more specifically, interply hybrid composites. Hybrid
composites contain either more than one fibre or more than one matrix system in a
laminate. The main four types of hybrid laminates are the following:
•
•
•
•
interply hybrid laminates
intraply hybrid laminates
interplay-intraply hybrids
resin hybrid laminates
In some cases it may be advantageous to intermingle different types of fibres, such as
glass and carbon or aramid and carbon, in the same unidirectional ply. Such composites
are called intraply hybrid composites. Of course, one could combine intraply hybrid
layers with other layers to form an intraply-interply hybrid composite.
Composite laminates are designated in a manner indicating the number, type, orientation
and stacking sequence of the plies. The configuration of the laminate indicating its ply
composition is called the layup. The configuration indicating the exact location or
sequence of the various plies (in addition to its ply composition) is called the stacking
sequence (Daniel & Ishai 2006).
Read more about these types of hybrid composites in section 1.4 in Kaw (2006:46–49).
1.13.2 Typical attributes of hybrid composites
The typical attributes of hybrid composites are the following:
•
•
•
stronger and tougher
higher impact resistance
low-cost production
1.13.3 Typical applications of hybrid composites
The typical applications of hybrid composites include the following:
•
•
•
lightweight structural components of land (e.g. automotive, civil infrastructure), water
(e.g. ship hulls) and air transport (e.g. landing-gear hatch, fuselage, rotor blades for
helicopters)
sporting goods
lightweight orthopaedic components
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1.14 SANDWICH COMPOSITES
Sandwich composites are structural composites consisting of two outer sheets, faces or
skins that are separated by a thicker core (see figure 1.6). The outer sheets are made of
stiff and strong material, usually aluminium alloys, steel and stainless steel, fibrereinforced plastics and plywood. The outer sheets carry bending loads.
Figure 1.6
Aluminium composite material panel structure
(Source: https://en.wikipedia.org/wiki/Sandwich_panel).
The core is lightweight with a lower modulus of elasticity, and lower tensile and
compressive stresses. It supports the outer sheets and holds them together. It provides
high shear stiffness in order to resist buckling. The core materials are less expensive and
typically made of rigid polymeric foams, wood and honeycomb.
1.14.1 Typical attributes of sandwich composites
The following are the typical attributes of sandwich composites:
•
•
•
•
lightweight
relatively high stiffness and strength
cost-effective
sound and vibration damping characteristics
1.14.2 Typical applications of sandwich composites
Sandwich composites are typically used in the following industries:
•
•
aviation (leading and trailing edges of aircraft, flaps, rudders, etc.)
construction (cladding for buildings, insulated roof and wall systems, etc.)
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•
•
automotive (head liners, luggage compartment floors, spare wheel covers, etc.)
marine (bulkheads, furniture, ceiling, partition panes, etc.)
1.15 NANOCOMPOSITES
Nanocomposites are a new class of composite materials. They are composed of
nanometre-sized particles. The three general nanoparticle types are (1) nanocarbons, (2)
nanoclays and (3) particulate nanocrystals. Processing is the main challenge in the
production of nanocomposites.
1.15.1 Typical attributes of nanocomposites
The typical attributes of nanocomposites are the following:
•
•
•
They can be designed to have mechanical, electrical, magnetic, optical, thermal,
biological and transport properties that are superior to those of conventional filler
materials.
The physical and chemical properties of a nanoparticle change dramatically when its
size decreases.
Their properties depend on the properties of both matrix and nanoparticle, shape and
content, as well as matrix and nanoparticle interfacial characteristics.
1.15.2 Typical applications of nanocomposites
The typical attributes of nanocomposites include the following:
•
•
•
•
•
•
gas-barrier coatings (nanocomposite thin film bags or containers)
energy storage (lithium-ion rechargeable batteries)
flame-barrier coatings (protection from combustion and decomposition)
dental restorations (filling material)
mechanical strength enhancements (wind turbine blades and sports equipment)
electrostatic dissipation
1.16 SUMMARY
•
•
A composite material is a combination of two or more different materials at the
microscopic level; or two inherently different materials (reinforcement phase, e.g.
fibres; and binder phase, e.g. compliant matrix) that when combined produce a
material with properties that exceed the constituent materials.
Composites are used in the aerospace, automotive and construction industries, in the
manufacture of sporting goods, and so on.
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•
The types of composites as classified by matrix material are polymer matrix
composites (PMCs), metal matrix composites (MMCs) and ceramic matrix composites
(CMCs).
The types of composites as classified based on the form of their structural constituents
are fibre composites, particle composites, laminar composites, flake composites and
filled composites.
Some new types of composites have also been also introduced, including carboncarbon composites, hybrid composites and nanocomposites.
A important aspect of composite materials is the investigation of the relationship
between the material’s structure and properties. The ability to manipulate this
relationship could enable large advances in technology.
In addition to the basic categories (metals, ceramics and polymers), advanced
materials have been discussed. These are highly processed basic materials with
special properties that enable their use in high technology applications. Students
should be able to name the main categories of advanced materials.
•
•
•
•
1.17 PRACTICE PROBLEMS
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
20
What is a composite?
Give a brief historical review of composites.
Give FOUR examples of naturally found composites. What are the constituents of
these?
What is the distinction between the matrix and reinforcement phases in a composite
material?
Give FOUR reasons why glass fibres are most commonly used for reinforcement.
How are composites classified?
Why is epoxy the most popular resin?
Find TEN applications of polymer matrix components other than those given in
chapter 1 of Kaw (2006).
For a polymer-matrix fibre-reinforced composite:
(a) Name THREE functions of the matrix.
(b) Give TWO reasons why there must be a strong bond between the fibre and
matrix at their interface.
Compare the advantages and disadvantages of MMCs and PMCs.
Find THREE applications of MMCs other than those given.
Find THREE applications of CMCs other than those given.
Find THREE applications of PMCs other than those given.
Define the following: fibre, matrix, lamina and laminate.
What is the main reason for fabricating laminar composites?
Briefly describe sandwich panels.
What is the main reason for fabricating sandwich panels?
What is the function of the faces and the core in sandwich panels?
What is a hybrid composite?
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(20) Name TWO important advantages of hybrid composites over normal fibre
composites.
(21) How are hybrid composites classified?
(22) What are advanced composites?
(23) What are the most common advanced composites?
(24) Name the various fibres used in advanced polymer composites.
(25) Are carbon and graphite the same? What is the difference, if any?
(26) What are the advantages of carbon-carbon composites?
(27) Name ONE typical method of processing a carbon-carbon composite.
(28) What are some of the applications of carbon-carbon composites?
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Study unit 1
2
PROCESSING OF COMPOSITES
2.1
LEARNING OBJECTIVES
After students have studied this study unit, they should be able to
•
describe the underlying principles and processes for the manufacturing of composite
materials, and list the advantages and limitations of those processes
apply the abbreviations used in the manufacturing of composites
•
2.2
INTRODUCTION
It is important to know how composites are made, because with composites we design
and build not only the structure, but also the structural material itself. The selection of a
fabrication process obviously depends on the constituent materials in the composite, with
the matrix material being the key, because the processes for polymer matrix, metal matrix
and ceramic matrix composites are quite different. The fabrication process also depends
on the application and/or design requirements.
The following important terms need to be explained:
•
Curing is the drying and hardening (or polymerisation) of the resin matrix of a finished
composite. This may be done unaided or by applying heat and/or pressure.
Layup is basically the process of arranging fibre-reinforced layers (or laminae) in a
laminate and shaping the laminate to make the part desired. (The term layup is also
used to refer to the laminate itself before curing.) Unless prepregs are used, layup
includes the actual creation of laminae by applying resins to the fibre reinforcements.
•
2.3
ABBREVIATIONS
To describe the modes of fabricating the composite piece, the professionals use many
abbreviations. Each is detailed below:
BMC: Bulk moulding compound
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RRIM: Reinforced reaction injection moulding
SRIM: Structural reaction injection moulding
RTM: Resin transfer moulding
SMC: Sheet moulding compound
RTP: Reinforced thermoplastics
RST: Reinforced stamped thermoplastics
ACTIVITY 2.1
Find the meanings of the following abbreviations:
ZMC
TMC
XMC
(a)
(b)
(c)
2.4
•
•
•
•
GUIDE TO PROCESSING COMPOSITES
The two phases are typically produced separately before being combined into the
composite part.
Processing techniques to fabricate MMC and CMC components are similar to those
used for powdered metals and ceramics.
Moulding processes are commonly used for PMCs with particles and chopped fibres.
Specialised processes have been developed for FRPs.
2.5
FABRICATION PROCESSES
The flowchart in figure 2.1 shows the steps found in moulding processes. Forming by
moulding processes varies depending on the nature of the part, the number of parts and
the cost. The mould material can be made out of metal, polymer, wood or plaster.
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Figure 2.1
Steps in moulding process (Gay & Hoa 2007)
2.5.1
Contact moulding
Contact moulding is open moulding (either male or female), as shown in figure 2.2. The
layers of fibres impregnated with resin (and accelerator) are placed on the mould.
Compaction is done using a roller to squeeze out the air pockets.
Figure 2.2
Contact moulding
(Source: Mechanciatech.com)
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Hand layup
•
Hand layup or contact moulding is the oldest and simplest way of making fibreglassresin composites. Applications include standard wind turbine blades and boats.
Spray-up
•
•
•
•
Continuous strands of fibreglass are pushed through a hand-held gun that both chops
the strands and combines them with a catalysed resin such as polyester.
The impregnated chopped glass is shot onto the mould surface in whatever thickness
the design requires and the human operator thinks is appropriate.
This process is good for large production runs at a reasonable cost, but produces
geometric shapes with less strength than other moulding processes and poor
dimensional tolerance.
Applications are lightly loaded structural panels, for example caravan bodies, truck
fairings, bathtubs and small boats.
Table 2.1 Advantages and limitations of hand layup and spray-up processes
Advantages
Limitations
Large and complex items can be
produced.
The process is labour intensive.
Minimum equipment investment is
necessary.
It is a low-volume process.
The start-up lead time and cost are
minimal.
Longer cure times may be required,
since room-temperature curing agents
are generally used.
Tooling cost is low.
Quality is related to the skill of the
operator.
Semiskilled workers are easily trained.
Product uniformity is difficult to
maintain within a single part or from
one part to another.
Design flexibility.
Only one good (moulded) surface is
obtained.
Moulded-in inserts and structural
changes are possible.
The waste factor is high.
Sandwich constructions are possible.
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2.5.2
Compression moulding
With compression moulding (see figure 2.3), the counter mould will close the mould after
the impregnated reinforcements have been placed on the mould. The whole assembly is
placed in a press that can apply a pressure of 1 to 2 bars. The polymerisation takes place
either at ambient temperature or higher.
Figure 2.3
Compression moulding (Gay & Hoa 2007)
Compression moulding
•
A "preform" or "charge" of SMC, BMC or sometimes prepreg fabric is placed into the
mould cavity.
The mould is closed and the material is compacted and cured inside by pressure and
heat.
Compression moulding offers excellent detailing for geometric shapes ranging from
pattern and relief detailing, complex curves and creative forms to precision
engineering, all within a maximum curing time of 20 minutes.
The major advantages of compression moulding are the following:
•
•
•
o Very large parts (>80 kg) can be produced with minimal fibreglass degradation,
yielding the strongest parts of all moulding processes.
o Material can be placed in the cavity to achieve optimum fibre orientation in critical
strength locations. The process is not limited by gate locations.
o Dissimilar materials can be placed in the mould, such as glass mat or
unidirectional glass, to improve part strength.
o It is an economical choice for small (<1000) to very large volumes using single
or multiple cavity tooling.
Compression moulding is very popular in the automotive industry because of its high
volume capabilities.
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2.5.3
Moulding with vacuum
This process is still called depression moulding or bag moulding. As in the case of contact
moulding, one uses an open mould on top of which the impregnated reinforcements are
placed. One sheet of soft plastic is used for sealing (this is adhesively bonded to the
perimeter of the mould). Vacuum is applied under the piece of plastic, as shown in figure
2.4. The piece is then compacted due to the action of atmospheric pressure and the air
bubbles are eliminated. Porous fabrics absorb excessive resin. The whole material is
polymerised using one of the following: an oven, autoclave pressure, heat, an electron
beam or x-rays. This process has applications for aircraft structures.
Figure 2.4
Vacuum moulding (Gay & Hoa 2007)
2.5.4
Resin injection moulding
With resin injection moulding (also called resin transfer moulding [RTM], see figure 2.5),
the reinforcements are put in place between the mould and the counter mould. The resin
(polyester or phenolic) is injected. The mould pressure is low. The investments are less
costly and have application in automobile bodies.
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Figure 2.5
Resin injection moulding
(Source: https://encryptedtbn0.gstatic.com/images?q=tbn:ANd9GcRAGBcWEkY34DcvUKpDLymr8ywq
RUxTkFEBDN3agEkG0ZfGS_3GQA)
RTM process
The resin transfer moulding process is suitable for the high-volume production of complex
or thick composite parts. The process may be briefly described as follows:
•
Fabrics are placed into a mould and wet resin is then injected into the mould. The
resin is typically pressurised and forced into a cavity which is under vacuum in the
RTM process.
Resin is entirely pulled into the cavity under vacuum in the vacuum-assisted resin
transfer moulding (VARTM) process.
This moulding process allows precise tolerances and detailed shaping, but can
sometimes fail to saturate the fabric fully, leading to weak spots in the final shape.
The process is expensive and the required tooling design complex.
•
•
•
2.5.5
Moulding by injection of a premix
This process allows automation of the fabrication cycle.
•
•
Thermoset resins can be used to make components of auto body.
Thermoplastic resins can be used to make mechanical components with high
temperature resistance.
2.5.6
Moulding by foam injection
Moulding by foam injection allows the processing of pieces of fairly large dimensions
made of polyurethane foam reinforced with glass fibres. These pieces remain stable over
time, they have good surface conditions, and their mechanical and thermal properties are
satisfactory.
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2.5.7
Moulding of components of revolution
The process of centrifugal moulding (see figure 2.6) is used for the fabrication of tubes. It
allows for the homogeneous distribution of resin with good surface conditions, including
the internal surface of the tubes.
Figure 2.6
Centrifugal moulding
(Source: https://nptel.ac.in/courses/101104010/lecture8/images/figure3.jpg)
The process of filament winding (see figure 2.7) can be integrated into a continuous chain
of production and can be used to fabricate tubes of long lengths. These can be used to
make missile tubes, torpillas, containers or tubes for transporting petroleum.
Figure 2.7
Filament winding
(Source: https://aliancys.com/pictures-categories/processing-techniques/aliancysfilament-winding-1519832342.png)
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By its nature, a filament winding process is best suited to products having surfaces of
revolution. The filament winding process can briefly be described as follows:
•
Machines pull fibre bundles through a wet bath of resin and wind them over a rotating
steel mandrel in specific orientations.
Parts are cured at either room temperature or elevated temperatures.
Mandrel is extracted, leaving a final geometric shape that can be left in some cases.
The process is highly automated.
It is relatively inexpensive and involves low manufacturing costs.
Filament winding is used to make glass fibre pipes, sailboats masts, etc.
It is suitable for making specialised structures, such as pressure vessels.
•
•
•
•
•
•
Table 2.2 Advantages and limitations of a filament winding process
Advantages
Limitations
The process may be automated and Winding reverse curvatures are difficult.
provides high production rates.
Highest-strength products are obtained Winding at low angles (parallel to
because of fibre placement control.
rotational axis) is difficult.
It can be used to produce products of Complex (double-curvature) shapes are
many different sizes.
difficult to obtain.
Strength control in different directions is The resulting external surface conditions
made possible.
are poor.
2.5.8
Pultrusion
Pultrusion is a manufacturing process when fibre-reinforced composite products are
produced with a constant cross-section in an effective way. The term pultrusion comes
from the two words “pull” and “extrusion”.
Extrusion is the process of creating objects of a fixed cross-sectional profile through a
pushing process. Therefore, in the course of pultrusion, reinforcement material goes
through pulling and pushing stages.
•
Fibre bundles and slit fabrics are pulled through a wet bath of resin and formed into
the rough part shape.
Saturated material is extruded from a heated closed die curing while being
continuously pulled through the die.
The process is productive. Potential applications are roadside reflector poles, ladder
rails, etc.
•
•
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Figure 2.8
The pultrusion process
(Source: http://basalt.today/images/2015/12/Pultrusion_Process.jpg)
Table 2.3 Advantages and limitations of a pultrusion process
Advantages
Limitations
Increased strength (fibre processed under
tension)
The axial direction (difficult to control fibre
orientation)
High fibre content
Fibre angles 0°
Highly automated
Not suitable for tapered and complex
shapes
Consistent quality
Difficult to control resin content
High production
Inconsistent quality (plastics stick to the die)
Low labour required
Low cost
2.6
COST COMPARISON
The diagram in figure 2.9 allows the comparison of the costs to fabricate composite
products. Note the important difference between the cost of composites produced in large
volume and the cost of high-performance composites.
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Figure 2.7
Cost comparison for different processes (Gay & Hoa 2007)
Read section 1.5 in Gibson (2016) before you continue.
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2.7
SUMMARY
The mixture of reinforcement or resin does not really become a composite material until
the last phase of the fabrication, that is when the matrix has hardened. After this phase, it
would be impossible to modify the material (e.g. as one would like to modify the structure
of a metal alloy using heat treatment).
In the case of polymer matrix composites, the reinforcement or resin has to be
polymerised, for example polyester resin. During the solidification process, the composite
passes from the liquid state to the solid state by copolymerisation with a monomer that is
mixed with a resin. The phenomenon leads to hardening. This can be done using either
a chemical (accelerator) or heat. This study unit described the principal processes for the
formation of composite parts (Gay & Hoa 2007).
2.8
PRACTICE PROBLEMS
(1)
(2)
(3)
What is glue and what is resin?
How does resin set?
What is hand lamination, vacuum infusion, vacuum bagging and autoclave
lamination?
(4) What are the advantages and disadvantages of the different processes of
manufacturing PMCs?
(5) What are the advantages and disadvantages of the different processes of
manufacturing MMCs?
(6) What are the advantages and disadvantages of the different processes of
manufacturing CMCs?
(7) Describe some practical physical limitations on the use of the RRIM process in the
moulding of chopped FRP matrix composites.
(8) Describe some practical physical limitations on the use of the RTM process in the
fabrication of composite sandwich structures that consist of composite face sheets
and a foam or honeycomb core.
(9) Describe a possible sequence of fabrication processes that might be used to
manufacture the helicopter rotor blade in figure 1.12 in Gibson (2016:22). Note that
several different materials and fibre layups are used.
(10) What are prepregs?
(11) What is another name used for resin transfer moulding?
(12) Describe ONE process that is used to manufacture CMCs.
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Study unit 1
3
PROPERTIES OF COMPOSITES
3.1
LEARNING OBJECTIVES
After students have studied this study unit, chapter 16 in Callister (2015) and chapter 2 in
Daniel and Ishai (2006), they you should be able to
•
•
•
•
•
describe and compare the basic properties of various composite materials
define general terminology used to describe the properties of composites
discuss the influence of fibre length
discuss the influence of fibre orientation and concentration
perform basic property analysis on composite material
3.2
GEOMETRIC AND PHYSICAL DEFINITIONS
Type of material
A material can be called a single-phase (or monolithic) material, a bi-phase (or two-phase)
material, a three-phase material or a multi-phase material, depending on the number of
constituents or phases of the material.
Homogeneity
A material is called homogeneous if its properties are the same at every point in the
material. If little unevenness is present from point to point on a macroscopic scale in the
material, the material is then referred to as quasi-homogeneous.
Heterogeneity
If the properties of the material vary from point to point, the material is referred to as
heterogeneous or inhomogeneous.
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Isotropy
When the properties of the material are the same in all directions or when they are
independent of the orientation of the reference axes, they are called isotropic. Material
properties such as stiffness, strength and thermal expansion are linked to a direction.
Anisotropy
If the properties of the material at a point vary with direction or are dependent on the
orientation of reference axes, then the material is anisotropic or orthotropic.
In figure 3.1, the material is considered homogeneous and anisotropic on a macroscopic
level, because it has similar composition at different locations (i.e. at A and B) but
properties varying with orientation. However, on a microscopic level, the material is
heterogeneous and isotropic, having different but orientation-independent properties in
characteristic volumes a and b.
Figure 3.1
Macroscopic (A, B) and microscopic (a, b) scales of observation for
unidirectional layers (Daniel & Ishai 2006)
The following important terms need to be explained:
Impact strength testing (IZOD)
IZOD is a measure of how much energy is absorbed by the material when it is broken by
a moving weight. There are many different test methods for measuring impact and IZOD
is but one of these methods. Higher numbers mean that the material will absorb more
energy before it is broken by a moving weight.
Specific gravity
Specific gravity is the ratio of the density of a material to the density of water. It is a
unitless number.
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Tensile strength
Tensile strength describes how much of a non-moving load a material can withstand
before it no longer returns to its original length upon removal of the load. Higher numbers
indicate materials that can withstand a stronger pull before failure.
Tensile modulus
Tensile modulus measures the ability of a material to withstand load without permanent
deformation. It is normally measured as the slope of the straight line portion of a plot of
stress vs strain.
Thermal conductivity
Thermal conductivity is known as the K factor. It measures the transfer of heat from one
side of a material to the other side. Higher numbers indicate that more heat is transferred
through a material in the same amount of time.
3.3
REINFORCEMENT OF COMPOSITE MATERIALS
The mechanical properties of reinforced plastics vary according to the kind, shape,
relative volume and orientation of the reinforcing material, and the length of the fibres.
Polymer matrix composites consist of a polymer resin as the matrix and fibres as the
reinforcement medium. In metal matrix composites and ceramic matrix composites, the
reinforcement may be in the form of particulates or fibres.
3.3.1
Particle-reinforced composites
Particle-reinforced composites consist of particles of various sizes and shapes randomly
dispersed in the matrix. Because of their random distribution, these composites can be
regarded as quasi-homogeneous on a scale larger than the particle size and spacing, and
quasi-isotropic. These types of composites may consist of non-metallic particles in a nonmetallic matrix (e.g. concrete, glass reinforced with mica flakes or brittle polymers
reinforced with rubberlike particles); metallic particles in non-metallic matrices (e.g.
aluminium particles in a polyurethane rubber); metallic particles in metallic matrices (e.g.
lead particles in copper alloys to improve machinability); and non-metallic particles in
metallic matrices (e.g. silicon carbide particles in aluminium).
For most of the large particle-reinforced composites, the reinforcing particle is harder and
stiffer than the matrix. These reinforcing particles tend to restrain the movement of the
matrix phase in the vicinity of each particle. In essence, the matrix transfers some of the
applied stress to the particles, which bear a fraction of the load applied. The degree of
improvement of mechanical properties depends on the strong bonding at the matrixparticle interface.
The diameters of smaller particles can range between 0.01 and 0.1 μm. The particle–
matrix interactions that lead to strengthening occur on the atomic or molecular level. The
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matrix bears the major portion of an applied load and the small dispersed particles hinder
the motion of dislocations. Thus, plastic deformation is restricted such that yield, tensile
strengths and hardness can improve.
3.3.2
Fibre-reinforced composites
Fibre-reinforced composites are sub-classified by the length of the fibre (i.e. discontinuous
or short fibres, and continuous or long fibres).
Discontinuous composites contain short fibres or whiskers as the reinforcing phase. The
fibres in short-fibre composites are too short to produce a significant improvement in
strength. They can be either all oriented along one direction (see figure 3.2) or randomly
oriented (see figure 3.3). If oriented along one direction, the composite material tends to
be distinctly anisotropic, whereas if randomly oriented the composite can be regarded as
quasi-isotropic.
Figure 3.2
Unidirectional discontinuous fibre composite (Daniel & Ishai 2006;
Callister & Rethwisch 2015)
Figure 3.3
Randomly oriented discontinuous fibre composite (Daniel & Ishai 2006)
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Continuous composites contain long fibres as the reinforcing phase. They are the most
efficient type in terms of stiffness and strength. The continuous fibres can be all parallel
(unidirectional continuous fibre composite) (see figure 3.4), they can be oriented at right
angles to each other (cross-ply or woven fabric continuous fibre composite) (see figure
3.5), or they can be oriented along several directions (multidirectional continuous fibre
composite) (see figure 3.6).
Figure 3.4
Unidirectional continuous fibre composite (Callister & Rethwisch 2015)
Figure 3.5
Cross-ply continuous fibre composite (Daniel & Ishai 2006)
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Figure 3.6
Multidirectional continuous fibre composite (Daniel & Ishai 2006)
Table 3.1 shows classes of fibre-reinforced composites according to the matrix used
(polymer, metal, ceramic or carbon matrix composites).
Table 3.1 Types of composite materials (Daniels & Ishai 2006)
Matrix type
Polymer
Metal
Ceramic
Carbon
Fibre
E-glass
S-glass
Carbon (graphite)
Aramid (Kevlar)
Boron
Boron
Borsic
Carbon (graphite)
Silicon carbide
Alumina
Silicon carbide
Alumina
Silicon nitride
Carbon
Matrix
Epoxy
Polyimide
Polyester
Thermoplastics
(PEEK, polysulfone, etc.)
Aluminium
Magnesium
Titanium
Copper
Silicon carbide
Alumina
Glass-ceramic
Silicon nitride
Carbon
INFLUENCE OF FIBRE LENGTH
•
The mechanical characteristics of a fibre-reinforced composite depend on the
properties of the fibre and on the degree of load transmittance to the matrix phase.
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•
Important to the degree of this load transmittance is the magnitude of the interfacial
bond between the fibre and matrix phases.
Under an applied stress, this fibre-matrix bond ceases at the fibre ends, yielding a
matrix deformation pattern (see figure 3.7). It means there is no load transference from
the matrix at each fibre extremity.
•
Figure 3.7
Deformation pattern in the matrix surrounding a fibre that is
subjected to an applied tensile load (Callister & Rethwisch 2015)
•
Stress can be transferred from matrix to fibre (or from fibre to matrix) through the
interface.
Critical fibre length for transferring stress
•
dependent on
𝑙𝑙𝑐𝑐 =
𝜎𝜎𝑓𝑓 𝑑𝑑
2𝜏𝜏𝑐𝑐
,
o the fibre diameter d,
o the fibre ultimate (or tensile) strength 𝜎𝜎𝑓𝑓 , and
o the fibre-matrix bond strength (or the shear yield strength of the matrix) 𝜏𝜏𝑐𝑐
•
For a number of glass and carbon fibre-matrix combinations, this lc is on the order of
1 mm, which ranges between 20 and 150 times the fiber diameter.
The stress-position profile shown in figure 3.8a result when a stress equal to 𝜎𝜎𝑓𝑓 is
applied to a fibre having just this critical length.
As fibre lengthlincreases, the fibre reinforcement becomes more effective, as
demonstrated in figure 3.8b.
Figure 3.8c shows the stress-position profile for l < lc.
•
•
•
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Figure 3.8
Stress-position profile when the fibre length l (a) is equal to the critical length lc, (b) is
greater the critical length, (c) is less than the critical length for a fibre-reinforced
composite that is subjected to a tensile stress equal to the fibre tensile strength 𝝈𝝈𝒇𝒇
(Callister & Rethwisch 2015)
•
•
•
For continuous fibre-reinforced composites: 𝑙𝑙 ≫ 𝑙𝑙𝑐𝑐 (normally 𝑙𝑙 > 15𝑙𝑙𝑐𝑐 ).
For discontinuous or short fibres: 𝑙𝑙 < 15𝑙𝑙𝑐𝑐 .
For discontinuous fibres of lengths significantly less than 𝑙𝑙𝑐𝑐 , the matrix deforms around
the fibre such that there is virtually no stress transference and little reinforcement by
the fibre.
FIBRE ORIENTATION AND CONCENTRATION: Unidirectional continuous fibre
composites
Tensile stress-strain behaviour with longitudinal loading
Figure 3.9
Longitudinal and transverse directions illustrated on a unidirectional
continuous fibre composite
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Assume the stress-strain behaviour of fibre and matrix phases that are shown in figure
3.10a. In this case, the fibre is considered to be completely brittle and the matrix to be
reasonably ductile. Also indicated in this figure are fracture strengths in tension for fibre
∗
∗
and matrix, 𝜎𝜎𝑓𝑓∗ and 𝜎𝜎𝑚𝑚
respectively. Their corresponding fracture strains are 𝜖𝜖𝑓𝑓∗ and 𝜖𝜖𝑚𝑚
.A
fibre-reinforced composite that consists of these fibre and matrix materials exhibits the
uniaxial stress-strain response illustrated in figure 3.10b.
•
•
•
•
•
In stage I, both fibre and matrix deform elastically.
In stage II, the fibre continues to deform elastically, but the matrix has yielded.
From stage I to stage II, the fibre picks up more load.
The onset of composite failure begins as the fibres start to fracture.
Composite failure is not catastrophic.
Figure 3.10
(a)
(b)
Schematic stress-strain curves for brittle fibre and ductile materials. Fracture
stresses and strains for both materials are noted.
Schematic stress-strain curve for an aligned fibre-reinforced composite that is
exposed to a uniaxial stress applied in the direction of alignment; curves for fibre
and matrix materials shown in part (a) are also superimposed (Callister &
Rethwisch 2015).
Elastic behaviour with longitudinal loading
•
•
The properties of a composite depend on the fibre direction.
Assume that the fibre-matrix interfacial bond is very good, such that deformation of
matrix and fibres is the same (Isostrain): 𝜖𝜖𝑐𝑐 = 𝜖𝜖𝑓𝑓 = 𝜖𝜖𝑚𝑚 .
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Total load subjected by the composite:
𝐹𝐹𝑐𝑐 = 𝐹𝐹𝑚𝑚 + 𝐹𝐹𝑓𝑓
From the definition of stress:
𝜎𝜎𝑐𝑐 𝐴𝐴𝑐𝑐 = 𝜎𝜎𝑚𝑚 𝐴𝐴𝑚𝑚 + 𝜎𝜎𝑓𝑓 𝐴𝐴𝑓𝑓
Dividing by the total cross-sectional area of the composite, Ac:
𝐴𝐴𝑚𝑚
𝐴𝐴𝑐𝑐
𝐴𝐴𝑓𝑓
𝐴𝐴𝑐𝑐
𝜎𝜎𝑐𝑐 = 𝜎𝜎𝑚𝑚
𝐴𝐴𝑓𝑓
𝐴𝐴𝑚𝑚
+ 𝜎𝜎𝑓𝑓
𝐴𝐴𝑐𝑐
𝐴𝐴𝑐𝑐
is the area fractions of the matrix.
is the area fractions of the fibre.
Using volume fraction, the composite stress becomes
𝜎𝜎𝑐𝑐 = 𝜎𝜎𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝜎𝜎𝑓𝑓 𝑉𝑉𝑓𝑓 .
The previous assumption of an isostrain state means that
𝜖𝜖𝑐𝑐 = 𝜖𝜖𝑓𝑓 = 𝜖𝜖𝑚𝑚 ,
therefore we can have
𝜎𝜎𝑓𝑓
𝜎𝜎𝑐𝑐 𝜎𝜎𝑚𝑚
=
𝑉𝑉𝑚𝑚 + 𝑉𝑉𝑓𝑓 .
𝜖𝜖𝑐𝑐 𝜖𝜖𝑚𝑚
𝜖𝜖𝑓𝑓
NOTE: 𝐸𝐸𝑐𝑐 = 𝜎𝜎𝑐𝑐 /𝜖𝜖𝑐𝑐 ; 𝐸𝐸𝑚𝑚 = 𝜎𝜎𝑚𝑚 /𝜖𝜖𝑚𝑚 ; 𝐸𝐸𝑓𝑓 = 𝜎𝜎𝑓𝑓 /𝜖𝜖𝑓𝑓
•
The modulus of elasticity of a continuous and aligned fibrous composite in the
direction of alignment (or longitudinal direction) is Ecl.
𝐸𝐸𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓
𝑉𝑉𝑚𝑚 + 𝑉𝑉𝑓𝑓 = 1
𝐸𝐸𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑚𝑚 (1 − 𝑉𝑉𝑓𝑓 ) + 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓
The rule of mixture is the following:
𝐸𝐸𝑐𝑐𝑐𝑐
is equal to the volume fraction weighted average of the moduli of elasticity of the
fibre and matrix phases.
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•
Other properties, including tensile strength, also have this dependence on volume
fractions.
Students can give this equation:
(TS)lc = ?
•
It can also be shown, for longitudinal loading, that the ratio of the load carried by the
fibres to that carried by the matrix is
𝐹𝐹𝑓𝑓
𝐹𝐹𝑚𝑚
=
𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓
𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚
.
A continuous and oriented fibre composite may be loaded in the transverse direction;
that is, the load is applied at a 90° angle to the direction of fibre alignment. For this
situation, the stress σ to which the composite and both phases are exposed is the same,
or
𝜎𝜎𝑐𝑐 = 𝜎𝜎𝑚𝑚 = 𝜎𝜎𝑓𝑓 = 𝜎𝜎.
This is termed an isostress state. In addition, the strain or deformation of the entire
composite is
𝜖𝜖𝑐𝑐 = 𝜖𝜖𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝜖𝜖𝑓𝑓 𝑉𝑉𝑓𝑓 ,
𝜖𝜖 =
since
𝜎𝜎
𝐸𝐸𝑐𝑐𝑐𝑐
𝜎𝜎
=
𝑉𝑉
𝐸𝐸𝑚𝑚 𝑚𝑚
+
1
=
𝑉𝑉𝑚𝑚
+
𝜎𝜎
𝑉𝑉 ,
𝐸𝐸𝑓𝑓 𝑓𝑓
𝜎𝜎
𝐸𝐸
where 𝐸𝐸𝑐𝑐𝑐𝑐 is the modulus of elasticity in the transverse direction.
Now, dividing through by σ yields
𝐸𝐸𝑐𝑐𝑐𝑐
𝐸𝐸𝑚𝑚
𝑉𝑉𝑓𝑓
𝐸𝐸𝑓𝑓
.
Longitudinal tensile strength
Typical longitudinal tensile strength values for three common fibrous composites are
listed in table 3.2. The fibre content for each is approximated to 50 vol%.
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Table 3.2 Typical longitudinal and transverse strengths for three unidirectional
fibre-reinforced composites (Callister & Rethwisch 2015)
Material
Longitudinal tensile
strength (MPa)
Transverse tensile
strength (MPa)
Glass polyester
700
20
Carbon (high modulus)/epoxy
1000
35
Kevlar/epoxy
1200
20
Transverse tensile strength
The strengths of unidirectional continuous fibre composites are highly anisotropic, and
such composites are commonly designed to be loaded along the longitudinal direction
(high-strength direction). Under circumstances in which transverse tensile loads are
present, premature failure may occur. Considering that transverse strength is usually
extremely low, it sometimes lies below the tensile strength of the matrix. Thus, the
reinforcing effect of the fibres is negative.
While longitudinal strength is dominated by fibre strength, transverse strength is
influenced by a variety of factors, which may include the properties of both the fibre and
the matrix, and the presence of voids. Measures used to improve the transverse strength
often involve modification of the matrix properties.
FIBRE ORIENTATION AND CONCENTRATION: Unidirectional discontinuous fibre
composites
•
The moduli of elasticity and the tensile strengths of short-fibre composites are about
50% to 90% of those of long fibre composites.
o When l > lc, the longitudinal strength is
𝑙𝑙
′
𝜎𝜎𝑐𝑐𝑐𝑐 = 𝜎𝜎𝑓𝑓 𝑉𝑉𝑓𝑓 �1 − 𝑐𝑐 � + 𝜎𝜎𝑚𝑚
�1 − 𝑉𝑉𝑓𝑓 �,
2𝑙𝑙
where 𝜎𝜎𝑐𝑐𝑐𝑐 is the fracture strength of the fibre, and
′
𝜎𝜎𝑚𝑚
is the stress in the matrix when the composite fails.
o When l < lc, the longitudinal strength is
𝜎𝜎𝑐𝑐𝑐𝑐 =
𝑙𝑙𝜏𝜏𝑐𝑐
𝑑𝑑
′
𝑉𝑉𝑓𝑓 + 𝜎𝜎𝑚𝑚
�1 − 𝑉𝑉𝑓𝑓 �,
where d is the fibre diameter, and
𝜏𝜏𝑐𝑐 is the shear yield strength of the matrix.
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FIBRE ORIENTATION AND CONCENTRATION: Randomly oriented fibre composites
•
A “rule of mixtures” expression for the elastic modulus Ecd is
𝐸𝐸𝑐𝑐𝑐𝑐 = 𝐾𝐾𝐾𝐾𝑓𝑓 𝑉𝑉𝑓𝑓 + 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚 ,
where K is a fibre efficiency parameter dependent on Vf and Ef/Em ratio (0,1 ~ 0,6).
Some of the mechanical properties of the unreinforced and reinforced polycarbonates for
discontinuous and randomly oriented glass fibres are given in table 3.3.
Table 3.3 Properties of unreinforced and reinforced polycarbonates with
randomly
oriented glass fibres (Callister & Rethwisch 2015)
Value for given amount of
reinforcement (vol%)
Property
Unreinforced
Specific gravity
Tensile strength (MPa)
Modulus
(GPa)
of
elasticity
Elongation (%)
Impact strength, notched
IZOD (N/cm)
20
30
40
1.19–1.22
1.35
1.43
1.52
59–62
110
131
159
2.24–2.345
5.93
8.62
11.6p
90–115
4–6
3–5
3–5
21–28
3.5
3.5
4.4
CHARACTERISTICS OF FIBRE-REINFORCEMENT MATERIALS
Small diameter fibres are much stronger than bulk material, especially in brittle materials.
Fibres are grouped into three different classes based on their diameter and character:
(1) Whiskers. These are very thin, single crystals with extremely large length-to-diameter
ratios. They are among the strongest known materials.
ACTIVITY 3.1
Name SIX whisker materials and tabulate their properties under the following
headings: specific gravity, tensile strength, specific strength, modulus of elasticity and
specific modulus.
(2)
46
Fibres. These are either polycrystalline or amorphous, and have small diameters.
Fibrous materials are largely polymers or ceramics.
EMT3701/1
ACTIVITY 3.2
Name SIX fibre materials and tabulate their properties under the following headings:
specific gravity, tensile strength, specific strength, modulus of elasticity and specific
modulus.
(3)
Wires. Fine wires have relatively large diameters. They are used as radial steel
reinforcement in tires, in rocket casings and in high-pressure hoses.
ACTIVITY 3.3
Name FOUR wire materials and tabulate their properties under the following headings:
specific gravity, tensile strength, specific strength, modulus of elasticity and specific
modulus.
3.4
PROPERTIES OF POLYMER MATRIX COMPOSITES
The properties of continuous and aligned (unidirectional) glass, carbon and aramid fibrereinforced epoxy composites are presented in table 3.4. The fibre volume fraction is 0.60.
Table 3.4 Properties of continuous and aligned glass, carbon and aramid fibrereinforced epoxy-matrix composites in longitudinal and transverse
directions (Callister & Rethwisch 2015)
Property
Specific gravity
Glass (E-glass)
Carbon (high
strength)
Aramid
(Kevlar 49)
2.1
1.6
1.4
Longitudinal (GPa)
45
145
76
Transverse (GPa)
12
10
5.5
1020
1240
1380
40
4130
Longitudinal
2.3
0.9
1.8
Transverse
0.4
0.4
0.5
Tensile modulus
Tensile strength
Longitudinal (MPa)
Transverse (MPa)
Ultimate tensile strain
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3.5
PROPERTIES OF METAL-MATRIX COMPOSITES
The properties of several common metal-matrix, continuous and aligned (unidirectional)
fibre-reinforced composites are presented in table 3.5.
Table 3.5 Properties of several metal-matrix composites reinforced with
continuous
and aligned fibres (Callister & Rethwisch 2015)
Fibre
Matrix
Carbon
6061 A1
41
2.44
320
620
Boron
6061 A1
48
–
207
1515
SiC
6061 A1
50
2.63
230
1480
Alumina
380.0 A1
24
–
120
340
Carbon
AZ31 Mg
38
1.83
300
510
Borsic
Ti
45
3.68
220
1270
3.6
Fibre
content
(vol%)
Density
(g/cm3)
Longitudinal
Longitudinal
tensile modulus tensile
(GPa)
strength
(MPa)
PROPERTIES OF CERAMIC MATRIX COMPOSITES
Increasing fibre content improves strength and fracture toughness, as demonstrated in
table 3.6 for SiC whisker-reinforced alumina. In addition, there is a significant reduction
in the scatter of fracture strengths for whisker-reinforced ceramics relative to their
unreinforced counterparts. Also, these CMCs exhibit improved high temperature creep
behaviour and resistance to failure resulting from sudden changes in temperature (i.e.
thermal shock).
Table 3.6 Room temperature fracture strengths and fracture toughnesses for
various SiC whisker contents in Al2O3 (Callister & Rethwisch 2015)
Whisker content (vol%)
Fracture strength (MPa)
0
–
10
455 ± 55
20
655 ± 135
7.5–9.0
40
850 ± 130
6.0
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Fracture toughness
(MPa√𝒎𝒎)
4.5
7.1
3.7
SUMMARY
The following are the main points of this study unit:
•
•
•
•
•
•
•
•
Materials can be single crystals or polycrystalline. Material properties generally vary
with single crystal orientation (i.e. they are anisotropic), but are generally nondirectional (i.e. they are isotropic) in polycrystals with randomly oriented grains.
For large-particle composites, upper and lower elastic modulus values depend on the
moduli and volume fractions of matrix and particulate phases according to the ruleof-mixtures expressions.
The potential for reinforcement efficiency is greatest for fibre-reinforced composites.
Significant reinforcement is possible only if the matrix-fibre bond is strong. Because
reinforcement discontinues at the fibre extremities, reinforcement efficiency depends
on fibre length.
Critical length (lc) exists for each fibre-matrix combination. It depends on fibre
diameter and strength, and fibre-matrix bond strength.
The length of fibres greatly exceeds this critical value (i.e. lc > 15lc), while shorter
fibres are discontinuous.
Based on fibre length and orientation, three types of fibre-reinforced composites are
possible, namely unidirectional continuous (or continuous and aligned) composites;
unidirectional discontinuous (or discontinuous and aligned) composites; and
randomly oriented discontinuous (or discontinuous and randomly oriented)
composites.
Based on diameter and material type, fibre reinforcements are classified as whiskers,
fibres and wires.
3.8
PRACTICE PROBLEMS
Example problem 3.1
A continuous and aligned glass-reinforced composite consists of 40 vol% of glass fibres
having a modulus of elasticity of 69 GPa and 60 vol% of a polyester resin that, when
hardened, displays a modulus of 3.4 GPa.
(a)
(b)
(c)
(d)
Compute the modulus of elasticity of this composite in the longitudinal direction.
If the cross-sectional area is 250 mm2 and a stress of 50 MPa is applied in this
longitudinal direction, compute the magnitude of the load carried by each of the
fibre and matrix phases.
Determine the strain that is sustained by each phase when the stress in part b is
applied.
Compute the elastic modulus of the composite material, but assume that the stress
is applied perpendicular to the direction of fibre alignment.
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Equations on the calculation for long fibre-reinforced matrix composites:
•
Longitudinal direction:
𝜖𝜖𝑐𝑐 = 𝜖𝜖𝑓𝑓 = 𝜖𝜖𝑚𝑚
𝜎𝜎𝑐𝑐 = 𝜎𝜎𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝜎𝜎𝑓𝑓 𝑉𝑉𝑓𝑓
𝐸𝐸𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓
𝐹𝐹𝑐𝑐 = 𝐹𝐹𝑚𝑚 + 𝐹𝐹𝑓𝑓
𝐹𝐹𝑓𝑓
𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓
=
𝐹𝐹𝑚𝑚 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚
•
Transverse direction:
1
𝑉𝑉𝑚𝑚 𝑉𝑉𝑓𝑓
=
+
𝐸𝐸𝑐𝑐𝑐𝑐 𝐸𝐸𝑚𝑚 𝐸𝐸𝑓𝑓
Answers:
We have
Ef = 69 GPa,
Em = 3,4 GPa,
Vf = 0,4, and
Vm = 0,6.
(a) The modulus of elasticity of the composite is calculated using equation
𝐸𝐸𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓 = (3,4 𝐺𝐺𝐺𝐺𝐺𝐺) × (0,6) + (69 𝐺𝐺𝐺𝐺𝐺𝐺) × (0,4) = 30 𝐺𝐺𝐺𝐺𝐺𝐺.
(b) To solve this portion of the problem, first find the ratio of the fibre load to matrix load
using equation
𝐹𝐹𝑓𝑓
𝐹𝐹𝑚𝑚
=
𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓
𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚
=
(69𝐺𝐺𝐺𝐺𝐺𝐺)×(0,4)
(3,4𝐺𝐺𝐺𝐺𝐺𝐺)×(0,6)
= 13,5.
In addition, the total force sustained by the composite Fc may be computed from the
applied stress and the composites cross-section Ac according to
𝐹𝐹𝑐𝑐 = 𝐴𝐴𝑐𝑐 𝜎𝜎 = (250 𝑚𝑚𝑚𝑚2 ) × (50 𝑀𝑀𝑀𝑀𝑀𝑀) = 12500 𝑁𝑁.
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However, this total load is just the sum of the loads carried by the fibre and matrix phases,
that is
𝐹𝐹𝑐𝑐 = 𝐹𝐹𝑓𝑓 + 𝐹𝐹𝑚𝑚 = 12500 𝑁𝑁.
Substitution for 𝐹𝐹𝑓𝑓 from the above yields
whereas
13,5𝐹𝐹𝑚𝑚 + 𝐹𝐹𝑚𝑚 = 12500 𝑁𝑁, 𝐹𝐹𝑚𝑚 = 862 𝑁𝑁,
𝐹𝐹𝑓𝑓 = 𝐹𝐹𝑐𝑐 − 𝐹𝐹𝑚𝑚 = 12500 𝑁𝑁 − 862 𝑁𝑁 = 11638 𝑁𝑁.
Thus, the fibre phase supports the majority of the applied load.
(c)
The stress for both fibre and matrix phases must be calculated. Then, by using the
elastic modulus for each (from part a), the strain values my determined.
For stress calculations, phase cross-sectional areas are necessary.
𝐴𝐴𝑚𝑚 = 𝑉𝑉𝑚𝑚 𝐴𝐴𝑐𝑐 = (0,6)(250𝑚𝑚𝑚𝑚2 ) = 150𝑚𝑚𝑚𝑚2 , and
thus
𝐴𝐴𝑓𝑓 = 𝑉𝑉𝑓𝑓 𝐴𝐴𝑐𝑐 = (0,4)(250𝑚𝑚𝑚𝑚2 ) = 100𝑚𝑚𝑚𝑚2 ,
𝐹𝐹𝑚𝑚
𝜎𝜎𝑚𝑚 =
𝐴𝐴𝑚𝑚
𝜎𝜎𝑓𝑓 =
=
𝐹𝐹𝑓𝑓
𝐴𝐴𝑓𝑓
862 𝑁𝑁
150𝑚𝑚𝑚𝑚2
=
= 5.75 𝑀𝑀𝑀𝑀𝑀𝑀, and
11640 𝑁𝑁
100𝑚𝑚𝑚𝑚2
= 116,4 𝑀𝑀𝑀𝑀𝑀𝑀.
Finally, strains are computed as
𝜀𝜀𝑚𝑚 =
𝜎𝜎𝑚𝑚
𝐸𝐸𝑚𝑚
𝜀𝜀𝑓𝑓 =
=
𝜎𝜎𝑓𝑓
𝐸𝐸𝑓𝑓
5,73 𝑀𝑀𝑀𝑀𝑀𝑀
3,4×103 𝑀𝑀𝑀𝑀𝑀𝑀
=
116,4 𝑀𝑀𝑀𝑀𝑀𝑀
= 1,69 × 10−3 , and
69×103 𝑀𝑀𝑀𝑀𝑀𝑀
= 1,69 × 10−3 .
Therefore, the strains for both matrix and fibre phases are identical, which they should
be.
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(d)
According to equation
1
𝐸𝐸𝑐𝑐𝑐𝑐
=
𝑉𝑉𝑚𝑚
𝐸𝐸𝑚𝑚
+
𝑉𝑉𝑓𝑓
𝐸𝐸𝑓𝑓
(3,4 𝐺𝐺𝐺𝐺𝐺𝐺)(69 𝐺𝐺𝐺𝐺𝐺𝐺)
𝐸𝐸𝑐𝑐𝑐𝑐 = (0,6)(69
,
𝐺𝐺𝐺𝐺𝐺𝐺)+(0,4)(3,4 𝐺𝐺𝐺𝐺𝐺𝐺)
= 5,5 𝐺𝐺𝐺𝐺𝐺𝐺.
This value for 𝐸𝐸𝑐𝑐𝑐𝑐 is slightly greater than that of the matrix phase, but it is only
approximately one-fifth of the modulus of elasticity along the fibre direction (𝐸𝐸𝑐𝑐𝑐𝑐 ), which
indicates the degree of anisotropy of continuous and oriented fibre composites.
Problem 3.1
The mechanical properties of aluminium may be improved by incorporating fine particles
of aluminium oxide (Al2O3). Given that the modulus of elasticity of these materials are
respectively 69 GPa and 393 GPa, plot the modulus of elasticity versus the volume per
cent of Al2O3 in Al from 0 to 100 vol%, using both upper- and lower-bound expressions.
Problem 3.2
Estimate the maximum and minimum thermal conductivity values for a cermet that
contains 90 vol% titanium carbide (TiC) particles in a cobalt matrix. Assume thermal
conductivities of 27 and 69 W/m.K for TiC and Co, respectively.
Problem 3.3
A large-particle composite consisting of tungsten particles in a copper matrix is to be
prepared. If the volume fractions of tungsten and copper are 0.60 and 0.40, respectively,
estimate the upper limit for the specific stiffness of this composite. Take the specific
gravities of tungsten and copper as 19.3 and 8.9 respectively; also, their respective moduli
of elasticity are 407 and 110 GPa.
Problem 3.4
(a)
For a fibre-reinforced composite, the efficiency of reinforcement η is dependent on
𝑙𝑙−2𝑥𝑥
fibre length l according to η = 𝑙𝑙 , where x represents the length of the fibre at
each end that does not contribute to the load transfer. Make a plot of η versus l to l
= 50 mm, assuming x = 0.8 mm.
(b)
What length is required for a 0.80 efficency of reinforcement?
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Problem 3.5
A continuous and aligned fibre-reinforced composite is to be produced consisting of 30
vol% silicon carbide fibres and 70 vol% of a polycarbonate matrix. The mechanical
characteristics of these two materials are as follows:
Modulus of elasticity
(GPa)
Tensile strength (MPa)
Silicon carbide
400
3900
Polycarbonate
2.4
65
Also, the stress on the polycarbonate matrix when the aramid fails is 45 MPa.
For this composite, compute:
(a)
(b)
the longitudinal tensile strength
the longitudinal modulus of elasticity
Problem 3.6
For a continuous and oriented fibre-reinforced composite, the moduli of elasticity in the
longitudinal and transverse direction are 19.7 and 3.66 GPa, respectively. If the volume
fraction of the fibres is 0.25, determine the moduli of elasticity of the fibre and matrix
phases.
Problem 3.7
Assume that the composite decribed in problem 5 has a cross-sectional area of 325 mm2
and is subjected to a longitudinal load of 44 600 N.
(a)
(b)
(c)
(d
Calculate the fibre-matrix load ratio.
Calculate the actual loads carried by both the fibre and matrix phases.
Compute the magnitude of the stress on each of the fibre and matrix phases.
What strain is experienced by the composite?
Problem 3.8
A continuous and aligned fibre-reinforced composite having a cross-sectional area of
1140 mm2 is subjected to an external tensile load. The stresses sustained by the fibre and
the matrix phases are 156 MPa and 2.75 MPa, respectively; the force sustained by the
fibre phase is 74 000 N; and a total longitudinal strain is 1.4 x 10–3.
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Determine:
(a)
(b)
(c)
the force sustained by the matrix phase
the modulus of elasticity of the composite material in the longitudinal direction
the moduli of elasticity for the fibre and matrix phases
Problem 3.9
Compute the longitudinal strength of an aligned carbon fibre/epoxy matrix composite
having a 0.25 volume fraction of fibres. Assume the following: (1) the average fibre
diameter is 20 x 10–3 mm; (2) the average fibre length is 5 mm; (3) the fibre fracture
strength is 2.5 GPa; (4) the fibre-matrix bond strength is 90 MPa; (5) the matrix stess at
fibre failure is 10 MPa; and (6) the matrix tensile strength is 80 MPa.
Problem 3.10
It is desired to produce an aligned carbon fibre/epoxy matrix composite having a
longitudinal tensile strength of 750 MPa. Calculate the volume fraction of fibres necessary
if (1) the average fibre diameter and length are 1.2 x 10–2 mm and 1 mm, respectively; (2)
the fibre fracture strength is 5000 MPa; (3) the fibre-matrix bond strength is 25 MPa; and
(4) the matrix stress at fibre failure is 10 MPa.
Problem 3.11
Which fibre factors contribute to the mechanical performance of a composite?
Problem 3.12
What are the matrix factors that contribute to the mechanical performance of composites?
Problem 3.13
What is an isotropic body?
Problem 3.14
What is a homogenous body?
Problem 3.15
What is an anisotropic material?
Problem 3.16
What is a non-homogenous/inhomogenous body?
Problem 3.17
Give an example of a homogenous body which is not isotropic.
Problem 3.18
Give an example of a non-homogenous body which is isotropic.
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4
Study unit 1
ELASTIC BEHAVIOUR OF COMPOSITE LAMINA
4.1
LEARNING OBJECTIVES
After students have studied this study unit and chapters 3 and 4 of Daniel and Ishai (2006),
they should be able to
•
•
•
discuss the basic principles of the various methods used for predicting the properties
of composite materials
apply the mechanics of materials and the Halpin-Tsai approaches to determine the
properties of composite materials
determine and analyse the behaviour of composite laminae on a micromechanics
level
4.2
INTRODUCTION
A composite lamina forms a basic building block of composite laminate and composite
structures. Its behaviour is a function of the constituent (reinforcement and matrix)
properties and constituent geometric characteristics (e.g. fibre volume ratio and geometric
parameters).
There are three known idealised packing geometries, namely rectangular, square and
hexagonal. It is proven that composites with a low fibre volume ratio tend to have a
random fibre distribution, while fibres in composites with a high fibre volume ratio tend
to nest in nearly hexagonal packing.
The properties of the unidirectional lamina do not only depend on the fibre volume ratio,
but also on the packing geometry of the fibres. The fibre volume ratios for the three fibre
packing geometries are related to the fibre radius and fibre spacing.
This study unit considers the elastic behaviour of the unidirectional lamina, mainly from
the micromechanics level of analysis. Various methods of analysis are reviewed.
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Particularly, two predominant methods are detailed, namely the mechanics of materials
approach and the Halpin–Tsai approach.
The mechanics of materials approach is based on simplifying assumptions of either
uniform strain or uniform stress in the constituents. Approaches based on assumptions of
simplified stress states do not yield accurate results. Hence, semi-empirical (Halpin–Tsai)
relationships have been developed.
The so-called Halpin–Tsai relations constitute a mathematical model for the prediction of
elasticity of composite material based on the geometry and orientation of the filler and
the elastic properties of the filler and matrix.
4.3
MICROMECHANICAL PREDICTIONS OF ELASTIC CONSTANTS
Composite materials are generally viewed and analysed at different levels and on different
scales. A particular view would be based on the particular set of characteristics and
behaviours under consideration. Micromechanics can be defined as the study of the
interactions of the constituents of composites on a microscopic level, that is at the
constituent level where the scale of observation is the order of the fibre diameter, particle
size or matrix spaces between reinforcement (Daniel & Ishai 2006).
One objective of micromechanics is to obtain functional relationships for the elastic
constants of the composite in the form
𝐶𝐶𝑖𝑖𝑖𝑖 = 𝑓𝑓�𝐸𝐸𝑓𝑓 , 𝐸𝐸𝑚𝑚 , 𝑣𝑣𝑓𝑓 , 𝑣𝑣𝑚𝑚 , 𝑉𝑉𝑓𝑓 , 𝑉𝑉𝑚𝑚 , 𝑆𝑆, 𝐴𝐴�,
where
C is the composite stiffness,
subscripts i, j = 1, 2, 3,
subscript f = fibre,
subscript m = matrix, and
S and A are geometrical parameters describing the shape and array of the
reinforcement, respectively.
4.3.1
Scope and approaches
As far as the in-plain stress–strain relations are concerned, the behaviour of the
unidirectional lamina can be fully characterised in terms of four independent basic lamina
properties, such as
(1)
(2)
(3)
56
the four reduced stiffnesses Q11, Q22, Q12, and Q66; or
the four compliances S11, S22, S12, and S66; or
the four engineering constants E1, E2, G12, and v12
(where E is Young’s modulus, G is shear modulus and v is the Poisson’s ratio).
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The different approaches used in various methods for predicting properties of composites
fall into the following general categories:
(1)
(2)
(3)
(4)
(5)
(6)
mechanics of materials
numerical
self-consistent field
bounding
semi-empirical
experimental
The mechanics of materials predictions approach is sufficient for longitudinal properties
such as Young’s modulus E1 and Poisson’s ratio v12, which are not sensitive to fibre shape
and distribution. At the same time, the transverse modulus (E2) and shear modulus (G12)
properties are underestimated.
The numerical approaches are time consuming and do not yield close form expressions.
Instead results are presented in the form of a group of curves, which is time consuming.
The self-consistent field and bounding approaches yield complex expressions for
transverse modulus in terms of other properties.
Actually, to overcome the difficulties experienced with the theoretical approaches listed
in methods (1) to (4), and to facilitate computation, semi-empirical relationships have
been developed. One of these is the so-called Halpin–Tsai relationships, which have a
consistent form for all properties.
The Halpin–Tsai equations are a set of semi-empirical relationships that enable the
property of a composite material to be expressed in terms of the properties of the matrix
and reinforcing phases, together with their proportions and geometry. These equations
are confirmed by experimental measurements. Here, only final expressions are given for
the determination of the basic elastic properties of a lamina (Daniel & Ishai 2006).
ACTIVITY 4.1
Discuss the basic principles of each one of the various methods stated above.
4.3.2
Longitudinal properties
Longitudinal modulus, as given by the following relation, assumes that the fibre can be
anisotropic with different properties in the axial and transverse (radial) directions, and
that the matrix is isotropic.
𝐸𝐸1 = 𝑉𝑉𝑓𝑓 𝐸𝐸1𝑓𝑓 + 𝑉𝑉𝑚𝑚 𝐸𝐸𝑚𝑚
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This prediction is called the rule of mixtures,
where
𝐸𝐸1 and 𝑣𝑣12 are properties related to loading in the fibre direction and are dominated by
fibres (usually stronger, stiffer and low ultimate strain fibres),
𝐸𝐸1𝑓𝑓 is the longitudinal fibre moduli,
𝐸𝐸𝑚𝑚 is the longitudinal matrix moduli,
𝑉𝑉𝑓𝑓 is the fibre volume ratio, and
𝑉𝑉𝑚𝑚 is the matrix volume ratio.
The rule of mixtures prediction for the major (longitudinal) Poisson’s ratio is given
by
𝑣𝑣12 = 𝑉𝑉𝑓𝑓 𝑣𝑣12𝑓𝑓 + 𝑉𝑉𝑚𝑚 𝑣𝑣𝑚𝑚 ,
where
𝑣𝑣12𝑓𝑓 is the longitudinal Poisson’s ratio of the fibre, and
4.3.3
𝑣𝑣𝑚𝑚 is the Poisson’s ratio of the matrix.
Transverse modulus
In the case of transverse normal loading, the transverse modulus is a matrix-dominated
property that is sensitive to the local state of stress.
In the mechanics of materials approach, where the fibres and matrix are assumed to be
under uniform stress, the transverse modulus tends to be underestimated. The composite
is represented by a series of models of fibre and matrix yielding the following prediction
relation for transverse modulus:
𝑉𝑉𝑓𝑓
1
𝑉𝑉𝑚𝑚
=
+
𝐸𝐸2 𝐸𝐸2𝑓𝑓 𝐸𝐸𝑚𝑚
or
𝐸𝐸2 = 𝑉𝑉
𝑓𝑓
where
𝐸𝐸2𝑓𝑓 𝐸𝐸𝑚𝑚
𝐸𝐸𝑚𝑚 +𝑉𝑉𝑚𝑚 𝐸𝐸2𝑓𝑓
,
𝐸𝐸2𝑓𝑓 is the transverse modulus of the fibre, and
𝐸𝐸𝑚𝑚 is the matrix modulus. It is usually replaced by
𝐸𝐸
𝐸𝐸′𝑚𝑚 = 1−𝑣𝑣𝑚𝑚 2 ,
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𝑚𝑚
therefore
𝐸𝐸2 =
𝐸𝐸2𝑓𝑓 𝐸𝐸′𝑚𝑚
.
𝑉𝑉𝑓𝑓 𝐸𝐸′𝑚𝑚 + 𝑉𝑉𝑚𝑚 𝐸𝐸2𝑓𝑓
The following Halpin–Tsai semi-empirical relationship is a more practical approach once
the choice for the parameter ξ has been made:
where
𝐸𝐸2 = 𝐸𝐸𝑚𝑚
and
η1 =
1+ξ1 η1 𝑉𝑉𝑓𝑓
1−η1 𝑉𝑉𝑓𝑓
,
𝐸𝐸2𝑓𝑓 − 𝐸𝐸𝑚𝑚
𝐸𝐸2𝑓𝑓 + ξ1 𝐸𝐸𝑚𝑚
ξ1 is the reinforcing efficiency factor for transverse loading.
For values of ξ1 that are between 1 and 2, the above Halpin–Tsai prediction tends to agree
with experimental results. If a reliable experimental value of 𝐸𝐸2 is available for a
composite, the obtained value of ξ1 can be used to predict 𝐸𝐸2 for a wide range of fibre
volume ratios on the same composite.
Transverse modulus as a function of fibre volume ratio for various composites obtained
by the Halpin–Tsai relation is shown in figure 4.1.
Figure 4.1
Transverse modulus of unidirectional composites as a function
of fibre volume ratio (Daniel & Ishai 2006)
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4.3.4
In-plane shear modulus
The behaviour of unidirectional composites under in-plain (longitudinal) shear loading is
also dominated by the matrix properties and the distribution of the local stress. The
mechanics of materials using a series model under uniform tress yields the following
prediction (this approach tends to underestimate the in-plain shear modulus):
𝑉𝑉𝑓𝑓
1
𝑉𝑉𝑚𝑚
=
+
𝐺𝐺12 𝐺𝐺12𝑓𝑓 𝐺𝐺𝑚𝑚
or
𝐺𝐺12 = 𝑉𝑉
𝑓𝑓
where
𝐺𝐺12𝑓𝑓 𝐺𝐺𝑚𝑚
𝐺𝐺𝑚𝑚 +𝑉𝑉𝑚𝑚 𝐺𝐺12𝑓𝑓
,
𝐺𝐺12𝑓𝑓 is the shear moduli of the fibre, and
𝐺𝐺𝑚𝑚 is the shear moduli of the matrix.
In this case the Halpin–Tsai relation is
𝐺𝐺12 = 𝐺𝐺𝑚𝑚
where
1+ξ2 η2 𝑉𝑉𝑓𝑓
1−η2 𝑉𝑉𝑓𝑓
𝐺𝐺12𝑓𝑓 −𝐺𝐺𝑚𝑚
η2 = 𝐺𝐺
12𝑓𝑓 +ξ2
𝐺𝐺𝑚𝑚
,
, and
ξ2 is the reinforcing efficiency factor for in-plain shear.
The best agreement with experimental results is obtained when ξ2 = 1, which changes
the relation to
12
�𝐺𝐺
+𝐺𝐺𝑚𝑚 �+𝑉𝑉𝑓𝑓 �𝐺𝐺12𝑓𝑓 −𝐺𝐺𝑚𝑚 �
= 𝐺𝐺𝑚𝑚 �𝐺𝐺12𝑓𝑓 +𝐺𝐺
12𝑓𝑓
.
𝑚𝑚 �−𝑉𝑉𝑓𝑓 �𝐺𝐺12𝑓𝑓 −𝐺𝐺𝑚𝑚 �
The variation of the in-plain shear modulus with fibre volume ratio for various composites
obtained by numerical analysis is shown in figure 4.2.
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Figure 4.2
In-plane shear modulus of unidirectional composites as a function
of fibre volume ratio (Daniel & Ishai 2006)
4.3.5
The composite property (Halpin–Tsai)
The general composite property P* is obtained from
or
where
𝑃𝑃 ∗ =
𝑃𝑃∗ =
𝑃𝑃𝑚𝑚 �1 + ξ η 𝑉𝑉𝑓𝑓 �
𝑟𝑟
𝑃𝑃𝑚𝑚 �𝑃𝑃𝑓𝑓 +ξ 𝑃𝑃𝑚𝑚 +ξ 𝑉𝑉𝑓𝑓 �𝑃𝑃𝑓𝑓 −𝑃𝑃𝑚𝑚 ��
𝑃𝑃𝑓𝑓 +ξ 𝑃𝑃𝑚𝑚 −𝑉𝑉𝑓𝑓 �𝑃𝑃𝑓𝑓 −𝑃𝑃𝑚𝑚 �
,
𝑃𝑃 −𝑃𝑃𝑚𝑚
η = 𝑃𝑃 𝑓𝑓+ξ 𝑃𝑃 ,
𝑓𝑓
𝑚𝑚
𝑃𝑃𝑓𝑓 is the fibre property, and
𝑃𝑃𝑚𝑚 is the matrix property.
For ξ → ∞ we obtain the parallel (Voigt) model
𝑃𝑃∗ = 𝑉𝑉𝑓𝑓 𝑃𝑃𝑓𝑓 + 𝑉𝑉𝑚𝑚 𝑃𝑃𝑚𝑚 .
For ξ = 0 we obtain the series (Reuss) model
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𝑉𝑉
𝑉𝑉
−1
𝑃𝑃∗ = �𝑃𝑃𝑓𝑓 + 𝑃𝑃𝑚𝑚 � .
𝑓𝑓
𝑚𝑚
For an experimental value of 𝑃𝑃 ∗ for a given value of 𝑉𝑉𝑓𝑓 , the parameter ξ is given by
ξ=
4.3.6
𝑃𝑃𝑓𝑓 (𝑃𝑃 ∗ −𝑃𝑃𝑚𝑚 )− 𝑉𝑉𝑓𝑓 𝑃𝑃∗ �𝑃𝑃𝑓𝑓 −𝑃𝑃𝑚𝑚 �
𝑃𝑃𝑚𝑚 ��𝑃𝑃𝑓𝑓 −𝑃𝑃∗ �− 𝑉𝑉𝑚𝑚 �𝑃𝑃𝑓𝑓 −𝑃𝑃𝑚𝑚 ��
.
Semi-empirical relation (Halpin–Tsai) for short fibres
By setting the parameter ξ as
𝑙𝑙
ξ = 𝑟𝑟 = 2𝑠𝑠,
where
s is the fibre aspect ratio = l/2r,
l is the length of the fibres, and
r is the fibre radius,
the longitudinal modulus of a short-fibre composite can be estimated as
𝐸𝐸1 =
or
𝐸𝐸𝑚𝑚 �𝐸𝐸1𝑓𝑓 +2𝑠𝑠 𝐸𝐸𝑚𝑚 +2𝑠𝑠 𝑉𝑉𝑓𝑓 �𝐸𝐸1𝑓𝑓 −𝐸𝐸𝑚𝑚 ��
,
𝐸𝐸1𝑓𝑓 +2𝑠𝑠 𝐸𝐸𝑚𝑚 −𝑉𝑉𝑓𝑓 �𝐸𝐸1𝑓𝑓 −𝐸𝐸𝑚𝑚 �
𝐸𝐸1 = 𝐸𝐸𝑚𝑚
𝐸𝐸1𝑓𝑓 �1+2𝑠𝑠 𝑉𝑉𝑓𝑓 �+2𝑠𝑠 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚
𝐸𝐸1𝑓𝑓 𝑉𝑉𝑚𝑚 +𝐸𝐸𝑚𝑚 �2𝑠𝑠+𝑉𝑉𝑓𝑓 �
.
From the relation above, as the fibre aspect ratio increases (𝑠𝑠 → ∞), the material becomes
a continuous-fibre composite.
4.4
STRESS-STRAIN RELATIONS IN MACROMECHANICS
The macromechanical analysis considers the unidirectional lamina as a quasihomogeneous anisotropic material with its own average stiffness and strength properties.
The properties of the constituents can be used to control and predict the average material
behaviour.
4.4.1
General anisotropic material
In an anisotropic material, there are no planes of material property symmetry. Therefore,
it has different physical properties in different directions relative to the crystal orientation
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of the materials; that is, the material properties are directionally dependent. The stressstrain relations for an anisotropic body can be written in the contracted notation as
(Daniel & Ishai 2006):
and
𝜎𝜎1
𝐶𝐶11
⎡𝜎𝜎2⎤ ⎡𝐶𝐶21
⎢𝜎𝜎 ⎥ ⎢𝐶𝐶
⎢ 3⎥ = ⎢ 31
⎢𝜏𝜏4 ⎥ ⎢𝐶𝐶41
⎢𝜏𝜏5 ⎥ ⎢𝐶𝐶51
⎣𝜏𝜏6 ⎦ ⎣𝐶𝐶61
𝜖𝜖1
𝑆𝑆11
⎡𝜖𝜖2 ⎤ ⎡𝑆𝑆21
⎢𝜖𝜖 ⎥ ⎢𝑆𝑆
⎢ 3 ⎥ = ⎢ 31
⎢𝛾𝛾4 ⎥ ⎢𝑆𝑆41
⎢𝛾𝛾5 ⎥ ⎢𝑆𝑆51
⎣𝛾𝛾6 ⎦ ⎣𝑆𝑆61
𝐶𝐶12
𝐶𝐶22
𝐶𝐶32
𝐶𝐶42
𝐶𝐶52
𝐶𝐶62
𝑆𝑆12
𝑆𝑆22
𝑆𝑆32
𝑆𝑆42
𝑆𝑆52
𝑆𝑆62
𝐶𝐶13
𝐶𝐶23
𝐶𝐶33
𝐶𝐶43
𝐶𝐶53
𝐶𝐶63
𝑆𝑆13
𝑆𝑆23
𝑆𝑆33
𝑆𝑆43
𝑆𝑆53
𝑆𝑆63
𝐶𝐶14
𝐶𝐶24
𝐶𝐶34
𝐶𝐶44
𝐶𝐶54
𝐶𝐶64
𝑆𝑆14
𝑆𝑆24
𝑆𝑆34
𝑆𝑆44
𝑆𝑆54
𝑆𝑆64
𝐶𝐶15
𝐶𝐶25
𝐶𝐶35
𝐶𝐶45
𝐶𝐶55
𝐶𝐶65
𝑆𝑆15
𝑆𝑆25
𝑆𝑆35
𝑆𝑆45
𝑆𝑆55
𝑆𝑆65
𝐶𝐶16
𝐶𝐶26 ⎤
⎥
𝐶𝐶36 ⎥
𝐶𝐶46 ⎥
𝐶𝐶56 ⎥
𝐶𝐶66 ⎦
𝑆𝑆16
𝑆𝑆26 ⎤
⎥
𝑆𝑆36 ⎥
𝑆𝑆46 ⎥
𝑆𝑆56 ⎥
𝑆𝑆66 ⎦
𝜖𝜖1
⎡𝜖𝜖2 ⎤
⎢𝜖𝜖 ⎥
⎢ 3⎥
⎢𝛾𝛾4 ⎥
⎢𝛾𝛾5 ⎥
⎣𝛾𝛾6 ⎦
𝜎𝜎1
⎡𝜎𝜎2 ⎤
⎢𝜎𝜎 ⎥
⎢ 3⎥
⎢ 𝜏𝜏4 ⎥
⎢ 𝜏𝜏5 ⎥
⎣ 𝜏𝜏6 ⎦
There are 21 independent elastic constants in the stress–strain relation as given above.
Normal stresses produce normal strains due to the Poisson effect and shear strains due to
the effect of mutual influence. In the same way, shear stresses produce shear strains and
normal strains.
4.4.2
Orthotropic material
By definition, an orthotropic material is the material that has three (or at least two)
mutually perpendicular planes of material symmetry, where material properties are
independent of the direction within each plane. The material behaviour is called specially
orthotropic, when the normal stresses are applied in the principal material directions. If
not, it is called general orthotropic, which behaves almost equivalent to anisotropic
material. The stress-strain relations for an orthotropic body can be written in the
contracted notation as (Daniel & Ishai 2006):
and
𝜎𝜎1
0
𝐶𝐶11 𝐶𝐶12 𝐶𝐶13 0
0
⎡𝜎𝜎2 ⎤ ⎡𝐶𝐶 𝐶𝐶 𝐶𝐶
0 ⎤
0
0
⎥
⎢𝜎𝜎 ⎥ ⎢ 12 22 23
0 ⎥
0
⎢ 3 ⎥ = ⎢𝐶𝐶13 𝐶𝐶23 𝐶𝐶33 0
0 ⎥
0 𝐶𝐶44 0
⎢ 𝜏𝜏4 ⎥ ⎢ 0 0
⎢ 𝜏𝜏5 ⎥ ⎢ 0 0
0 0 𝐶𝐶55 0 ⎥
⎣ 𝜏𝜏6 ⎦ ⎣ 0 0
0
0 𝐶𝐶66 ⎦
0
𝜖𝜖1
⎡𝜖𝜖2 ⎤
⎢𝜖𝜖 ⎥
⎢ 3⎥
⎢𝛾𝛾4 ⎥
⎢𝛾𝛾5 ⎥
⎣𝛾𝛾6 ⎦
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𝜖𝜖1
𝑆𝑆11 𝑆𝑆12 𝑆𝑆13 0 0 0
⎤
⎡𝜖𝜖2 ⎤ ⎡𝑆𝑆 𝑆𝑆 𝑆𝑆
0 0 0
11
22
23
⎢
⎥
⎢𝜖𝜖 ⎥
⎢ 3 ⎥ = ⎢𝑆𝑆13 𝑆𝑆23 𝑆𝑆33 0 0 0 ⎥
⎢𝛾𝛾4 ⎥ ⎢ 0 0 0 𝑆𝑆44 0 0 ⎥
⎢𝛾𝛾5 ⎥ ⎢ 0 0 0 0 𝑆𝑆55 0 ⎥
⎣𝛾𝛾6 ⎦ ⎣ 0 0 0 0 0 𝑆𝑆66 ⎦
𝜎𝜎1
⎡𝜎𝜎2 ⎤
⎢𝜎𝜎 ⎥
⎢ 3⎥
⎢ 𝜏𝜏4 ⎥
⎢ 𝜏𝜏5 ⎥
⎣ 𝜏𝜏6 ⎦
There are nine independent elastic constants in the stiffness matrix as given below for a
specially orthotropic material. From the stress-strain relation, it is clear that normal
stresses applied in one of the principal material directions cause elongation in the
direction of the applied stresses and contractions in the other two transverse directions
simultaneously. In addition, normal stresses applied in any other direction will create
both extensional and shear deformations.
4.4.3
Transversely isotropic material
An orthotropic material is called transversely isotopic when one of its principal planes is
a plane of isotropy. This means at every point there is a plane on which the mechanical
properties are the same in all directions. A lot of unidirectional composites with fibres
packed in a hexagonal array (or close to the hexagonal array) are usually considered
transversely isotropic, with the 2–3 plane (normal to the fibres) is the plane of isotropy
(see figure 4.3). This is the case with unidirectional carbon/epoxy, aramid/epoxy and
glass/epoxy composites with relatively high fibre volume ratios.
Figure 4.3
Orthotropic material with transverse isotropy (Daniel & Ishai 2006)
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The stress-strain relation for a transversely isotropic material reduce to:
and
0
𝜎𝜎1
0 ⎤
0
⎡𝐶𝐶11 𝐶𝐶12 𝐶𝐶12
0
⎡𝜎𝜎2 ⎤
0 ⎥
0
⎢𝐶𝐶 𝐶𝐶 𝐶𝐶
⎢𝜎𝜎 ⎥ ⎢ 12 22 22
0
0 ⎥
0
3
𝐶𝐶
𝐶𝐶
𝐶𝐶
⎢ ⎥ = ⎢ 12 23 23 𝐶𝐶22 − 𝐶𝐶23
𝜏𝜏
0 ⎥
0
0
⎢ 4⎥ ⎢ 0 0
2
⎢ 𝜏𝜏5 ⎥
𝐶𝐶55 0 ⎥⎥
0
⎢ 0 0
0
⎣ 𝜏𝜏6 ⎦
0 𝐶𝐶55 ⎦
0
⎣ 0 0
0
𝜖𝜖1
𝑆𝑆11
⎡𝜖𝜖2 ⎤ ⎡𝑆𝑆
⎢𝜖𝜖 ⎥ ⎢ 11
⎢ 3 ⎥ = ⎢𝑆𝑆13
⎢ 𝛾𝛾4 ⎥ ⎢ 0
⎢𝛾𝛾5 ⎥ ⎢ 0
⎣𝛾𝛾6 ⎦ ⎣ 0
𝑆𝑆12 𝑆𝑆12
0
0 0
⎤
𝑆𝑆22 𝑆𝑆22
0
0 0
⎥
0
0 0 ⎥
𝑆𝑆23 𝑆𝑆23
0 0 2(𝑆𝑆22 − 𝑆𝑆23 ) 0 0 ⎥
𝑆𝑆55 0 ⎥
0
0 0
0
0 𝑆𝑆55 ⎦
0 0
There are five independent elastic constants for these materials.
4.4.4
𝜖𝜖1
⎡𝜖𝜖2 ⎤
⎢𝜖𝜖 ⎥
⎢ 3⎥
⎢𝛾𝛾4 ⎥
⎢𝛾𝛾5 ⎥
⎣𝛾𝛾6 ⎦
𝜎𝜎1
⎡𝜎𝜎2 ⎤
⎢𝜎𝜎 ⎥
⎢ 3⎥
⎢ 𝜏𝜏4 ⎥
⎢ 𝜏𝜏5 ⎥
⎣ 𝜏𝜏6 ⎦
Isotropic material
In an isotropic material, the properties are the same in all directions (axial, lateral and in
between). An isotropic material is characterised by an infinite number of planes of
material property symmetry passing through a point, which means that material properties
are directionally independent. Therefore, there are two independent elastic constants,
such as the stiffnesses C11 and C12. Then the stress–strain relations are reduced to (Daniel
& Ishai 2006):
0
0
0
𝜎𝜎1
⎡𝐶𝐶11 𝐶𝐶12 𝐶𝐶12
⎤
0
0
0
⎡𝜎𝜎2 ⎤ ⎢𝐶𝐶 𝐶𝐶 𝐶𝐶
⎥
0
⎢𝜎𝜎 ⎥ ⎢ 12 11 12
0
0
⎥
⎢ 3 ⎥ = ⎢𝐶𝐶12 𝐶𝐶12 𝐶𝐶11 𝐶𝐶11 − 𝐶𝐶12
0
0
⎥
0 0 0
⎢ 𝜏𝜏4 ⎥
𝐶𝐶11 − 𝐶𝐶12
0
⎢
⎥
2
⎢ 𝜏𝜏5 ⎥
0 0 0
𝐶𝐶
−
𝐶𝐶
⎢
⎥
0
11
12
2
⎣ 𝜏𝜏6 ⎦
0
0
0
⎦
⎣
0
0
2
𝜖𝜖1
⎡𝜖𝜖2 ⎤
⎢𝜖𝜖 ⎥
⎢ 3⎥
⎢𝛾𝛾4 ⎥
⎢𝛾𝛾5 ⎥
⎣𝛾𝛾6 ⎦
Tensile normal stresses applied in any direction on an isotropic material cause elongation
in the direction of the applied stresses and contractions in the other two transverse
directions. It does not yield shear strain in the material. Likewise, shear stresses will only
yield corresponding shear strains.
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In table 4.1, the required number of independent elastic constants for the various types
of composite materials are summarised.
Table 4.1 Independent elastic constants for various types of materials (Daniel &
Ishai
2006)
Material
General anisotropic material
Anisotropic material considering symmetry of
stress and strain tensors �𝜎𝜎𝑖𝑖𝑖𝑖 = 𝜎𝜎𝑗𝑗𝑗𝑗 , 𝜀𝜀𝑖𝑖𝑖𝑖 = 𝜀𝜀𝑗𝑗𝑗𝑗 �
Anisotropic
material
with
elastic
energy
considerations
General orthotropic material
Orthotropic material with transverse isotropy
Isotropic material
4.5
No. of independent elastic
constants
81
36
21
9
5
2
PROBLEMS
Problem 4.1
Determine the transverse modulus 𝐸𝐸2 of a carbon/epoxy composite with the following
properties:
𝐸𝐸2𝑓𝑓 = 14.8 Pa
𝐸𝐸𝑚𝑚 = 3.45 Pa
𝑣𝑣𝑚𝑚 = 0.36
𝑉𝑉𝑓𝑓 = 0.65
Use the mechanics of materials approach and the Halpin-Tsai relationship with ξ1 = 1.
Answer: 7.56 GPa; 8.13 GPa
Problem 4.2
Determine the transverse modulus 𝐸𝐸2 of silicon carbide/aluminium (SiC/Al) composite
with the following properties:
𝐸𝐸2𝑓𝑓 = 366 Pa
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𝐸𝐸𝑚𝑚 = 69 Pa
𝑣𝑣𝑚𝑚 = 0.33
𝑉𝑉𝑓𝑓 = 0.40
Use the mechanics of materials approach and the Halpin-Tsai relationship with ξ1 = 2.
Problem 4.3
Determine the in-plane shear modulus 𝐺𝐺12 of a glass/epoxy composite with the following
properties:
𝐺𝐺𝑓𝑓 = 28.3 Pa
𝐺𝐺𝑚𝑚 = 1270 Pa
𝑉𝑉𝑚𝑚 = 0.55
Use the mechanics of materials approach and the Halpin-Tsai relationship with ξ2 = 1.
Answer: 2.68 GPa; 3.84 GPa
Problem 4.4
In the general Halpin-Tsai expression for composite properties, prove that the value of
parameter ξ = 0 corresponds to the series model and ξ → ∞ corresponds to the parallel
model.
Problem 4.5
In the general Halpin-Tsai expression, find the limiting values of parameter η and the
corresponding composite properties for the cases of rigid inclusions (fibres),
homogeneous material (fibres of the same material as the matrix) and voids (totally
debonded fibres).
Answer:
η = 1, 𝑃𝑃∗ = 𝑃𝑃𝑚𝑚
1 + ξ𝑉𝑉𝑓𝑓
𝑉𝑉𝑚𝑚
η = 0, 𝑃𝑃∗ = 𝑃𝑃𝑚𝑚
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1
1 + ξ𝑉𝑉𝑚𝑚
η = − , 𝑃𝑃∗ = 𝑃𝑃𝑚𝑚
ξ
ξ + 𝑉𝑉𝑓𝑓
Problem 4.6
The measured transverse modulus E2 of a unidirectional carbon/epoxy composite is
E2 = 10.3 GPa. Given that Em = 3.45 GPa and Vf = 0.65, determine the transverse fibre
Modulus E2f of the fibre using the Halpin–Tsai relation with ξ = 1.5.
Answer: E2 = 21.86 GPa
Problem 4.7
A unidirectional glass/epoxy composite with properties Em = 3.45 GPa, E2f = 69 GPa
and Vf = 0.55 has a transverse modulus of E2 = 8.56 GPa. Determine the appropriate
value of ξ in the Halpin-Tsai relation; and then determine the transverse modulus of a
composite of the same constituents but with a fibre volume ratio of Vf = 0.65.
Problem 4.8
The in-plane shear modulus of a unidirectional carbon/epoxy composite was measured
to be G12 = 6.9 GPa. Determine the value of parameter ξ in the Halpin-Tsai relation for
the following properties:
Gm = 1.27 GPa
G12f= 13.1 GPa
Vf = 0.60
Answer: ξ = 13.29
Problem 4.9
The in-plane shear modulus of a unidirectional carbon/epoxy composite was measured
to be G12 = 6.9 GPa. Use the Halpin–Tsai relation for ξ = 10 and the following properties:
Gm = 1.27 GPa
Vf = 0.60
Determine the in-plane shear modulus of the fibre G12f.
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Problem 4.10
The measured shear modulus of a boron/epoxy composite with a fibre volume ratio of Vf
= 0.50 is G12 = 5.4 GPa. Using the Halpin-Tsai relation, determine the appropriate value
of ξ and shear modulus G12 for a similar material with Vf = 0.70 and the following
constituent properties:
G12f = 165 GPa
Gm = 1.27 GPa
Answer: ξ = 2.425; G12 = 10.59 GPa
Problem 4.11
The longitudinal modulus of a glass/epoxy composite containing short aligned fibres of
length l is El = 40 GPa. Using Halpin’s semi-empirical relation, determine the length l of
the fibres for the following properties:
Vf = 0.60
df = 10 μm
Ef = 70 GPa
Em = 3.5 GPa
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Study unit 1
5
DAMAGE IN COMPOSITES
5.1
LEARNING OBJECTIVES
After students have studied this study unit and part 4 of chapter 35 (sections 35.2 and
35.3) in Peters (1998), they should be able to
•
define terminology associated with damage in composite materials as outlined in this
study unit
describe the various composite materials damage mechanisms
apply the Griffith model for the mechanics of fractures, and distinguish between this
analysis and other techniques of composite fracture mechanics such as the stress
intensity approach, the complex stress function approach and the strain energy release
rate approach
•
•
5.2
INTRODUCTION
If a purpose for a designed structure is to carry loads, it is the designer’s responsibility to
ensure that is has enough load-carrying capacity for the specific application. If the said
structure is to function over a period, then it must be designed to function without losing
its integrity during that period. This is a generic requirement, regardless of the material
used.
Note that there are significant differences in the design procedures using monolithic
materials and those involving the use of composite materials. Certain parameters, such as
heterogeneity and anisotropy, lead to significantly different characteristics in composite
materials. These differences relate to how they deform and fail compared to monolithic
materials. This study unit reviews those characteristics.
In contrast to monolithic materials, the inherent behaviour of a composite can change
due to damage incurred in service. While monolithic materials can fail due to the unstable
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growth of a crack, the heterogeneous internal structure of a composite leads to the
formation of multiple cracks.
The following important terms need to be explained (Talreja & Singh 2012):
•
•
•
•
•
•
•
Fracture is usually understood to be the breakage of material or the breakage of
atomic bonds in a material.
Fracture mechanics a field that deals with conditions for the formation and
enlargement of the surfaces of material separation.
Damage is a collection of all the irreversible changes brought about in a material by
a set of energy dissipating physical or chemical processes, resulting from the
application of thermomechanical loadings.
Damage mechanics a field that deals with conditions for the initiation and progression
of distributed changes as well as with consequences of those changes for the response
of a material to external loading.
Failure is the inability of a given material system (and consequently, a structure made
from it) to perform its design function. Fracture is one example of a possible failure,
although a material can fracture and still perform its design function. In actuality, the
failure event associated with composite structures is preceded and influenced by the
progressive occurrence and interaction of various damage mechanisms.
Structural integrity is the ability of a structure to remain intact (not breaking up into
pieces) and functional upon the application of loads. Note that composites can lose
their functionality by suffering degradation in their stiffness properties while still
carrying significant loads.
Durability is a term whose meaning is close to the meaning of structural integrity, but
it specifically defined as the structure’s ability to retain adequate properties (i.e.
strength, stiffness and environmental resistance) throughout its life to the extent that
any deterioration can be controlled and repaired. The long-term durability of a
composite structure is an important design requirement in civil engineering,
infrastructure projects and the aerospace industry.
5.3
DAMAGE MECHANISMS
The following are the reasons for the complexities observed in geometrical features of
micro-level failure or micro-cracks:
(1)
(2)
(3)
(4)
the heterogeneous microstructure of composites
the large differences between constituent properties
the presence of interfaces (e.g. between fibres and matrices, and between plies in a
laminate)
the directionality of reinforcement that induces anisotropy in overall properties
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Interfacial debonding
The performance of a fibre-reinforced composite is influenced by the properties of the
interface between the fibre and the matrix resin, because the interface plays an important
role in stress transfer between the fibre and matrix. The control of interfacial properties is
therefore critical to the performance of composite structures. In unidirectional
composites, for instance, a weak interface causes debonding (or separation) between the
fibre and matrix, as shown in figure 5.1.
Figure 5.1
Debonds in a fibre-reinforced composite (Talreja & Singh 2012)
Interfacial sliding
An example of interfacial sliding in a composite is when the fibres and matrix are not
bonded together by an adhesive, but instead are shrink fit due to their differences in
thermal expansion properties. When the fibres and matrix in a composite are adhesively
bonded together, interfacial sliding can occur following a debonding if a compressive
normal stress on the interface is present.
Matrix micro-cracking or intralaminar (ply) cracking
Fibre-reinforced composites develop cracks along fibres due to generally low strength
and stiffness in the transverse directions. These cracks are also referred to as transverse,
intralaminar, ply or matrix micro-cracks. They can be caused by tensile and fatigue
loadings as well as by temperature changes. The matrix micro-cracks originating from
fibre/matrix debonding and manufacturing-induced voids and inclusions are shown in
figure 5.2.
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Figure 5.2
Matrix crack initiation from: (a) fibre debonds; and (b) void results
(Talreja & Singh 2012)
Delamination or interlaminar cracking
Interlaminar cracking is the cracking that occurs in the plane between two adjoining plies
in a laminate. This type of cracking causes separation of the plies (delamination). Sources
of interlaminar cracking include low-velocity impacts, low interlaminar strength and low
fracture toughness.
Fibre breakage
Fibre-reinforced composites offer high strength and stiffness properties, especially in the
longitudinal direction. The failure of fibre-reinforced composites is the ultimate result of
the breakage of fibres.
Fibre microbuckling
Unidirectional composites that are loaded in compression are susceptible to this type of
fibre microbuckling. Two idealised modes of the microbuckling of fibres (i.e. extensional
and shear modes) are illustrated in figure 5.3.
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Figure 5.3
Extensional and shear modes of fibre microbuckling (Talreja & Singh 2012)
Particle cleavage
Particle cleavage is the main mode of damage when brittle particles such as ceramics are
placed in a ductile, strong and tough matrix. This mode of damage is found in particulate
metal matrix composites.
Void growth
Voids are one of the primary defects occurring in all types of composite materials. The
formation of voids is part of the defects that are induced during manufacturing. The
presence of voids has a detrimental effect on the overall material behaviour.
Damage modes
Interactions between the individual mechanics described above further complicate the
damage situation. For clarity of treatment, the full scope of damage can be divided into
damage modes. These modes are then treated individually and their interactions are
examined.
The determination of the damage mechanisms that become active in a given life period
of a composite structure is mainly dependent on the following:
(1)
(2)
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the properties of the base material (matrix)
architecture (misalignment, irregular distribution in the cross-section, material
breakages)
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(3)
(4)
(5)
(6)
(7)
(8)
orientation
distribution
volume fraction of the reinforcing agent (fibre)
the properties of the interface
loading
environmental conditions
The dominant damage mechanisms in long fibre composites are the following:
(1)
(2)
(3)
(4)
intralaminar cracking
interlaminar cracking
fibre fracture
microbuckling
The major damage mechanisms in particulate composites are (1) the debonding of the
particle and (2) cavity nucleation (see figure 5.4).
Figure 5.4
Damage mechanisms in particulate composites (Talreja & Singh 2012)
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5.4
DEVELOPMENT OF DAMAGE IN COMPOSITE LAMINATES
The damage accumulation process is the most significant single feature of damage in
composites. Damage development usually involves several damage modes that create a
widely distributed damage state. Failure is usually the result of a statistical accumulation
of damage rather than the statistical occurrence of damage (Peters 1998). These multiple
damage accumulations on failure modes are closely related to the manner in which the
composite is made (i.e. the inhomogeneity and anisotropic nature of the material). The
predominant damage mode in composite materials is micro-cracking, typically in the
matrix material. A common scenario for the development of such cracks is the formation
of matrix cracks as a function of an increasing load or increasing cycles of loading.
Matrix crack formation releases stored energy in the cracked ply or material, and changes
the stiffness of the material (Peters 1998). However, the density of cracks in the ply of a
laminate reaches a stable saturation value called the characteristic damage state (CDS) of
the ply. The CDS is a function only of the properties of the plies, their thickness and their
stacking sequence. Figure 5.5 shows that the CDS is formed by static or cyclic loading.
Figure 5.5
Spacing of cracks in –45° plies of [𝟎𝟎/𝟗𝟗𝟗𝟗/±𝟒𝟒𝟒𝟒]𝒔𝒔 graphite/epoxy laminates as a function
of quasi-static and fatigue loading (Talreja & Singh 2012)
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Figure 5.6 is a schematic depiction of damage development in composite laminates in
tension. There are five identifiable damage mechanisms, which are given in the order of
their occurrence. The figure provides the basic details for quasi-static loading.
The early stage of damage accumulation is dominated by multiple matrix cracking in the
layers that have fibres aligned transversely to the applied load direction. Depending upon
the laminate configuration, the transverse matrix cracks can initiate at 0.4% (Talreja &
Singh 2012). The initiation begins at locations of defects or at areas of high fibre volume
fraction or even resin-rich areas. Ply cracks grow unstably through the width direction
and then span the specimen width. More and more cracks appear as the applied load
increases.
Figure 5.6
Development of damage in composite laminate (Talreja & Singh 2012)
5.5
DAMAGE MECHANICS
The objectives of damage mechanics analysis are generalised as follows:
(1)
(2)
(3)
(4)
(5)
(6)
to understand the conditions for initiation of the first damage event
to predict the evolution of progressive damage
to characterise and quantify damage in the structure
to analyse the effect of damage on thermomechanical response
to assess the criticality of damage and the durability of the structure
to provide input into the overall structure and design
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5.6
ANALYSIS OF FRACTURE
The purpose of this section is to introduce the analysis of fracture of composites due to
cracks, particularly as outlined in Gibson (2016).
5.6.1
Fracture mechanics analysis of through-thickness cracks
The origin of fracture mechanics can be traced back to seminal work of Griffith (1920),
in which the discrepancy between the measured and predicted strength of glass is
explained by considering the stability of a small crack. The stability criterion was
developed by using an energy balance on the crack.
Figure 5.7 shows the through-thickness crack in the uniaxially loaded homogeneous,
isotropic and linear elastic plate of infinite width. From the stress analysis, Griffith
estimated that the strain energy released by the creation of the crack under plane stress
conditions would be
𝑈𝑈𝑟𝑟 =
where
𝜋𝜋𝜎𝜎2 𝑎𝑎2 𝑡𝑡
𝐸𝐸
,
𝑈𝑈𝑟𝑟 is the strain energy released,
𝜎𝜎 is the applied stress,
𝑎𝑎 is half-crack length,
𝑡𝑡 is plate thickness, and
𝐸𝐸 is modulus of elasticity of the plate.
Figure 5.7
Griffith crack: A through-thickness crack in a uniaxially stressed
plate of infinite width (Gibson 2016)
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The volume of the given ellipse with lengths 4a and 2a (see figure 5.7) is
𝑉𝑉 = 𝜋𝜋(2𝑎𝑎)(𝑎𝑎)(𝑡𝑡) = 2𝜋𝜋𝑎𝑎2 𝑡𝑡.
Thus, the strain energy released due to the relaxation of the elliptical volume around the
crack is
1 𝜎𝜎 2
𝜋𝜋𝜎𝜎 2 𝑎𝑎2 𝑡𝑡
𝑉𝑉 =
.
𝑈𝑈𝑟𝑟 =
2 𝐸𝐸
𝐸𝐸
Another assumption by Griffith is that the creation of new crack surfaces requires the
absorption of an amount of energy given by
where
𝑈𝑈𝑠𝑠 = 4𝑎𝑎𝑎𝑎𝛾𝛾𝑠𝑠 ,
𝑈𝑈𝑠𝑠 is the energy absorbed by creation of new crack surfaces, and
𝛾𝛾𝑠𝑠 is the surface energy per unit area.
As the crack grows and if the rate at which energy is absorbed by creating new surfaces
is greater than the rate at which strain energy is released, then
𝜕𝜕𝜕𝜕𝑠𝑠
>
𝜕𝜕𝜕𝜕𝑟𝑟
,
𝜕𝜕𝜕𝜕𝑟𝑟
>
𝜕𝜕𝜕𝜕𝑠𝑠
,
𝜕𝜕𝜕𝜕𝑟𝑟
=
𝜕𝜕𝜕𝜕𝑠𝑠
,
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
and the crack growth is stable. If the strain energy is released at a greater rate than it is
absorbed, then the conditions are
𝜕𝜕𝜕𝜕
𝜕𝜕𝜕𝜕
and the crack growth is unstable. The condition of neutral equilibrium is therefore
or
𝜕𝜕𝜕𝜕
𝜋𝜋𝜎𝜎2 𝑎𝑎
𝐸𝐸
𝜕𝜕𝜕𝜕
= 2𝛾𝛾𝑠𝑠 .
Thus, for self-sustaining extension of the crack in plane stress, the critical stress 𝜎𝜎𝑐𝑐 is
2𝐸𝐸𝛾𝛾𝑠𝑠
𝜎𝜎𝑐𝑐 = �
𝜋𝜋𝜋𝜋
,
or the critical flaw size for plane stress at stress 𝜎𝜎 is
𝑎𝑎𝑐𝑐 =
2𝐸𝐸𝛾𝛾𝑠𝑠
𝜋𝜋𝜎𝜎2
.
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Fracture toughness, Kc
It can be seen from above equations that
𝜎𝜎√𝜋𝜋𝜋𝜋 = �2𝐸𝐸𝛾𝛾𝑠𝑠 ,
where
𝜎𝜎√𝜋𝜋𝜋𝜋 depends on loading and geometry, and
�2𝐸𝐸𝛾𝛾𝑠𝑠 depends on the material properties.
When the stress 𝜎𝜎 reaches the critical fracture stress 𝜎𝜎𝑐𝑐 , then
the term 𝜎𝜎√𝜋𝜋𝜋𝜋 becomes 𝜎𝜎𝑐𝑐 √𝜋𝜋𝜋𝜋, which is referred to as the fracture toughness, Kc.
Many of the difficulties presented by the application of the Griffith-type analysis to
composites have been solved over the years since his work was first published. Two of
the several analytical techniques used to solve problems encountered in the development
of composite fracture mechanics are the stress intensity factor approach and the strain
energy release rate approach.
5.6.2
Stress intensity factor approach
The Griffith analysis was originally developed for homogeneous, isotropic materials in
simple, uniaxial states of stress. By considering the stress distribution around the crack
tip, another interpretation of the Griffith analysis can be developed and applied equally
to homogeneous isotropic or anisotropic materials, as well as to other states of stress.
Using the complex stress function approach and the information in figure 5.8, it can be
shown that the stresses for the isotropic case at a point P defined by polar coordinates
(r, θ) can be expressed as
𝜎𝜎𝑥𝑥 =
𝜎𝜎𝑦𝑦 =
80
√2𝜋𝜋𝜋𝜋
𝐾𝐾𝐼𝐼
√2𝜋𝜋𝜋𝜋
𝜏𝜏𝑥𝑥𝑥𝑥 =
where
Thus,
𝐾𝐾𝐼𝐼
𝑓𝑓1 (𝜃𝜃)
𝑓𝑓2 (𝜃𝜃)
𝐾𝐾𝐼𝐼
𝑓𝑓 (𝜃𝜃),
√2𝜋𝜋𝜋𝜋 3
𝐾𝐾𝐼𝐼 is the stress intensity factor for the crack opening mode = 𝜎𝜎√𝜋𝜋𝜋𝜋.
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the critical value of the stress intensity factor, 𝐾𝐾𝐼𝐼𝐼𝐼 , which corresponds to the
critical stress 𝜎𝜎𝑐𝑐 , is the fracture toughness or critical stress intensity factor,
𝑓𝑓𝑖𝑖 (𝜃𝜃) is the trigonometric function of the angle,
the term 𝜎𝜎√𝜋𝜋𝜋𝜋 controls the magnitudes of the stresses at a point (r, θ) near the
crack tip (Gibson 2016), and
𝐾𝐾𝐼𝐼𝐼𝐼 is the material property that can be determined experimentally.
Figure 5.8
Stresses at the tip of a crack under plane stress (Gibson 2016)
Three basic modes of crack deformation
Figure 5.9 shows the three basic modes of crack deformation.
For mode I (crack opening mode), the stress intensity factor is 𝐾𝐾𝐼𝐼 .
For mode II (the in-plane shear mode), the stress intensity factor is 𝐾𝐾𝐼𝐼𝐼𝐼 .
For mode III (the anti-plane shear mode), the stress intensity factor is 𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 .
For example, for the cases of pure shear loading in mode II and mode III, we have
𝐾𝐾𝐼𝐼𝐼𝐼 = 𝜏𝜏√𝜋𝜋𝜋𝜋 and 𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 = 𝜏𝜏√𝜋𝜋𝜋𝜋, respectively, where 𝜏𝜏 is different for the two modes.
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Figure 5.9
Three basic modes of crack deformation (Gibson 2016)
One of the major shortcomings of this approach is that a stress analysis of the crack tip
region is required. A useful alternative approach is the strain energy release rate approach.
5.6.3
Strain energy release rate approach
This approach has a physical interpretation that is valid for both isotropic and anisotropic
materials. It is a powerful tool in both experimental and computational studies of crack
growth.
Consider a through-thickness cracked linear elastic plate under a uniaxial load, as shown
in figure 5.10(a). From the unloaded condition, an increase in the load P will cause a
linearly proportional change in the displacement, u, at the point of application of the load
(see the load-displacement plot in figure 5.10(b)).
Figure 5.10
Loaded plate and corresponding load-displacement curve used for strain
energy release rate analysis: (a) plate under uniaxial load and
(b) load-displacement curve (Gibson 2016)
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From further analysis of the system shown in Figure 5.10 above (although not detailed
here), the system compliance s is given by
𝑢𝑢
𝑠𝑠 = 𝑃𝑃,
where
s is the system compliance (not the material compliance S defined
as a ratio of strain to stress),
u is the displacement, and
P is the load applied.
The potential energy of the plate in figure 5.10(a) is
1
1
𝑈𝑈 = 2 𝑃𝑃𝑃𝑃 = 2 𝑠𝑠𝑃𝑃2 .
The incremental work done during the crack extension is approximately
∆𝑊𝑊 = 𝑃𝑃(∆𝑢𝑢).
For a plate of constant thickness t, the strain energy release rate GI for mode I crack
deformation is
𝐺𝐺𝐼𝐼 =
𝑃𝑃 2 𝜕𝜕𝜕𝜕
2𝑡𝑡 𝜕𝜕𝜕𝜕
.
NOTE: GI is not to be confused with the shear modulus G.
𝜕𝜕𝜕𝜕
The critical strain energy release rate for mode I corresponds to the value Pc and �𝜕𝜕𝜕𝜕� at
fracture, that is
𝐺𝐺𝐼𝐼𝐼𝐼 =
𝑃𝑃𝑐𝑐 2
2𝑡𝑡
𝜕𝜕𝜕𝜕
𝑐𝑐
�𝜕𝜕𝜕𝜕� .
𝑐𝑐
For mode I, crack deformation in isotropic materials under plane stress,
so that
𝐾𝐾𝐼𝐼 2 = 𝐺𝐺𝐼𝐼 𝐸𝐸,
𝐾𝐾𝐼𝐼𝐼𝐼 2 = 𝐺𝐺𝐼𝐼𝐼𝐼 𝐸𝐸.
Example 5.1
A unidirectional E-glass/epoxy composite plate having a central through-thickness crack
of length 2a is subjected to a uniaxial stress 𝜎𝜎, as shown in figure 5.7. The unidirectional
fibres are oriented at an angle 𝛼𝛼 with respect to the direction of the crack, where 𝛼𝛼 is in
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radians. The mode I fracture toughness of the composite,𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 , varies with the angle 𝛼𝛼
according to the empirical equation
𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 = [0.739𝛼𝛼 2 + 0.19𝛼𝛼 + 1]𝐾𝐾𝐼𝐼𝐼𝐼0,
where
The applied stress is
𝐾𝐾𝐼𝐼𝐼𝐼0 = 1.47 MPa m1⁄2 is the fracture toughness at the
angle 𝛼𝛼 = 0 (i.e. when the crack is parallel to the fibre
direction).
𝜎𝜎 = 100 MPa.
Determine the critical crack size ac for the cases, where the crack is (a) perpendicular to
the fibres and (b) parallel to the fibres.
Solution:
For case (a), 𝛼𝛼 = 1.57 rad,
𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 = [0.739(1.57)2 + 0.19(1.57) + 1](1.47) = 4.59 MPa m1⁄2 ,
and the critical crack size is
𝑎𝑎𝑐𝑐 =
𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 2
𝜋𝜋𝜎𝜎2
(4.59)2
= 𝜋𝜋(100)2 = 0.00067 m = 0.67 mm.
For case (b), 𝛼𝛼 = 0, 𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 = 𝐾𝐾𝐼𝐼𝐼𝐼0 = 1.47 MPa m1⁄2 and the critical crack size is
𝑎𝑎𝑐𝑐 =
𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 2
𝜋𝜋𝜎𝜎2
(1.47)2
= 𝜋𝜋(100)2 = 0.00007 m = 0.07 mm.
Thus, the fracture toughness and the critical crack size are both greater for case (a) than
they are for case (b). It is also important to note that a non-destructive inspection
technique must be able to detect smaller cracks when the cracks are parallel to the fibres
rather than when the cracks are perpendicular to the fibres.
Example 5.2
A quasi-isotropic graphite/epoxy laminate has a fracture toughness 𝐾𝐾𝐼𝐼𝐼𝐼 = 30 MPa m1⁄2
and a tensile strength of 500 MPa. As shown in figure 5.11, a 25 mm wide structural
element made from this material has an edge crack of length a = 3 mm. If the element is
subjected to a uniaxial stress, 𝛼𝛼, determine the critical value of the stress that would cause
unstable propagation of the crack. Compare this stress with the tensile strength of the
material, which does not take cracks into account.
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Figure 5.11
Single edge crack in a plate under uniaxial stress for example 5.2 (Gibson 2016)
Solution
The stress intensity factor for the single edge crack in figure 5.11 is
𝐾𝐾𝐼𝐼 = σ√𝜋𝜋𝜋𝜋𝑓𝑓(𝑎𝑎⁄𝑏𝑏),
where the function 𝑓𝑓(𝑎𝑎⁄𝑏𝑏)is given by the empirical formula
𝑓𝑓(𝑎𝑎⁄𝑏𝑏) = 1.12 − 0.231(𝑎𝑎/𝑏𝑏) + 10.55(𝑎𝑎/𝑏𝑏)2 − 21.72(𝑎𝑎/𝑏𝑏)3 + 30.39(𝑎𝑎/𝑏𝑏)4 ,
which is said to be accurate within 0.5% when 𝑎𝑎⁄𝑏𝑏 ≤ 0.6.
For this case,
𝑎𝑎⁄𝑏𝑏 = 3/25 = 0.12, and
𝑓𝑓(𝑎𝑎⁄𝑏𝑏) = 1.213.
The critical stress is then
𝜎𝜎𝑐𝑐 =
𝐾𝐾𝐼𝐼𝐼𝐼
√𝜋𝜋𝜋𝜋𝑓𝑓(𝑎𝑎⁄𝑏𝑏 )
=
30
√𝜋𝜋(0.003)(1.213)
= 255 MPa.
Comparing this stress with the tensile strength of 500 MPa, we see that in this case, the
cracked element can sustain only about 50% of the stress that an uncracked element
could withstand.
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Example 5.3
A foam core sandwich beam in four-point flexural loading is shown in figure 5.12, along
with the shear force and bending moment diagrams. The overall dimensions of the beam
are s = 120 mm; d = 41.6 mm; hc = 12.7 mm; tf = 0.711 mm; and b = 25.4 mm. The
fibres in the unidirectional carbon/epoxy face sheets are aligned with the beam axis. The
longitudinal Young’s modulus of the face sheets is Efs = 139.4 Pa and the shear modulus
is Gfs =3.36 GPa. The isotropic foam core has a Young’s modulus Ec = 0.092 GPa and a
shear modulus Gc = 0.035 GPa. Core shear fracture is observed to occur in the regions
of maximum shear force V. The critical stress intensity factor for mode II shear fracture in
the foam core is 𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 = 0.00654 MPa m1⁄2 and a shear crack of size 2aII = 1.566 mm is
located at the point of maximum core shear stress.
Determine the critical value of the total applied load, Pc.
Figure 5.12
Sandwich beam in four-point flexural loading, along with corresponding
shear force and bending moment diagrams (Gibson 2016)
Solution
For the mode II crack shown if figure 5.13, the critical stress intensity factor is
𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼 = τ√𝜋𝜋𝑎𝑎𝐼𝐼𝐼𝐼 ,
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so the critical shear stress is
𝜏𝜏𝑐𝑐 =
𝐾𝐾𝐼𝐼𝐼𝐼𝐼𝐼
√𝜋𝜋𝑎𝑎𝐼𝐼𝐼𝐼
=
0.0654
�𝜋𝜋(0.000783)
= 1.319 MPa.
Figure 5.13
Mode II shear crack for example 5.3 (Gibson 2016)
It can be shown that the maximum transverse shear stress in the foam core occurs at the
middle surface in the regions of the maximum shear force 𝑉𝑉𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 /2, between the
loading points and the support points. From laminated beam theory, the transverse shear
stress at the inner edge of the kth layer is given by equation
(𝜏𝜏𝑥𝑥𝑥𝑥 )𝑘𝑘 =
𝐸𝐸
𝑉𝑉
𝑓𝑓 𝐼𝐼𝑦𝑦𝑦𝑦
𝑧𝑧𝑧𝑧
⁄2
∑𝑁𝑁
𝑗𝑗=𝑘𝑘 ∫𝑧𝑧𝑧𝑧−1(𝐸𝐸𝑥𝑥 )𝑗𝑗 𝑧𝑧 𝑑𝑑𝑑𝑑 =
𝑉𝑉
2𝐸𝐸𝑓𝑓 𝐼𝐼𝑦𝑦𝑦𝑦
⁄2
2
2
∑𝑁𝑁
𝑗𝑗=𝑘𝑘 (𝐸𝐸𝑥𝑥 )𝑗𝑗 �𝑧𝑧𝑗𝑗 − 𝑧𝑧𝑗𝑗−1 �.
For the sandwich beam described in figure 5.12, the above equation evaluated at
the middle surface yields the following result for the maximum shear stress:
(𝜏𝜏𝑥𝑥𝑥𝑥 )1 =
𝑉𝑉�0.092�6.352 −0�+139.4�7.0612 −6.352 ��
2(38.08)(25.4)(14.122)3 /12
= 0.002936𝑉𝑉 MPa,
where V is in Newtons. Setting this result equal to the critical shear stress
𝜏𝜏𝑐𝑐 = 1.319 MPa, we find that the corresponding critical shear force is
𝑉𝑉 = 𝑉𝑉𝑐𝑐 = 449.25 N,
and the critical applied load is 𝑃𝑃𝑐𝑐 = 2𝑉𝑉𝑐𝑐 = 898.5 N.
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5.7
PROBLEMS
Problem 5.1
A randomly oriented, shorter-fibre-reinforced composite plate having a central throughthickness crack of length 2a is subjected to a uniaxial stress 𝜎𝜎, as shown in figure 5.7. If
the composite has a fracture toughness KIc = 50 MPa m1/2 and the applied stresses
𝜎𝜎 = 200 MPa, determine the critical crack size ac for unstable and catastrophic crack
growth.
Problem 5.2
The thin-walled tubular shaft shown in figure 5.14 is made of a randomly oriented, shortfibre-reinforced metal matrix composite. The shaft has a longitudinal through-thickness
crack of length 2a and is subjected to a torque T=1 kNm. If the mode II fracture toughness
of the composite is KIIc = 40 MPa m1/2, determine the critical crack size for self-sustaining
crack growth.
Figure 5.14
Thin-walled tubular composite shaft with longitudinal crack (Gibson 2016)
Problem 5.3
(a) Determine the allowable torque, T, if the crack length for the shaft in figure 5.14 is
2a = 10 mm. Use the same dimensions and fracture toughness values that were
given in problem 5.2.
(b) If the uniaxial yield stress for the shaft material is Υ = 1200 MPa, and the crack is
ignored, compare the answer to part (a) with the allowable torque based on the
maximum shear stress criterion for yielding.
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Problem 5.4
The tube shown in figure 5.14 is subjected to an internal pressure, p = 5 MPa, instead of
a torque. Neglecting the stress along the longitudinal axis of the tube, and assuming that
the mode I fracture toughness is KIc = 10 MPa m1/2, determine the critical crack size.
Answer: ac = 12.7 mm
Problem 5.5
As in problem 5.4, assume that the tube in figure 5.14 is subjected only to an internal
pressure and neglect the longitudinal stress.
(a)
(b)
Determine the allowable internal pressure, p, if the crack length in figure 5.14 is
2a = 10 mm. Use the same dimensions and fracture toughness values that were
given in problem 5.4.
Using the yield stress from problem 5.3 and ignoring the crack, compare the answer
to part (a) of this problem with the allowable internal pressure based on the
maximum shear stress criterion for yielding.
Problem 5.6
A 3 mm thick composite specimen is tested, as shown in figure 5.10(a), and the
compliance, s = u/P, as a function of the half-crack length, a, is shown in figure 5.15. In
a separate test, the critical load for self-sustaining crack propagation, Pc, is measured for
different crack lengths, and the critical load corresponding to a crack length 2a = 50 mm
is found to be 100 N. Determine the critical mode I strain energy release rate, GIc.
Figure 5.15
Variation of specimen compliance with crack length for problem 5.6 (Gibson 2016)
Answer: GIc = 0.1667; N/mm = 166.7 J/m2
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Problem 5.7
The sandwich beam described in example 5.3 is subjected to a total applied load
P = 500 N. Assuming that a shear crack is located at the middle surface of the beam in
the region of maximum shear force, determine the critical crack size for mode II core
shear fracture.
5.8
SUMMARY
Damage mechanisms relating to the deformation and failure of composite materials were
summarised in this study unit. An overview of damage development in composites was
also provided.
The Griffith analysis applies to a crack in an infinite width plate.
NOTE: The stress intensity factor in some publications is defined as 𝑘𝑘1 = 𝜎𝜎√𝑎𝑎. This
corresponds to the cancellation of √𝜋𝜋 in both the numerator and the denominator of some
equations and thus leading to 𝐾𝐾𝐼𝐼 = 𝑘𝑘1 √𝜋𝜋.
Expressions for stress distributions for other types of loading and crack geometries in
isotropic materials can be found referenced in Gibson (2016). While such analyses have
been performed for a variety of loading conditions and crack geometries for isotropic
materials, the corresponding analyses for anisotropic materials have only been done for
few cases due to mathematical difficulties.
5.9
ACTIVITIES
Activity 5.1
Define the following terms relating to composites:
(1)
(2)
(3)
damage
fracture
failure
Activity 5.2
Discuss the interfacial sliding mechanisms in the following materials:
(1)
(2)
(3)
(4)
90
CMCs
PMCs
MMCs
SFCs (short-fibre composites)
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Activity 5.3
Discuss the transverse cracking mechanisms in the following materials:
(1)
(2)
(3)
(4)
CMCs
PMCs
MMCs
SFCs (short-fibre composites)
Activity 5.4
Use schematic diagrams to illustrate the two idealised modes of microbuckling.
Activity 5.5
List FOUR damage mechanisms dominant in long-fibre composites.
Activity 5.6
Use the illustration in figure 5.5 to describe in detail how damage develops in composite
laminates.
Activity 5.7
What is the most pervasive damage mode in composite materials?
Activity 5.8
What are some of the major drawbacks of the Griffith-type analysis?
Activity 5.9
What are some of the major drawbacks of the stress intensity approach?
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Study unit 1
6
FATIGUE OF COMPOSITES
6.1
LEARNING OBJECTIVES
After students have studied this study unit, they should be able to
•
•
•
describe the fatigue behaviour of fibre composite materials
describe and illustrate the purpose of fatigue life diagrams in composites
discuss the effects of constituent properties deriving from composite action
6.2
INTRODUCTION
Since the early 1970s, advances have been made in characterising and modelling the
mechanical behaviour of composite materials, and developing tools and methodologies
for predicting their fracture and fatigue. This study unit presents the concept of fatigue as
related to this area of composites. Fatigue is treated separately from damage because of
its particular complexities that require systematic interpretation schemes that have been
developed for this purpose. The fracture surface of a metal sample failed in fatigue differs
uniquely from the fracture surface of a metal sample failed in the application of a
monotonically (consistently) increasing load. The fracture surface of a unidirectional fibrereinforced composite, loaded along fibres monotonically or cyclically, does not clearly
indicate mechanisms that precede failure in either case; following the events from their
initiation until separation is generally difficult.
When the loading is applied in a cyclic manner, it is normal to assume that the
complexities of damage observed under quasi-static loading would be greater. A
systematic conceptual framework for fatigue life and failure interpretations (for more
general cases of loading as well as for more general fibre orientations) takes the form of a
two-dimensional plot called the fatigue life diagram. The diagram is a means of
interpreting the roles or effects of fibres (e.g. fibre stiffness), the matrix (e.g. matrix
ductility) and interfaces and laminate configuration parameters (e.g. ply orientation,
sequence and thickness).
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6.3
FATIGUE LIFE DIAGRAM AND THE FATIGUE BEHAVIOUR OF
COMPOSITES
The unidirectional composite (or ply) is a basic unit in laminates. The fatigue life diagram
for this composite under tension–tension loading forms the baseline diagram from which
more cases evolve. This diagram is shown in figure 6.1. The y-axis is the maximum strain
attained at the first application of maximum stress in a load-controlled fatigue test. This
quantity provides upper and lower limits to the fatigue behaviour. Consequently, the
strain to failure (of fibre) forms the upper limit, while the strain corresponding to the
fatigue (primarily a matrix property) forms the lower limit. The strain values can always
be converted to applied stress. The regions shown in the diagram provide clarity about
the governing mechanisms dictated by the properties of the constituent. This diagram can
also serve the purpose of facilitating mechanisms-based life prediction modelling.
Figure 6.1
Fatigue life diagram of a unidirectional fibre-reinforced composite subjected
to cyclic tension in the fibre direction (Talreja & Singh 2012)
6.4
EFFECTS OF CONSTITUENT PROPERTIES
Fibres of different material (glass, carbon and SiC) have different axial moduli and fail at
different axial tensile strains. For instance, depending on processing and surface
treatment, carbon fibres can fail at strains of ~0.5% or those in excess of 1.8%. In most
composites, stiffness and failure strain in the fibre direction are mainly determined by the
fibre properties.
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The effect on composite fatigue of changing fibres and/or matrix properties can be viewed
on the fatigue life diagram as shown in figure 6.2.
Figure 6.2
Trends in fatigue life diagrams due to constituent properties (Talreja & Singh 2012)
Activity 6.1
Identify the trends in figure 6.2, where the fibre-bridged cracking is the progressive
mechanism.
6.5
UNIDIRECTIONAL COMPOSITES LOADED PARALLEL TO THE
FIBRES
The fatigue life diagram in figure 6.2 has been developed using generic considerations of
damage mechanisms. This section deals with the illustration of the interpretation of
fatigue behaviour of unidirectional composites under cyclic on-axis tension by
considering test data (Talreja & Singh 2012).
6.5.1
PMCs
The fatigue life diagram is used as a baseline diagram for interpreting the fatigue of PMCs
system. Fatigue for other material systems (MMCs and CMCs) then becomes easy to
interpret.
Figure 6.3 shows the fatigue life data for a glass/epoxy composite of three different fibre
volume fractions. These data are plotted in the conventional manner with the applied
stress amplitude on the y-axis.
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Figure 6.3
Stress/life data of a unidirectional glass/epoxy composite loaded in
tension parallel to the fibres (Talreja & Singh 2012)
In figure 6.4, the data are replotted using the maximum strain applied in the first cycle as
the vertical axis, in accordance with the fatigue life diagram. As seen in figure 6.4, the
data for the three volume fractions are found to fall together. The horizontal scatter band
of composite failure strain is drawn as region I; and the fatigue limit of the epoxy resin in
strain control testing, reported to be at 0.6% strain (Talreja & Singh 2012), has been drawn
as the assumed fatigue limit of the glass/epoxy composites. A scatter band placed about
the fatigue life data indicates region II. Plotting fatigue life against strain allows for an
interpretation that is more meaningful. It also confirms that the fatigue limit of the matrix
is a good indication of the composite fatigue limit when plotted in the strain coordinate.
The existence of region I is not strongly indicated by the glass/epoxy data.
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Figure 6.4
Fatigue life diagram of a unidirectional glass/epoxy composite loaded
in tension parallel to the fibres (Talreja & Singh 2012)
Consider a set of unidirectional carbon/epoxy composites where each composite has
different types of carbon fibre and the same epoxy resin:
Two examples of stress–strain behaviour, one with relatively low stiffness fibres and the
other with relatively high stiffness fibres, are shown in figure 6.5(a) and (b), respectively.
Figure 6.5
Effect of fibre stiffness and strain to failure on composite stiffness
in a unidirectional composite in longitudinal loading (a) composite with low stiffness
fibres; and (b) composite with high stiffness fibres (Talreja & Singh 2012)
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NOTE:
𝜀𝜀𝑚𝑚 is the matrix fatigue limit.
𝜀𝜀𝑐𝑐 is the composite failure strain.
𝜀𝜀𝑐𝑐 is lower for higher fibre stiffness.
Therefore the following is true:
•
•
The result of changing carbon fibre stiffness is an increase or decrease the extent of
region II.
The result of composite failing at 𝜀𝜀𝑐𝑐 < 𝜀𝜀𝑚𝑚 is that no fatigue progression would be
possible; that is, region II would not exist as 𝜀𝜀𝑚𝑚 would lie above region I. Thus, only a
horizontal scatter band resembling region I will appear in the fatigue life diagram, as
illustrated in figure 6.6 (using fatigue life data for a carbon/epoxy composite with high
stiffness fibres). The 𝜀𝜀𝑚𝑚 , assumed for epoxy to be 0.6% strain, has been marked in
figure 6.6, along with the average 𝜀𝜀𝑐𝑐 , at about 0.48% strain.
Figure 6.6
Fatigue life diagram of unidirectional composite reinforced by stiff fibres
with low strain to failure (Talreja & Singh 2012)
NOTE: There is no fatigue degradation, since the mechanism is non-progressive fibre
breakage only.
The set of data in figure 6.7 is for carbon/epoxy with fibres of stiffnesses lower than those
used in the composite mentioned above (medium stiffness). The data suggest the
following:
•
•
There is no fatigue degradation when viewed without the fatigue life diagram.
When the scatter band of region I and 𝜀𝜀𝑚𝑚 of epoxy are placed in the diagram, the
progressive fatigue mechanism of region II is seen to exist in a narrow range of strain.
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Figure 6.7
Fatigue life diagram of unidirectional composite reinforced by medium stiffness fibres,
showing a narrow range of strain where fatigue occurs (Talreja & Singh 2012)
The set of data in figure 6.8 is for lower stiffness carbon/epoxy. The data suggest the
following: Depending on where the fatigue limit lies, there would be a region II of
progressive fatigue damage. The fatigue limit in the figure is indicated at 0.6% strain as
reference comparison with other cases.
Figure 6.8
Fatigue life diagram of a unidirectional composite with low stiffness fibres, with
a relatively wide range of strain where fatigue occurs (Talreja & Singh 2012)
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For the set of data of carbon/epoxy fatigue shown in figure 6.9, the regions of the fatigue
life diagram appear distinctly. The value of recognising the existence of region I is evident.
Without this, the error introduced in assessing the fatigue life would be significant.
Figure 6.9
Fatigue life of a unidirectional carbon fibre/epoxy composite
with a distinct region I (Talreja & Singh 2012)
Using fatigue life diagrams, a fatigue performance comparison between different material
systems can be carried out. In addition, material systems of unknown constituent
composition can thus be compared and the best selection for a particular application
made. For further illustration of the fatigue life diagrams, figures 6.10 and 6.11 show test
data for Kevlar/epoxy and Kevlar/J2 polymer, respectively.
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Figure 6.10
Fatigue life diagram of a unidirectional Kevlar fibre/epoxy composite (Talreja & Singh
2012)
Figure 6.11
Fatigue life diagram of a unidirectional Kevlar fibre/J2
polymer composite (Talreja & Singh 2012)
6.5.2
MMCs
This section discusses the changes in the diagram when the matrix material is a metal.
Note the role of fibres in modifying the fatigue mechanisms taking place in the matrix.
The three regions of the fatigue life diagram for MMCs are discussed (Talreja & Singh
2012).
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Region I
This region is established by fibre failures. For PMCs it is argued that the fibre failures
occurred in a manner that did not have an accumulation of fibre failures in a localised
zone, leading to final failure of composite from random sites at random number of cycles.
However, the cyclic plastic deformation of a metal matrix around a broken fibre
redistributes stresses in the neighbouring fibres. This allows an accumulative fibre failure
process to occur. In consequence, a localised progressive degradation is introduced, and
on reaching a critical level, composite failure will manifest. As a result, the horizontal
scatter band of region I (in PMCs), will now have a downward slope.
Region II
The mechanism of fibre-bridged matrix cracking is also expected to be the primary
progressive mechanism for MMCs. The difference with respect to PMCs lies in the role of
fibre/matrix debonding. The fibre/matrix bond in MMCs is generally stronger, which leads
to a shorter extent of the interface failure. Moreover, the increased ductility of the metal
matrix leads to increased failure of the bridging fibres. The effect of the ductility of the
matrix will thus be as assumed above in describing the trend in region II of the fatigue life
diagram.
Region III
This region is expected to be the same as in PMCs. The composite fatigue limit is also
expected to be related to the matrix fatigue limit.
6.5.3
CMCs
Ceramics have insignificant irreversibility of deformation compared with polymers and
metals. However, when ceramics are reinforced by fibres with which they bond quickly,
a dissipative mechanism becomes available from reversed frictional sliding at interfaces.
This mechanism plays a role in causing fatigue of CMCs.
When considering fatigue, the first question to ask is: What happens in the material in the
second and following load cycles that is different from the damage caused in the first load
cycle? The answer lies in knowing the source of irreversibility in the material. Because
ceramics have insignificant plastic deformation, the likely source of irreversibility is
frictional sliding at the interface.
The discussion of the fatigue limit in CMCs is rather theoretical because the energy
dissipating in the mechanism of frictional sliding at debonded interfaces depends on
loading frequency and specimen geometry. The reason for this is that the time rate at
which the conduction of the heat generated by frictional sliding occurs affects the rate
per cycle of energy dissipation by frictional sliding.
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Activity 6.2
Discuss the existence and nature of the three regions of the fatigue life diagram for CMCs.
6.6
FATIGUE OF LAMINATES
As discussed previously, composite structures are built by placing fibres in different
orientations in order to carry multi-axial loading effectively. In this section, we consider
the influence of multidirectional fibre placement in a laminate on the mechanisms of
fatigue damage. We also consider how the influence translates into changing the basic
fatigue life diagram described above. The laminate under consideration is subjected to a
cyclic tensile load.
6.6.1
Angle-ply laminates
Angle-ply laminates have two fibre orientations, as in the [±𝜃𝜃𝑛𝑛 ]𝑠𝑠 illustrated in figure 6.12.
When loaded in the axial (0°) direction, a 𝜃𝜃-ply in the laminate behaves differently from
a unidirectional composite loaded off-axis at the same 𝜃𝜃-angle. Figure 6.12 depicts
multiple cracking and the associated delamination schematically.
The key elements of the fatigue failure process in laminates are illustrated by the angleply fatigue. They can be summarised as follows:
•
•
•
•
•
•
•
•
•
multiple ply cracking
delamination formation and growth
(possibly) more ply cracking
delamination merger in ply interfaces
separation of plies
overloading of individual plies
ply failure
fibre failures
laminate failure
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Figure 6.12
Multiple matrix cracks in the off-axis ply of a laminate (left) and
subsequent delamination caused by fatigue (right) (Talreja & Singh 2012)
(For clarity, cracks and delamination are shown for one ply
only; the other ply is indicated in broken lines.)
ACTIVITY 6.3
Discuss the fatigue life diagram for angle-ply laminates subjected to a cyclic tensile
load.
6.6.2
Cross-ply laminates
Cross-ply laminates,[0𝑛𝑛 /90𝑚𝑚 ]𝑠𝑠 , are orthogonal angle-ply laminates. Loading on cross-ply
laminates is usually applied in one of the two fibre directions. Figure 6.13 shows data for
a carbon/epoxy cross-ply laminate plotted on the strain scale. The location of the fatigue
limit strain has been taken at the value of stress (converted to strain) reported as the value
where the first transverse cracking was found (Talreja & Singh 2012).
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Figure 6.13
Experimental data verifying the anticipated fatigue life diagram
of cross-ply laminates (Talreja & Singh 2012)
Note the following features of the fatigue life diagram:
•
•
The fibre breakage process is non-progressive.
The fatigue limit is given by strain to transverse cracking leading to delamination.
ACTIVITY 6.4
Discuss the fatigue life diagram for cross-ply laminates under cyclic axial tension.
6.6.3
General multidirectional laminates
Practical structures of composites are designed to meet a variety of requirements, such as
to resist bending, torsion and thermal expansion. A common composite design is a
laminate, which consists of plies, each with unidirectional fibres, stacked in such a way
that the resulting structure possesses the required combination of properties. The number
of ply orientations is often kept to three. The most used ones are 0°, 45°, –45° and 90°.
The presence of 0° plies provides region I, which lies as a scatter band about the fibre
failure strain. The fatigue limit for a laminate is determined by the first cracking
mechanism. Thus, if 90° ply orientation is present in a laminate, the strain at which the
first transverse cracking occurs will determine the fatigue limit.
The progressive fatigue damage is represented by region II. It appears as a sloping scatter
band, starting at a low number of cycles and approaching the fatigue limit at a high
number of cycles. A life prediction model is needed to predict this slope.
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Figure 6.14 shows the fatigue life diagram for a glass/epoxy [0/±45/90]𝑠𝑠 laminate under
tension–tension loading along 0° direction. The failure strain of fibres (which is the same
as that of the laminate) is taken to place the scatter band of region I. The scatter band has
been drawn based on other similar data on fibre failure strain. The fatigue limit was placed
at 0.46% strain based on information about the strain at which transverse cracking is
apparent. It is noted that the scatter band of region II (placed around the fatigue life test
data) is nearly straight and meets the region I band at 102 to 103 cycles. The lower end of
the region II band is almost 107 cycles.
Figure 6.14
Fatigue life data for a glass/epoxy [𝟎𝟎/±𝟒𝟒𝟒𝟒/𝟗𝟗𝟗𝟗]𝒔𝒔 laminate under
tension–tension loading along 0° direction (Talreja & Singh 2012)
(The fatigue life diagram is superimposed on the data.)
ACTIVITY 6.5
Another set of data to consider is for a carbon/epoxy [0/±45/90]𝑠𝑠 laminate under
tension–tension loading along the 0° direction. Show the fatigue life diagram and
describe the procedure used for its construction.
6.7
FAILURE CRITERION FOR A LAMINATE
The following facts about a laminate have been established:
•
•
•
•
A laminate will fail under increasing mechanical and thermal loads.
A laminate failure may not be catastrophic.
Failed plies may still contribute to the stiffness and strength of the laminate.
When a ply fails and the cracks occur parallel to the fibres, the ply is still capable of
taking load parallel to the fibres.
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The procedure for finding successive loads between first ply failure and last ply failure
given by Kaw (2006) follows the fully discounted method and is outlined in steps (1) to
(7) below. The procedure for the partial discounting of fibres is more complicated.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
6.8
Given the mechanical loads, apply loads in the same ratio as the applied loads.
However, apply the actual temperature change and moisture content.
Use laminate analysis to find the mid-plane strains and curvatures.
Find the local stresses and strains in each ply under the assumed load.
Use the ply-by-ply stresses and strains in ply failure theories to find the strength
ratio. Multiplying the strength ratio to the applied load gives the load level of the
failure of the first ply. This load is called the first ply failure load.
Degrade fully the stiffness of the damaged ply or plies. Apply the actual load level
of previous failure.
Go to step (2) to find the strength ratio in the undamaged plies.
If the strength ratio is more than one, multiply the strength ratio to the applied load
to give the load level of the next ply failure, and go to step (2).
If the strength ratio is less than one, degrade the stiffness and strength properties of
all the damaged plies and go to step (5).
Repeat the above steps until all the plies in the laminate have failed. The load at
which all the plies in the laminate have failed is called the last ply failure.
SUMMARY
An overview of a systematic conceptual framework for interpretation of the fatigue
process in composites was provided in this study unit. An understanding of the physical
mechanisms underlying fatigue and incorporating them in fatigue life diagrams were
emphasised. Among other functions, these diagrams generate bases for material selection
and give useful guidelines for mechanisms-based modelling. It can be deduced that from
a fatigue point of view, the assessment of laminates is exceptionally simple. Most research
efforts have taken an empirical route due to the challenges of addressing the mechanisms
of fatigue damage accumulation.
6.9
ACTIVITIES
ACTIVITY 6.6
Describe the purpose of fatigue life diagrams with the aid of illustration diagrams.
ACTIVITY 6.7
Discuss the consequence of changing carbon fibre stiffness in unidirectional
carbon/epoxy composites with the aid of relevant diagrams.
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ACTIVITY 6.8
Discuss the THREE regions of the fatigue life diagram for MMCs.
ACTIVITY 6.9
Name at least TWO benefits of fatigue life diagrams.
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Study unit 1
7
DESIGN OF COMPOSITES
7.1
LEARNING OBJECTIVES
After students have studied this study unit, they should be able to
•
•
•
outline the method used to design ply layouts that achieve the structural design goals
for composite parts
describe the benefits of structural design using reinforced materials
apply the design methodology described to design a composite part
7.2
INTRODUCTION
A design process for composites is guided fundamentally by certain specific
considerations and optimisation criteria. For example, weight savings considerations play
a major role in aerospace applications. Commercially, automotive and sports industries
are led by cost competitiveness.
This study unit presents various aspects considered in the design of laminates and
provides insight into the numerous options for optimising materials for particular needs.
The basic equations are presented and design procedures outlined. Because simple
computer codes that embody these equations are now widely available, we no longer
need to solve these equations by hand. To demonstrate concepts, examples and sample
problems are included. The design of components determined by mechanical
performance requirements such as stiffness, durability or strength are also a feature of this
study unit.
The distinction between material properties and material strength is established. The term
material properties is used to include extensional (tensile) and compressive moduli of
elasticity, Poisson ratios, in-plane shear modulus, coefficients of thermal expansion and
coefficients of moisture expansion. The term material strengths refer specifically to
tension, compression, in-plane shear, interlaminar shear and bearing.
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7.3
DESIGN METHODOLOGY
A design process for structures of composites involves the following:
(1)
(2)
(3)
(4)
material selection
process specification
optimisation (of laminate configuration)
design of the structural components
Design objectives would vary following the structural application. Specific application
requirements may include one or more of the following objectives:
(1)
(2)
(3)
(4)
(5)
Design for stiffness.
Design for strength.
Design for dynamic stability.
Design for environmental stability.
Design for damage tolerance.
In table 7.1, various design objectives, structural requirements, material requirements,
and typical materials and applications are summarized
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Table 7.1 Design methodology for structural composite materials (Daniel & Ishai
2006)
Design objective
Design for stiffness
Structural
requirements
Small deflections
Material
requirements
High-stiffness fibres
in sandwich or
hybrid laminates for
high flexural rigidity
Typical material
Typical application
Carbon, graphite,
boron, and Kevlar
fibre composites
Aircraft control
surfaces
Underground,
underwater vessels
Thin skins in
comparison
Sporting goods
Marine structures
High lamina strength
with high degree of
fibre utilisation
High stiffness to
strength Ratio (𝜌𝜌𝐸𝐸𝐸𝐸 )
Carbon, Kevlar (in
tension), and S-glass
fibre
Composites
Pressure vessels
Trusses (tension
members)
Thin skins in
sandwich panels,
ribs, joints
Marine structures
Long fatigue life
High resonance
frequency
High-strength fibres
Fibres with high
specific stiffness (E/ρ)
Carbon, graphite
fibres
Thermoplastic
matrices
Vibration control
Low centrifugal forces
Ductile matrices or
hybrids with highdamping layers
Engine components
Aircraft components
Helicopter rotor
blades
Flywheels
High dimensional
stability under
extreme
environmental
fluctuations
Low coefficients of
thermal and moisture
expansion
High buckling loads
Low weight
Design for strength
High load capacity
(static, dynamic)
Low weight
High interlaminar
strength
Design for dynamic
control and stability
Design for
environmental
stability and durability
High corrosion
resistance
Design for damage
tolerance
High impact
resistance
High compressive
strength after impact
damage
Resistance to damage
growth
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Laminate design for
hygrothermal
isotropy
High-stiffness
anisotropic fibres
High fracture
toughness (intra- and
interlaminar)
Energy-absorbent
interlayers
Textile laminates
Interleaving with
thermoplastic layers
Carbon, graphite
fibre composites
Fabric composite
coatings
Kevlar fibre
composites
Tough epoxy
matrices,
thermoplastic
matrices
Interleaving
Radar and space
antennae
Space mirrors,
telescopes
Solar reflectors
Marine structures
Ballistic armor
Bulletproof vests,
helmets
Impact-resistant
structures
Rotor blades
(helicopters, wind
tunnels, wind
turbines)
Like every other mechanical part, a composite part has to withstand loadings. A designer
of a composite piece has to keep in mind the following characteristic properties of
composites:
(1) Fibre orientation enables the optimisation of the mechanical behaviour along a
specific direction.
(2) The material is elastic up to rupture. Unlike classical metallic materials, it cannot
yield by local plastic deformation.
(3) Fatigue resistance is excellent.
(4) The percentage elongation is not the same as that for metals (attention must be paid
to the metal/composite joints).
(5) Complex forms can be easily moulded.
(6) The number of parts can be reduced and the amount of processing work limited.
The importance of establishing and articulating design requirements cannot be
overstated. Unsuccessful applications are often the result of unclear or poorly defined
design requirements.
7.4
FATIGUE RESISTANCE
The specific fatigue resistance is expressed by the ratio 𝜎𝜎/𝜌𝜌, with 𝜎𝜎 being the normal
stress and 𝜌𝜌 the specific mass. This specific resistance is three times higher than for
aluminium alloys, and twice as high as the specific resistance of high strength steel and
titanium alloys, because the fatigue resistance is equal to
(1) 90% of the static fracture strength for a composite
(2) 35% of the static fracture strength for aluminium alloys
(3) 50% of the static fracture strength for titanium alloys
The above is illustrated by figure 7.1.
Figure 7.1
Comparison of the fatigue behaviour of a composite and aluminium (Gay & Hoa 2007)
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7.5
GUIDELINE VALUES FOR PREDESIGN
To assist designers in choosing a composite in the predesign phase, a comparison
between different materials is shown in figure 7.2.
Figure 7.2
Comparison of the characteristics of different materials (Gay & Hoa 2007)
Figure 7.3 shows a comparison of the principal specific properties of the fibres that make
up the plies. The specific modulus and specific strength are presented with regard to
lightweight structural materials.
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Figure 7.3
Specific characteristics of different fibres (Gay & Hoa 2007)
Safety factors
To take care of design uncertainties, certain safety factor values are defined. The
uncertainties for consideration are the following:
(1)
(2)
(3)
(4)
(5)
the magnitude of mechanical characteristics of reinforcement and matrix
the stress concentrations
the imperfection of the hypotheses for calculation
the fabrication process
the aging of materials
The safety factor values are given as follows:
High volume composites:
Static loading
short duration:
long duration:
Intermittent loading over a long term:
Cyclic loading:
Impact loading:
2
4
4
5
10
High performance composites:
1.3 to 1.8
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7.6
THE LAMINATE
Advanced composite materials are typically supplied as a thin layer called ply or lamina.
Laminated composites consist of thin layers (or plies) of different materials bonded
together, such as bimetals, clad metals, plywood, Formica and so on, with proper
orientations in each ply through the hand layup operation. A unidirectional ply or lamina
can be flat or curved layers of fibres orientated in one direction and held together by a
matrix material. Figure 7.4 is a schematic diagram of the various levels of consideration
and the corresponding types of analysis. The stresses perpendicular to the planar surface
are taken as zero.
Figure 7.4
Levels of observation and types of analysis for composite materials (Daniel & Ishai
2006)
7.6.1
Unidirectional layers
The advantages of unidirectional layers include the following:
(1)
(2)
(3)
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High rigidity.
The ply can be used to wrap over a long distance. Then the load transmission of the
fibres is continuous over a great distance.
There is less waste.
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The disadvantages of unidirectional layers include the following:
(1)
(2)
7.6.2
Wrapping takes long.
Wrapping is not suitable for complex shapes.
Fabrics
The advantages of fabrics include the following:
(1) Reduced wrapping time.
(2) Complex forms can be shaped using the deformation of the fabric.
(3) Different types of fibres can be combined in the same fabric.
The disadvantages of fabrics include the following:
(1) Fabrics have a lower modulus and strength than unidirectional layers.
(2) More material is wasted after cutting.
(3) Joints are required when wrap large parts are wrapped.
7.6.3
Ply orientation
The fundamental advantage of laminates is their ability to adapt and control fibre
orientation in such a way that the material can best resist loadings. It is therefore important
to know how plies contribute to laminate resistance. Figures 7.5 to 7.8 show situations
that must be encouraged and the ones that should be avoided.
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Figure 7.5
Effect of ply orientation (Gay & Hoa 2007)
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Recall the Mohr circle:
In figure 7.6, the Mohr circle for stresses show that the 45° fibres support the
compression, 𝜎𝜎1 = −𝜏𝜏 (where 𝜏𝜏 is the arithmetic value of shear stress), while the resin
supports the tension, 𝜎𝜎2 = 𝜏𝜏, with low fracture limit.
Figure 7.6
Poor design (Gay & Hoa 2007)
The fibres in figure 7.7 support the tension, 𝜎𝜎1 = 𝜏𝜏, while the resin supports the
compression, 𝜎𝜎2 = −𝜏𝜏. In figure 7.8, the fibres are deposited at 45° and –45°. Taking
into account the previous remarks, the 45° fibres can support the tension 𝜎𝜎1 = 𝜏𝜏. While
the –45° fibres can support the compression, 𝜎𝜎2 = −𝜏𝜏. The resin is less loaded than
previously.
Figure 7.7
Mediocre design (Gay & Hoa 2007)
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Figure 7.8
Good design (Gay & Hoa 2007)
While providing a weight savings due to the difference in material densities, with equal
fibre distribution in multiple directions and rendering an effectively quasi-isotropic
material, composites can approximate metals. Take into account, however, their relative
orientation with respect to the loading directions. The designer must take advantage of
being able to tailor the properties of the material. The result is a material with different
properties in different directions (anisotropic).
7.6.4
Laminate design
The unique features of composites are highly direction-dependent properties. Examples
of such unique properties include the following:
(1)
(2)
(3)
Poisson’s ratios greater than unity or even negative
bending–twisting coupling
zero to negative coefficients of thermal expansion (CTE)
Because load-carrying fibre is in effectively all directions, it is specified initially that a
laminate will be constructed of plies oriented with fibres in a few preselected directions,
in which case only the percentage distribution in each orientation must then be
determined. This measure is taken in order to simplify the analysis.
Π/4 laminates are those with plies distributed in the 0°, 45°, 90° or –45° directions. Plies
for Π/3 laminates are distributed every 60° (i.e. 0°, 60° or –60° directions). An equal
percentage of plies in each of the preselected orientations results in a quasi-isotropic
laminate in both cases. This is the performance baseline, because load-carrying fibre is in
effectively all directions. The performance of a laminate can only be improved beyond
that of a quasi-isotropic laminate as fibre is biased into load directions, since, of course,
fibre would never be put in unnecessary directions.
Although they are not optimal in strength-to-weight or stiffness-to-weight ratios, quasiisotropic laminates are used for the following reasons:
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(1)
(2)
They have properties similar to the properties of metals.
They give predictable responses that are familiar.
Composite materials are more than mere lightweight substitutes for heavyweight metals.
Structural performances that are not possible with metals can be easily achievable. Highly
coupled deformation and load-carrying capability can be designed into the laminate. The
most successful structural applications are those where the inherent advantages of
reinforced materials can be translated into performance advantages for the manufactured
part. These advantages include the following:
(1)
(2)
(3)
(4)
(5)
(6)
stiffness-to-density ratios
strength-to-density ratios
low thermal expansion characteristics
resistance to specific environments
thermal conductivity
fatigue characteristics
7.6.5
Arrangement of plies
The proportion and the number of plies to be placed in each of the directions (i.e. 0°,
90°, 45° and –45°; see figure 7.9) must take into account the mechanical loading to be
applied to the laminate at the particular location. Once the number of layers and
orientations are defined, the following conditions are to be observed as much as possible:
•
•
90° plies are placed on the surface, followed by 45° and –45° plies, when the
predominant stress resultant is oriented along the 0° direction.
No more than four consecutive plies are placed along the same direction.
Figure 7.9
Common orientations (Gay & Hoa 2007)
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A current case consists of membrane loading, which is the loading of the laminate in its
plane. The mechanical loadings can take the form of stresses (𝜎𝜎𝑥𝑥 , 𝜎𝜎𝑦𝑦 , 𝜏𝜏𝑥𝑥𝑥𝑥 ) or stress
resultants (𝑁𝑁𝑥𝑥 , 𝑁𝑁𝑦𝑦 , 𝑇𝑇𝑥𝑥𝑥𝑥 ), as shown if figure 7.10(a) and (b), respectively. The stress
resultants are the products of the stresses and thickness h of the laminate.
Figure 7.10
Stresses and stress resultants (Gay & Hoa 2007)
The three general criteria to be considered by the designer for the ply configuration are
the following:
(1)
(2)
(3)
Support the loading without the deterioration of the laminate.
Limit the deformation of the loaded piece.
Minimise the weight of the material used.
NOTE: Certain combinations of the criteria may not always be possible, for example
minimum thickness and high rigidity, or high rigidity with minimum weight.
7.7
STRENGTHS OF COMPOSITE MATERIALS
The subject of material design data assumes greater importance in composite materials
than in conventional materials mainly because the engineering development process
encompasses designing both the material and the structure.
Material data are required to make key design decisions. The type and extent of the data
depend on the particular application. Most typically, data on the stiffnesses, strengths and
densities of selected material are needed.
The relative ranges of specific tensile modulus for composites with various fibre
reinforcements are shown in figure 7.11.
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Figure 7.11
The specific tensile modulus of various composite materials (Peters 1998)
Specific modulus refers to the ratio of composite modulus to composite density. It is a
measure of stiffness per kilogram of material that is commonly used in material
comparisons. The ranges of material costs for these same groups of materials are shown
in figure 7.12.
Figure 7.12
Costs of composite materials (Peters 1998)
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There are three more or less distinct regions of composites:
(1) glass-reinforced composites
(2) intermediate modulus (IM) graphite and aramid fibre-reinforced composites
(3) high and ultra-high modulus (HM) graphite fibre composites
Figure 7.12 explains why aramid and graphite have replaced metals in applications where
the market is prepared to pay for performance. Also, glass replaces metals in applications
where increased environmental resistance is a higher priority than some kind of
performance. An intermediate modulus graphite fibre composite is usually selected based
on performance. Material cost is a major portion of product cost in some applications; in
other applications, material cost overshadowed by the manufacturing costs and/or other
lifecycle costs.
A design that maximises modulus in one direction, minimises modulus in the transverse
direction and also minimises the in-plane shear modulus. Strength in the transverse
direction and in-plane shear strength will be reduced in magnitude. Highly directional
laminates typically behave like this, which severely limits their ability to resist load and
deformation in these directions.
Multidirectional reinforcement offers a stronger design because strengths and properties
are dominated by fibre properties in all in-plane directions. In addition, laminates with
multidirectional reinforcement offer more desirable cure characteristics.
A typical list of materials data required for structural design using reinforced composite
materials is provided in table 7.2. The mechanical properties and strengths of four fibrereinforced materials are shown. These are the basic data from which laminate values are
calculated. Lamination theory simply uses layer values to determine engineering
constants and to estimate strengths for any desired laminate. As a result, material testing
is conducted primarily at the layer level. Laminate test samples are employed to confirm
predictions and workmanship. However, strengths (e.g. bearing strength and interlaminar
shear strength) are laminate-specific, but they generally do not influence material
selection decisions.
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Table 7.2 Typical materials data for a preliminary design (Peters 1998)
Material
Mechanical properties
Fibre
volume
fraction
Density
Strengths
Modulus
Tensile
Compressive
(g/cm3)
Long.
Trans.
Long.
Trans.
Long.
Trans.
(GPa)
(GPa)
(MPa)
(MPa)
(MPa)
(MPa)
T300 fabric
0.6
1.55
68.9
68.9
620
620
414
414
M60J tape
0.6
1.69
248
5.52
993
27.6
496
172
P100 tape
0.6
1.74
414
4.14
827
27.6
414
138
Aramid
fabric
0.6
1.6
37.2
37.2
827
827
138
138
7.8
DESIGN EXAMPLE 7.1
The methodology typically employed in preliminary design is illustrated in this section
and an example of a trade study performed for material selection purposes is provided.
The example consists of the design of a composite beam.
The structure selected is a beam of constant cross-section that is fixed against
displacement and rotation at both ends, and loaded by a uniform load along the entire
length l, as shown in figure 7.13.
Figure 7.13
Example: Trade study of beam with a uniform load (Peters 1998)
The design requirements are as follows:
(1)
(2)
(3)
(4)
The maximum beam weight is not to exceed 5.0 kg or 3.33 g/mm, excluding end
fittings.
The maximum beam deflection (at midspan) must be less than 2.5 mm under the
load shown.
Maximum stresses in the beam must not exceed allowables, including a safety factor
of 2.0.
The cross-section of the beam must be closed and rectangular, as shown.
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Four materials will be considered for this application:
(1)
(2)
(3)
(4)
aluminium (7075 alloy)
E-glass/epoxy composite
T300 graphite/epoxy composite
M60J graphite/epoxy composite
Formulas:
(1) For deflection:
𝑑𝑑 = (𝑤𝑤𝑙𝑙 4 ⁄384𝐸𝐸𝐸𝐸 ),
where
(2) Maximum stress:
𝐸𝐸𝐸𝐸=(𝐸𝐸𝐸𝐸𝐸𝐸ℎ2 )/2
𝑓𝑓𝑐𝑐 = 2𝑀𝑀𝑀𝑀/𝐼𝐼
𝑓𝑓𝑐𝑐 = 2𝑀𝑀/ℎ𝑏𝑏𝑏𝑏
= (𝑤𝑤𝐿𝐿2 /4ℎ𝑏𝑏𝑏𝑏)
𝑊𝑊 = 𝑣𝑣(2ℎ + 2𝑏𝑏)𝑡𝑡 < 33.3 g/mm
(3) Weight:
One additional constraint must be introduced to the design. Buckling of one side of the
rectangular section is governed by elastic moduli and by the width-to-thickness ratio of
that side.
•
In order to prevent compressive or shear buckling of the sides and flanges, a rule of
thumb is to limit the side dimension h to no more than 20 times the thickness t, and
to limit the flange dimension b to no more than 15 times the thickness t.
Using these relations, h and b are eliminated from the equations and replaced by
multiples of t.
The three equations are then solved by iteration for each of the four materials using
the properties and strengths given in table 7.3.
•
•
Table 7.3 Results of design trade study of composite beam (Peters 1998)
Materiala
Alum
(7075)
Modulus
(GPa)
68.9
Compressive Density
strength
(MPa)
(g/cm3)
482
2.68
Wall
thickness
Weight
(mm)
(g/mm)
2.7
1.37
E-glass
34.5
475
1.93
3.2
1.38
M60J
248
379
1.69
2.0
0.47
T300
99.3
572
1.50
2.5
0.66
Design values for each composite material are developed assuming a laminate with the following
proportions: 65% 0° plies; 25% 45° plies; and 10% 90° plies.
a
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The summary table presents a comparison of the calculated design thicknesses and
corresponding beam weights for each of the four candidate materials. The following
conclusions can be made from this comparison:
(1) Aluminium (Al) and E-glass designs are comparable on a weight basis.
(2) Additional weight introduced by metallic end fittings (i.e. if they were taken into
account) would probably cause the detailed E-glass design to be heavier than the
aluminium design.
(3) The T300/epoxy design offers significant weight savings over Al and E-glass.
(4) The additional weight savings associated with M60J is relatively small.
(5) The cost differential is going to be substantial for M60J because prepreg costs over
$200 per kilogram, while T300 prepreg costs about $20 per kilogram.
The next calculation is a cost estimation in order to ascertain the cost differential.
In a real design situation, the trade would probably be a bit more complex. The trade
methodology remains the same, but perhaps additional characteristics would need to be
considered.
7.9
DESIGN EXAMPLE 7.2
A thin-wall cylindrical pressure vessel is loaded by internal pressure, p, and an external
torque, T, as shown in figure 7.14.
Figure 7.14
Thin-wall cylindrical pressure vessel under internal pressure and
torque loading (Daniel & Ishai 2006)
p = 2.07 MPa
T = 283 kN.m
D = 89 cm
It is also given that the vessel operates at room temperature and dry conditions, and that
curing residual stresses can be neglected. We need to find the optimum composite
material system and layup to achieve minimum weight and make the vessel comparable
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to an aluminium reference vessel. The allowable safety factor is Sall = 2.0. The design of
the aluminium vessel is based on the Von Mises criterion, with a material yield strength
σyp = 242 MPa. The density of aluminium is given as ρ = 2.8 g/cm3. The design of the
composite laminate is based on the Tsai–Wu failure criterion for first ply failure (FPF).
Balanced symmetric laminates are to be investigated for three candidate composite
materials, namely S-glass/epoxy, Kevlar/epoxy and carbon/epoxy.
The unit loads acting on an element of the cylindrical shell along the axial and hoop
directions (x and y) are obtained as follows:
𝑝𝑝𝑝𝑝
4
𝑝𝑝𝑝𝑝
𝑁𝑁𝑦𝑦 = 𝜎𝜎𝑦𝑦 ℎ =
2
2𝑇𝑇
𝑁𝑁𝑠𝑠 = 𝜏𝜏𝑠𝑠 ℎ ≅
𝜋𝜋𝐷𝐷2
(1)
𝑁𝑁𝑦𝑦 = 920 kN/m
(2)
𝑁𝑁𝑥𝑥 = 𝜎𝜎𝑥𝑥 ℎ =
Substituting the data given, we obtain the following:
𝑁𝑁𝑥𝑥 = 460 kN/m
𝑁𝑁𝑠𝑠 = 228 kN/m
The principal stresses for the above state of stress are as follows:
1.014
ℎ
366
𝜎𝜎2 =
ℎ
𝜎𝜎1 =
𝜎𝜎1 = 0
(in kPa)
(in kPa)
(3)
Aluminium reference vessel
According to the Von Mises yield criterion,
[(𝜎𝜎1 − 𝜎𝜎2 )2 + (𝜎𝜎2 − 𝜎𝜎3 )2 + (𝜎𝜎3 − 𝜎𝜎1 )2 ]1⁄2 =
√2𝜎𝜎𝑦𝑦𝑦𝑦
𝑆𝑆𝑎𝑎𝑎𝑎𝑎𝑎
(4)
Substituting the numerical results of equation (3) and the given data in equation (4), we
obtain
1.257
ℎ𝑎𝑎
= 170766 kPa,
which yields
ha = 7.36 mm.
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Cross-ply [0m/90n]s laminates
Since the ratio of hoop stress to axial stress is 2:1, a similar ratio of the number of 90°
and 0° layers, or n:m, is selected initially. The process of optimisation for a given type of
layup is best carried out by using one of several available computer programs.
Initially the safety factor Sf is obtained for a [0/902]s layup of the material investigated, the
thickness of which is ho = 6t (i.e. six ply thicknesses). The multiples mi and ni for the
initial trial are obtained as
𝑚𝑚𝑖𝑖 =
𝑛𝑛𝑖𝑖
2
≅
𝑆𝑆𝑎𝑎𝑎𝑎𝑎𝑎
𝑆𝑆𝑓𝑓
2
= 𝑆𝑆 ,
(5)
𝑓𝑓
and the allowable laminate thickness is ha = 6mt = mho. The optimum choice from the
point of view of weight is reached by trying different values of m and n around the initial
guess until the sum (m + n) is minimised. Results for the three materials investigated are
tabulated in table 7.4.
Table 7.4 Optimum [0m/90n]s layup for three composite materials (Daniel &
Ishai 2006)
S-glass/Epoxy
Kevlar/Epoxy
Carbon/Epoxy
Ply thickness (t, mm)
0.165
0.127
0.127
m
10
12
10
n
28
29
22
Safety factor, Sf
2.017
2.029
2.043
Optimum layup*
[010/9028]s
[012/9029]s
[010/9022]s
Laminate thickness (h, mm)
12.54
10.41
8.13
*To reduce interlaminar stresses, we intersperse the plies and minimise layer thicknesses.
Angle-ply [±𝛉𝛉]ns laminates
Optimisation of this type of laminate involves only one variable, θ. This is accomplished
by selecting the angle θ for the basic laminate unit [±θ]s that maximises the safety factor
Sf. The basic laminate unit has a thickness ho = 4t (i.e. four ply thicknesses). Then the
allowable laminate thickness is
ℎ𝑎𝑎 =
𝑆𝑆𝑎𝑎𝑎𝑎𝑎𝑎
𝑆𝑆𝑓𝑓
8𝑡𝑡
ℎ𝑜𝑜 = 𝑆𝑆 .
(6)
𝑓𝑓
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Figure 7.15
Effect of lamination angle on allowable thickness of [±θ]ns
angle-ply laminate in pressure vessel (Daniel & Ishai 2006)
To find the optimum θ, the allowable (required) thickness ha was computed and plotted
versus θ for the three materials considered in figure 7.15. It is interesting to note that the
optimum angle θ corresponding to the minimum allowable thickness is almost the same
for all three materials, namely 55° for S-glass/epoxy and carbon/epoxy, and 54° for
Kevlar/epoxy. Although the three materials considered have comparable strength
properties, the variation of the required minimum laminate thickness with angle θ is very
different for each material (see figure 7.15). The curve for Kevlar/epoxy shows the sharpest
variation with angle, but it has roughly the same minimum (ha = 4.24 mm) as that of
carbon/epoxy (ha = 4.14 mm). Although the strength properties of S-glass/epoxy are
higher than those of Kevlar/epoxy, the required minimum thickness for S-glass/epoxy is
much higher (ha = 11.37 mm). The results above are tabulated in table 7.5.
The results obtained illustrate the important fact that the structural efficiency of a laminate
is not only a function of the lamina strength properties, but also of its lamina stiffnesses
and their ratios (degree of anisotropy).
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Table 7.5 Optimum [±θ]ns layup for three composite materials (Daniel & Ishai
2006)
S-glass/Epoxy
Kevlar/Epoxy
Carbon/Epoxy
Ply thickness (t, mm)
0.165
0.127
0.127
Optimum θ (degrees)
55
54
55
Safety factor (Sf, n = 1)
0.116
0.240
0.246
Minimum allowable thickness
(ha, mm)
11.37
4.24
4.14
2.091
[±54]9𝑠𝑠
2.125
[±55]9𝑠𝑠
11.89
4.57
4.57
Optimum layup
Safety factor (Sf, optimum layup)
Laminate thickness (h, mm, optimum
layup)
±55]18𝑠𝑠
2.209
[𝟗𝟗𝟗𝟗/±𝛉𝛉]ns Laminates
Optimisation of the [90/±θ]ns laminate also involves only one variable, θ. Safety factors
are computed for the basic laminate unit [90/±θ]s for the three materials investigated for
various values of θ. The minimum allowable thickness for each laminate is obtained as
ℎ𝑎𝑎 =
𝑆𝑆𝑎𝑎𝑎𝑎𝑎𝑎
𝑆𝑆𝑓𝑓
ℎ𝑜𝑜 =
12𝑡𝑡
𝑆𝑆𝑓𝑓
.
(7)
Results are tabulated in table 7.6. The optimum angle θ was found to be 48°, 45° and
45° for the S-glass/epoxy, Kevlar/epoxy and carbon/epoxy materials, respectively. Again,
as in the previous case of [±θ]ns laminates, the Kevlar/epoxy material appears much better
than the S-glass/epoxy because of its higher laminate efficiency and fibre utilisation
factors.
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Table 7.6 Optimum [90/±θ]ns layup for three composite materials (Daniel & Ishai
2006)
S-glass/Epoxy
Kevlar/Epoxy Carbon/Epoxy
Ply thickness (t, mm)
0.165
0.127
0.127
Optimum θ (degrees)
48
45
45
Safety factor (Sf, n = 1)
0.155
0.240
0.335
Minimum allowable thickness
(ha, mm)
12.76
6.35
4.55
[90/±48]13𝑠𝑠
2.018
[90/±45]9𝑠𝑠
2.159
[90/±45]6𝑠𝑠
12.87
6.86
4.57
Optimum layup
Safety factor (Sf, optimum layup)
Laminate thickness (h, mm,
optimum layup)
2.012
[𝟎𝟎/±𝛉𝛉]ns Laminates
The optimisation of the [0/±θ]ns laminate is similar to the previous laminate. Safety factors
and minimum allowable laminate thicknesses are calculated as before using equation (7).
Results are tabulated in table 7.7. The optimum angle θ was found to be 75°, 67° and
67° for the S-glass/epoxy, Kevlar/epoxy and carbon/epoxy materials, respectively. As in
the previous case, the required laminate thickness for the S-glass/epoxy material was
approximately double that for the other two materials.
Table 7.7 Optimum [0/±θ]ns layup for three composite materials (Daniel & Ishai
2006)
Ply thickness (t, mm)
Optimum θ (degrees)
Safety factor (Sf, n = 1)
Minimum allowable thickness
(ha, mm)
Optimum layup
Safety factor (Sf, optimum layup)
Laminate thickness (h, mm,
optimum layup)
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S-Glass/Epoxy
0.165
75
0.157
Kevlar/Epoxy Carbon/Epoxy
0.127
0.127
0.254
0.293
67
67
12.61
6.01
5.21
[0/±75]13𝑠𝑠
2.041
[0/±67]8𝑠𝑠
2.029
[0/±67]7𝑠𝑠
12.87
6.10
5.33
2.047
Quasi-isotropic [𝟎𝟎/±𝟒𝟒𝟒𝟒/𝟗𝟗𝟗𝟗]ns laminates
Quasi-isotropic [0/±45/90]ns laminates are investigated for reference purposes. Safety
factors are calculated for the basic unit (n = 1) and allowable thicknesses computed as
before, using
ℎ𝑎𝑎 =
𝑆𝑆𝑎𝑎𝑎𝑎𝑎𝑎
𝑆𝑆𝑓𝑓
ℎ𝑜𝑜 =
16𝑡𝑡
𝑆𝑆𝑓𝑓
.
(8)
Results are tabulated in table 7.8. As can be seen, this is the least efficient layup for all
three materials.
Table 7.8 Optimum [0/±45/90]ns layup for three composite materials (Daniel &
Ishai 2006)
S-glass/Epoxy
Kevlar/Epoxy
Carbon/Epoxy
Safety factor (Sf, n = 1)
0.181
0.254
0.361
Minimum allowable thickness
(ha, mm)
14.59
7.91
5.63
Minimum n
12
8
6
[0/±45/90]12𝑠𝑠
[0/±45/90]8𝑠𝑠 [0/±45/90]6𝑠𝑠
Optimum layup
Safety factor (Sf, optimum layup)
2.173
Laminate thickness (h, mm,
optimum layup)
15.84
2.055
2.169
8.13
6.10
Summary and comparison of results
Results of the optimum layups for the three composite materialsp considered and the
relative weight savings compared with an aluminium pressure vessel are summarised in
table 7.9. The optimum layup for all three materials is the angle-ply [±θ]ns layup. Given
the fixed ply thicknesses for the materials, total laminate thicknesses were obtained that
resulted in safety factors slightly higher than the allowable one (Sall = 2.0). Both the
Kevlar/epoxy and the carbon/epoxy materials resulted in the same laminate thickness,
which is less than half of the required one for the S-glass/epoxy material. The relative
weight savings compared with the aluminium reference pressure vessel were calculated
as follows:
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Weight savings =
or
∆𝑊𝑊 𝑊𝑊𝑎𝑎𝑎𝑎 − 𝑊𝑊𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
=
𝑊𝑊
𝑊𝑊𝑎𝑎𝑎𝑎
𝜌𝜌𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ℎ𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
∆𝑊𝑊
= 1−
𝑊𝑊
𝜌𝜌𝑎𝑎𝑎𝑎 ℎ𝑎𝑎𝑎𝑎
(9)
Table 7.9 Summary of optimum layups for three composite materials (Daniel &
Ishai 2006)
S-glass/Epoxy Kevlar/Epoxy Carbon/Epoxy
Density (ρ, g/cm3)
2.0
0.127
0.127
Ply thickness (t, mm)
0.165
0.127
0.127
Optimum layup
[±55]18𝑠𝑠
2.091
[±54]9𝑠𝑠
2.125
[±55]9𝑠𝑠
11.89
4.57
4.57
–15.4
69.0
64.5
Safety factor (Sf, optimum layup)
Laminate thickness (h, mm,
optimum layup)
Weight savings compared to
aluminium
(∆𝑊𝑊/𝑊𝑊, %)
2.209
As shown in table 7.9, there are weight savings of 69% and 64.5% in the Kevlar/epoxy
and carbon/epoxy designs, but a weight increase of 15.4% in the S-glass/epoxy design.
Ranking of composite laminates
The results above are summarised in a bar graph in figure 7.16. Here the different
composite laminate options are ranked according to their weight per unit wall area. A
clear trend is observed that is common for the three material systems considered, namely
a minimum weight for [±θ]ns angle-ply configurations with 𝜃𝜃 ≅ 55° and significantly
higher weights for cross-ply [0m/90n]s and quasi-isotropic [0/±45/90]ns layups.
The design procedure illustrated before can be very time consuming if all potential layups
are examined for each material system considered. Based on this illustration and prior
experience, a shortened ranking procedure is recommended:
(1) Select a material system and determine the best layup for this system to achieve
minimum weight.
(2) Compare different material systems for this layup.
(3) Select the material system giving the lowest weight in step (2) and repeat step (1) for
this material system.
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Figure 7.16
Ranking of different material systems and laminate layups according
to weight for pressure vessel design example (Daniel & Ishai 2006)
7.10 DESIGN EXAMPLE 7.3
Design of a tubular composite shaft (Callister & Rethwisch 2015)
A tubular composite shaft must be designed. It must have an outside diameter of 70 mm,
an inside diameter of 50 mm and a length of 1.0 m, and is represented schematically in
figure 7.17. The mechanical characteristic of prime importance is bending stiffness in
terms of the longitudinal modulus of elasticity. Strength and fatigue resistance are not
significant parameters for this application when filament composites are used. Stiffness is
to be specified as maximum allowable deflection in bending. When subjected to threepoint bending as in figure 7.18 (i.e. support points at both tube extremities and load
application at the longitudinal midpoint), a load of 1000 N is to produce an elastic
deflection of no more than 0.35 mm at the midpoint position.
Continuous fibres that are oriented parallel to the tube axis will be used. Possible fibre
materials are glass and carbon in standard, intermediate and high modulus grades. The
matrix material is to be an epoxy resin. The maximum allowable fibre volume fraction is
0.60.
This design problem calls for us to do the following:
(a) Decide which of the four fibre materials, when embedded in the epoxy matrix, meet
the stipulated criteria.
(b) Of these possibilities, select the one fibre material that will yield the cheapest
composite material (assuming fabri cation costs are the same for all fibres).
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Elastic modulus, density and cost data for the fibre and matrix materials are given in table
7.10.
Figure 7.17
Schematic representation of a tubular composite shaft (Callister & Rethwisch 2015)
Figure 7.18
A three-point loading scheme for measuring the stress–strain behaviour and
flexural strength of brittle ceramics, including expressions for computing stress
for rectangular and circular cross-sections (Callister & Rethwisch 2015)
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Table 7.10 Elastic modulus, density and cost data for glass, various carbon fibres
and epoxy resin (Callister & Rethwisch 2015)
Material
Elastic modulus
Density
Cost
(GPa)
(g/cm3)
($US/kg)
Glass fibres
72.5
2.58
2.10
Carbon fibres
230
1.80
60.00
285
1.80
95.00
400
1.80
250.00
2.4
1.14
6.00
(standard modulus)
Carbon fibres
(intermediate modulus)
Carbon fibres
(high modulus)
Epoxy resin
Solution
(a)
We must first determine the required longitudinal modulus of elasticity for this
composite material in line with the stipulated criteria. This computation requires the
use of the three-point deflection expression
𝐹𝐹𝐿𝐿3
∆𝑦𝑦 =
,
48 𝐸𝐸𝐸𝐸
in which y is the midpoint deflection, F is the applied force, L is the support point
separation distance, E is the modulus of elasticity and I is the cross-sectional moment
of inertia.
For a tube having inside and outside diameters of di and do, respectively,
𝜋𝜋
𝐼𝐼 =
�𝑑𝑑 4 − 𝑑𝑑𝑖𝑖 4 �
64 𝑜𝑜
and
4𝐹𝐹𝐿𝐿3
For this shaft design,
𝐸𝐸 = 3𝜋𝜋 ∆𝑦𝑦�𝑑𝑑
𝑜𝑜
4
−𝑑𝑑𝑖𝑖 4 �
.
𝐹𝐹 = 1000 N,
𝐿𝐿 = 1.0 m,
∆𝑦𝑦 = 0.35 mm,
𝑑𝑑𝑜𝑜 = 70 mm, and
𝑑𝑑𝑖𝑖 = 50 mm.
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Thus, the required longitudinal modulus of elasticity for this shaft is
4(1000 N)(1.0 m)3
𝐸𝐸 = 3𝜋𝜋(0.35×10−3 m)[(70×10−3 m)4 −(50×10−3 m)4 ] = 69.3 Pa .
The next step is to determine the fibre and matrix volume fractions for each of the
four candidate fibre materials. This can be done using the rule-of-mixtures
expression,
𝐸𝐸𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓 = 𝐸𝐸𝑚𝑚 �1 − 𝑉𝑉𝑓𝑓 � + 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓 .
Table 7.11 lists the Vm and Vf values required for Ecs = 69.3 GPa. The equation
above and the moduli data in table 7.10 were used in these computations. Only the
three carbon fibre types are possible candidates because their Vf values are less than
0.6.
Table 7.11 Fibre and matrix volume fraction for glass and three carbon fibre
types as required to give a composite modulus of 69.3 GPa
(Callister & Rethwisch 2015)
Fibre types
Vf
Vm
Glass fibres
0.954
0.046
0.293
0.707
0.237
0.763
0.168
0.832
Carbon fibres
(standard modulus)
Carbon fibres
(intermediate modulus)
Carbon fibres
(high modulus)
(b)
At this point, it becomes necessary to determine the volume of fibres and matrix for
each of the three carbon types. The total tube volume Vc in centimetres is
𝜋𝜋𝜋𝜋
�𝑑𝑑𝑜𝑜 4 − 𝑑𝑑𝑖𝑖 4 �
4
𝜋𝜋(100 cm)
[(7.0 cm)2 − (5.0 cm)2 ]
=
4
𝑉𝑉𝑐𝑐 =
= 1885 cm3 .
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Thus, fibre and matrix volumes result from products of this value and the Vf and Vm values
cited in table 7.11. These volume values are presented in table 7.12 and are then
converted into masses using densities (see table 7.10) and finally into material costs, from
the per unit mass cost (also given in table 7.10).
As may be noted in table 7.12, the material of choice (i.e. the least expensive material) is
the standard-modulus carbon fibre composite. The relatively low cost per unit mass of
this fibre material offsets its relatively low modulus of elasticity and required high volume
fraction.
Table 7.12 Fibre and matrix volumes, masses, costs and total material cost for
three carbon fibre epoxy-matrix composites (Callister & Rethwisch
2015)
Fibre
volume
Fibre
mass
Fibre
cost
Matrix
volume
Matrix
mass
Mass
cost
Total cost
Fibre type
(cm3)
(kg)
($US)
(cm3)
(kg)
($US)
($US/kg)
Carbon fibres
(standard modulus)
552
0.994
59.60
1333
1.520
9.10
68.70
Carbon fibres
(intermediate
modulus)
447
0.805
76.50
1438
1.639
9.80
86.30
Carbon fibres (high
modulus)
317
0.571
142.80
1568
1.788
10.70
153.50
7.11 DESIGN PROBLEMS
(1)
It is desired to produce an aligned and continuous fibre-reinforced epoxy composite
having a maximum of 40 vol% fibres. In addition, a minimum longitudinal modulus
of elasticity of 55 GPa is required, as is a minimum tensile strength of 1200 MPa.
Of E-glass, carbon (PAN standard modulus) and aramid fibre materials, which are
possible candidates and why? The epoxy has a modulus of elasticity of 3.1 GPa and
a tensile strength of 69 MPa. In addition, assume the following stress levels on the
epoxy matrix at fibre failure: E-glass, 70 MPa; carbon (PAN standard modulus), 30
MPa; and aramid, 50 MPa. Other fibre data are given in tables B.2 and B.4 in
Appendix B of Callister and Rethwisch (2015). For aramid fibres, use the minimum
of the range of strength values provided in table B.4 (Callister & Rethwisch 2015).
(2)
It is desired to produce an aligned and continuous fibre-reinforced epoxy composite
having a maximum of 50 vol% fibres. In addition, a minimum longitudinal modulus
of elasticity of 55 GPa is required, as well as a minimum tensile strength of
1310 MPa of E-glass, carbon (PAN standard modulus) and aramid fibre materials,
which are possible candidates and why? The epoxy has a modulus of elasticity of
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3.1 GPa and a tensile strength of 75 MPa. In addition, assume the following stress
levels on the epoxy matrix at fibre failure: E-glass, –70 MPa; carbon (PAN standard
modulus), –30 MPa; and aramid, –50 MPa. Other fibre data are given in tables B.2
and B.4 in Appendix B. For aramid and carbon fibres, use average strengths
computed from the minimum and maximum values provided in table B.4 (Callister
& Rethwisch 2015).
(3)
It is desired to produce a continuous and oriented carbon fibre-reinforced epoxy
having a modulus of elasticity of at least 69 GPa in the direction of fibre alignment.
The maximum permissible specific gravity is 1.40. Given the data in the following
table, is such a composite possible? Why or why not? Assume that compositespecific gravity may be determined using a relationship similar to the equation
𝐸𝐸𝑐𝑐𝑐𝑐 = 𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓 .
Specific
gravity
(4)
Carbon fibre
1.80
260
Epoxy
1.25
2.4
It is desired to produce a continuous and oriented carbon fibre-reinforced epoxy
having a modulus of elasticity of at least 83 GPa in the direction of fibre alignment.
The maximum permissible specific gravity is 1.40. Given the data in the following
table, is such a composite possible? Why or why not? Assume that composite
specific gravity may be determined using a relationship similar to the equation 𝐸𝐸𝑐𝑐𝑐𝑐 =
𝐸𝐸𝑚𝑚 𝑉𝑉𝑚𝑚 + 𝐸𝐸𝑓𝑓 𝑉𝑉𝑓𝑓 .
Specific
gravity
(5)
138
Modulus of
elasticity [GPa]
Modulus of
elasticity [GPa]
Carbon fibre
1.80
260
Epoxy
1.25
2.4
It is desired to fabricate a continuous and aligned glass fibre-reinforced polyester
having a tensile strength of at least 1250 MPa in the longitudinal direction. The
maximum possible specific gravity is 1.80. Using the following data, determine
whether such a composite is possible. Justify your decision. Assume a value of 20
MPa for the stress on the matrix at fibre failure.
EMT3701/1
Specific
gravity
(6)
Modulus of
elasticity [MPa]
Carbon fibre
2.50
3500
Polyester
1.35
50
It is desired to fabricate a continuous and aligned glass fibre-reinforced polyester
having a tensile strength of at least 1410 MPa in the longitudinal direction. The
maximum possible specific gravity is 1.65. Using the following data, determine
whether such a composite is possible. Justify your decision. Assume a value of
18 MPa for the stress on the matrix at fibre failure.
Specific
gravity
Modulus
of
elasticity [MPa]
Carbon fibre
2.50
3500
Polyester
1.35
50
(7)
It is necessary to fabricate an aligned and discontinuous glass fibre-epoxy matrix
composite having a longitudinal tensile strength of 1200 MPa using a 0.35 volume
fraction of fibres. Compute the required fibre fracture strength, assuming that the
average fibre diameter and length are 0.015 mm and 5.0 mm, respectively. The
fibre–matrix bond strength is 80 MPa and the matrix stress at composite failure is
6.55 MPa.
(8)
It is necessary to fabricate an aligned and discontinuous carbon fibre-epoxy matrix
composite having a longitudinal tensile strength of 1900 MPa using a 0.50 volume
fraction of fibres. Compute the required fibre fracture strength assuming that the
average fibre diameter and length are 10 × 10−3 mm and 3.5 mm, respectively. The
fibre-matrix bond strength is 40 MPa and the matrix stress at fibre failure is 12 MPa.
(9)
A tubular shaft similar to that shown in figure 7.17 is to be designed with an outside
diameter of 100 mm and a length of 1.25 m. The mechanical characteristic of prime
importance is bending stiffness in terms of the longitudinal modulus of elasticity.
Stiffness is to be specified as maximum allowable deflection in bending. When
subjected to three-point bending as in figure 7.18, a load of 1700 N is to produce
an elastic deflection of no more than 0.20 mm at the midpoint position.
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Continuous fibres that are oriented parallel to the tube axis will be used. Possible
fibre materials are glass and carbon in standard, intermediate and high modulus
grades. The matrix material is to be an epoxy resin and the fibre volume fraction is
0.40.
(a)
(b)
(c)
Decide which of the four fibre materials are possible candidates for this
application.
For each candidate, determine the required inside diameter consistent with
the preceding criteria.
For each candidate, determine the required cost and, on this basis, specify the
fibre that would be the least expensive to use.
Elastic modulus, density and cost data for the fibre and matrix materials are given
in table 7.10.
(10) A tubular shaft similar to that shown in figure 7.17 is to be designed with an outside
diameter of 80 mm and a length of 0.75 m. The mechanical characteristic of prime
importance is bending stiffness in terms of the longitudinal modulus of elasticity.
Stiffness is to be specified as maximum allowable deflection in bending. When
subjected to three-point bending as in figure 7.18, a load of 1000 N is to produce
an elastic deflection of no more than 0.40 mm at the midpoint position.
Continuous fibres that are oriented parallel to the tube axis will be used. Possible
fibre materials are glass and carbon in standard, intermediate and high modulus
grades. The matrix material is to be an epoxy resin and the fibre volume fraction is
0.35.
(a)
(b)
(c)
Decide which of the four fibre materials are possible candidates for this
application.
For each candidate, determine the required inside diameter consistent with
the preceding criteria.
For each candidate, determine the required cost and, on this basis, specify the
fibre that would be the least expensive to use.
Elastic modulus, density, and cost data for the fibre and matrix materials are given
in table 7.10.
7.12 DESIGN VERIFICATION PROCESS
A design verification process is more than non-destructive testing. It is an integral part of
both the design and manufacturing phases, and it serves to ensure that a component fulfils
all design requirements. Figure 7.19 identifies the verification activities in each phase of
the component development process.
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Depending on the industry, these activities range from formal, documented stages to
undocumented ones. The main advantage of documenting the evaluation process is
traceability. These records can be used to identify specific trends in development or
production. The disadvantage of such a process is the costs involved.
Figure 7.19
Component verification process (Peters 1998)
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Study unit 1
8
NON-DESTRUCTIVE TESTING OF COMPOSITES
8.1
LEARNING OBJECTIVES
After students have studied this study unit and part 4 of chapter 38 in Peters (1998), they
should be able to
•
•
•
describe various techniques that can be used for anomaly detection in composites
list the advantages and disadvantages of the various techniques used for nondestructive testing
categorise various techniques used for non-destructive testing according to their
orking principles
8.2
INTRODUCTION
The principal consideration in the development and selection of non-destructive
evaluation techniques is the nature of advanced composites as typically layered,
anisotropic materials. Included in the list of materials of interest are fibre-reinforced
plastics such as fibreglass and carbon epoxy, as well as some of the other materials like
the metal-matrix or ceramic-matrix composites. Naturally occurring composites such as
wood may be treated with approaches that are similar to those used for fabricated
composites.
The advantages obtainable from composites are focused on the high strength and low
weight properties of typical constituents. However, if the materials are to exhibit high
strength, they must maintain their integrity in service. Non-destructive testing (NDT)
presents a technology to help assure the reliability of the composite materials.
While the service record for composites has been excellent in a number of applications
(e.g. the aerospace, automotive, marine and construction industries), they are subject to
damage from sources such as overload, hail, lightning, low velocity impact ballistic
rounds and moisture invasion. Material defects are a major source of composite failures.
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These defects can show up as matrix cracking, fibre fracture, material delamination and
fibre pull-out.
This study unit describes many NDT methods that can be used to detect anomalies in
composites during manufacture and in service. It considers the capabilities, advantages
and disadvantages of most common methods in composite NDT applications, such as
visual inspection, tap testing, ultrasonic testing, radiographic testing, acoustic emission,
eddy current testing, thermography and Shearography testing. The methods are
categorised based on their basic characteristics and their applications.
8.3
INHOMOGENEITY FACTORS THAT CAN AFFECT COMPOSITE
PERFORMANCE
Inhomogeneity factors that may affect the performance of a composite material include
the following:
•
•
•
•
•
concentration of constituents (fibre-to-resin ratio, resin starvation, etc.)
orientation and distribution of reinforcement
voids
matrix-reinforcement bonding
other similar characteristics
8.4
THE PURPOSE OF NON-DESTRUCTIVE TESTING
The purpose of NDT in composites is to detect the above-mentioned inhomogeneities as
well as the following:
•
•
•
•
•
•
•
•
•
foreign material
fibre breakage
degradation due to moisture
degradation due to ultraviolet (UV) light
cracks
abrasion
impact damage
fire or excessive heat
other similar characteristics
Many testing methods have been automated for production applications, but in-service
inspection is frequently executed using conventional manual inspection equipment.
Inspection processes that follow manual approaches can be time consuming. The
interpretation of inspection results may require specially trained personnel.
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8.5
VISUAL INSPECTION
Many of the more severe conditions associated with composites are visually detectable.
Punctures, surface ply delaminations, scratches, gouges and heat damage can often be
detected during a visual inspection. The separation of a composite skin and some
substructure may also be detectable as a blister in the skin or a distortion in the geometry
of the component.
Translucent composites can be inspected using transmitted light. This straightforward
approach can be used in material such as non-pigmented glass-reinforced plastic (GRP)
to detect inhomogeneities such as voids, delaminations or inclusions.
For the detection of impact damage, composite surfaces are painted with a paint
containing micro-encapsulated dye for visual inspection. When crushed by the impact,
dye is released and reveals the location of the impact. Dyes can be formulated either for
visual observation of a colour change or using UV-excited fluorescence in the dye.
Another visual inspection approach that can be used to enhance the detectability of
surface-related damage is by using visual aids, such as, borescopes and television
cameras.
Further, this type of inspection cannot be expected to detect all forms of damage that may
be present in a composite structure. When damage is detected, it is essential to use other
tools to assess the extent of the damage (Peters 1998).
8.6
TAP TEST
The tap test method (see figure 8.1) uses either a coin or a special tap hammer. The
obvious reason for the adoption of this test method is that it does not require expensive
equipment. Another reason is that many of the composites in use consist of thin laminates
in low strain designs. The tap method can be used to detect problems in relatively large
areas of laminate, particularly where the substructure of the tested skin is reasonably
consistent. This method of testing is sensitive only to laminar-type flaws, such as
delaminations, unbonds or separation. It relies on different acoustic resonances of the
loose upper layer compared to the surrounding material.
In complex geometries, the tap method often suffers from subjective interpretation,
variable application, declining sensitivity with flaw depth and an inability to calibrate
effectively for either flaw size or depth. In many cases, applications involving thicker
laminates and more highly loaded designs make this approach inadequate. Machine-type
tapper and instrumentation have been developed, but suffer from many of the same
disadvantages as manual tapping, with the additional disadvantages of increased cost
(Peters 1998).
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Figure 8.1
Tap test with tap hammer
(Source: http://content.aviation-safety-bureau.com/allmembers/faa-h-8083-31amt-airframe-vol-1/sections/chapter7.php)
8.7
ULTRASONIC METHODS
Ultrasonic inspection (see figure 8.2) makes use of frequencies above 20 kHz mechanical
vibrations, with typical frequencies for inspection of composites in the megahertz range.
The ultrasonic signal is typically introduced in a pulse mode (Peters 1998).
Figure 8.2
Ultrasonic testing method
(Source: http://content.aviation-safety-bureau.com/allmembers/faa-h-808331-amt-airframe-vol-1/sections/chapter7.php)
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8.7.1
Ultrasonic through-transmission testing
Ultrasonic through-transmission testing is probably the most commonly used production
inspection method for composite structures. These systems measure the signal strength of
a pulse of ultrasonic energy transmitted through the structure under test. Where there
could be a delamination or perhaps a foreign material, a reduced exit ultrasonic intensity
will show. The method requires access to both sides of the part and the alignment of
ultrasonic units on opposite sides of the part. These factors restrict the usefulness of this
test method for in-service inspection (Peters 1998).
8.7.2
Ultrasonic pulse-echo testing
The ultrasonic pulse-echo test (see figure 8.3) approach uses a single search unit as both
the transmitter and the receiver. This test approach requires access to only one side of the
structure to be tested. Flaws are detected by monitoring the time of arrival and/or the
signal strength of returning echoes. The main advantage of the pulse-echo system is that
flaws at multiple depths can be distinguished from one another. It is also advantageous
in that it offers increased sensitivity to foreign material inclusions associated with the
manufacturing process for laminated composites. Sometimes foreign materials, such as
the paper and plastic materials that are used in handling and transporting uncured
composite materials, find their way into a composite laminate, but fortunately they can
be detected (Peters 1998).
Figure 8.3
Pulse-echo test equipment
(Source: http://content.aviation-safety-bureau.com/allmembers/faa-h-8083-31amt-airframe-vol-1/sections/chapter7.php)
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8.7.3
Ultrasonic polar backscatter
Ultrasonic polar backscatter makes use of slightly angled ultrasonic beams to detect flaws.
The angle orientation allows the user to associate flaws with a particular ply orientation.
This method is sensitive to linear voids, but it is particularly useful for characterising
matrix cracking in the composite plies. It is successfully used to characterise the various
levels of damage in impacted laminates. This test approach has also been used to measure
directional velocity variations and elastic properties in composites. Using these
properties, anisotropic elastic properties can be determined. Inspection times in the field
can get long because the angulating mechanism is rather difficult to manipulate and
control (Peters 1998).
8.7.4
Ultrasonic resonance
Ultrasonic resonance is a one-sided inspection method used to detect laminar
discontinuities in composites or bonded structures. This is accomplished through setting
up a continuous ultrasonic resonance wave in the material and sensing the mechanical
stiffness of the material. Material delamination reduces the normal surface stiffness of the
material, which reduces the surface loading on the ultrasonic probe. This can be sensed
as a phase, amplitude or resonant frequency shift in the ultrasonic element. The ultrasonic
resonance method is particularly useful in complex bonded structures where access
limitation restricts the use of ultrasonic through-transmission testing and the complex
internal reflections make pulse-echo signals difficult to interpret (Peters 1998).
8.7.5
Ultrasonic correlation
The ultrasonic correlation approach has proven to be effective in the evaluation of thick
and highly attenuated materials where conventional pulsed ultrasonic systems have
trouble penetrating the material. It achieves increased sensitivity using a continuous
wave, a cross-correlation technique that enhances the sensitivity of the test at the expense
of inspection speed.
By way of using continuous generation and accumulation of the ultrasonic signal, the
maximum possible efficiency of data accumulation can occur (Peters 1998).
8.8
X-RADIOGRAPHY
X-radiography imaging relies on the differential absorption or scattering of the X-ray
photons passing through a material. The significant effect of flaws that allow more X-ray
photons to pass, to be absorbed or to scatter can be imaged. The low density of most
composite materials permits the use of low energy X-rays, which helps to enhance
sensitivity.
The X-radiology approach can be used to detect porosity, matrix cracks and some foreign
materials. Boron and silicon carbide fibres are typically deposited on a tungsten filament,
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which can be imaged. This allows the user to detect fibre fractures and to determine fibre
orientations and placements, provided the number of plies does not get too large. On the
other hand, carbon fibres are not generally imaged by X-rays.
X-radiography is considered to be particularly useful for the detection of honeycomb core
defects in bonded sandwich assemblies. Core defects include blown core, crushed core,
condensed core, fatigued core, corroded or cut core and foaming adhesive voids (Peters
1998).
8.8.1
X-ray backscatter imaging
The X-ray backscatter imaging approach uses a camera with a slot. The backscattered
X-rays are detected by an array of scintillation detectors. The intensity information of the
backscatter is obtained as a function of detector position; this translates into different
depths in the inspection object.
The X-ray backscatter inspection method is particularly useful for the inspection of
laminated structures such as pressure vessels and rocket motor cases. Quantitative
information about variations in density caused by changes in material or delaminations,
and the location of such variations within the material depth, is contained by the X-ray
backscatter signal (Peters 1998).
8.8.2
Computed tomography
A tomographic image looks like a slice that is taken across the inspection object. In
tomographic inspection, a parallel single pencil beam of X-rays is directed at the sample,
which is shifted and rotated relative to the X-ray beam. The X-ray beam intensity is then
measured at each position and rotation. These measurements allow a computer
reconstruction of a density map of the inspection object. The major advantage of this
approach is that the resultant image shows a true three-dimensional view of all the
variations across the image slice (Peters 1998).
8.8.3
Neutron radiography
In neutron radiography testing, X-rays are attenuated as a function of the density of the
material through which they pass. This technique enables us to detect variations in the
organic matrix materials and moisture take-up of composites (Peters 1998).
8.9
ACOUSTIC EMISSION
Acoustic emission testing involves the detection of elastic energy. Components are
required to be under load during testing. Materials, including composites, release the
energy spontaneously when they undergo deformation (under load). Acoustic emission
testing is used (Peters 1998) as follows:
(i)
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(ii)
for monitoring and characterising damage growth mechanisms in composites under
cyclic loading
(iii) for detecting and characterising matrix cracking, delamination and fibre breakage
(iv) largely in the testing of composite pressure vessels
(v) in the detection of moisture and corrosion in honeycomb assemblies
8.10 ACOUSTO-ULTRASONICS
The acousto-ultrasonic test method is also called the stress wave factor. It uses an
ultrasonic transducer to inject a simulated acoustic emissions pulse into the inspection
object. Damage to the material will impede the motion of the stress wave through the
material. The acousto-ultrasonic method can be used to detect matrix cracking and
laminate porosity; and it is sensitive to fibre breakage and delaminations (Peters 1998).
8.11 EDDY CURRENT TESTING
Eddy current test methods rely on the principles of magnetic induction to examine a
material under test. Current loops (or eddy currents) are induced in a conducting material
by means of a varying magnetic field. In order to form current loops, multiple fibres (i.e.
carbon fibres) must make electrical contact with one another at various places along the
length of the material.
Eddy current techniques can be used to monitor fibre orientation and to detect fibre
breakage. They provide effective results for many damage mechanisms in carbon fibre
composites, including impact damage and fatigue damage. Eddy current testing is limited
to carbon fibres, because most resin matrix materials are very poor electrical conductors
(Peters 1998).
8.12 INFRARED THERMAL TESTING
Infrared thermal testing, or thermography, is used on bodies with a temperature above
absolute zero. Such bodies emit electromagnetic radiation by virtue of the motion of the
constituent atoms. The spectrum and intensity of the radiation depend on the surface
temperature and the nature of the surface. Typically, to produce surface temperature
patterns that can easily be detected with an infrared imaging system, thermographic
applications would involve the introduction of a controlled thermal load on the object of
interest.
Impact damage often results in matrix damage near the surface of a composite material,
which can be detected by infrared imaging. Composites typically offer an excellent
combination of thermal properties for the useful application of infrared thermal testing
(Peters 1998).
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8.13 LASER SHEAROGRAPHY OR HOLOGRAPHY
A hologram is an interference pattern formed when two wave-fronts (an object beam and
a reference beam) superposition on a recording material such as a photographic film. A
technique called holographic interferometry is used to permit observation of the pattern.
A holographic inspection approach is sensitive to displacements as small as one-quarter
wavelength of the laser light being used. An inspection objects may be a sandwich panel
consisting of graphite/epoxy laminate skins and a foam core (Peters 1998).
8.14 MICROWAVE TESTING
Microwave testing uses microwave energy to inspect and characterise composite
materials. Successful results of microwave techniques have been reported for the
measurement of fibre content and orientation, material thickness and porosity content.
Also, this method offers excellent sensitivity to conditions such as matrix porosity and the
cure state of the matrix, which are difficult to establish using more conventional NDT
techniques (Peters 1998).
8.15 CONTACT METHODS AND NON-CONTACT METHODS
The basic types of non-destructive evaluation (NDE) or non-destructive testing (NDT)
include contact methods and non-contact methods between the sensor and the tested
composite surface.
ACTIVITY 8.1
Use table 8.1 below to categorise all the NDT methods mentioned above according to
their contact and non-contact nature. One example of each has been given.
Table 8.1 Contact and non-contact NDT methods
Contact methods
Non-contact methods
Example: Eddy current testing
Holography
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8.16 PHYSICAL PROPERTIES AND STRUCTURAL INTEGRITY
In analysing the best NDT method to use for the testing of composite materials, sufficient
attention must be paid to factors such as safety, efficiency and cost. Non-destructive tests
can be categorised based on the factors that they evaluate, as shown in table 8.2. The
term structural integrity, as used in table 8.2, can be described as a formalised process
that utilises advanced NDT methods for the purpose of detecting, localising and
determining the size of a damage incurred in a composite material.
Table 8.2 Category of NDT methods based on the detecting factors (Gholizadeh
2016)
Category
The estimation of
the physical and
mechanical
properties, and
material defects
detection in
composites
Determining the
integrity of
structural
components that
are manufactured
from composites
Applications
Measurement of the following:
dynamic mechanical analysis (DMA) (Šturm et al 2015)
fibre amount of portion (El-Sabbagh et al 2013)
mechanical strength and stiffness (Ray 2006)
elastic constants (Rojek et al 2005)
material content (El-Sabbagh et al 2013)
damage failing initiation and subsequent damage evolution
(Talreja 2008)
• delamination (Ghadermazi et al 2015)
• construction connected with laminate (Scarselli et al 2015)
• condition of resin cure (Aggelis & Paipetis 2012)
• condition regarding to fibre/matrix interface (Kersemans et al
2014)
Detection of the following:
•
•
•
•
•
•
•
•
•
•
cracks and debonding (Giurgiutiu 2016)
mechanical rubbing (Gostautas et al 2005)
fibre pull-out (Short et al 2002)
fibre breakage (Narita et al 2014)
A full reference list for table 8.2 is available in Gholizadeh (2016).
8.17 INSPECTION TYPE VERSUS NDT METHOD
The inspection type and NDT methods used for each are presented in table 8.3 to provide
users with a quick recommendation when they need to evaluate a specific type of
composite structure.
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Table 8.3 Inspection type and NDT methods (Gholizadeh 2016)
Inspection type
NDT method
Ultrasonic testing
Damage identification in aircraft composite
Thermographic testing
structures
Vibration methods
Aircraft composites assessment
Infrared thermography
Health monitoring of aerospace composite
Shearography
structures
X-ray computed tomography (XCT)
Health monitoring of a composite wing-box
Ultrasonic testing
structure
Structural health monitoring
Ultrasonic testing
Damage in glass fibre reinforced plastic
Thermographic testing
(GFRP)
Radiography
Auto-detection of impact damage in carbon
fibre composites
Characterising damage in carbon fibre
Thermographic testing
reinforced polymer composites (CFRP)
Radiography
structures
Impact damage in glass/epoxy with
Infrared thermography
manufacturing defects
Damage assessment in sandwich structures
Parameters influencing the damping of a
structure
The structures behaviour
Vibration methods
Dynamic characteristics for damage
detection of structures
Skin damage statistical detection and
restoration assessment
Multiple cracks detection
Neutron radiography
8.18 CONCLUSION
A variety of non-destructive techniques can be used to evaluate many composite
structures. The field of non-destructive evaluation (NDE) or non-destructive testing (NDT)
involves the identification and characterisation of damages on the surface and interior of
materials without altering it physically. The selection of the most suitable test technique
for a particular application can be a challenging task. Table 8.4 provides a summary of
inpection methods related to composite inhomogeneities. However, experience, training,
experimentation and a clear understanding of the inspection objective are required to
develop effective NDT applications.
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Table 8.4 Summary of applicability of NDT methods (Peters 1998)
8.19 ACTIVITIES
(1)
(2)
(3)
(4)
What is the purpose of non-destructive evaluation in composites?
Apart from using the classical methods for controlling the surface defects (e.g.
imperfect bonding, delaminations and inclusions), which allow the repair of
external delaminations of laminated facings, make a list of other techniques that
allow the identification and repair of external defects due to fabrication or due to
damages in service.
Give at least THREE inhomogeneity factors that can affect composite performance.
Tabulate the advantages and disadvantages of the following testing techniques:
•
•
•
•
•
•
•
•
•
visual inspection
tap test
ultrasonic methods
X-radiography
acoustic emission
eddy current testing
infrared thermal testing
laser shearography
microwave testing
8.20 REFERENCE LIST
Callister, WD & Rethwisch, DG. 2015. Materials science and engineering. 9th edition.
Hoboken, NJ: John Wiley & Sons.
Daniel, IM & Ishai, O. 2006. Engineering mechanics of composite materials. New York:
Oxford University Press.
Gay, D & Hoa, SV. 2007. Composite materials: design and applications. 2nd edition.
Boca Raton, FL: CRC Press.
Gholizadeh, S. 2016. A review of non-destructive testing methods of composite
materials. Procedia Structural Integrity 1:50–57.
Gibson, R. 2016 Principles of composite material mechanics. 4th edition. Boca Raton,
FL: CRC Press.
Griffith, AA. 1920. The phenomena of rupture and flow in in solids. Philosophical
Transactions of the Royal Society 221A:163–198.
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