Analysis and Performance of Fiber Composites E-Book

Bhagwan D. Agarwal

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 730

Veröffentlichungsjahr: 2017

Beschreibung

Updated and expanded coverage of the latest trends and developments in fiber composite materials, processes, and applications

Analysis and Performance of Fiber Composites, Fourth Edition features updated and expanded coverage of all technical aspects of fiber composites, including the latest trends and developments in materials, manufacturing processes, and materials applications, as well as the latest experimental characterization methods.

Fiber reinforced composite materials have become a fundamental part of modern product manufacturing. Routinely used in such high-tech fields as electronics, automobiles, aircraft, and space vehicles, they are also essential to everyday staples of modern life, such as containers, piping, and appliances. Little wonder, when one considers their ease of fabrication, outstanding mechanical properties, design versatility, light weight, corrosion and impact resistance, and excellent fatigue strength. This Fourth Edition of the classic reference�the standard text for composite materials courses, worldwide�offers an unrivalled review of such an important class of engineering materials.

Still the most comprehensive, up-to-date treatment of the mechanics, materials, performance, analysis, fabrication, and characterization of fiber composite materials available, Analysis and Performance of Fiber Composites, Fourth Edition features:

• Expanded coverage of materials and manufacturing, with additional information on materials, processes, and material applications
• Updated and expanded information on experimental characterization methods�including many industry specific tests
• Discussions of damage identification techniques using nondestructive evaluation (NDE)
• Coverage of the influence of moisture on performance of polymer matrix composites, stress corrosion of glass fibers and glass reinforced plastics, and damage due to low-velocity impact
• New end-of-chapter problems and exercises with solutions found on an accompanying website
• Computer analysis of laminates

No other reference provides such exhaustive coverage of fiber composites with such clarity and depth. Analysis and Performance of Fiber Composites, Fourth Edition is, without a doubt, an indispensable resource for practicing engineers, as well as students of mechanics, mechanical engineering, and aerospace engineering.

Visit the Companion Website at: https://www.wiley.com/WileyCDA/Section/id-830336.html

Leseprobe

Table of Contents

COVER

TITLE PAGE

PREFACE

ABOUT THE COMPANION WEBSITE

1 INTRODUCTION

1.1 DEFINITION

1.2 CLASSIFICATION

1.3 PARTICULATE COMPOSITES

1.4 FIBER-REINFORCED COMPOSITES

1.5 APPLICATIONS OF FIBER-REINFORCED POLYMER COMPOSITES

EXERCISE PROBLEMS

REFERENCES

2 FIBERS, MATRICES, AND FABRICATION OF COMPOSITES

2.1 REINFORCING FIBERS

2.2 MATRIX MATERIALS

2.3 FABRICATION OF FIBER COMPOSITE PRODUCTS

SUGGESTED READING

3 MICROMECHANICS OF UNIDIRECTIONAL COMPOSITES

3.1 INTRODUCTION

3.2 LONGITUDINAL LOADING: DEFORMATION, MODULUS, AND STRENGTH

3.3 TRANSVERSE LOADING: MODULUS AND STRENGTH

3.4 SHEAR MODULUS

3.5 POISSON'S RATIOS

3.6 EXPANSION COEFFICIENTS AND TRANSPORT PROPERTIES

3.7 FAILURE OF UNIDIRECTIONAL COMPOSITES

3.8 TYPICAL PROPERTIES OF UNIDIRECTIONAL FIBER COMPOSITES

EXERCISE PROBLEMS

REFERENCES

4 SHORT-FIBER COMPOSITES

4.1 INTRODUCTION

4.2 LOAD TRANSFER TO FIBERS

4.3 PREDICTING MODULUS AND STRENGTH OF SHORT-FIBER COMPOSITES

4.4 INFLUENCE OF MATRIX DUCTILITY ON PROPERTIES

EXERCISE PROBLEMS

REFERENCES

5 MACROMECHANICS ANALYSIS OF AN ORTHOTROPIC LAMINA

5.1 INTRODUCTION

5.2 STRESS–STRAIN RELATIONS FOR UNIDIRECTIONAL COMPOSITES

5.3 HOOKE'S LAW AND STIFFNESS AND COMPLIANCE MATRICES

5.4 STRENGTHS OF AN ORTHOTROPIC LAMINA

EXERCISE PROBLEMS

REFERENCES

6 ANALYSIS OF LAMINATED COMPOSITES

6.1 CLASSICAL LAMINATION THEORY

6.2 LAMINATE DESCRIPTION SYSTEM

6.3 DESIGN, CONSTRUCTION, AND PROPERTIES OF LAMINATES

6.4 FAILURE OF LAMINATES

6.5 HYGROTHERMAL STRESSES IN LAMINATES

6.6 LAMINATE ANALYSIS THROUGH COMPUTERS

EXERCISE PROBLEMS

REFERENCES

7 ANALYSIS OF LAMINATED PLATES AND BEAMS

7.1 INTRODUCTION

7.2 GOVERNING EQUATIONS FOR PLATES

7.3 APPLICATION OF PLATE THEORY

7.4 DEFORMATIONS DUE TO TRANSVERSE SHEAR

7.5 ANALYSIS OF LAMINATED BEAMS

EXERCISE PROBLEMS

REFERENCES

8 ADVANCED TOPICS IN FIBER COMPOSITES

8.1 INTERLAMINAR STRESSES AND FREE-EDGE EFFECTS

8.2 FRACTURE MECHANICS OF FIBER COMPOSITES

8.3 JOINTS FOR COMPOSITE STRUCTURES

EXERCISE PROBLEMS

REFERENCES

9 PERFORMANCE OF FIBER COMPOSITES: FATIGUE, IMPACT, AND ENVIRONMENTAL EFFECTS

9.1 FATIGUE

9.2 IMPACT

9.3 ENVIRONMENTAL-INTERACTION EFFECTS

EXERCISE PROBLEMS

REFERENCES

10 EXPERIMENTAL CHARACTERIZATION OF COMPOSITES

10.1 INTRODUCTION

10.2 MEASUREMENT OF PHYSICAL PROPERTIES

10.3 MEASUREMENT OF MECHANICAL PROPERTIES

10.4 DAMAGE IDENTIFICATION USING NONDESTRUCTIVE EVALUATION TECHNIQUES

10.5 GENERAL REMARKS ON CHARACTERIZATION

EXERCISE PROBLEMS

REFERENCES

11 EMERGING COMPOSITE MATERIALS

11.1 NANOCOMPOSITES

11.2 CARBON–CARBON COMPOSITES

11.3 BIOCOMPOSITES

11.4 COMPOSITES IN “SMART” STRUCTURES

11.5 FURTHER EMERGING TRENDS

SUGGESTED READING

APPINDEX 1: MATRICES AND TENSORS

A1.1 MATRIX DEFINITIONS

A1.2 MATRIX OPERATIONS

A1.3 TENSORS

REFERENCES

APPINDEX 2: EQUATIONS OF THEORY OF ELASTICITY

A2.1 ANALYSIS OF STRAIN

A2.2 ANALYSIS OF STRESS

A2.3 STRESS–STRAIN RELATIONS FOR ISOTROPIC MATERIALS

REFERENCES

APPENDIX 3: LAMINATE ORIENTATION CODE

A3.1 STANDARD CODE ELEMENTS

A3.2 POSITIVE AND NEGATIVE ANGLES

A3.3 SYMMETRIC LAMINATES

A3.4 SETS

A3.5 HYBRID LAMINATES

APPENDIX 4: PROPERTIES OF FIBER COMPOSITES

APPENDIX 5: COMPUTER PROGRAMS FOR LAMINATE ANALYSIS

APPINDEX 6: INTRODUCTION TO MATLAB

A6.1 INTRODUCTION: GETTING STARTED

A6.2 VECTORS AND MATRICES

A6.3 PROGRAMMING IN MATLAB

A6.4 PLOTTING TOOLS

INDEX

SUPPLEMENTAL IMAGES

END USER LICENSE AGREEMENT

List of Tables

Chapter 1

Table 1.1 Properties of Fibers and Conventional Bulk Materials

Table 1.2 Properties of Conventional Structural Materials and Bidirectional (Cross-ply) Fiber Composites

Chapter 2

Table 2.1 Properties of E-Glass and S-Glass Fibers

Table 2.2 Typical Compositions of E-Glass and S-Glass Fibers

Table 2.3 Properties of Carbon Fibers

Table 2.4 Typical Properties of Kevlar Fibers

Table 2.5 Properties of Boron Fiber (with tungsten, core)

Table 2.6 Properties of Ceramic Fibers

Table 2.7 Properties of High-Performance Polyethylene (HPPE) Fibers

Table 2.8 Effect of External Variables on Polymer Properties

Table 2.9 Transition Temperatures for Polymers

Table 2.10 Properties of a Typical Cast Thermosetting Polyester

Table 2.11 Properties of a Typical Cast Epoxy Resin (at 23°C)

Table 2.12 Typical Properties of Vinyl Esters, Polyimides, and Phenolics

Table 2.13 Typical Properties of Some Thermoplastic Resins

Table 2.14 Properties of Some Aluminum-Alloy Matrix Materials

Chapter 3

Table 3.1 Typical Properties of Unidirectional-Fiber-Reinforced-Epoxy Composites

Table 3.2 Summary of Influence of Constituents on Properties of Unidirectional Polymer Composites

Chapter 4

Table 4.1 Average-Maximum Fiber Stress Ratios

Table 4.2 Properties of Different Blends of Matrix

Chapter 5

Table 5.1 Number of Elastic Constants

Chapter 7

Table 7.1 Maximum Deflection (

w

0

, 10

–6

m) Predicted by the Navier Series Solution

Table 7.2 Center Deflection and Stresses in Square Plates with Different Support Conditions

Table 7.3 Vibration Frequencies of a Simply Supported Square Plate

Table 7.4 First Five Natural Frequencies of a Simply Supported Plate

Chapter 8

Table 8.1 Experimental Fracture Toughness Values of Some Composites and Structural Metals

Table 8.2 Advantages and Disadvantages of Adhesively Bonded Joints

Table 8.3 Advantages and Disadvantages of Mechanically Fastened Joints

Chapter 9

Table 9.1 Typical Impact-Energy Values for Various Materials—Standard Charpy V Notched Impact Tests

Table 9.2 Impact Properties of Unidirectional Fiber–Epoxy Composites

Table 9.3 Summary of Experimental Data on the Effect of Moisture and Temperature on the Tensile Strength of Composites

Table 9.4 Summary of Experimental Data on the Effects of Moisture and Temperature on the Elastic Modulus of Composite Materials

Chapter 10

Table 10.1 Absorption Coefficients for 0.098-Å Wavelength X-Rays

Table 10.2 Material Thickness at Which X-Ray Intensity Reduces to Half Its Incident Value

Chapter 11

Table 11.1 Properties of Single-Walled Carbon Nanotubes

Table 11.2 Properties of Various Natural Fiber Reinforcements

Appendix 4

Table A4.1 Properties of Some Commercial Fiber Composites

Appendix 5

Table A5.1 Commercially Available Software Packages

List of Illustrations

Chapter 1

Figure 1.1.

Classification of composite materials.

Figure 1.2.

Growth of composites in the United States over five decades: comparison with steel, aluminum, and GDP.

Figure 1.3.

Use of composites in U.S. by application industries: Estimates for year 2015.

Figure 1.4.

Use of composites in Europe by application industries: Estimates for year 2015.

Figure 1.5.

Global demand for carbon-fiber-reinforced polymers in 1,000 tonnes (* estimated).

Figure 1.6.

Boeing 787 Dreamliner structural material distribution: predominance of fiber composites is obvious.

Figure 1.7.

Bell-Boeing V-22: the military aircraft used over 50% fiber composites as its structural materials in 1989.

Figure 1.8.

Ford Raptor fender and hood are made of fiber composites.

Figure 1.9.

Cross section of a fiber composite bridge manufactured at the Missouri University of Science and Technology.

Figure 1.10.

The fiber composite bridge installed at the campus of Missouri University of Science and Technology.

Chapter 2

Figure 2.1.

Commercial forms of fibers.

Figure 2.2.

Process for producing glass fibers.

Figure 2.3.

Global demand for carbon fibers by application industries: Estimates for year 2015.

Figure 2.4.

Atomic structure in carbon fibers.

Figure 2.5.

Process of converting precursor PAN fibers to carbon fibers.

Figure 2.6.

Usable temperature ranges for composites with different types of matrix materials.

Figure 2.7.

Specific volume of amorphous and semicrystalline polymers: variation with temperature.

Figure 2.8.

Variation of elastic modulus of polymers with temperature: (

a

) thermoplastic, amorphous (high molecular weight or lightly cross-linked); (

b

) thermoset, highly cross-linked; (

c

) semicrystalline.

Figure 2.9.

Tensile stress–strain curves of a thermoplastic polymer at different strain rates and temperatures.

Figure 2.10.

Spray-up molding process.

Figure 2.11.

Bag molding processes: (

a

) pressure bag, (

b

) vacuum bag.

Figure 2.12.

An autoclave (3 ft. in diameter and 6 ft. long) at the Missouri University of Science and Technology.

Figure 2.13.

Schematic representation of autoclave molding arrangement.

Figure 2.14.

Typical laminate lay-up for bagging.

Figure 2.15.

Resin-transfer molding configurations.

Figure 2.16.

Filament winding operation.

Figure 2.17.

Filament winding patterns.

Figure 2.18.

Pultruded samples made at the Missouri University of Science and Technology.

Figure 2.19.

Pultrusion process scheme.

Figure 2.20.

A Labstar pultrusion machine at the Missouri University of Science and Technology.

Figure 2.21.

Manufacturing scheme of sheet molding compound.

Figure 2.22.

Compression molding.

Figure 2.23.

Production of polymer coated continuous fiber roving.

Figure 2.24.

Thermostamping process.

Figure 2.25.

Typical lay-up and construction of a sandwich panel.

Figure 2.26.

A typical honeycomb core structure.

Chapter 3

Figure 3.1.

A unidirectional composite represented schematically.

Figure 3.2.

Cross section of unidirectional composites (from a single ply): (

a

) glass–epoxy; (

b

) Fiber FP (alumina fiber) in aluminum matrix.

Figure 3.3.

Model of unidirectional composite used to predict longitudinal behavior.

Figure 3.4.

Longitudinal modulus as a function of fiber volume fraction.

Figure 3.5.

Longitudinal stress–strain diagrams of composites with: (

a

) linear, and (

b

) nonlinear matrix material.

Figure 3.6.

Percentage of longitudinal load carried by the fibers in unidirectional composites.

Figure 3.7.

Longitudinal stress–strain curves for unidirectional composites with ductile and brittle fibers and a typical ductile matrix.

Figure 3.8.

Longitudinal strength as a function of fiber volume fraction.

Figure 3.9.

Transverse loading of a unidirectional composite.

Figure 3.10.

Model used to predict transverse modulus of unidirectional composites.

Figure 3.11.

Transverse modulus predicted using the model shown in Figure 3.10.

Figure 3.12.

Comparison of predicted transverse modulus with the experimental measurements on a boron–epoxy lamina (

,

,

,

).

Figure 3.13.

Transverse modulus predicted through numerical calculations.

Figure 3.14.

Transverse modulus predicted by Halpin–Tsai equation [Eq. (3.36)].

Figure 3.15.

Stress distributions in matrix surrounding a single cylindrical inclusion:

,

,

Figure 3.16.

Maximum principal stress in matrix surrounding multiple fibers (

,

).

Figure 3.17.

Model used to predict shear modulus.

Figure 3.18.

Shear modulus predicted through numerical calculations.

Figure 3.19.

Shear modulus predicted by Halpin–Tsai equation [Eq. (3.53)].

Figure 3.20.

Predicted shear modulus (by Halpin–Tsai equation [Eq. (3.53)]) and experimentally measured shear modulus of unidirectional glass–epoxy lamina (

,

).

Figure 3.21.

Model used to predict major Poisson's ratio.

Figure 3.22.

Model used to predict longitudinal coefficient of thermal expansion.

Figure 3.23.

Coefficients of thermal expansion for unidirectional composites.

Figure 3.24.

Coefficient of thermal expansion of unidirectional high-modulus graphite–epoxy composites as a function of temperature.

Figure 3.25.

Longitudinal thermal conductivity of unidirectional carbon–epoxy composites at 20°C.

Figure 3.26.

Transverse thermal conductivity of unidirectional carbon–epoxy composites at 20°C.

Figure 3.27.

Longitudinal electrical conductivity of unidirectional carbon–epoxy composites at 20°C.

Figure 3.28.

Transverse electrical conductivity of unidirectional carbon–epoxy composites at 20°C.

Figure 3.29.

Matrix diffusivity and longitudinal and transverse diffusivities of graphite–epoxy composites.

Figure 3.30.

Multiple fiber-breaks in a unidirectional composite loaded in longitudinal direction.

Figure 3.31.

Separation of fibers from matrix (i.e., debonding) in a glass–epoxy composite (5000X).

Figure 3.32.

Microcracking in a glass–epoxy laminate during fatigue loading (800X).

Figure 3.33.

Separation of laminae (i.e., delamination) in a glass–epoxy laminate during fatigue loading (200X).

Figure 3.34.

Cumulative number of fiber breaks with increasing longitudinal load.

Figure 3.35.

Failure modes of a unidirectional composite subjected to longitudinal tensile load: (

a

) brittle failure, (

b

) brittle failure with fiber pullout, and (

c

) brittle failure with debonding and/or matrix failure.

Figure 3.36.

Photographs of unidirectional composite specimens fractured under longitudinal tensile loads. Cracks at different cross sections joined up to cause ultimate failure.

Figure 3.37.

Transverse tensile failure (i.e., transverse splitting) of unidirectional composite caused by a longitudinal compressive load.

Figure 3.38.

Comparison of longitudinal compressive strength, predicted by transverse splitting model, with experimental data.

Figure 3.39.

(

a

) Fiber microbuckling in extensional mode, and (

b

) fiber microbuckling in shear mode in unidirectional composites subjected to longitudinal compressive load.

Figure 3.40.

Photographs show microbuckling of fibers in unidirectional composites produced by compressive stresses on fibers due to matrix shrinkage. Parallel fibers buckle in phase (i.e., in shear mode) at separations of up to 10 fiber diameters (

a

,

b

). Fibers buckle independently only at very large separations of 50 fiber diameters in extension mode (

c

).

Figure 3.41.

Shear failure of a unidirectional composite under longitudinal compressive load.

Figure 3.42.

Photograph shows shear failure of specimen under longitudinal compressive load (50X). Localized rotation of carbon fibers may have occurred before or during failure process.

Figure 3.43.

Failure of unidirectional composite under transverse tensile load.

Figure 3.44.

Fracture surfaces of unidirectional graphite–fiber composites produced by transverse tensile loads when fibers are: (

a

) high modulus, and (

b

) high tensile strength.

Figure 3.45.

Shear failure of unidirectional composite subjected to transverse compressive load.

Figure 3.46.

Photographs showing shear failure of unconstrained unidirectional carbon-fiber-reinforced plastics subjected to transverse compressive loads.

Figure 3.47.

Failure of a unidirectional composite subjected to in-plane shear load.

Figure 3.48.

Fiber packing in unidirectional composites (Exercise Problem 3.1).

Figure 3.49.

Stress-strain curves for matrices A and B (Exercise Problem 3.9).

Chapter 4

Figure 4.1.

Internal forces on a small length of fiber for its equilibrium.

Figure 4.2.

Idealized shear-stress–shear-strain curve for a rigid, perfectly plastic matrix material.

Figure 4.3.

Fiber stress and interfacial shear stress on fibers of different lengths but equal stress on the composite.

Figure 4.4.

Fiber stress on a fiber longer than its critical length for different composite stresses.

Figure 4.5.

Fiber stress and interfacial shear stress from elastic FEA.

.

Figure 4.6.

Matrix stresses in axial and radial directions from elastic FEA.

.

Figure 4.7.

Fiber stress and interfacial shear stress from elastoplastic FEA.

; matrix yield strain

].

Figure 4.8.

Model of an aligned short-fiber composite.

Figure 4.9.

Influence of fiber aspect ratio (

l

/

d

) and fiber volume fraction on longitudinal modulus

.

Figure 4.10.

Influence of fiber aspect ratio (

l

/

d

) and fiber volume fraction on longitudinal modulus

.

Figure 4.11.

Model of a randomly oriented short-fiber composite.

Figure 4.12.

Comparison of experimentally measured and theoretically predicted tensile strength of randomly oriented short-fiber composites.

Figure 4.13.

Photomicrographs of injection-molded glass-fiber-reinforced nylon (100X) show (

a

) an area where fibers are aligned due to flow and (

b

) an area where fibers are randomly oriented.

Figure 4.14.

Stress–strain curves for composites with ductile and brittle matrices.

Figure 4.15.

Tensile strength of composites with ductile and brittle matrices.

Figure 4.16.

Notched Izod impact strength of composites with ductile and brittle matrices.

Chapter 5

Figure 5.1.

Deformation of isotropic plate under (

a

) uniaxial tension, and (

b

) pure shear. Undeformed plate is shown by broken lines.

Figure 5.2.

Deformation of anisotropic or arbitrarily oriented orthotropic lamina under (

a

) uniaxial tension, and (

b

) pure shear. Undeformed lamina is shown by broken lines.

Figure 5.3.

Deformation of unidirectional lamina loaded parallel to material axes (L & T) in (

a

) uniaxial tension, and (

b

) pure shear. Undeformed lamina is shown by broken lines.

Figure 5.4.

An orthotropic lamina loaded along material (L & T) axes.

Figure 5.5.

Strains in a lamina due to longitudinal stress only.

Figure 5.6.

Strains in a lamina due to transverse stress only.

Figure 5.7.

Strains in a lamina due to shear stress only.

Figure 5.8.

Loaded off-axis lamina.

Figure 5.9.

Elastic constants of a glass–epoxy lamina: variation with fiber orientation.

Figure 5.10.

Elastic constants of a graphite–epoxy lamina: variation with fiber orientation.

Figure 5.11.

Elastic constants of a boron–epoxy lamina: variation with fiber orientation.

Figure 5.12.

Elastic constants of a balanced lamina: variation with fiber orientation.

Figure 5.13.

State of stress on the lamina for Example 5.2.

Figure 5.14.

Components of stress tensor on a cube element.

Figure 5.15.

Invariant and variable components of stiffness: variation with fiber orientation.

Figure 5.16.

Off-axis strength predicted by maximum-stress and maximum-strain theories of failure.

Figure 5.17.

State of stress on a glass–epoxy lamina for Example 5.6.

Figure 5.18.

Off-axis strength predicted by maximum-work (Tsai–Hill) and maximum-stress theories of failure.

Figure 5.19.

Failure envelopes for different strength ratios but zero shear stress on a normalized stress plane.

Figure 5.20.

Change in size of failure envelope for different shear stresses.

Figure 5.21.

Sign convention for stress components: (

a

) positive stresses and (

b

) negative stresses.

Figure 5.22.

Principal stresses when shear stress is applied parallel to L and T axes.

Figure 5.23.

Principal stresses when shear stress is applied 45° to L and T axes.

Figure 5.24.

Transformation of coordinate axes when

x

1

x

2

is a plane of symmetry.

Figure 5.25.

Transformation of coordinate axes when

x

2

x

3

is a plane of symmetry.

Chapter 6

Figure 6.1.

A four-ply laminate.

Figure 6.2.

Deformation of a line element of a laminate during bending in the

xz

plane.

Figure 6.3.

Variation of strain and stress in a hypothetical three-ply laminate.

Figure 6.4.

Sign convention for resultant forces and moments (positive forces and moments are shown).

Figure 6.5.

Description of a multilayered laminate geometry

Figure 6.6.

Two-ply laminate for Example 6.1.

Figure 6.7.

Twisting of an asymmetric (±θ) laminate due to in-plane axial force.

Figure 6.8.

Three-ply laminate for Example 6.2.

Figure 6.9.

Applied forces defined on laminate for Example 6.8.

Figure 6.10.

Coordinate axes for (

a

) 0° lamina, and (

b

) 45° lamina.

Figure 6.11.

Lamina stresses and strains along the reference axes (Example 6.8).

Figure 6.12.

Lamina stresses and strains along the longitudinal and transverse axes (Example 6.7).

Figure 6.13.

Load-deformation behavior of a hypothetical laminate.

Figure 6.14.

Experimental and theoretical stress–strain curves for a [0/90]

2

s

laminate.

Figure 6.15.

Experimental and theoretical stress–strain curves for a [0/902]

s

laminate.

Figure 6.16.

Load–elongation curve predicted for the quasi-isotropic laminate in Example 6.10.

Figure 6.17.

How thermal strains and stresses are produced in a three-ply symmetric laminate.

Figure 6.18.

Residual stresses (Example 6.10).

Figure 6.19.

Flowchart for laminate stress analysis.

Figure 6.20.

Flowchart for laminate strength analysis.

Chapter 7

Figure 7.1.

A flat plate subjected to transverse load.

Figure 7.2.

Differential elements with (

a

) in-plane force resultants, and (

b

) moment resultants, shear force resultants, and applied transverse load.

Figure 7.3.

Rectangular plate geometry defined for bending problem.

Figure 7.4.

Deflection of a simply supported plate under uniformly distributed load.

Figure 7.5.

Variation of bending stresses (σ

x

and σ

y

) in a rectangular plate: simply supported and subjected to uniformly distributed load.

Figure 7.6.

A rectangular plate subjected to in-plane loads.

Figure 7.7.

Nondimensional buckling load for rectangular plates with different aspect ratios.

Figure 7.8.

Buckling loads for rectangular plates subjected to uniaxial and biaxial compressive loads.

Figure 7.9.

Modes of vibration for simply supported square plates. Dashed lines represent nodal lines.

Figure 7.10.

Deformed shape of a simply supported plate vibrating in first mode.

Figure 7.11.

Effect of transverse shear on center deflection of a symmetric cross-ply [0/90]s laminate subjected to sinusoidal transverse load.

Figure 7.12.

Center deflection, predicted by different theories, of a symmetric cross-ply [0/90]s laminate.

Figure 7.13.

The transverse shear stress, τ

xz

, predicted by the first-order and higher order theories.

Figure 7.14.

Transverse shear stress, τ

yz

, predicted by the first-order and higher order theories.

Figure 7.15.

Transverse load applied to a beam.

Figure 7.16.

A uniformly loaded beam: (

a

) simply supported, and (

b

) clamped at both ends.

Figure 7.17.

Axial compressive load applied to a simply supported beam.

Chapter 8

Figure 8.1.

A four-ply laminate subjected to a uniaxial force in the

x

direction.

Figure 8.2.

Schematic representation of free-edge delamination.

Figure 8.3.

Model of a symmetric angle-ply laminate used for calculating interlaminar stresses.

Figure 8.4.

Variation of stresses across width of the laminate shown in Fig. 8.3.

Figure 8.5.

Change in interlaminar shear stress as ply orientation (θ) changes in angle-ply laminates.

Figure 8.6.

Comparison of experimentally measured and theoretically calculated surface displacements in the laminate shown in Fig. 8.3.

Figure 8.7.

Interlaminar shear stresses in cross-ply laminates for different ply lay-ups.

Figure 8.8.

Interlaminar stresses in [45/−45/0]

s

laminates for different fibers (carbon or glass): (

a

) shear stresses τ

xz

and τ

yz

and (

b

) normal stress σ

z

.

Figure 8.9.

Comparison of interlaminar stresses from Whitney's approximate solution and exact elasticity solution.

Figure 8.10.

Free-edge delamination-suppression concepts.

Figure 8.11.

A model of local failure events near the crack tip in fracture-process zone.

Figure 8.12.

A damage zone formed ahead of the crack tip in a short-fiber composite.

Figure 8.13.

A solid body subjected to external forces: (

a

) without a crack and (

b

) with a crack.

Figure 8.14.

Loading and coordinate system defined for stress analysis of a plate with a crack.

Figure 8.15.

Modes of crack extension: (

a

) opening mode (mode I), (

b

) shear mode (mode II), and (

c

) anti-plane strain or tearing mode (mode III).

Figure 8.16.

An arbitrary line contour for evaluating

J

-integral.

Figure 8.17.

A plate with a circular hole of radius

R

.

Figure 8.18.

A plate with a crack of length 2

c

.

Figure 8.19.

Experimentally measured and theoretically predicted strengths of [0/±45/90]

2

S

glass–epoxy laminates containing circular holes.

Figure 8.20.

Experimentally measured and theoretically predicted strengths of [0/±45/90]

2

S

glass–epoxy laminates containing sharp cracks.

Figure 8.21.

Experimentally measured and theoretically predicted fracture toughness of [0/±45/90]

2

S

glass–epoxy laminates.

Figure 8.22.

Mechanisms of adhesive bonding: (

a

) chemical bonding, (

b

) mechanical interlocking, and (

c

) electrostatic bonding.

Figure 8.23.

Adhesively bonded joint configurations.

Figure 8.24.

Failure modes in adhesively bonded joints.

Figure 8.25.

Interlaminar stresses (normal and shear) in a single-lap joint.

Figure 8.26.

Failure modes in mechanically fastened joints: (

a

) bearing, (

b

) tension, (

c

) shear-out, and (

d

) cleavage.

Chapter 9

Figure 9.1.

Fatigue failure initiation: (

a

) single crack in cross-ply, and (

b

) multiple cracks in cross-plies.

Figure 9.2.

A delamination crack initiates at the tip of a cross-ply crack.

Figure 9.3.

Longitudinal-ply crack appears in specimen cross section.

Figure 9.4.

Extensive delamination observed in a cross section near fracture surface after fatigue failure.

Figure 9.5.

Modes of fatigue-crack growth in fiber-reinforced composites: (

a

) shear-crack initiation at fiber break, (

b

) tensile splitting of interface ahead of matrix crack, (

c

) matrix crack bypassing a strong fiber, (

d

) crack initiation in ductile fiber ahead of matrix crack, and (

e

) fracture of brittle fiber ahead of matrix crack.

Figure 9.6.

Loss of strength and modulus of a laminate during fatigue is a result of the increase in the number of cracks in cross plies.

Figure 9.7.

Correlation between loss of modulus and the crack pitch.

Figure 9.8.

Temperature rises and load decays during constant-deflection flexural fatigue cycling.

Figure 9.9.

Comparison of fatigue strength of glass-reinforced plastic laminates with different matrix materials.

Figure 9.10.

Fatigue strength for different fiber orientations and laminate constructions.

Figure 9.11.

S

–

N

curves for different laminate constructions.

Figure 9.12.

Axial fatigue strength as a function of glass content.

Figure 9.13.

Rotating bending fatigue strength as a function of glass content.

Figure 9.14.

Shear fatigue strength of unidirectional glass–epoxy composite.

Figure 9.15.

Shear fatigue strength of unidirectional boron–epoxy composite.

Figure 9.16.

Master diagram showing influence of mean stress on fatigue strength.

Figure 9.17.

S

–

N

curve for a unidirectional graphite–epoxy laminate.

Figure 9.18.

S

–

N

curve for a [0

4

/±45

2

/90] graphite–epoxy laminate.

Figure 9.19.

Longitudinal stress–rupture curves for unidirectional graphite–epoxy composite under different environmental conditions.

Figure 9.20.

S

–

N

curves for unidirectional boron–epoxy composite.

Figure 9.21.

S

–

N

curves for [0/±45/90] boron–epoxy laminate.

Figure 9.22.

Fatigue characteristics of unidirectional composites compared with aluminum.

Figure 9.23.

Approximate fatigue behavior of several reinforced plastics. CSM refers to chopped-strand mat (curve G), which generally has 5 cm long randomly oriented fibers, and DMC refers to dough-molding compound, which has less than 1 cm long fibers.

Figure 9.24.

Fatigue data for CSM–PR specimens at zero mean stress.

Figure 9.25.

The onset of transverse fiber debonding and resin cracking in fatigue under zero mean-stress.

Figure 9.26.

Effect of holes on fatigue strength of CSM–PR specimens.

Figure 9.27.

Fatigue endurance of glass-fortified polyacetal and polystyrene.

Figure 9.28.

Fatigue endurance of glass-fortified rigid polyvinylchloride, polypropylene, and polysulfone.

Figure 9.29.

Fatigue endurance of glass-fortified polycarbonate, 6/10 nylon, and 6/6 nylon.

Figure 9.30.

A model of local failure events near the crack tip in fracture-process zone.

Figure 9.31.

Photograph of a matrix crack formed in a glass–epoxy composite (900X).

Figure 9.32.

Fracture surface of a glass–epoxy composite shows fibers pulled out of matrix (600X).

Figure 9.33.

Three successive frames, recorded at a speed of 6000 frames per second, show development of delamination in a composite laminate during an impact test.

Figure 9.34.

Impact test arrangement.

Figure 9.35.

Influence of fiber orientation on energy absorbed by a unidirectional glass–epoxy composite.

Figure 9.36.

Influence of fiber orientation on energy absorbed by cross-ply laminate of a glass–epoxy composite.

Figure 9.37.

Influence of interface strength on impact energy of a glass–polyester composite.

Figure 9.38.

Influence of interface strength on impact energy of a glass–epoxy composite.

Figure 9.39.

Initiation and propagation energies during impact of composites.

Figure 9.40.

Influence of adding glass fibers to a graphite–epoxy laminate on its impact energy.

Figure 9.41.

Size of internal delamination surfaces produced by impacts at different velocities on cross-ply laminates.

Figure 9.42.

Matrix cracking patterns on (

a

) impacted surface, and (

b

) surface opposite to impact.

Figure 9.43.

Residual tensile strength of graphite–epoxy laminates after repeated impacts with different energies.

Figure 9.44.

Residual compressive strength of graphite–epoxy laminates after repeated impacts with different energies.

Figure 9.45.

Static tensile fatigue strength E-glass fibers at different temperatures.

Figure 9.46.

Stress–rupture properties of boron fibers.

Figure 9.47.

Appearance of fracture surface of a GRP exposed to sulfuric acid under stress.

Figure 9.48.

Strengths of E-glass fibers in various pH solutions.

Figure 9.49.

The stress-corrosion failure time (

t

f

) of single E-glass fibers under varying applied strains (ε

a

) in 0.5 M H

2

SO

4

(○), 0.5 M NaHSO

4

(•) and 0.01 M H

2

SO

4

(+).

Figure 9.50.

Correlation between stress parallel to fibers and time to composite pipe failure in 0.65 M HCL at 20°C for different resins.

Figure 9.51.

Appearance of fracture surfaces of GRP samples fractured in (

a

) air, and (

b

) acid.

Figure 9.52.

Moisture absorption by a carbon–epoxy laminate at 24°C.

Figure 9.53.

Thermal degradation of glass–phenolic composites.

Figure 9.54.

Master curve for decomposition of a phenolic–glass composites.

Figure 9.55.

Master curve for stiffness and strength of a phenolic–glass composites.

Figure 9.56.

Stress–rupture behavior of unidirectional graphite–epoxy composites subjected to transverse load at different temperatures.

Figure 9.57.

Stress–rupture behavior of unidirectional boron–epoxy composites subjected to transverse load.

Figure 9.58.

Stress–rupture behavior of boron–epoxy [±45] laminates.

Chapter 10

Figure 10.1.

Moisture-absorption curve for determining diffusivity.

Figure 10.2.

Tension-test specimens: (

a

) dog-bone, and (

b

) straight-sided with end tabs.

Figure 10.3.

End connections for tension-test specimens: (

a

) pin type, and (

b

) serrated-jaw type.

Figure 10.4.

Deformed shape of off-axis tension specimen when: (

a

) grips are free to rotate in-plane, and (

b

) unusual buckling may occur when grips rotation is suppressed.

Figure 10.5.

End brooming under compressive loading represents premature failure.

Figure 10.6.

Modified IITRI compression test fixture and specimen dimensions.

Figure 10.7.

Photograph of an IIRTI compression test fixture.

Figure 10.8.

Torsion tube test specimen for determining shear properties.

Figure 10.9.

Schematic representation of Iosipescu shear test loading mechanism.

Figure 10.10.

Free body diagram of Iosipescu shear test specimen shows external forces on it. Shear-force and bending moment on the specimen are shown below the specimen.

Figure 10.11.

Photograph of an Iosipescu shear test fixture.

Figure 10.12.

[±45]

S

coupon for measuring shear modulus by tension test.

Figure 10.13.

Off-axis coupon for determining shear-stress–strain response by tension test.

Figure 10.14.

Schematic representation of picture frame test for in-plane shear properties.

Figure 10.15.

Schematic representation of rail shear test.

Figure 10.16.

Sandwich cross-beam test specimen.

Figure 10.17.

Three-point loading and associated shear-force and bending-moment diagrams.

Figure 10.18.

Four-point loading and associated shear-force and bending-moment diagrams.

Figure 10.19.

Three-point bend test fixture.

Figure 10.20.

Four-point bend test fixture.

Figure 10.21.

Normal and shear stresses across thickness of a beam during bending of rectangular cross section beam of homogeneous material.

Figure 10.22.

Representation of interlaminar shear stresses in a laminated material.

Figure 10.23.

Staggered two-notch specimen for determination of interlaminar shear-strength by tension test.

Figure 10.24.

Double-cantilever-beam (DCB) specimen for fracture toughness measurement.

Figure 10.25.

Load-displacement behavior of DCB specimens at different crack lengths.

Figure 10.26.

Area method for evaluation of GIC.

Figure 10.27.

A plate with a crack to measure GIC by tension test.

Figure 10.28.

Fracture toughness test specimens: (

a

) single-edge notched (SEN), (

b

) double-edge notched (DEN), and (

c

) notch bend test specimen.

Figure 10.29.

An

R

curve and

K

I

curves for constant loads.

Figure 10.30.

Load–COD curves for different initial crack lengths.

Figure 10.31.

Crack length estimation curve for 25mm wide specimens.

Figure 10.32.

Instantaneous compliance evaluation procedure.

Figure 10.33.

(

a

) Determination of strain energies at different displacements, and (

b

) energy curves at constant displacements.

Figure 10.34.

Impact test arrangements: (

a

) Charpy test and (

b

) Izod test.

Figure 10.35.

Typical load history during impact test on composite laminates.

Figure 10.36.

Load and energy histories recorded during an instrumented Charpy test on a glass–epoxy laminate. Tested specimen is also shown.

Figure 10.37.

Load and energy histories during low-energy impact on a graphite–epoxy laminate.

Figure 10.38.

Load and energy histories during high-energy impact on a graphite–epoxy laminate.

Figure 10.39.

Ultrasonic pulse–echo test configuration.

Figure 10.40.

Ultrasonic pitch–catch test configuration.

Figure 10.41.

Ultrasonic through transmission test configuration.

Figure 10.42.

A C-scan of a graphite–epoxy laminate. The blank spaces indicate defects.

Figure 10.43.

Schematic diagram of an acoustic emission system.

Figure 10.44.

A typical thermography inspection arrangement.

Figure 10.45.

A typical laser shearography system configuration.

Figure 10.46.

Typical “butterfly” fringe patterns of a strain concentration obtained by shearography.

Chapter 11

Figure 11.1.

Structure of some important biopolyesters.

Appendix 1

Figure A1.1.

Representation of a vector by (

a

) a directed line segment, and (

b

) components.

Figure A1.2.

Representation of stress as (

a

) an average force vector and a unit normal, and (

b

) components.

Figure A1.3.

Cartesian components of stress.

Figure A1.4.

Two coordinate systems defined.

Figure A1.5.

Transformation angles defined in two dimensions.

Figure A1.6.

Transformation angles defined in three dimensions.

Figure A1.7.

Coordinate axes rotated about

x

3

axis.

Figure A1.8.

Two coordinate systems for Example A1.25.

Appendix 2

Figure A2.1.

A line segment deforms.

Figure A2.2.

Two orthogonal line segments deform.

Figure A2.3.

Two sets of coordinate axes defined.

Figure A2.4.

Internal forces at a point in a loaded solid body.

Figure A2.5.

Three-dimensional stress components.

Figure A2.6.

Stresses on a parallelepiped element in equilibrium inside a solid body.

Figure A2.7.

A tetragonal volume element on the surface of a solid body with applied load.

Figure A2.8.

Stresses on two-dimensional triangular elements in equilibrium inside a solid body.

Appendix 3

Figure A3.1.

Sign convention for laminate orientation code.

Appendix 4

Figure A4.1.

Longitudinal tensile stress–strain curve for a unidirectional graphite-fiber (T300)–epoxy laminate.

Figure A4.2.

Longitudinal compression stress–strain curve for a unidirectional graphite-fiber (T300)–epoxy laminate.

Figure A4.3.

Shear stress–strain curve for a unidirectional graphite-fiber (T300)–epoxy laminate.

Figure A4.4.

Transverse tension stress–strain curve for a unidirectional graphite-fiber (T300)–epoxy laminate.

Figure A4.5.

Transverse compression stress–strain curve for a unidirectional graphite-fiber (T300)–epoxy laminate.

Figure A4.6.

Longitudinal stress–strain curves for [±45] graphite–epoxy laminate.

Appendix 6

Figure A6.1.

MATLAB interface.

Figure A6.2.

Plots of sine and cosine functions.

Supplemental Images

Figure 1.2.

Growth of composites in the United States over five decades: comparison with steel, aluminum, and GDP.

Figure 1.3.

Use of composites in U.S. by application industries: Estimates for year 2015.

Figure 1.4.

Use of Composites in Europe by application industries: Estimates for year 2015.

Figure 1.6.

Boeing 787 Dreamliner structural material distribution: predominance of fiber composites is obvious.

Figure 1.7.

Bell-Boeing V-22: the military aircraft used over 50% fiber composites as its structural materials in 1989.

Figure 1.8.

Ford Raptor fender and hood are made of fiber composites.

Figure 2.1.

Commercial forms of fibers.

Figure 2.3.

Global demand for carbon fibers by application industries: Estimates for year 2015.

Figure 2.12.

An autoclave (3 ft. in diameter and 6 ft. long) at the Missouri University of Science and Technology.

Figure 2.18.

Pultruded samples made at the Missouri University of Science and Technology.

Figure 2.20.

A Labstar pultrusion machine at the Missouri University of Science and Technology.

Figure 2.25.

Typical lay up and construction of a sandwich panel.

Figure 10.19.

Three-point bend test fixture.

Figure 10.20.

Four-point bend test fixture.

Figure A6.1.

MATLAB interface.

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E1

ANALYSIS AND PERFORMANCE OF FIBER COMPOSITES

FOURTH EDITION

Bhagwan D. Agarwal

ConsultantHoffman Estates, Illinois, USA

Lawrence J. Broutman

ConsultantChicago, Illinois, USA

K. Chandrashekhara

Missouri University of Science and TechnologyRolla, Missouri, USA

This edition first published 2018

© 2018 John Wiley & Sons, Inc.

Edition History

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PREFACE

The need to include composite materials courses in engineering and science curricula at colleges and universities has been steadily increasing over the past 40 years. This need is caused by the growing worldwide usage of composite materials. The advantages of fiber composites in structural applications include outstanding mechanical properties, design versatility, light weight, corrosion and impact resistance, and excellent fatigue strength. In addition, their strength and stiffness properties are easily controlled by their fiber and layer composition. No wonder that these materials are now a major player in the universe of materials available to the design engineer. Thus, engineering and science students, particularly civil, materials, mechanical, and aerospace engineers need to be educated on all aspects of composites from the materials science to the engineering design of products manufactured from composites. The inclusion of new courses into a curriculum is greatly aided by the availability of suitable textbooks. This also lessens the need for the teacher to be an expert in the specific field. Prior editions of the book have well served the needs of colleges and universities for over three decades. The revised edition, with updates and extensive rewrites and reorganization, provides an improved teaching tool and is better focused for students and practicing engineers using the book for reference. The new edition was substantially developed from the feedback of students who used previous editions in their composites courses.

The book retains its complete coverage of the subject, with chapters on materials and manufacturing, micro- and macromechanics analyses, structural analysis, and test methods. Additional examples are presented of polymer composites used in demanding applications such as the Boeing Dreamliner passenger jet, the Bell-Boeing V-22, and the Ford Raptor truck.

A very useful structural analysis software, MATLAB, has been described in a new appendix and its use demonstrated by example problems in chapters 5, 6, and 7. The MATLAB code for exercise problems is provided in a solutions manual for instructors.

The authors would like to acknowledge the help of Zhen Huo, Sudharshan Anandan, Gurjot S. Dhaliwal, Bo Wang, Cheng Yan, and Shouvik Ganguly, all graduate students at the Missouri University of Science and Technology, Rolla. They provided useful suggestions, aided in typing the manuscript, prepared many new figures, and developed MATLAB codes for the solution of example and exercise problems. The authors also thank Dr. Sanjay Mazumdar for providing several updated as well as new figures.

BHAGWAN D. AGARWALLAWRENCE J. BROUTMANK. CHANDRASHEKHARAMay 2017

ABOUT THE COMPANION WEBSITE

This book is accompanied by a companion website:

www.wiley.com/go/agarwal/fiber

Password: density

The website includes a solutions manual.

1INTRODUCTION

1.1 DEFINITION

The word composite means “consisting of two or more distinct parts.” Thus, a material having two or more distinct constituent materials or phases may be considered a composite material. However, we recognize materials as composites only when the constituent phases have significantly different physical properties, and thus the composite properties are noticeably different from the constituent properties. The difference in properties will be more obvious when the properties of one constituent are much greater (≥5 times) than the other, when this phase is in fiber or platelet form, and its volume fraction is greater than 10%. Many combinations of constituents do not result in a new material with significantly different properties. Such materials are not classified as composites. For example, common metals almost always contain unwanted impurities or alloying elements; plastics generally contain small quantities of fillers, lubricants, ultraviolet absorbers, and other materials for commercial reasons such as economy and ease of processing, yet these generally are not classified as composites. In the case of metals, the constituent phases often have nearly identical properties (e.g., modulus of elasticity), the phases are not generally fibrous in character, and one of the phases usually is present in small-volume fractions. Thus, the modulus of elasticity of a steel alloy is insensitive to the amount of the carbide present, and metallurgists generally have not considered metal alloys as composites, particularly from the point of view of analysis. Nevertheless, two-phase metal alloys are good examples of particulate composites in terms of structure. Although plastics, which are filled with small amounts of additives to reduce cost, are composites, they need not be considered as such if their physical properties are not greatly affected by the additives.

Within the wide range of composite materials, a definition may be adopted to suit one's requirements. For the purpose of discussion in this book, composites can be considered to be materials consisting of two or more chemically distinct constituents, on a macroscale, having a distinct interface separating them. This definition encompasses the fiber composites, which are of primary interest in this text. This definition also encompasses many other types of composites that are not treated specifically in this book.

1.2 CLASSIFICATION

Composites consist of one or more discontinuous phases embedded in a continuous phase. The discontinuous phase usually has higher stiffness and strength than the continuous phase and is called the reinforcement or reinforcing material, whereas the continuous phase is termed the matrix. Ceramic matrix composites could be exceptions since matrix may have higher stiffness than the reinforcement. Properties of composites are strongly influenced by the properties of constituent materials, their distribution, and the interaction among them. Therefore, proper description of a composite material as a system requires, besides the constituent materials and their properties, the geometry of the reinforcement (shape, size, and size distribution) and its concentration, concentration distribution, and orientation with reference to the system.

Most composite materials have, so far, been developed to improve mechanical properties such as strength, stiffness, toughness, and high-temperature performance. The mechanism of improving these properties strongly depends on the geometry of the reinforcement. Therefore, it is quite convenient to classify composite materials on the basis of the microstructure of a representative unit of reinforcement to study together the composites that have a common strengthening mechanism. Figure 1.1 represents a commonly accepted classification scheme for composite materials. With regard to this classification, the distinguishing characteristic of a particle is that it is nonfibrous in nature with all its dimensions approximately equal. It may be spherical, cubic, tetragonal, a platelet, or of other regular or irregular shape. A fiber is characterized by its length being much greater than its cross-sectional dimensions. Particle-reinforced composites are sometimes referred to as particulate composites. Fiber-reinforced composites are, understandably, called fiber composites.

Figure 1.1. Classification of composite materials.

1.3 PARTICULATE COMPOSITES

Particle-reinforced composites are called particulate composites. A particle generally has no long dimension, with the exception of platelets. The dimensions of the reinforcement determine its capability of contributing its properties to the composite. Also, a reinforcement with a long dimension inhibits the growth of cracks normal to the reinforcement that otherwise might lead to failure, particularly with brittle matrices. Therefore, particles, in general, are not very effective in improving fracture resistance. However, particles of rubberlike substances in brittle polymers improve fracture resistance by promoting and then arresting crazing in the brittle matrices. Other types of particles, such as ceramic, metal, or inorganic particles, produce reinforcing effects in metallic matrices by different strengthening mechanisms. The particles, because they are harder than the matrix, restrict deformation of the matrix material between them and thus increase stiffness of the material. The particles also share the load, but to a much smaller extent than the fibers that are parallel to the load. Thus, the particles enhance the stiffness of the composites but do not offer much potential for strengthening. On the other hand, hard particles placed in a brittle matrix reduce strength because they produce stress concentrations in the adjacent matrix. Particle fillers, however, are used widely to improve other properties of matrix materials, such as the thermal and electrical conductivities, improve performance at elevated temperature, reduce friction, increase wear and abrasion resistance and machinability, increase surface hardness, and reduce shrinkage. In many cases, they are used simply to reduce cost.

The particles and matrix material in a particulate composite can be any combination of metallic and nonmetallic materials. The choice of a particular combination depends on the desired end properties. Particles of lead are mixed with copper alloys and steel to improve their machinability. In addition, lead is a natural lubricant in bearings made of copper alloys. Particles of many brittle metals such as tungsten, chromium, and molybdenum are incorporated into ductile metals to improve their elevated temperature performance while maintaining ductile characteristics at room temperature. Particles of tungsten, molybdenum, or their carbides are used widely in silver and copper matrices for electrical-contact applications, which require high thermal and electrical conductivities, high melting point, and low friction and wetting characteristics. These materials are also used for electrodes and related applications in the welding industry.

Cermets are composites of ceramic and metal. Oxide-based cermets are used extensively as tool materials for high-speed cutting, thermocouple protection tubes, furnace mufflers, and a variety of high-temperature erosive applications. Carbide-based cermets mostly have particles of tungsten, chromium, and titanium carbides. Tungsten carbide in a cobalt matrix produces very high surface hardness and is widely used in cutting tools, wiredrawing dies, valve parts, and precision gauges. Chromium carbide in a cobalt matrix is highly resistant to corrosion and abrasion and has a coefficient of thermal expansion close to that of steel. This makes it useful for valve parts, nozzles, and high-load bearings that operate at very high temperatures. Titanium carbide in a nickel or cobalt matrix is well suited for high-temperature applications such as turbine parts, torch tips, and hot-mill parts.

Inorganic fillers are extensively used to improve properties of plastics, such as surface hardness and shrinkage reduction, and to eliminate crazing in moldings, improve fire retardancy, provide color and improve appearance, modify the thermal and electrical conductivities, and, most important, greatly reduce cost without necessarily sacrificing the desirable properties. Many commercially important elastomers are filled with carbon black or silica to improve their strength and abrasion resistance while maintaining their necessary extensibility. Cold solders consist of metal powders suspended in thermosetting resins so that the composite is hard and strong and conducts heat and electricity. Copper in epoxy increases its conductivity immensely. Lead content in plastics acts as a sound deadener and shield against gamma radiation. Fluorocarbon-based plastics are being used as bearing materials. Metallic inclusions are incorporated to increase thermal conductivity, lower the coefficient of expansion, and drastically reduce the wear rate.

Thin flakes offer attractive features to be effective reinforcement. They have a primarily two-dimensional geometry and thus impart equal strength in all directions in their plane compared with fibers that are unidirectional reinforcements. Flakes, when laid parallel, can be packed more closely than fibers or spherical particles. Mica flakes are used in electrical and heat-insulating applications. Composites of mica flakes in a glassy matrix can be machined easily and are used in electrical applications. Aluminum flakes in paints and other coatings orient themselves parallel to the surface and give the coating exceptionally good properties. Silver flakes are employed where good conductivity is required. It has not been possible to fully exploit the attractive possibilities of flake-reinforced composites because of fabrication difficulties.

Nanocomposites, which are emerging new composites, are discussed in Chapter 11. Clay-reinforced nanocomposites are particulate composites. While nanotubes are fibers by character, their size is very small compared with conventional reinforcing fibers. Therefore, nanotube-reinforced composites may also be analyzed as particulate composites, especially since nanotube concentration is very small.

Particulate composites are an important class of composite materials. The discussion in this text, however, deals primarily with fiber composites.

1.4 FIBER-REINFORCED COMPOSITES

The fiber-reinforced composites, or simply fiber composites, have become the most important class of composite materials because they are capable of achieving high strength and have found applications in industries such as automotive, construction, appliances, marine, corrosion, electrical insulation, and aerospace. The fiber composites achieve high strength because the reinforcing fibers possess high strength and high stiffness. Properties of some common fibers are given inTable 1.1, along with properties of some conventional materials. For comparison of properties on the weight basis, specific strength and specific modulus are also given. Strength and specific strength of fibers are superior to those of conventional bulk materials. Graphite, boron, and Kevlar 49 fibers also have much higher specific modulus, but glass fibers have specific modulus comparable only with that of aluminum. Thus, importance of fibers in achieving high strengths is obvious from Table 1.1.

Table 1.1Properties of Fibers and Conventional Bulk Materials

Material

Tensile Modulus (

E

) (GPa)

Tensile Strength (σ

u

) (GPa)

Density (ρ) (g/cm

3

)

Specific Modulus (

E

/ρ)

Specific Strength (σ

u

/ρ)

Fibers

E-glass

72.4 

3.5

a

2.54

28.5

1.38

S-glass

85.5

4.6

a

2.48

34.5

1.85

Graphite (high modulus)

390.0

2.1 

1.90

205.0

1.1 

Graphite (high tensile strength)

240.0

2.5 

1.90

126.0

1.3 

Boron

385.0

2.8 

2.63

146.0

1.1 

Silica

72.4

5.8 

2.19

33.0

2.65

Tungsten

414.0

4.2 

19.30

21.0

0.22

Beryllium

240.0

1.3 

1.83

131.0

0.71

Kevlar 49 (aramid polymer)

130.0

2.8 

1.50

87.0

1.87

Conventional materials

Steel

210.0 

0.34–2.1

7.8 

26.9

0.043–0.27

Aluminum alloys

70.0

0.14–0.62

2.7 

25.9

0.052–0.23

Glass

70.0

0.7–2.1

2.5 

28.0

0.28–0.84

Tungsten

350.0

1.1–4.1

19.30

18.1

0.057–0.21

Beryllium

300.0

0.7 

1.83

164.0

0.38

aVirgin strength values. Actual strength values prior to incorporation into composites are approximately 2.1 (GPa).

The high strength of glass fibers is attributed to being defect free or being free from inherent flaws, which, in bulk glass and other brittle materials, drastically reduces strength. Graphite, Kevlar 49 (aramid fibers), and many other polymeric fibers attain high strength as a result of improved orientation of their atomic or molecular structure. E-glass fibers are the most important reinforcing fibers because they are relatively inexpensive yet very effective reinforcement for polymers. However, boron, graphite, and the Kevlar 49 (aramid polymer) fibers are most exceptional because of their high stiffness, which is an essential requirement for effective reinforcement. Of these, the graphite fibers offer the largest number of combinations of strength and modulus values because their structure can be effectively controlled during manufacturing.

Fibers, because of their small cross-sectional dimensions, are not directly usable as structural materials. They are, therefore, embedded in matrix material to form fiber composites. The matrix binds the fibers together to provide shape to the fiber composite, transfers applied load to the fibers, and protects them against environmental attack and damage due to handling.

The practical structural elements of fiber composites are multilayered, with several distinct layers. Each layer or lamina is usually very thin (typical thickness of 0.1 mm) and hence cannot be used directly. When all layers of a multilayered composite are made of the same constituent materials, it is called simply laminate. When layers are made up of different constituent materials, the composite is called hybrid laminate or hybrid composite. For example, one layer of a hybrid laminate may be a glass-fiber-reinforced epoxy, whereas another layer may be graphite-fiber-reinforced epoxy. It is possible, but not as common, to find a hybrid laminate having different fibers within the single layer.