Composite Structures: Design, Mechanics, Analysis, Manufacturing, and Testing

761 Pages·2018·128.52 MB·English

by  Manoj Kumar Buragohain

Composite Structures
Design, Mechanics, Analysis,
Manufacturing, and Testing

Composite Structures
Design, Mechanics, Analysis,
Manufacturing, and Testing
Manoj Kumar Buragohain
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Contents
Preface ........................................................................................................................xxi
Author .....................................................................................................................xxiii
Book Road Map ........................................................................................................xxv
Part I Introduction, Mechanics, and analysis
Chapter 1 Introduction to Composites ......................................................................3
1.1 Chapter Road Map ..........................................................................3
1.2 Introduction ....................................................................................3
1.3 History of Composites ....................................................................3
1.4 Characteristics of Composite Materials ..........................................4
1.4.1 Definition ............................................................................4
1.4.2 Classification ......................................................................5
1.4.2.1 Polymer Matrix Composites .................................5
1.4.2.2 Metal Matrix Composites .....................................5
1.4.2.3 Ceramic Matrix Composites ................................6
1.4.2.4 Carbon/Carbon Composites .................................6
1.4.2.5 Particulate Composites .........................................7
1.4.2.6 Short Fiber Composites ........................................7
1.4.2.7 Flake Composites .................................................8
1.4.2.8 Unidirectional Composites ...................................8
1.4.2.9 3D Composites .....................................................8
1.4.2.10 Laminated Composites .........................................8
1.4.2.11 Sandwich Composites ...........................................8
1.4.3 Characteristics and Functions of Reinforcements and Matrix ....8
1.4.4 Composites Terminologies .................................................9
1.5 Advantages and Disadvantages of Composites ............................10
1.5.1 Advantages .......................................................................10
1.5.2 Disadvantages ...................................................................13
1.6 Applications of Composites ..........................................................14
1.7 Summary ......................................................................................18
Exercise Problems ..................................................................................19
References and Suggested Reading ........................................................19
Chapter 2 Basic Solid Mechanics............................................................................21
2.1 Chapter Road Map ........................................................................21
2.2 Principal Nomenclature ................................................................21
2.3 Introductory Concepts ..................................................................23
2.3.1 Solid Mechanics and Continuum ......................................23
2.3.2 Spatial Point, Material Point, and Configuration ..............23
2.3.3 Fundamental Principles and Governing Equations ..........23
2.4 Kinematics ....................................................................................24
2.4.1 Normal Strain and Shear Strain .......................................25
2.4.2 Types of Strain Measures: 1D Approach ..........................26
2.4.2.1 Engineering Strain .............................................26
vii
viii Contents
2.4.2.2 True Strain ..........................................................26
2.4.2.3 Green Strain .......................................................27
2.4.2.4 Almansi Strain ...................................................27
2.4.3 Displacement at a Point ....................................................28
2.4.4 Deformation Gradient and Displacement Gradient ..........30
2.4.5 Infinitesimal Strain and Finite Strain Theories ................32
2.4.6 Infinitesimal Strain at a Point ...........................................33
2.4.7 Finite Strain at a Point ......................................................36
2.4.7.1 Finite Strain Tensor ............................................36
2.4.7.2 Physical Meaning of Finite Strain Tensor
Components ........................................................38
2.4.8 Strain–Displacement Relations in Cylindrical
Coordinates .......................................................................40
2.4.9 Transformation of Strain Tensor .......................................41
2.4.10 Compatibility Conditions ..................................................42
2.5 Kinetics .........................................................................................43
2.5.1 Forces on a Body ..............................................................43
2.5.2 Cauchy’s Stress Principle and Stress Vector .....................43
2.5.3 State of Stress at a Point and Stress Tensor ......................44
2.5.4 Transformation of Stress Tensor .......................................46
2.5.5 Stress Tensor–Stress Vector Relationship .........................49
2.5.6 Principal Stresses ..............................................................50
2.5.7 Equilibrium Equations ......................................................53
2.6 Thermodynamics ..........................................................................54
2.7 Constitutive Modeling ..................................................................56
2.7.1 Idealization of Materials ...................................................56
2.7.2 Elastic Materials ...............................................................57
2.7.3 Generalized Hooke’s Law .................................................58
2.7.3.1 Symmetry of Stress and Strain Tensors .............59
2.7.3.2 Symmetry of Elastic Stiffness Matrix ................61
2.7.3.3 Anisotropic Materials .........................................61
2.7.3.4 Monoclinic Materials .........................................61
2.7.3.5 Orthotropic Materials .........................................63
2.7.3.6 Transversely Isotropic Materials ........................67
2.7.3.7 Cubic Symmetry.................................................68
2.7.3.8 Isotropic Materials..............................................68
2.8 Plane Elasticity Problems .............................................................69
2.8.1 Plane Stress .......................................................................69
2.8.1.1 Plane Stress Problem in Orthotropic Materials .....70
2.8.1.2 Plane Stress Problem in Isotropic Materials .......71
2.8.2 Plane Strain ......................................................................72
2.8.2.1 Plane Strain Problem in Orthotropic Materials .....73
2.8.2.2 Plane Strain Problem in Isotropic Materials ......73
2.9 Summary ......................................................................................74
Exercise Problems ..................................................................................74
References and Suggested Reading ........................................................78
Chapter 3 Micromechanics of a Lamina .................................................................79
3.1 Chapter Road Map ........................................................................79
3.2 Principal Nomenclature ................................................................79
3.3 Introduction ..................................................................................82
Contents ix
3.4 Basic Micromechanics ..................................................................84
3.4.1 Assumptions and Restrictions ..........................................84
3.4.2 Micromechanics Variables ...............................................84
3.4.2.1 Elastic Moduli and Strengths of Fibers
and Matrix ..........................................................84
3.4.2.2 Volume Fractions ................................................84
3.4.2.3 Mass Fractions ....................................................86
3.4.3 Representative Volume Element .......................................87
3.5 Mechanics of Materials-Based Models ........................................88
3.5.1 Evaluation of Elastic Moduli ............................................88
3.5.1.1 Longitudinal Modulus (E ) ................................88
1c
3.5.1.2 Transverse Modulus (E ) ...................................90
2c
3.5.1.3 Major Poisson’s Ratio (ν ) ................................93
12c
3.5.1.4 In-Plane Shear Modulus (G ) ...........................95
12c
3.5.2 Evaluation of Strengths .....................................................99
3.5.2.1 Longitudinal Tensile Strength (σT ) ...............100
1c ult
3.5.2.2 Longitudinal Compressive Strength (σC) ......107
1c ult
3.5.2.3 Transverse Tensile Strength (σT ) .................110
2c ult
3.5.2.4 Transverse Compressive Strength (σC) .........113
2c ult
3.5.2.5 In-Plane Shear Strength (τ ) ........................114
12c ult
3.5.3 Evaluation of Thermal Coefficients .................................116
3.5.4 Evaluation of Moisture Coefficients ...............................119
3.6 Elasticity-Based Models .............................................................123
3.7 Semiempirical Models ................................................................124
3.7.1 General Form of Halpin–Tsai Equations ........................125
3.7.2 Halpin–Tsai Equations for Elastic Moduli ......................125
3.7.2.1 Longitudinal Modulus ......................................125
3.7.2.2 Transverse Modulus .........................................126
3.7.2.3 Major Poisson’s Ratio .......................................126
3.7.2.4 In-Plane Shear Modulus ...................................127
3.8 Summary ....................................................................................128
Exercise Problems ................................................................................129
References and Suggested Reading ......................................................131
Chapter 4 Macromechanics of a Lamina ..............................................................133
4.1 Chapter Road Map ......................................................................133
4.2 Principal Nomenclature ..............................................................133
4.3 Introduction to Lamina ...............................................................134
4.4 Constitutive Equations of a Lamina ...........................................135
4.4.1 Specially Orthotropic Lamina ........................................136
4.4.1.1 Constitutive Relation ........................................136
4.4.1.2 Restrictions on Elastic Constants .....................143
4.4.2 Generally Orthotropic Lamina .......................................144
4.5 Engineering Constants of a Generally Orthotropic Lamina .......152
4.6 Strength ......................................................................................164
4.6.1 Strength of an Orthotropic Lamina ................................165
4.6.2 Failure Criteria ...............................................................167
4.6.2.1 Maximum Stress Failure Criterion ...................167
4.6.2.2 Maximum Strain Failure Criterion ...................170
4.6.2.3 Tsai–Hill Failure Criterion ...............................172