Textbook "Composite Materials"

Contents

 

Preface

 

PART I Composite Materials

 

CHAPTER  1 Basic Features of Composite Materials
- 1.1 Composite Materials
- 1.1.1 Definition
- 1.1.2 General Characteristics
- 1.2 Classification of Composite Materials 
- 1.2.1 Classification by the Form of Constituents
- 1.2.2 Classification by the Nature of Constituents
- 1.3 Why Composite Materials ?
- 1.3.1 Specific Mechanical Characteristics 
- 1.3.2 Caractéristiques mécaniques des matériaux
- 1.3.3 Composite Materials
- 1.4 Volume and Weight Fractions
- 1.4.1 Introduction
- 1.4.2 Vomume Fraction
- 1.4.3 Weight Fraction
- 1.4.4 Relations between Volume and Weight Fractions 
- 1.4.5 Presence of Porosity
- Exercises
  

CHAPTER  2 The Constituents of a Composite Material
- 2.1 Introduction
- 2.2 Resin Systems
- 2.2.1 The Various Types of Resins
- 2.2.2 Thermosetting Resins
- 2.2.3 Thermoplastic Resins 
- 2.2.4 Thermostable Resins
- 2.3 Fillers and Additives
- 2.3.1 Introduction
- 2.3.2 Fillers
- 2.3.3 Additives
- 2.4 Fiber and Cloth Reinforcements
- 2.4.1 Basics
- 2.4.2 Fiber Forms
- 2.4.3 Surface Tissues 
- 2.4.4 Multidirectional Woven Structures
- 2.5 Different Fibers
- 2.5.1 Glass Fibers
- 2.5.2 Carbon Fibers
- 2.5.3 Aramid Fibers with High Mechanical Properties
- 2.5.4 Ceramic Fibers
- 2.5.5 Thermostable Synthetic Fibers
- 2.5.6 Other Fibers

 

CHAPTER  3 Molding Processes abd Architecture of Composite Materials
- 3.1 Introduction
- 3.2 Molding Processes 
- 3.2.1 Contact Molding
- 3.2.2 Vacuum Molding
- 3.2.3 Compression Molding
- 3.2.4 Continuous Molding 
- 3.2.5 Pultrusion Molding
- 3.2.6 Centrifugal Molding
- 3.2.7 Filament Winding
- 3.3 Use of Prepregs and Compounds
- 3.3.1 Introduction
- 3.3.2 Prepregs
- 3.3.3 Molding Compounds
- 3.4 Architecture of Composite Materials
- 3.4.1 Introduction
- 3.4.2 Laminates
- 3.4.3 Sandwich Composites
- 3.4.4 Other Architectures 
- 3.4.5 Consequences on the Study of the Mechanical Behavior of Composite Materials

 

PART II  Basic Concepts of the Mechanical Behavior of Materials

 

CHAPTER  4 Mathematical Basics
- 4.1 Transformation of Coordinate Systems
- 4.1.1 General Expression
- 4.1.2 Rotation around an Axis
- 4.2 Second-Order Tensor
- 4.2.1 Introduction
- 4.2.2 Change of Reference system
- 4.2.3 Diagonalization of a matrix. Eigenvectors and Eigenvalues
- 4.2.4 Inversion of a Symmetric Matrix of Order Three

 

CHAPTER  5 Stresses
- 5.1 Stress State in a Solid
- 5.1.1 Stress Tensor
- 5.1.2 Force Acting at a Point on a Surface Element
- 5.2 Properties of the Stress Tensor
- 5.2.1 Physical Interpretation of the Stress Components
- 5.2.2 Normal and Tangential Components of the Stress Vector
- 5.2.3 Principal Directions, Principal Stresses
- 5.2.4 Change of Reference System
- 5.3 Particular States of Stresses
- 5.3.1 Spherical Tensor and Stress Deviator 
- 5.3.2 Spherical Compression or Tension
- 5.3.3 Uniaxial Tension or Compression 
- 5.3.4 Shear State
- 5.3.5 State of Plane Stress
- 5.3.6 Arbitrary Stress State
- 5.4 Engineering Matrix Notation
- 5.4.1 Introduction of the Notation
- 5.4.2 Change of Reference System
-  Exercises

 

CHAPTER  6 Strains
- 6.1 The Strain Tensor
- 6.1.1 Strains at a Point
- 6.1.2 Strain Tensor
- 6.1.3 Interpretation of the Strain Components
- 6.1.4 Compatibility Conditions
- 6.2 Strain State at a Point
- 6.2.1 Elongation per Unit Length
- 6.2.2 Shear Strain
- 6.2.3 Strain Tensor in the Principal Directions
- 6.2.4 Change of Reference System
- 6.3 Particular States of Strains
- 6.3.1 Spherical Tensor and Strain Deviator 
- 6.3.2 Particular States
- 6.4 Engineering Matrix Notation
- 6.4.1 Introduction of the Notation
- 6.4.2 Change of Refernce System
-  Exercies

 

CHAPTER  7 The Elastic Behavior of Materials
- 7.1 Stress-Strain Relations for Anisotropic Materials
- 7.1.1 Introduction
- 7.1.2 Stiffness Matrix
- 7.1.3 Compliance Matrix
- 7.1.4 Change of Reference System
- 7.1.5 Anisotropic Materials
- 7.2 Isotropic Materials
- 7.2.1 Elasticity Relations
- 7.2.2 Elasticity Moduli
- 7.2.3 Relations between the Coefficients of Elasticity
- 7.2.4 Expressions for the Stiffness and Compliance Matrices
-  Exercices

 

CHAPTER  8 The Mechanics of Deformable Solids 
- 8.1 Fundamental Equations of Motion 
- 8.2 Formulation of the Structural Analysis
- 8.2.1 Statement of the Problem
- 8.2.2 Equations in Cartesian Coordinates 
- 8.2.3 Equations in Cylindrical Coordinates
- 8.3 Energy Formulation
- 8.3.1 Variation of a Functional
- 8.3.2 The Virtual Work Theorem
- 8.3.3 Dynamics of Solids
- 8.4 Variational Methods
- 8.4.1 Principle
- 8.4.2 Convergence

 

PART III  Mechanical Behavior of Composite Materials

 

CHAPTER  9 Elastic Behavior of Unidirectional Composite Materials
- 9.1 Effective Moduli
- 9.1.1 The Concept of Homogenization
- 9.1.2 Homogenized Moduli
- 9.2 Hooke's law for a Unidirectional Composite
- 9.2.1 Constitution of a unidiectional Composite Material
- 9.2.2 Stiffness and Compliance Matrices
- 9.3 Engineering Constants
- 9.3.1 Longitudinal Tensile Test
- 9.3.2 Transverse Tensile Test
- 9.3.3 Longitudinal Shear Test
- 9.3.4 Transverse Shear Test
- 9.3.5 Lateral Hydrostatic Compression
- 9.3.6 Moduli as Functions of the Stiffness and Compliance Constants
- 9.3.7 The Stiffness and Compliance Constants as Functions of the Engineering Constants
- 9.3.8 Restrictions on the Engineering Constants
- 9.4 Theoretical Approaches to Evaluating Engineering Constants
- 9.4.1 Different Approaches to the Problem
- 9.4.2 Bounds on the Engineering Constants
- 9.4.3 Exact Solutions
- 9.4.4 Simplified Approaches
- 9.4.5 Halpin-Tsai Equations
- 9.5 Numerical Values of the Engineering Constants
- 9.5.1 Experimental Values of Moduli
- 9.5.2 Comparison of Experimental and Calculated Values of Moduli
- 9.5.3 Conclusions
-  Exercises

 

CHAPTER  10  Elastic Behavior of an Orthotropic Composite
- 10.1 Hooke's Law for an Orthotropic Composite
- 10.1.1 Orthotropic Composite
- 10.1.2 Stiffness and Compliance Matrices
- 10.2 Engineering Constants
- 10.2.1 Tensile Test in the Warp Direction
- 10.2.2 Tensile Test in the Weft Direction
- 10.2.3 Transverse Tensile Test
- 10.2.4 Relation between Young's moduli and Poisson Ratios
- 10.2.5 Shear Tests
- 10.2.6 Conclusion
- 10.3 Stiffness and Compliance Constants as Functions of the Engineering Constants
- 10.3.1 Compliance Constants
- 10.3.2 Stiffness Constants
- 10.3.3 Restrictions on the Elasticity Constants
-  Exercices

 

CHAPTER  11 Off-Axis Behavior of Composite Materials
- 11.1 Stress-Strain Relations for Off-Axis Layers
- 11.1.1 Introduction
- 11.1.2 Stiffness and Compliance Matrices
- 11.1.3 Other Expressions for Stiffness Matrices
- 11.2 Engineering Constants
- 11.2.1 Expressions for Off-Axis Moduli
- 11.2.2 Variations in the Moduli of Elasticity of a Unidirectional Composite
- 11.3 Plane Stress State
- 11.3.1 Introduction
- 11.3.2 Two-dimensional Stress State
- 11.3.3 Elasticity Equations for Plane Stress State
- 11.3.4 Reduced Stiffness Matrix in Principal Directions
- 11.3.5 Relations between the Off-Axis and Principal Axes Reduced Stiffness Constants
- 11.3.6 Conclusions
- 11.3.7 Example
- 11.4 Experimental Determination of Engineering Constants
- 11.4.1 Introduction
- 11.4.2 Longitudinal Tensile Test
- 11.4.3 Transverse Tensile Test
- 11.4.4 Off-Axis Tension
- 11.4.5 Specimens for Tensile Tests
-  Exercises

 

CHAPTER  12 Fracture Mechanisms and Damage of Composite Materials
- 12.1 Fracture Processes Induced in Composite Materials
- 12.1.1 Introduction
- 12.1.2 Fracture Mechanisms Induced in a Unidirectional Composite
- 12.1.3 Unidirectional Composite Subjected to Longitudinal Tension
- 12.1.4 Unidirectional Composite Subjected to Transverse Tension
- 12.1.5 Laminate Fracture Modes
- 12.1.6 Observation of Fracture Mechanisms
- 12.2 Failure Criteria
- 12.2.1 Introduction
- 12.2.2 Maximum Stress Criterion
- 12.2.3 Maximum Strain Criterion
- 12.2.4 Interactive Criteria
-  Exercises

 

PART IV Modeling the Mechanical Behavior of Laminates and Sandwich Plates

 

CHAPTER  13 Basics of Laminate Theory
- 13.1 Introduction
- 13.1.1 Architecture
- 13.1.2 Notations and Objective
- 13.2 Displacement Field
- 13.2.1 General Expressions
- 13.2.2 Deformation of a Normal
- 13.2.3 First-Order Theory
- 13.3 Strain Field
- 13.3.1 General Expressions
- 13.3.2 First-Order Theory 
- 13.4 Stress Field
- 13.4.1 General Expression
- 13.4.2 Simplification in the Context of the Theory of Plates
- 13.5 Resultants and moments
- 13.5.1 In-Plane Resultants
- 13.5.2 Transverse Shear Resultants
- 13.5.3 Resultant Moments
- 13.6 Fundamental Equations for Plates in a First-Order Theory
- 13.6.1 Fundamental Equations of the Mechanics of Materials
- 13.6.2 Fundamental Equations for In-Plane Resultants
- 13.6.3 Fundamental Equations for Transverse Shear Resultants
- 13.6.4 Fundamental Equations of Moments 
- 13.6.5 Summary of Fundamental Equations
- 13.6.6 Statics Problems
-  Exercises  

 

CHAPTER  14 Classical Laminate Theory
- 14.1 Strain Field
- 14.1.1 Assumptions of the Classical Laminate Theory
- 14.1.2 Expression for the Strain Field
- 14.2 Stress Field
- 14.2.1 Form of the Stress Field
- 14.2.2 Stress Expression
- 14.3 Resultant and Moment Expressions
- 14.3.1 In-Plane Resultants
- 14.3.2 Resultant Moments
- 14.4 Mechanical Behavior Equation of a Laminate
- 14.4.1 Constitutive Equation
- 14.4.2 Stiffness Matrix
- 14.4.3 Examples
- 14.5 Determination of Strains and Stresses
- 14.5.1 The Problem to Be Solved
- 14.5.2 In-Plane Strains and Curvatures
- 14.5.3 Strain Field
- 14.5.4 Stress Field
- 14.5.5 Example
-  Exercises

 

CHAPTER  15 Effect of the Stacking Sequence. Mat and Cloth Reinforced Materials
- 15.1 Effect of the Stacking Sequence
- 15.1.1 Case of One Layer
- 15.1.2 Symmetric Laminates
- 15.1.3 Antisymmetric Laminates
- 15.1.4 Cross-Ply Laminates
- 15.1.5 Angl-Ply Laminates
- 15.1.6 Laminates with Isotropic Layers
- 15.1.7 Arbitrary Laminates
- 15.2 Engineering Constants of Mat and Cloth Reinforced Materials
- 15.2.1 Introduction
- 15.2.2 Caracterization of a Cloth Reinforcement
- 15.2.3 Laminate Analogy
- 15.2.4 In-Plane Behavior of a Cloth Reinforced Layer
- 15.2.5 In-Plane Moduli of a Cloth Reinforced Layer
- 15.2.6 Numerical Applications
- 15.2.7 Mat Reinforced Layer
- 15.2.8 Laminate with Mat and Cloth Reinforced Layers
-  Exercises

 

CHAPTER  16 Governing Equations and Energy Formulation of the Classical Laminate Theory
- 16.1 Governing Equations
- 16.1.1 General Relations
- 16.1.2 Symmetric Laminates
- 16.1.3 Antisymmetric Laminates
- 16.1.4 Expressions for Resultants and Moments
- 16.1.5 Expressions for Stresses
- 16.2 Boundary Conditions
- 16.2.1 Basics
- 16.2.2 Simply Supported Edge
- 16.2.3 Clamped Edge
- 16.2.4 Free Edge
- 16.3 Energy Formulation of Laminate Theory
- 16.3.1 Introduction
- 16.3.2 Strain Energy of a Laminate
- 16.3.3 Kinetic Energy of a Laminate
- 16.3.4 Energy of External Loads

 

CHAPTER  17 Including Transverse Shear Deformation in Laminat Theory
- 17.1 Limitations of the Classical Laminate Theory 
- 17.2 Strain and Stress Fields
- 17.2.1 Displacement Field
- 17.2.2 Starin Field
- 17.2.3 Stress Field
- 17.3 Fundamental Equations of Laminates, Including Transverse Shear Deformation 
- 17.3.1 Constitutive Equation
- 17.3.2 Fundamenta Equetions
- 17.3.3 Boundary Conditions
- 17.3.4 Stresses in the Layers
- 17.4 Introduction of Shear Coefficients
- 17.4.1 Assumptions of Laminate Theory
- 17.4.2 Evaluation of Shear Correction Factors in the Case of Orthotropic Plates
- 17.4.3 Evaluation of Shear Correction Factors in the Case of a laminated Plate
- 17.5 Conclusions
-  ExerciSes

 

CHAPTER  18 Theory of Sandwich Plates
- 18.1 Introduction
- 18.2 Strain and Stress Fields
- 18.2.1 Assumptions for Sandwich Theory
- 18.2.2 Displacement Field
- 18.2.3 Strain Field
- 18.2.4 Stress Field
- 18.3 Governing Equations of Sandwich Plates
- 18.3.1 Constitutive Equation
- 18.3.2 Fundamental Equations
- 18.4 Sandwich Materials with Thick Skins
-  Exercises

 

PART V Analysis of the Mechanical Behavior of Composite Material Structures

 

CHAPTER  19 Cylindrical Bending
- 19.1 Introduction
- 19.2 Classical Laminate Theory
- 19.2.1 Equations 
- 19.2.2 Uniform Load
- 19.2.3 Sinusoidal Load
- 19.3 Including the Transverse Shear Effect
- 19.3.1 Orthotropic Laminate
- 19.3.2 Angle-Ply Laminate
- 19.4 Exact Solution
- 19.5 Comparison between the Different Theories
- 19.6 Cylindrical Bending of Sandwich Plates
-  Exercises

 

CHAPTER  20 Bending of Laminate and Sandwich Plates
- 20.1 Introduction
- 20.2 Classical Laminate Theory
- 20.2.1 General Expressions
- 20.2.2 Three-Point Bending
- 20.2.3 Four-Point Bending
- 20.3 Including the Transverse Shear Deformation
- 20.3.1 General Equations
- 20.3.2 Three-Point Bending
- 20.3.3 Four-Point Bending
- 20.4 Bending of Sandwich Beams
- 20.4.1 General Expressions
- 20.4.2 Comparison between Sandwich Theory and Laminate Theory with Transverse Shear
-  Exercises

 

CHAPTER  21 Bending of Orthotropic Laminate Plates
- 21.1 Introduction
- 21.2 Simply Supported Rectangular Plates
- 21.2.1 General Expressions
- 21.2.2 Case of Uniform Load
- 21.2.3 Case of Load Distributed over a Rectangle
- 21.3 Rectangular Plates with Two Simply Supported Edges
- 21.3.1 Case of an Arbitrary Load
- 21.3.2 Case of Uniform Loading
- 21.4 Rectangular Plates with Various Boundary Conditions
- 21.5 Clamped Rectangular Plates
- 21.5.1 Introduction
- 21.5.2 Solution Approximated by Polynomial Functions
- 21.5.3 Solution Approximated by Beam Functions
- 21.5.4 Comparison between the Approximate Solutions
- 21.6 Simply Supported Sandwich Plates
-  Exercises

 

CHAPTER  22 Bending of Plates Made of Symmetric, Cross-Ply, or Angle-Ply Laminates
- 22.1 Symmetric Laminate Plates
- 22.1.1 General Expressions
- 22.1.2 Simply Supported Symmetric Laminate Plates
- 22.1.3 Clamped Symmetric Laminate Plates
- 22.2 Rectangular Cross-Ply Laminate Plates
- 22.2.1 General Expressions
- 22.2.2 Influence of the Moduli
- 22.2.3 Influence of the Length-to-Width Ratio
- 22.3 Rectangular Angle-Ply Laminate Plates
 Exercises

 

CHAPTER  23 Buckling of Laminate or Sandwich Beams and Plates
- 23.1 Governing Equations Including Buckling
- 23.1.1 Introduction
- 23.1.2 Plate Equations Taking Account of Buckling
- 23.1.3 Equations of the Classical Laminate Theory Taking Account of Transverse Displacement
- 23.1.4 Energy Formulation of Buckling
- 23.1.5 Equations of the Classical Laminate Theory Taking Account of Transverse Displacement
- 23.1.6 Equations of the Transverse Shear Theory Taking Account of Transverse Displacement
- 23.2 Buckling under Cylindrical Bending
- 23.2.1 Classical Laminate Theory
- 23.2.2 Effect of Transverse Shear
- 23.2.3 Buckling of a Sandwich Plate
- 23.3 Buckling of Beams
- 23.3.1 Bucling Equations
- 23.3.2 Simply Supported Beam
- 23.3.3 Clamped Beam
- 23.3.4 Other Support Conditions
- 23.3.5 Effect of Transverse Shear
- 23.3.6 Buckling of a Sandwich Beam
- 23.4 Buckling of Orthotropic Plates under Biaxial Compression
- 23.4.1 General Expressions
- 23.4.2 Uniaxial Compression
- 23.4.3 Square Plate under Biaxial Compression 
- 23.5 Buckling of Orthotropic Plates under Arbitrary Conditions
- 23.5.1 General Expressions
- 23.5.2 Clamped Orthotropic Plates Subjected to Uniform Shear
-  Exercises

 

CHAPTER  24 Bibrations of Laminate or Sandwich Beams and Plates
- 24.1 Introduction
- 24.2 Cylindrical Bending
- 24.2.1 Classical Laminate Theory
- 24.2.2 Effect of Transverse Shear
- 24.2.3 Vibrations of Sandwich Plates
- 24.3 Vibrations of Beams
- 24.3.1 General Equation
- 24.3.2 Simply Supported Beam
- 24.3.3 Clamped Beam
- 24.3.4 Beam Clamped at One End and Simply Supported at the Other
- 24.3.5 Beam Clamped at One End and Free at the Other
- 24.3.6 Beam with Two Free Ends
- 24.4 Vibrations of Simply Supported Rectangular Orthotropic Plates
- 24.5 Vibrations of Orthotropic Plates with Various Conditions along the Edges
- 24.5.1 General Expressions
- 24.5.2 Rayleigh's Approximation
- 24.5.3 Two-Term Approximation
- 24.5.4 Orthotropic Plates with Simply Supported or Clamped Edges
- 24.6 Vibrations of Symmetric Laminate Plates
- 24.6.1 General Expressions
- 24.6.2 Symmetric Plates with Clamped or Free Edges
- 24.7 Vibrations of Nonsymmetric Laminate Plates
- 24.7.1 Plate Made of an Antisymmetric Cross-Ply Laminate
- 24.7.2 Plate Made of an Angle-Ply Laminate 
-  Exercises

 

CHAPTER  25 Expansional Strain Effects on Laminate Mechanical Behavior
- 25.1 Introduction
- 25.2 Elasticity Relations Including Expansional Strain Effects
- 25.2.1 Elasticity Relations in Material Directions
- 25.2.2 Off-Axis Elasticity Relations
- 25.3 Governing Equations
- 25.3.1 Constitutive Equation
- 25.3.2 Examples 
- 25.3.3 Fundamental Relations
- 25.3.4 Strain Energy
- 25.4 Behavior of Rectangular Plates
- 25.4.1 Rectangular Plate Made of a Symmetric Laminate
- 25.4.2 Rectangular Plate Made of an Angle-Ply Antisymmetric Laminate
- 25.4.3 Thermal Effects
 Exercises

 

CHAPTER  26 Predesigning Laminate and Sandwich Structures
- 26.1 Problem of Designing
- 26.2 Basic Elements of Composite Structures
- 26.2.1 Simple Beams
- 26.2.2 Profiles
- 26.2.3 Sandwich Beams 
- 26.2.4 Plates
- 26.3 Evaluation of the Characteristics of the Mechanical Behavior of Materials
- 26.3.1 Moduli
- 26.3.2 Fracture Characteristics
- 26.4 Structural Analysis by the Finite Element Method
- 26.4.1 Introduction
- 26.4.2 The Finite Element Method
- 26.4.3 Validation 
- 26.5 Examples of Predesigning
- 26.5.1 Predesigning the Hull of a Yatch
- 26.5.2 Predesigning the Hood of a Car

 

APPENDIX A  Clamped-Clamped Polynomial Function

APPENDIX B           Characteristic Function of a Beam with Clamped Ends

 

References

 

Index