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# Composite laminates

About: Composite laminates is a research topic. Over the lifetime, 10087 publications have been published within this topic receiving 208227 citations.

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01 Jan 1980TL;DR: In this paper, the authors present an analysis of the properties of fiber-reinforced composites under different types of stress and failure modes, such as failure under longitudinal tensile loads, failure under transverse tensile load, and failure under In-Plane Shear Load.

Abstract: Preface. 1 Introduction. 1.1 Definition. 1.2 Characteristics. 1.3 Classification. 1.4 Particulate Composites. 1.5 Fiber-Reinforced Composites. 1.6 Applications of Fiber Composites. Exercise Problems. References. 2 Fibers, Matrices, and Fabrication of Composites. 2.1 Advanced Fibers. 2.1.1 Glass Fibers. 2.1.2 Carbon and Graphite Fibers. 2.1.3 Aramid Fibers. 2.1.4 Boron Fibers. 2.1.5 Other Fibers. 2.2 Matrix Materials. 2.2.1 Polymers. 2.2.2 Metals. 2.3 Fabrication of Composites. 2.3.1 Fabrication of Thermosetting Resin Matrix Composites. 2.3.2 Fabrication of Thermoplastic-Resin Matrix Composites (Short-Fiber Composites). 2.3.3 Fabrication of Metal Matrix Composites. 2.3.4 Fabrication of Ceramic Matrix Composites. Suggested Reading. 3 Behavior of Unidirectional Composites. 3.1 Introduction. 3.1.1 Nomenclature. 3.1.2 Volume and Weight Fractions. 3.2 Longitudinal Behavior of Unidirectional Composites. 3.2.1 Initial Stiffness. 3.2.2 Load Sharing. 3.2.3 Behavior beyond Initial Deformation. 3.2.4 Failure Mechanism and Strength. 3.2.5 Factors Influencing Longitudinal Strength and Stiffness. 3.3 Transverse Stiffness and Strength. 3.3.1 Constant-Stress Model. 3.3.2 Elasticity Methods of Stiffness Prediction. 3.3.3 Halpin-Tsai Equations for Transverse Modulus. 3.3.4 Transverse Strength. 3.4 Prediction of Shear Modulus. 3.5 Prediction of Poisson's Ratio. 3.6 Failure Modes. 3.6.1 Failure under Longitudinal Tensile Loads. 3.6.2 Failure under Longitudinal Compressive Loads. 3.6.3 Failure under Transverse Tensile Loads. 3.6.4 Failure under Transverse Compressive Loads. 3.6.5 Failure under In-Plane Shear Loads. 3.7 Expansion Coefficients and Transport Properties. 3.7.1 Thermal Expansion Coefficients. 3.7.2 Moisture Expansion Coefficients. 3.7.3 Transport Properties. 3.7.4 Mass Diffusion. 3.8 Typical Unidirectional Fiber Composite Properties. Exercise Problems. References. 4 Short-Fiber Composites. 4.1 Introduction. 4.2 Theories of Stress Transfer. 4.2.1 Approximate Analysis of Stress Transfer. 4.2.2 Stress Distributions from Finite-Element Analysis. 4.2.3 Average Fiber Stress. 4.3 Modulus and Strength of Short-Fiber Composites. 4.3.1 Prediction of Modulus. 4.3.2 Prediction of Strength. 4.3.3 Effect of Matrix Ductility. 4.4 Ribbon-Reinforced Composites. Exercise Problems. References. 5 Analysis of an Orthotropic Lamina. 5.1 Introduction. 5.1.1 Orthotropic Materials. 5.2 Stress-Strain Relations and Engineering Constants. 5.2.1 Stress-Strain Relations for Specially Orthotropic Lamina. 5.2.2 Stress-Strain Relations for Generally Orthotropic Lamina. 5.2.3 Transformation of Engineering Constants. 5.3 Hooke's Law and Stiffness and Compliance Matrices. 5.3.1 General Anisotropic Material. 5.3.2 Specially Orthotropic Material. 5.3.3 Transversely Isotropic Material. 5.3.4 Isotropic Material. 5.3.5 Specially Orthotropic Material under Plane Stress. 5.3.6 Compliance Tensor and Compliance Matrix. 5.3.7 Relations between Engineering Constants and Elements of Stiffness and Compliance Matrices. 5.3.8 Restrictions on Elastic Constants. 5.3.9 Transformation of Stiffness and Compliance Matrices. 5.3.10 Invariant Forms of Stiffness and Compliance Matrices. 5.4 Strengths of an Orthotropic Lamina. 5.4.1 Maximum-Stress Theory. 5.4.2 Maximum-Strain Theory. 5.4.3 Maximum-Work Theory. 5.4.4 Importance of Sign of Shear Stress on Strength of Composites. Exercise Problems. References. 6 Analysis of Laminated Composites. 6.1 Introduction. 6.2 Laminate Strains. 6.3 Variation of Stresses in a Laminate. 6.4 Resultant Forces and Moments: Synthesis of Stiffness Matrix. 6.5 Laminate Description System. 6.6 Construction and Properties of Special Laminates. 6.6.1 Symmetric Laminates. 6.6.2 Unidirectional, Cross-Ply, and Angle-Ply Laminates. 6.6.3 Quasi-isotropic Laminates. 6.7 Determination of Laminae Stresses and Strains. 6.8 Analysis of Laminates after Initial Failure. 6.9 Hygrothermal Stresses in Laminates. 6.9.1 Concepts of Thermal Stresses. 6.9.2 Hygrothermal Stress Calculations. 6.10 Laminate Analysis Through Computers. Exercise Problems. References. 7 Analysis of Laminated Plates and Beams. 7.1 Introduction. 7.2 Governing Equations for Plates. 7.2.1 Equilibrium Equations. 7.2.2 Equilibrium Equations in Terms of Displacements. 7.3 Application of Plate Theory. 7.3.1 Bending. 7.3.2 Buckling. 7.3.3 Free Vibrations. 7.4 Deformations Due to Transverse Shear. 7.4.1 First-Order Shear Deformation Theory. 7.4.2 Higher-Order Shear Deformation Theory. 7.5 Analysis of Laminated Beams. 7.5.1 Governing Equations for Laminated Beams. 7.5.2 Application of Beam Theory. Exercise Problems. References. 8 Advanced Topics in Fiber Composites. 8.1 Interlaminar Stresses and Free-Edge Effects. 8.1.1 Concepts of Interlaminar Stresses. 8.1.2 Determination of Interlaminar Stresses. 8.1.3 Effect of Stacking Sequence on Interlaminar Stresses. 8.1.4 Approximate Solutions for Interlaminar Stresses. 8.1.5 Summary. 8.2 Fracture Mechanics of Fiber Composites. 8.2.1 Introduction. 8.2.2 Fracture Mechanics Concepts and Measures of Fracture Toughness. 8.2.3 Fracture Toughness of Composite Laminates. 8.2.4 Whitney-Nuismer Failure Criteria for Notched Composites. 8.3 Joints for Composite Structures. 8.3.1 Adhesively Bonded Joints. 8.3.2 Mechanically Fastened Joints. 8.3.3 Bonded-Fastened Joints. Exercise Problems. References. 9 Performance of Fiber Composites: Fatigue, Impact, and Environmental Effects. 9.1 Fatigue. 9.1.1 Introduction. 9.1.2 Fatigue Damage. 9.1.3 Factors Influencing Fatigue Behavior of Composites. 9.1.4 Empirical Relations for Fatigue Damage and Fatigue Life. 9.1.5 Fatigue of High-Modulus Fiber-Reinforced Composites. 9.1.6 Fatigue of Short-Fiber Composites. 9.2 Impact. 9.2.1 Introduction and Fracture Process. 9.2.2 Energy-Absorbing Mechanisms and Failure Models. 9.2.3 Effect of Materials and Testing Variables on Impact Properties. 9.2.4 Hybrid Composites and Their Impact Strength. 9.2.5 Damage Due to Low-Velocity Impact. 9.3 Environmental-Interaction Effects. 9.3.1 Fiber Strength. 9.3.2 Matrix Effects. Exercise Problems. References. 10 Experimental Characterization of Composites. 10.1 Introduction. 10.2 Measurement of Physical Properties. 10.2.1 Density. 10.2.2 Constituent Weight and Volume Fractions. 10.2.3 Void Volume Fraction. 10.2.4 Thermal Expansion Coefficients. 10.2.5 Moisture Absorption and Diffusivity. 10.2.6 Moisture Expansion Coefficients. 10.3 Measurement of Mechanical Properties. 10.3.1 Properties in Tension. 10.3.2 Properties in Compression. 10.3.3 In-Place Shear Properties. 10.3.4 Flexural Properties. 10.3.5 Measures of In-Plane Fracture Toughness. 10.3.6 Interlaminar Shear Strength and Fracture Toughness. 10.3.7 Impact Properties. 10.4 Damage Identification Using Nondestructive Evaluation Techniques. 10.4.1 Ultrasonics. 10.4.2 Acoustic Emission. 10.4.3 x-Radiography. 10.4.4 Thermography. 10.4.5 Laser Shearography. 10.5 General Remarks on Characterization. Exercise Problems. References. 11 Emerging Composite Materials. 11.1 Nanocomposites. 11.2 Carbon-Carbon Composites. 11.3 Biocomposites. 11.3.1 Biofibers. 11.3.2 Wood-Plastic Composites (WPCs). 11.3.3 Biopolymers. 11.4 Composites in "Smart" Structures. Suggested Reading. Appendix 1: Matrices and Tensors. Appendix 2: Equations of Theory of Elasticity. Appendix 3: Laminate Orientation Code. Appendix 4: Properties of Fiber Composites. Appendix 5: Computer Programs for Laminate Analysis. Index.

1,912 citations

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01 Jan 1997

TL;DR: In this paper, the authors present a one-dimensional analysis of fiber-reinforced composite materials and their properties, including the properties of the components of a Lamina and their relationship with other components.

Abstract: Introduction and Mathematical Preliminaries Fiber-Reinforced Composite Materials. Vectors and Tensors. Matrices. Transformation of Vector and Tensor Components. Integral Relations. Equations of Anisotropic Elasticity Classification of Equations. Kinematics. Kinetics. Constitutive Equations. Equations of Thermoelasticity and Electroelasticity. Summary. Virtual Work Principles and Variational Methods Virtual Work. The Variational Operator and Functionals. Extrema of Functionals. Virtual Work Principles. Variational Methods. Summary. Introduction to Composite Materials Basic Concepts and Terminology. Constitutive Equations of a Lamina. Transformation of Stresses and Strains. Plane Stress Constitutive Relations. Classical and First-Order Theories of Laminated Composite Plates Introduction. An Overview of ESL Laminate Theories. The Classical Laminated Plate Theory. The First-Order Laminated Plate Theory. Stiffness Characteristics for Selected Laminates. One-Dimensional Analysis of Laminated Plates Introduction. Analysis of Laminated Beams Using CLPT. Analysis of Laminated Beams Using FSDT. Cylindrical Bending Using CLPT. Cylindrical Bending Using FSDT. Closing Remarks. Analysis of Specially Orthotropic Plates Using CLPT Introduction. Bending of Simply Supported Plates. Bending of Plates with Two Opposite Edges Simply Supported. Bending of Rectangular Plates with Various Boundary Conditions. Buckling of Simply Supported Plates Under Compressive Loads. Buckling of Rectangular Plates Under Inplane Shear Load. Vibration of Simply Supported Plates. Buckling and Vibration of Plates with Two Parallel Edges Simply Supported. Closure. Analytical Solutions of Rectangular Laminates Using CLPT Governing Equations in Terms of Displacements. Admissible Boundary Conditions for the Navier Solutions. Navier Solutions of Antisymmetric Cross-Ply Laminates. The Navier Solutions of Antisymmetric Angle-Ply Laminates. The LTvy Solutions. Analysis of Midplane Symmetric Laminates. Transient Analysis. Summary. Analytical Solutions of Rectangular Laminates Using FSDT Introduction. Simply Supported Antisymmetric Cross-Ply Laminates. Simply Supported Antisymmetric Angle-Ply Laminates. Antisymmetric Cross-Ply Laminates with Two Opposite Edges Simply Supported. Antisymmetric Angle-Ply Laminates with Two Opposite Edges Simply Supported. Transient Solutions. Summary. Finite Element Analysis of Composite Laminates Introduction. Laminated Beams and Plate Strips by CLPT. Timoshenko Beam/Plate Theory. Numerical Results for Beams and Plate Strips. Finite Element Models of Laminated Plates (CLPT). Finite Element Models of Laminated Plates (FSDT). Summary. Refined Theories of Laminated Composite Plates Introduction. A Third-Order Plate Theory. Higher-Order Laminate Stiffness Characteristics. The Navier Solutions. LTvy Solutions of Cross-Ply Laminates. Displacement Finite Element Model. Layerwise Theories and Variable Kinematic Models In troduction. Development of the Theory. Finite Element Model. Variable Kinematic Formulations. Nonlinear Analysis of Composite Laminates Introduction. Nonlinear Stiffness Coefficients. Solution Methods for Nonlinear Algebraic Equations. Computational Aspects and Numerical Examples. Closure. Index Most chapters include Exercises and References for Additional Reading

1,344 citations

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TL;DR: In this article, the limitations of classical laminated plate theory are investigated by comparing solutions of several specific boundary value problems in this theory to the corresponding theory of elasticity solutions, and it is shown that conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios.

Abstract: Limitations of classical laminated plate theory are investigated by comparing solutions of several specific boundary value problems in this theory to the corresponding theory of elasticity solutions. The general class of problems treated involves the geometric configuration of any number of isotropic or orthotropic layers bonded together and subjected to cylindrical bending. In general it is found that conventional plate theory leads to a very poor description of laminate response at low span-to-depth ratios, but converges to the exact solution as this ratio increases. The analysis presented is also valid in the study of sandwich plates under cylindrical bending.

1,194 citations

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28 Feb 1986TL;DR: In this paper, the authors introduce the concept of anisotropic elasticity and composite Laminate Theory for composite materials, and present a test standard for polymer matrix composites.

Abstract: Preface to the Second Edition. Preface to the First Edition. 1. Introduction to Composite Materials. 2. Anisotropic Elasticity and Composite Laminate Theory. 3. Plates and Panels of Composite Materials. 4. Beams, Columns and Rods of Composite Materials. 5. Composite Material Shells. 6. Energy Methods For Composite Material Structures. 7. Strength and Failure Theories. 8. Joining of Composite Material Structures. 9. Introduction to Composite Design. Appendices: A-1. Micromechanics. A-2. Test Standards for Polymer Matrix Composites. A-3. Properties of Various Polymer Composites. Author Index. Subject Index.

1,144 citations

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TL;DR: In this article, the response of a finite-width composite laminate under uniform axial strain is treated through the application of classical elasticity theory, and finite-difference solution techniques are employed to obtain solutions for stresses and displacements throughout the region.

Abstract: The response of a finite-width composite laminate under uniform axial strain is treated through the application of classical elasticity theory. Finite-difference solution techniques are employed to obtain solutions for stresses and displacements throughout the region. Results for material properties typical of a high modulus graphite-epoxy composite material system are presented which explain the mechanism of shear transfer within a symmetric laminate. In addition, results of this work are compared to those given in a recent approximate formulation.

1,048 citations