SOLID MECHANICS AND ITS APPLICATIONS Jack R. Vinson and Robert L. Sierakowski The Behavior of Structures Composed of Composite Materials Second Edition KLUWER ACADEMIC PUBLISHERS
The Behavior of Structures Composed of Composite materials
The Behavior of Structures Composed of Composite Materials
SOLID MECHANICS AND ITS APPLICATIONS Volume 105 Series editor: GML. GLadWELL University of Waterloo Waterloo, Ontario, Canada n2L 3GI Aims and Scope of the Series The fundamental questions arising in mechanics are: Why ?, How?, and How much The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations: computational mechanics statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos: the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability: soils, rocks and geomechanics; fracture; tribology; experimental mechanics: biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are mono- graphs defining the current state of the field; others are accessible to final year under graduates; but essentially the emphasis is on readability and clarity For a list of related mechanics titles, see final pages
SOLID MECHANICS AND ITS APPLICATIONS Volume 105 Series Editor: G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada N2L 3GI Aims and Scope of the Series The fundamental questions arising in mechanics are: Why?, How?, and How much? The aim of this series is to provide lucid accounts written by authoritative researchers giving vision and insight in answering these questions on the subject of mechanics as it relates to solids. The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics; variational formulations; computational mechanics; statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and structures; dynamical systems and chaos; the theories of elasticity, plasticity and viscoelasticity; composite materials; rods, beams, shells and membranes; structural control and stability; soils, rocks and geomechanics; fracture; tribology; experimental mechanics; biomechanics and machine design. The median level of presentation is the first year graduate student. Some texts are monographs defining the current state of the field; others are accessible to final year undergraduates; but essentially the emphasis is on readability and clarity. For a list of related mechanics titles, see final pages
The behavior of Structures Composed of Composite materials Second edition JACKR VINSON H. Fletcher Brown Porfessor of Mechanical Aerospace Engineering The Center for Composite Materials and The College of Marine Studies, Department of Mechanical Engineering University of delaware, Newark Delaware U.S.A ROBERT L. SIERAKOWSK Chief scientist, AFRL/MN Eglin AFB, Florida U.S.A KLUWER ACADEMIC PUBLISHERS NEW YORK. BOSTON. DORDRECHT. LONDON. MOSCOW
The Behavior of Structures Composed of Composite Materials Second Edition by JACK R. VINSON H. Fletcher Brown Porfessor of Mechanical & Aerospace Engineering, The Center for Composite Materials and The College of Marine Studies, Department of Mechanical Engineering, University of Delaware, Newark, Delaware, U.S.A. and ROBERT L. SIERAKOWSKI Chief Scientist, AFRL/MN Eglin AFB, Florida, U.S.A. KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
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tiful wife, Midge, for providing the wonderfu d In loving memory of Nina, and also to my wonderful children, Sandy and Steve -RLS
To my beautiful wife, Midge, for providing the wonderful environment, love, patience and encouragement to complete this text - JRV In loving memory of Nina, and also to my wonderful children, Sandy and Steve - RLS
Preface to the second edition of mle The purpose of this text is to educate the engineering reader in the various aspects anics for using composite materials in the design and analysis of composite structures and product In Chapter I, the text acquaints the reader with the description of a composite material, and its constituents. Then, methods by which to manufacture composite materials are discussed, followed by a description of the uses of composite materials early in the twenty-first century. Chapter 2 provides the fundamentals of anisotropic elasticity, and the methods to characterize and mathematically describe composite laminae and laminates which are the building blocks"of composite structures. Also discussed are thermal, hygrothermal high strain rate and piezoelectric considerations in modern composites. Chapter 3 then deals exclusively with the static and dynamic response of composite plates and panels subjected to a variety of mechanical and environmental load in great detail. This includes stresses, deformations, buckling loads, natural frequencies d response to blast loads. Chapter 4 analogously treats a special case of the above, amely beams, columns and rods. In Chapter 5, cylindrical composite shells are discussed, both in determining the stresses and deformations due to static loads, but in treating the buckling of these shells under various loads and their combinations. The peculiar behavior of shells,(such as the bending boundary layer) compared to plates and beams is discussed in detail Because so many practical structural problems are too difficult or complex to structural design problems using energy principles and variational methods. Thus, the engineer can always obtain a solution to a problem Chapter 7 provides various strength and failure theories widely used today, and their comparison. Chapter 8 provides suggested ways to analyze and design adhesive bonded joints and mechanically fastened joints Chapter 9 has been added to provide a needed introduction to composite design Appendix I provides a discussion of micromechanics Appendix 2 list or most of the test standards for polymer matrix composite and Appendix 3 lists the mechanical properties of many composite in use today At the end of each chapter are numerous problems, which can be useful omework problems or modified for examination problems. Professors may contact authors for solutions to these problen student at the University of Delaware, who meticulously typed the text through its evolution. His accuracy, stamina and diligence are greatly appreciated. Appreciation is also expressed to Dr. Gregg Schoeppner for his contributions to Chapter I and the Appendices, and to Ms. Jill O Donnell for her manuscript readin Jack R. vinson
Preface to the Second Edition The purpose of this text is to educate the engineering reader in the various aspects of mechanics for using composite materials in the design and analysis of composite structures and products. In Chapter 1, the text acquaints the reader with the description of a composite material, and its constituents. Then, methods by which to manufacture composite materials are discussed, followed by a description of the uses of composite materials early in the twenty-first century. Chapter 2 provides the fundamentals of anisotropic elasticity, and the methods to characterize and mathematically describe composite laminae and laminates which are the “building blocks” of composite structures. Also discussed are thermal, hygrothermal, high strain rate and piezoelectric considerations in modern composites. Chapter 3 then deals exclusively with the static and dynamic response of composite plates and panels subjected to a variety of mechanical and environmental loads in great detail. This includes stresses, deformations, buckling loads, natural frequencies and response to blast loads. Chapter 4 analogously treats a special case of the above, namely beams, columns and rods. In Chapter 5, cylindrical composite shells are discussed, both in determining the stresses and deformations due to static loads, but in treating the buckling of these shells under various loads and their combinations. The peculiar behavior of shells, (such as the bending boundary layer) compared to plates and beams is discussed in detail. Because so many practical structural problems are too difficult or complex to obtain analytical solutions, Chapter 6 provides in-depth knowledge of attacking real life structural design problems using energy principles and variational methods. Thus, the engineer can always obtain a solution to a problem. Chapter 7 provides various strength and failure theories widely used today, and their comparison. Chapter 8 provides suggested ways to analyze and design adhesive bonded joints and mechanically fastened joints. Chapter 9 has been added to provide a needed introduction to composite design philosophy. Appendix 1 provides a discussion of micromechanics basics; Appendix 2 lists all or most of the test standards for polymer matrix composite and Appendix 3 lists the mechanical properties of many composite in use today. At the end of each chapter are numerous problems, which can be useful as homework problems or modified for examination problems. Professors may contact the authors for solutions to these problems. Appreciation is hereby expressed to James T. Arters, an engineering student at the University of Delaware, who meticulously typed the text through its evolution. His accuracy, stamina and diligence are greatly appreciated. Appreciation is also expressed to Dr. Gregg Schoeppner for his contributions to Chapter 1 and the Appendices, and to Ms. Jill O’Donnell for her manuscript reading. Jack R. Vinson Robert L. Sierakowski
Preface to the First Edition While currently available tests dealing with the subject of high performance composite materials touch upon a spectra of topics such as mechanical metallurgy physical metallurgy, micromechanics and macromechanics of such systems, it is the specific purpose of this text to examine elements of the mechanics of structural components composed of composite materials. This text is intended for use in training engineers in this new technology and rational thought processes necessary to develop a better understanding of the behavior of such material systems for use as structural The concepts are further exploited in terms of the structural format and development to which the book is dedicated. To this end the development progresses systematically by first introducing the notion and concepts of what these new material classes are, the fabrication processes involved and their unique features relative to conventional monolithic materials. Such introductory remarks, while far too short in texts of this type, appear necessary as a precursor for engineers to develop a better understanding for design purposes of both the threshold limits to which the properties of such systems can be pushed a swell as the practical limitations on their manufacture Following these introductory remarks, an in-depth discussion of the important differences between composites and conventional monolithic material types is discussed in terms of developing the concepts associated with directional material properties. That is, the ideas of anisotropic elasticity for initially homogeneous bodies in the phenomenological sense are described and presented. The use of such analytical tools is then presented through exemplification of selected problems for a number of classical ype problems of various geometric shapes including plane stress, plane strain and the bending of a simply suppor rted beam These ideas are carried forward and developed for continuous fiber composites in Chapter Two which discusses both single ply laminae and multi-ply laminate theory This is then followed by a series of chapters, each of which deals with functional aspect of structural design in which the basic building blocks of a structural system are made. That is, plates and panels; beams, columns and rods; and cylindrical and spherical shells are each discussed within the framework of their potential use in a functional environment. Thus the traditional topics of conventional monolithic (isotropic)material structural elements such as structures subjected to static loads, thermal and other environmental loads, structural instability and vibratory reso materials included along with hapters on energy methods and failure theories of composi Energy methods have been included to present a tool for solving difficult problems of various types encountered in practice. Indeed, in many instances closed form solutions are not possible and approximate solutions must be sought. Energy methods thus provide both an alternative for the formulation of such problems plus means of generating approximate solutions The chapter on failure theories is a generic presentation in the senses that any and/or all of the above structural components consisting of various multi-ply construction an fail when subjected to a sufficiently large loading combination. It is emphasized that he failure of composites is a complicated, changing issue because of the diverse ways in which such structural systems can fail due both to the geometric ply arrangement of the
Preface to the First Edition While currently available tests dealing with the subject of high performance composite materials touch upon a spectra of topics such as mechanical metallurgy, physical metallurgy, micromechanics and macromechanics of such systems, it is the specific purpose of this text to examine elements of the mechanics of structural components composed of composite materials. This text is intended for use in training engineers in this new technology and rational thought processes necessary to develop a better understanding of the behavior of such material systems for use as structural components. The concepts are further exploited in terms of the structural format and development to which the book is dedicated. To this end the development progresses systematically by first introducing the notion and concepts of what these new material classes are, the fabrication processes involved and their unique features relative to conventional monolithic materials. Such introductory remarks, while far too short in texts of this type, appear necessary as a precursor for engineers to develop a better understanding for design purposes of both the threshold limits to which the properties of such systems can be pushed a swell as the practical limitations on their manufacture. Following these introductory remarks, an in-depth discussion of the important differences between composites and conventional monolithic material types is discussed in terms of developing the concepts associated with directional material properties. That is, the ideas of anisotropic elasticity for initially homogeneous bodies in the phenomenological sense are described and presented. The use of such analytical tools is then presented through exemplification of selected problems for a number of classical type problems of various geometric shapes including plane stress, plane strain and the bending of a simply supported beam. These ideas are carried forward and developed for continuous fiber composites in Chapter Two which discusses both single ply laminae and multi-ply laminate theory. This is then followed by a series of chapters, each of which deals with functional aspect of structural design in which the basic building blocks of a structural system are made. That is, plates and panels; beams, columns and rods; and cylindrical and spherical shells are each discussed within the framework of their potential use in a functional environment. Thus the traditional topics of conventional monolithic (isotropic) material structural elements such as structures subjected to static loads, thermal and other environmental loads, structural instability and vibratory response are included along with chapters on energy methods and failure theories of composite materials. Energy methods have been included to present a tool for solving difficult problems of various types encountered in practice. Indeed, in many instances closed form solutions are not possible and approximate solutions must be sought. Energy methods thus provide both an alternative for the formulation of such problems plus a means of generating approximate solutions. The chapter on failure theories is a generic presentation in the senses that any and/or all of the above structural components consisting of various multi-ply construction can fail when subjected to a sufficiently large loading combination. It is emphasized that the failure of composites is a complicated, changing issue because of the diverse ways in which such structural systems can fail due both to the geometric ply arrangement of the
components, complicated load paths, and the diversity of failure mechanisms which can be activated. Therefore, this should serve in a global sense at best as a guide to the prediction of structural integrity, while more common and accep phenomenological failure theories are being developed Finally, a chapter on joining is included to discuss to some detail the two methods y which composite material structural components can be joined: namely, adhesive bonding and mechanical fastening. Again, the material presented is an introduction to the ubject which is rapidly changing and developing At the end of each chapter are several problems, charact covered which can be used. Some answers are given in an appendi ristic of the material Knowing that nothing is perfect, the authors welcome any notification of errors and ambiguities, and if addresses are provided, authors will forward errata sheets riodically Appreciation is hereby expressed to many students at the University of Delaware, University of Florida, Ohio State University, The Ballistics Research Laboratory, and the Argentine Air Force who have helped directly or indirectly in refining, improving and orrecting the text, as well as working various problems and examples. In addition appreciation is expressed to Dr. w.J. Renton, Vought Corporation, who has used portions of the text at the University of Texas-Arlington, and made suggestions and corrections Jack. vi Robert L. sierak
X components, complicated load paths, and the diversity of failure mechanisms which can be activated. Therefore, this chapter should serve in a global sense at best as a guide to the prediction of structural integrity, while more common and acceptable phenomenological failure theories are being developed. Finally, a chapter on joining is included to discuss to some detail the two methods by which composite material structural components can be joined: namely, adhesive bonding and mechanical fastening. Again, the material presented is an introduction to the subject which is rapidly changing and developing. At the end of each chapter are several problems, characteristic of the material covered which can be used. Some answers are given in an appendix. Knowing that nothing is perfect, the authors welcome any notification of errors and ambiguities, and if addresses are provided, authors will forward errata sheets periodically. Appreciation is hereby expressed to many students at the University of Delaware, University of Florida, Ohio State University, The Ballistics Research Laboratory, and the Argentine Air Force who have helped directly or indirectly in refining, improving and correcting the text, as well as working various problems and examples. In addition appreciation is expressed to Dr. W.J. Renton, Vought Corporation, who has used portions of the text at the University of Texas-Arlington, and made suggestions and corrections. Jack R. Vinson Robert L. Sierakowski
Preface to the second edition Preface to the First Edition L. Introduction to Composite Materials I. General History 2. Composite Material Description .3. Types of Composite Materials 1. 4. Constituent Properties 15.Co te Manufacturing. Fabrication and Process 1.6 Uses of Composite Materials 1. 7. Design and Analyses with Composite Materials 8. References 36 9. Journals 36 L10. Problems 37 2. Anisotropic Elasticity and Composite Laminate Theory 21. Introduction 2. 2. Derivation of the Anisotropic Elastic Stiffness and Compliance Matrices 23. The Physical Meaning of the Components of the Orthotropic Elasticity ensor 2. 4. Methods to Obtain Composite Elastic Properties from Fiber and Matrix 2.5. Thermal and Hygrothermal Considerations 2.7. High Strain Rate Effects on Mateniar site Materials 2.6. Time-Temperature Effects on Com 2.8. Laminae of Composite Materials .9. Laminate Analyses 2.10. Piezoelectric Effects 2.11. References 3789667978 3. Plates and Panels of C te materials 3. 1. Introduction 3. 2. Plate Equilibrium Equations 3.3. The Bending of Composite Material Laminated Plates: Classical Theory 91 3.4. Classical Plate Theory Boundary Conditions 3.5. Navier Solutions for Rectangular Composite Material Plates 3.6. Navier Solution for a Uniformly Loaded Simply Supported Plate-An Example Problem 98 3.7. Levy Solution for Plates of Composite Materials
Contents Preface to the Second Edition VII Preface to the First Edition IX 1. Introduction to Composite Materials 1 1 2 6 8 11 21 33 36 36 37 39 39 40 46 50 53 57 58 59 66 76 77 79 87 87 87 91 94 95 98 102 1.1. 1.2. 1.3. 1.4. 1.5. 1.6. 1.7. 1.8. 1.9. 1.10. General History Composite Material Description Types of Composite Materials Constituent Properties Composite Manufacturing, Fabrication and Processing Uses of Composite Materials Design and Analyses with Composite Materials References Journals Problems 2. Anisotropic Elasticity and Composite Laminate Theory 2.1. 2.2. 2.3. 2.4. 2.5. 2.6. 2.7. 2.8. 2.9. Introduction Derivation of the Anisotropic Elastic Stiffness and Compliance Matrices The Physical Meaning of the Components of the Orthotropic Elasticity Tensor Methods to Obtain Composite Elastic Properties from Fiber and Matrix Properties Thermal and Hygrothermal Considerations Time-Temperature Effects on Composite Materials High Strain Rate Effects on Material Properties Laminae of Composite Materials Laminate Analyses 2.10. 2.11. 2.12. Piezoelectric Effects References Problems 3. Plates and Panels of Composite Materials 3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7. Introduction Plate Equilibrium Equations The Bending of Composite Material Laminated Plates: Classical Theory Classical Plate Theory Boundary Conditions Navier Solutions for Rectangular Composite Material Plates Navier Solution for a Uniformly Loaded Simply Supported Plate – An Example Problem Levy Solution for Plates of Composite Materials