Laminar Composites, Second Edition

466 Pages·2015·20.23 MB·English

Laminar Composites
To Ellen, Dan, Ben, and Jen
Laminar Composites
Second Edition
George H. Staab
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Contents
Preface ix
1 Introduction to composite materials 1
1.1 Historic and introductory comments 1
1.2 Characteristics of a composite material 3
1.3 Composite materials classifications 4
1.4 Fundamental composite material terminology 6
1.5 Advantages afforded by composite materials 8
1.6 Selected manufacturing techniques for composites 11
References 15
2 A review of stress–strain and material behavior 17
2.1 Introduction 17
2.2 Strain–displacement relations 17
2.3 Stress and stress transformations 23
2.4 Stress–strain relationships 25
2.5 Strain–stress relationships 29
2.6 Thermal and hygral effects 30
2.7 Complete anisotropic response 31
2.8 Problems 33
References 36
3 Lamina analysis 37
3.1 Introduction 37
3.2 Mechanical response of lamina 37
3.3 Thermal and hygral behavior of lamina 57
3.4 Prediction of lamina properties (micromechanics) 68
3.5 Problems 93
References 97
4 Mechanical test methods for lamina 99
4.1 Introduction 99
4.2 Strain gages applied to composites 99
4.3 Experimental determination of mechanical properties 110
4.4 Physical properties 125
vi Contents
4.5 Material properties of selected composites 127
4.6 Testing lamina constituents 130
4.7 Problems 133
References 136
5 Lamina failure theories 139
5.1 Introduction 139
5.2 Maximum stress theory 140
5.3 Maximum strain theory 141
5.4 The significance of shear stress 146
5.5 Interactive failure theories 149
5.6 Buckling 163
5.7 Design examples incorporating failure analysis 171
5.8 Problems 181
References 185
6 Laminate analysis 189
6.1 Introduction 189
6.2 Classical lamination theory 189
6.3 Thermal and hygral effects 199
6.4 Laminate codes 203
6.5 Laminate analysis 208
6.6 Laminate failure analysis 234
6.7 In-plane laminate strength analysis 247
6.8 Invariant forms of [A], [B], [D] 252
6.9 Analysis of hybrid laminates 258
6.10 Short fiber composites 262
6.11 Delamination and edge effects 270
6.12 Problems 276
References 282
7 Laminated composite beam analysis 285
7.1 Introduction 285
7.2 Equations of equilibrium for beams, rods, and columns 285
7.3 Elementary beam analysis 291
7.4 Advanced beam theory 297
7.5 Superposition 317
7.6 Beams with shear deformation 320
7.7 Buckling 324
7.8 Curved rings and beams 328
7.9 Beam vibrations 339
7.10 Problems 345
References 350
Contents vii
8 Laminated composite plate analysis 351
8.1 Introduction 351
8.2 Plate geometry and governing assumptions 351
8.3 Equations of motion 352
8.4 Boundary conditions 358
8.5 Plate bending 360
8.6 Plate vibrations 375
8.7 Effects of shear deformation 378
8.8 Stability 384
8.9 Problems 387
References 388
9 Analysis of laminated composite shells 391
9.1 Introduction 391
9.2 Strain–displacement relations for cylindrical shells 391
9.3 Equations of motion 393
9.4 Unidirectional laminate, axisymmetric loading: Static analysis 396
9.5 Anisotropic cylindrical shells 415
9.6 Problems 420
References 421
Appendix A: Generalized transformations 423
Appendix B: Summary of useful equations 427
Glossary 443
Index 449
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Preface
As an introduction to composite materials, the texts that have been published present
topics from either a materials science or applied mechanics viewpoint. This text pre-
sents the subject from an applied mechanics point of view and limits discussions to
continuous fiber composites. Topics are developed at a level suitable for terminal
undergraduate students and beginning graduate students. As a prerequisite, students
should have completed a course in strength of materials. Additionally, they should
be familiar with stress–strain relations for isotropic materials and load–stress relation-
ships. The philosophy behind this text is that it should be fundamentally simple
enough for a senior undergraduate to understand and apply the concepts forwarded,
while at the same time not too trivial for a beginning graduate student.
The scope of this text is limited to topics associated with the analysis and design of
continuous fiber-laminated composite materials. Lamina and laminate analysis is pre-
sented with a blend of theoretical developments and examples. The analysis of lam-
inated composites relies heavily on concepts developed in undergraduate statics and
mechanics of materials courses. Examples presented in this text require an under-
standing of free-body diagrams and analysis techniques introduced in undergraduate
mechanics courses. Experimental techniques applicable to defining the constitutive
relationships for orthotropic lamina are presented, as are failure theories for orthotro-
pic materials.
After establishing the stress–strain relationships, discussing special testing consid-
erations, and covering failure criteria for orthotropic lamina, classical lamination the-
ory is developed. An attempt has been made to present material in an easy-to-follow,
logical manner. Loading conditions involving mechanical, thermal, and hygral loads
are considered after the effect of each is discussed and developed independently.
Chapters on beams, plates, and shells have been added to the original text. The
chapter on beams should prove useful to undergraduates. Beams are a fundamental
structural element and this chapter is an extension of what undergraduates learned
in their introductory strength of materials courses. Although the plates and shells
chapters may be too difficult for undergraduates, they have been added for complete-
ness, and to serve as a starting point for students interested in these topics. These two
chapters are necessarily brief since the solutions to many types plate and shell prob-
lems require numerical techniques beyond the scope of this text.
Many of the topics covered in this text are a compilation of the topics covered in
preceding books, such as Primer on Composite Materials: Analysis by Ashton,
Halpin, and Petit; Mechanics of Composite Materials by Jones; Introduction to
Composite Materials by Tsai and Hahn; Experimental Mechanics of Fiber Reinforced