This book studies metallic and composite materials and their mechanical properties in terms of stiffness and strength, illustrated through several case studies and exercises.
Rheology, Physical and Mechanical Behavior of Materials 4 focuses on the replacement of metal and wood products with fiber composites, which offer highly interesting directional mechanical properties. It studies various tests used to characterize the fiber-bonding pair in orthotropic layers and axes and also presents methods used to obtain stiffness and flexibility matrices, maximum stresses and deformations, and rupture envelopes. Finally, it presents various laminates, such as membrane and bending plates, tubular torsion, beat, buckling, twisting and sandwich structures.
This book is aimed at researchers involved in the mechanics of deformation, those studying or teaching this topic and industrial design and manufacturing departments.
Table of Contents
Preface ix
List of Symbols xi
List of Abbreviations and Definitions xvii
Introduction xxiii
Chapter 1 Types of Composites 1
1.1 Fibers, matrices, fabrics, laminates and cellular arrays 1
1.1.1 Fibers 1
1.1.2 Matrices 5
1.1.3 Fabrics, laminates and sandwiches 8
1.1.4 Cellular solids: wood and foams 17
1.2 Stiffness and elastic resistances of composites on the basis of the volume fraction Vf of fibers and Vm of binding agents (matrix) 23
1.2.1 The case of unidirectional composites 23
1.2.2 Influence of the stress distribution between fiber and matrix in the law of mixtures 30
1.3 Measurements of rigidities and resistances 36
1.3.1 Shear 37
1.3.2 Measurements of EL, ET and νLT by bending 39
1.4 Values of the elasticity and resistance moduli 40
1.4.1 Woods 40
1.4.2 Glass-polyester composites 45
1.4.3 Hybrid or mixed composites 48
1.4.4 Elastic constants of a ply for various fiber composites of carbon, boron, glass and Kevlar 53
1.5 Critical length and use of short fibers 55
1.5.1 Use of short fibers: example using reinforced thermoplastic granules (TPR) 57
1.5.2 Fracturing energy Gc of fibrous composites 59
1.6 Particulate composites 60
1.6.1 Example 61
1.6.2 Fillers 62
Chapter 2 Rigidity and Flexibility of Matrices 63
2.1 Matrices of rigidity [Q] and flexibility [S] in a UD membrane, inside and outside of orthotropy axes L and T 63
2.1.1. Stiffness and flexibility of a layer on its orthotropic axes l, t (or x, y depending on the notation) 63
2.1.2 Stiffness and flexibility matrices off of orthotropic axes 65
2.2 Method for calculating the rigidity and flexibility of an off-axis UD layer 67
2.2.1 Examples: UD carbon-epoxy and wood 69
2.2.2 Rigidities of spruce and maple woods 73
2.2.3 Rigidities and flexibility of an off-axis layer: summary for UD 74
2.3 Strains due to the forces of membranes: the case of strains occurring due to the forces of the UD 79
2.4 Rigidity [A] and flexibility [a] matrices in membrane laminates 80
2.4.1 Calculation of matrices 82
2.5 Matrices of rigidity [D] and flexibility [d] in during bending of laminates 91
2.5.1 Bending of laminates 92
2.5.2 Simplified bending calculation of sandwich beams, sag value δ 95
2.6 Vibration and acoustic mechanics, vibration modes 99
2.6.1 Example: case of a musical instrument 101
2.6.2 Membrane and bending stiffness of wood and carbon laminates 103
2.6.3 Comparison of acoustic responses between wooden violins and carbon-based laminate prototypes 106
Chapter 3 Elastic Behavior, Scaling 113
3.1 Elastic behavior of tubes - rigidity, strain 113
3.1.1 Bending 113
3.1.2 Torsion 116
3.1.3 Cylindrical tubular laminates 120
3.2 General behavior of laminated plates 123
3.2.1 Total strain 123
3.2.2 Forces and resulting moments 127
3.2.3 Equations of the laminates, rigidities: study of thin plates and deformations 128
3.2.4 Stresses and strains of the different layers given the loading stresses on the average plane 135
3.3 Elastic behavior and design of parts: bending and torsion behavior, the case of buckling and beating of tubes 138
3.3.1 Metal shaft 138
3.3.2 Composite shaft 141
3.4 Elastic limit behavior 148
3.4.1 Fracture mechanisms 148
3.4.2 Criteria for fracture 153
3.5 Design in primary strains 163
3.5.1 Principal stresses and strains 163
3.5.2 Constants of stresses and strains 163
3.5.3 Scaling of isotropes 164
3.5.4 Scaling of directional materials 166
Appendix 171
References 187
Index 189
