Nielsen Composite Materials

Properties as Influenced by Phase Geometry
1. Auflage 2005
ISBN: 978-3-540-27680-7
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 264 Seiten

In the past ?ve decades considerable attention has been devoted to comp- ite materials. A number of expressions have been suggested by which mac- scopic properties can be predicted when the properties, geometry, and volume concentrations of the constituent components are known. Many expressions are purely empirical or semi-theoretical. Others, however, are theoretically well founded such as the exact results from the following classical boundary studies: Bounds for the elastic moduli of composites made of perfectly coherent homogeneous, isotropic linear elastic phases have been developed by Paul [1] and Hansen [2] for unrestricted phase geometry and by Hashin and Shtrikman [3] for phase geometries, which cause macroscopic homogeneity and isotropy. The composites dealt with in this book are of the latter type. For two speci?c situations (later referred to), Hashin [4] and Hill [5] derived exact - lutionsforthebulkmodulusofsuchmaterials.Hashinconsideredtheso-called Composite Spheres Assemblage (CSA) consisting of tightly packed congruent composite elements made of spherical particles embedded in concentric - trix shells. Hill considered materials in which both phases have identical shear moduli. In the ?eld of predicting the elastic moduli of homogeneous isotropic c- posite materials in general the exact Hashin and Hill solutions are of th- retical interest mainly. Only a few real composites have the geometry de?ned by Hashin or the sti?ness distribution assumed by Hill. The enormous sign- icance, however, of the Hashin/Hill solutions is that they represent bounds which must not be violated by sti?ness predicted by any new theory claiming to consider geometries in general.

Autoren/Hrsg.

Nielsen, Lauge Fuglsang

Inhaltsverzeichnis

1;Overview;6
1.1;Readers Guidance;7
2;Contents;9
3;1 Introduction;14
3.1;1.1 Objectives of This Work;17
3.1.1;1.1.1 Summary of Composites Considered;18
4;2 Classification of Composites;19
4.1;2.1 Volume Concentrations;19
4.2;2.2 Geometry at Fixed Phase Concentrations;20
4.2.1;2.2.1 Geometrical Classification;21
4.3;2.3 Composites with Variable Geometry;22
4.3.1;2.3.1 Geometrical Classification;22
4.3.2;2.3.2 Some Composite Examples;26
5;3 Preliminaries on Stress/Strain;29
5.1;3.1 Stiffness;29
5.1.1;3.1.1 Dilute Suspension;31
5.2;3.2 Stress;32
5.3;3.3 Composite Sti.ness Estimated by SCS;32
6;4 Composite Stress and Geometry;35
6.1;4.1 Volumetric Stress;35
6.1.1;4.1.1 CSA-Composites;35
6.1.2;4.1.2 Any Composite – Geometry Function;36
6.1.3;4.1.3 Geometry Function and Shape Function;37
6.1.4;4.1.4 Shape Functions – A Closer Look;39
6.1.5;4.1.5 Summary;42
6.2;4.2 Deviatoric Stress;43
6.2.1;4.2.1 Stress and Geometry;43
6.3;4.3 Summary on Stress and Geometry;44
6.3.1;4.3.1 Stress;44
6.3.2;4.3.2 Geo-Function;44
7;5 Composite Stiffness and Geometry;46
7.1;5.1 Bulk Modulus and Shear Modulus;46
7.1.1;5.1.1 Porous Materials and Stiff Pore Systems;46
7.2;5.2 Young’s Modulus and Poisson’s Ratio;47
7.3;5.3 Special Composites and Observations;47
7.3.1;5.3.1 CSA-Composites;48
7.3.2;5.3.2 Composites with Special Shear Moduli Geo-Independent Bulk Moduli;48
7.3.3;5.3.3 Paul/Hansen versus Geo-Functions;49
8;6 Composite Eigenstrain/Stress;50
8.1;6.1 Basics;50
8.1.1;6.1.1 Simple Composites;51
8.2;6.2 General Geometry;51
8.2.1;6.2.1 Eigenstrain and Eigenstress;51
8.2.2;6.2.2 Pore Pressure in Porous Materials;52
9;7 Quantification of Geometry;53
9.1;7.1 Shape Factors;57
9.1.1;7.1.1 DC-Composites;57
9.1.2;7.1.2 CD-Composites;63
9.1.3;7.1.3 MM-Composites;64
9.2;7.2 Shape Functions and Geo-Path;67
9.2.1;7.2.1 Default;67
9.2.2;7.2.2 Alternative I;70
9.2.3;7.2.3 Alternative II;71
9.3;7.3 Geo-Paths;72
10;8 Composite Theory – Elasticity;74
10.1;8.1 Illustrative Examples;74
10.1.1;8.1.1 DC-CD Composite;74
10.1.2;8.1.2 Crumbled Foils Composite;76
10.1.3;8.1.3 Particulate (DC-DC) Composite;78
10.2;8.2 Other Examples;80
10.2.1;8.2.1 Cracks;80
10.2.2;8.2.2 Special DC-CD Composites Isotropy;84
10.3;8.3 FEM-Analysis versus Theory;87
10.3.1;8.3.1 FEM-Analysis;87
10.3.2;8.3.2 Particulate Composite;89
10.3.3;8.3.3 Defective Particulate Composite;91
10.3.4;8.3.4 Pearls on a String Composite;96
10.3.5;8.3.5 Grid Composite;100
10.3.6;8.3.6 Cracked Material;103
10.3.7;8.3.7 Discussion of FEM-Analysis;104
10.4;8.4 Conclusion;107
11;9 Composite Theory – Conductivity;108
11.1;9.1 Theory;108
11.2;9.2 Illustrative Examples;109
11.2.1;9.2.1 Porous Materials and Stiff Pore Systems;109
11.2.2;9.2.2 Dilute Porous Materials and Stiff Pore Systems;111
11.2.3;9.2.3 Cracked Materials (Soft and Stiff Cracks);111
11.2.4;9.2.4 Crumbled Foils Composite;113
11.3;9.3 Theory versus Experiments;113
11.3.1;9.3.1 Chloride Diffusion in HCP and HCP with Silica Fume;113
11.3.2;9.3.2 Thermal Conductivity of Plane-Isotropic Fiber Composite;116
11.4;9.4 Theory versus SCS-Estimates;118
11.5;9.5 Conclusion;118
12;10 Simplified Composite Theory – Elasticity;121
12.1;10.1 Basis of Analysis;123
12.1.1;10.1.1 Geometry;123
12.1.2;10.1.2 Quantification of Composite Geometry;125
12.1.3;10.1.3 Preparation of Composite Analysis;129
12.2;10.2 Analysis;130
12.2.1;10.2.1 Bounds and Other Accurate Stiffness Expressions;131
12.2.2;10.2.2 Test of Theory;131
12.3;10.3 Illustrative Examples;133
12.3.1;10.3.1 Composites with Spherical Particles (CSAP);134
12.3.2;10.3.2 Nearly CSAP Composites;134
12.3.3;10.3.3 Phase Symmetric Composites;135
12.3.4;10.3.4 Eigenstrain/Stress versus Geometry;140
12.3.5;10.3.5 Porous Materials;140
12.4;10.4 Theory and Experiments;145
12.4.1;10.4.1 Some Irregular Geometries Non-Flexible Geometry – Interference;145
12.4.2;10.4.2 Various Porous Materials;148
12.4.3;10.4.3 Sulphur Impregnated Cement/Silicate System;152
12.4.4;10.4.4 Salt Infected Bricks;154
12.4.5;10.4.5 Non-Flexible Particles in Particulate Composite;155
12.4.6;10.4.6 Defective Phase Contact in Concrete;157
12.4.7;10.4.7 Hydrating Cement Paste and Concrete;159
12.5;10.5 Conclusion;162
13;11 Simplified Composite Theory – Conductivity;163
13.1;11.1 Illustrative Example;163
13.1.1;11.1.1 On the Accuracy of Simplification;164
13.2;11.2 Applications;164
13.2.1;11.2.1 Thermal Conductivity of Fire-Brick;164
13.2.2;11.2.2 Electrical Conductivity of Binary Metallic Mixtures;164
13.2.3;11.2.3 Chloride Di.usion in Cement Paste System;166
13.3;11.3 Conclusion;169
14;12 Diagnostic Aspects of Theory;170
14.1;12.1 Stiffness;172
14.1.1;12.1.1 Examination of Sti.ness Expressions Isotropy Check;172
14.2;12.2 Conductivity;178
14.2.1;12.2.1 Examination of SCS-Expressions Spheres: Böttcher/ Landauer;178
14.3;12.3 Discussion;181
15;13 Aspects of Materials Design;184
15.1;13.1 Geometries versus Properties;184
15.2;13.2 Design;185
15.3;13.3 Illustrative Examples;185
15.3.1;13.3.1 Stiffness;185
15.3.2;13.3.2 Conductivity;187
15.4;13.4 Discussion;189
16;14 Viscoelasticity;190
16.1;14.1 Stress-Strain Relations;191
16.1.1;14.1.1 Analogy Young’s Modulus;192
16.1.2;14.1.2 Vibrations;194
16.2;14.2 Models of Viscoelastic Materials;196
16.2.1;14.2.1 Simple Models;197
16.2.2;14.2.2 Less Simple Models;197
16.3;14.3 Summary, Analysis, and Approximate Analysis;202
16.3.1;14.3.1 Approximate Analysis;203
17;15 Viscoelastic Composites;206
17.1;15.1 Composite Analysis;207
17.1.1;15.1.1 Accurate Analysis;207
17.1.2;15.1.2 Approximate Analysis;207
17.2;15.2 Applications;209
17.2.1;15.2.1 Porous Materials and Stiff Pore Systems;210
17.2.2;15.2.2 Particulate Composite;210
17.2.3;15.2.3 Mature Cement Concrete;211
17.2.4;15.2.4 Young Concrete;217
17.2.5;15.2.5 In.uence of Geometry on Viscoelastic Composite Behavior Particulate Composite versus Grid Reinforced Composite;217
17.2.6;15.2.6 Monomer Impregnated HCP and Porous Glass;222
17.2.7;15.2.7 Damping of Wood;225
17.3;15.3 Discussion;227
18;16 Final Remarks;228
19;A Elasticity;230
19.1;A.1 Isotropy;230
19.1.1;A.1.1 Composite Aspects;230
19.1.2;A.1.2 Stress-Strain;230
19.2;A.2 Cubic Elasticity;231
19.2.1;A.2.1 Poly-Cubic Elasticity;232
19.2.2;A.2.2 Composite Aspects;233
20;B Dilute Particulate Composites;234
20.1;B.1 Cubic Stiffness, Shape Parameters, and Stress;234
20.1.1;B.1.1 Particle Stress;235
20.1.2;B.1.2 Isotropic Stiffness, Shape Coefficients, and Stress;237
20.1.3;B.1.3 Particle Stress;237
21;C SCS-Analysis;238
21.1;C.1 Stiffness;238
21.1.1;C.1.1 Spherical Particles;239
21.1.2;C.1.2 Various Particle Shapes and Cracks;240
21.1.3;C.1.3 Multi-Shaped Particles;241
21.2;C.2 Other Physical Properties;242
21.2.1;C.2.1 Spherical Particles;243
21.2.2;C.2.2 Particles of Various Shapes and Cracks;243
21.2.3;C.2.3 Multi-Shaped Particles;245
22;D General Viscoelastic Models;246
23;E HCP and Concrete;248
23.1;E.1 Volume Models;248
23.2;E.2 Porosity of Hardening Cement Paste;249
24;Notations;251
25;References;254