Lauge Fuglsang Nielsen. Composite Materials. Properties as Influenced by Phase Geometry. With 241 Figures ABC

Transcription

1 Composite Materials

2 Lauge Fuglsang Nielsen Composite Materials Properties as Influenced by Phase Geometry With 241 Figures ABC

3 Lauge Fuglsang Nielsen Technical University of Denmark Dept. Civil Engineering, Bld Lyngby, Denmark Library of Congress Control Number: ISBN -10 ISBN Springer Berlin Heidelberg New York Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com c Springer-Verlag Berlin Heidelberg 2005 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors and TechBooks using a Springer LATEX macro package Cover design: deblik, Berlin Printed on acid-free paper SPIN: /3141/jl

4 To my family and friends

5 Overview The subject dealt with in this book is the mechanical and physical behavior of composites as influenced by composite geometry. This subject has a high priority in the general study of composite materials. A better understanding of the behavior of natural composites, improvement of such materials, and design of new materials with prescribed properties are just three examples in modern materials research where more knowledge on geometry versus materials property is absolutely necessary. An analysis of various composite properties versus composite geometries is presented in this book as the result of integrating the results of two substudies: One study is made on composite properties as these can be related to composite geometry in general by so-called geometry functions. The second study is made on geometry functions as these are related to the geometry of specific composites, such as particulate composites, impregnated materials, laminated composites, and composites made by compaction of powders. In other words, global solutions for composite properties are developed in the first study, which apply for any composite. Final solutions for composites with specific geometries are then obtained from the global solutions introducing specific geometry functions developed in the second study. Special composite properties considered are stiffness, shrinkage, hygrothermal behavior, viscoelastic behavior, and internal stress states. Other physical properties considered are thermal and electrical conductivities, diffusion coefficients, dielectric constants and magnetic permeability. Special attention is given to the effect of pore shape on the mechanical and physical behavior of porous materials. The theories and the methods developed are verified by results obtained from a FEM-analysis presented, and by experimental and theoretical data from the composite literature. A number of examples are presented which illustrate the very decisive influence of the internal geometry on the mechanical and physical properties of composites.

6 VIII Overview As a spin-off result the composite theory developed is re-organized to become a diagnostic tool with respect to quality control of empirical or semitheoretical prediction methods suggested in the field of composite materials. Aspects of materials design are also considered. It is emphasized that strength is not considered as a genuine materials property in this book. It is a phenomenon where discontinuities in the materials structure suddenly occur as the result of violating local potentials to carry stress and/or strain for example. As such strength is a materials property that can be calculated from stress/strain results obtained in this book. Examples of such strength predictions for composite materials are presented. Readers Guidance Roughly speaking the book is divided into two parts. A theoretical part, and a more applicative part, starting at Chap. 10 where the theories developed are simplified, adapted, and generalized for most practice. Readers, who are interested primarily in applications, may start at this chapter. Any problem considered in Chap. 10 and subsequent chapters can be solved using the software package COM-APPL developed for easy composite analysis 1. Lists of notations and references used are presented at the end of the book. The former list should be consulted frequently. Symbols and notations used in the book are generally explained only at their first appearance in the text. The following superior concept of notations is emphasized: Whenever needed to distinguish single component properties from composite properties, subscripts P and S refer to property of component P and property of component S respectively while composite property is not subscripted. Usually the subscripts g and k are used to indicate quantities obtained from or used in deviatoric analysis and in volumetric analysis respectively. Formally these analyses are very often identical. In such cases only the volumetric analysis is presented with deviatoric results referred to by analogy. Alternatively both subscripts k and g are dropped when the feature discussed applies in principles for both volumetric and deviatoric behavior. A special subscript, Q, is used in conductivity studies to distinguish results obtained in these studies from similar quantities obtained in the analysis of elastic behavior. A number of auxiliary expressions are presented in appendix sections at the end of the book: Basic information is given on isotropic elasticity and cubical elasticity in Appendix A. A method is presented in Appendix B for the numerical determination of stresses in ellipsoidal particles in isotropic dilute 1 COM-APPL can be downloaded from

7 Overview IX suspensions. A generalized version of the so-called SCS-analysis (Self Consistency Scheme) of composite materials is presented in Appendix C. General viscoelastic models are presented in Appendix D. And finally, models are presented in Appendix E for volume compositions of hardening Portland cement paste and concrete.

8 Contents 1 Introduction ObjectivesofThisWork SummaryofCompositesConsidered Classification of Composites VolumeConcentrations GeometryatFixedPhaseConcentrations Geometrical Classification CompositeswithVariableGeometry Geometrical Classification SomeCompositeExamples Preliminaries on Stress/Strain Stiffness Dilute Suspension Stress CompositeStiffnessEstimatedbySCS Composite Stress and Geometry VolumetricStress CSA-Composites AnyComposite GeometryFunction GeometryFunctionandShapeFunction ShapeFunctions ACloserLook Summary Deviatoric Stress Stress and Geometry SummaryonStressandGeometry Stress Geo-Function... 32

9 XII Contents 5 Composite Stiffness and Geometry Bulk Modulus and Shear Modulus Porous Materials and Stiff Pore Systems Young smodulusandpoisson sratio SpecialCompositesandObservations CSA-Composites Composites with Special Shear Moduli Paul/Hansen versus Geo-Functions Composite Eigenstrain/Stress Basics SimpleComposites GeneralGeometry EigenstrainandEigenstress Pore Pressure in Porous Materials Quantification of Geometry ShapeFactors DC-Composites CD-Composites MM-Composites ShapeFunctionsandGeo-Path Default AlternativeI AlternativeII Geo-Paths Composite Theory Elasticity IllustrativeExamples DC-CDComposite CrumbledFoilsComposite Particulate (DC-DC) Composite OtherExamples Cracks SpecialDC-CDComposites FEM-AnalysisversusTheory FEM-Analysis Particulate Composite Defective Particulate Composite Pearls on a String Composite Grid Composite CrackedMaterial Discussion of FEM-Analysis Conclusion... 98

10 Contents XIII 9 Composite Theory Conductivity Theory IllustrativeExamples Porous Materials and Stiff Pore Systems Dilute Porous Materials and Stiff Pore Systems Cracked Materials (Soft and Stiff Cracks) CrumbledFoilsComposite TheoryversusExperiments Chloride Diffusion in HCP and HCP with Silica Fume Thermal Conductivity ofplane-isotropicfibercomposite TheoryversusSCS-Estimates Conclusion Simplified Composite Theory Elasticity BasisofAnalysis Geometry Quantification of Composite Geometry Preparation of Composite Analysis Analysis Bounds and Other Accurate Stiffness Expressions TestofTheory Illustrative Examples Composites with Spherical Particles (CSA P ) Nearly CSA P Composites Phase Symmetric Composites Eigenstrain/Stress versus Geometry PorousMaterials TheoryandExperiments Some Irregular Geometries Various Porous Materials Sulphur Impregnated Cement/Silicate System SaltInfectedBricks Non-Flexible Particles in Particulate Composite DefectivePhaseContactinConcrete Hydrating Cement Paste and Concrete Conclusion Simplified Composite Theory Conductivity Illustrative Example OntheAccuracyofSimplification Applications Thermal Conductivity of Fire-Brick Electrical Conductivity of Binary Metallic Mixtures

11 XIV Contents Chloride Diffusion in Cement Paste System Conclusion Diagnostic Aspects of Theory Stiffness Examination of Stiffness Expressions Conductivity Examination of SCS-Expressions Discussion Aspects of Materials Design Geometries versus Properties Design Illustrative Examples Stiffness Conductivity Discussion Viscoelasticity Stress-Strain Relations AnalogyYoung smodulus Vibrations Models of Viscoelastic Materials SimpleModels LessSimpleModels Summary, Analysis, and Approximate Analysis Approximate Analysis Viscoelastic Composites CompositeAnalysis AccurateAnalysis Approximate Analysis Applications Porous Materials and Stiff Pore Systems Particulate Composite MatureCementConcrete YoungConcrete Influence of Geometry onviscoelasticcompositebehavior Monomer Impregnated HCP and Porous Glass Damping of Wood Discussion Final Remarks...221

12 Contents XV A Elasticity A.1 Isotropy A.1.1 CompositeAspects A.1.2 Stress-Strain A.2 CubicElasticity A.2.1 Poly-Cubic Elasticity A.2.2 CompositeAspects B Dilute Particulate Composites B.1 Cubic Stiffness, Shape Parameters, and Stress B.1.1 Particle Stress B.1.2 Isotropic Stiffness, Shape Coefficients, and Stress B.1.3 Particle Stress C SCS-Analysis C.1 Stiffness C.1.1 Spherical Particles C.1.2 Various Particle Shapes and Cracks C.1.3 Multi-Shaped Particles C.2 OtherPhysicalProperties C.2.1 Spherical Particles C.2.2 Particles of Various Shapes and Cracks C.2.3 Multi-Shaped Particles D General Viscoelastic Models E HCP and Concrete E.1 VolumeModels E.2 PorosityofHardeningCementPaste Notations References...249