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Hygrothermoelasticity - George C. Sih


By: George C. Sih (Editor), J. G. Michopoulos (Editor), S.C. Chou (Editor)

Hardcover Published: 30th September 1986
ISBN: 9789024733569
Number Of Pages: 260

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This book contains results of more than a decade's effort on coupled deformation and diffusion obtained in research performed at the Institute of Fracture and Solid Mechanics, Lehigh University. Despite the overwhelming number of theories on this subject, little is known on the assessment of coupling effects because of the inherent difficulties associated with experimentation. A case in point is couple thermoelasticity, a theory that has remained virtually unused in practice. This is indicative of the inadequacy of conventional approaches. The interdependence of heat, moisture and deformation arises in many engineerĀ­ ing problems of practical interest. Whether these effects are coupled or not depend on the transient character of the boundary conditions. Special attention is given to finding the coupling constants. Invoked is the assumption that the physical parameters should be independent of the specified boundary conditions. They can thus be extracted from known experimental data for situations where coupling effects are relatively weak and then applied to predict strong coupling effects as boundary conditions are altered. This is illustrated for the T300/5208 material commonly used in composites and permits a more reliable evaluation of material behaving under extreme environmental conditions. The lack of this knowledge can often be a major deterrent to the achievement of new technological advances. The reader will recognize that the material in this book does not follow the main stream of research on moisture-temperature diffusion and deformation.

`The book should be read by all working on the mechanical properties of porous or composite materials. ... The authors are to be congratulated on presenting such a complex subject in a clear and concise way.' The Institute of Metals Materials Science & Technology

1 Classical diffusion theories.- 1.1 Introduction.- 1.2 Thermal diffusion: heat conduction.- 1.2.1 Law of heat conduction.- 1.2.2 Temperature field.- 1.3 Moisture diffusion.- 1.3.1 Moisture concentration field.- 1.3.2 Non-steady state moisture distribution.- 1.3.3 Time dependence.- 1.3.4 Temperature variation.- 1.3.5 Effect of relative humidity.- 1.3.6 Non-Fickian behavior.- 1.3.7 Dependency on concentration history.- 1.3.8 Influence of internal stress.- 1.3.9 Experimental results.- 1.4 Appendix: Anisotropic character of diffusion coefficient in fiber reinforced composite.- References.- 2 Coupled diffusion of temperature and moisture.- 2.1 Introduction.- 2.2 Dufour and Soret effects.- 2.3 Linear dependence of moisture and temperature in two-phase system.- 2.3.1 Vapor diffusion.- 2.3.2 Heat diffusion.- 2.3.3 Coupled diffusion.- 2.4 Solution by normal coordinates.- 2.4.1 One-dimensional.- 2.4.2 Three-dimensional.- 2.4.3 Time dependent external conditions.- 2.5 Evaluation of coupling constants.- 2.5.1 Change in moisture content.- 2.5.2 Change in heat content.- 2.5.3 Numerical results on coupling constants.- 2.6 Temperature and moisture diffusion in T300/5208 graphite/epoxy system.- 2.6.1 Determination of coupling coefficients.- 2.6.2 Transient temperature and moisture distribution in slab.- 2.7 Appendix A: Additional models of moisture and temperature coupling.- 2.7.1 Direct determination of moisture mass.- 2.7.2 Interaction of moisture energy.- 2.7.3 Phase transformation of liquid and vapor.- 2.8 Appendix B: Diffusion parameters for simultaneous moisture and temperature boundary conditions.- References.- 3 Analytical solutions of transient hygrothermal stresses in elastic bodies.- 3.1 Introduction.- 3.2 One-dimensional stress and strain expressions.- 3.2.1 Small deformation theory.- 3.2.2 Internal stresses.- 3.2.3 Material properties.- 3.3 Symmetric through thickness diffusion.- 3.3.1 Surface moisture boundary condition.- 3.3.2 Surface temperature boundary condition.- 3.4 Anti-symmetric through thickness diffusion.- 3.4.1 Sudden moisture change.- 3.4.2 Sudden temperature change.- 3.5 Spherical cavity in infinite solid.- 3.5.1 Problem statement and solution form.- 3.5.2 Discussion of special cases.- 3.5.3 Displacement and stress expressions.- 3.5.4 Coupled and uncoupled solutions.- 3.6 Appendix A: Elastic properties of T300/5208 graphite/epoxy laminate.- 3.7 Appendix B: General solution for coupled diffusion problems.- 3.7.1 Moisture and temperature distribution.- 3.7.2 Hygrothermal stresses.- References.- 4 Time dependent finite element formulation of hygrothermal elasticity problems.- 4.1 Introduction.- 4.2 Finite element applied to coupled diffusion equations.- 4.2.1 Discretization of temperature and moisture field.- 4.2.2 Variational calculus.- 4.2.3 Matrix decomposition.- 4.3 Laplace transformation and eigenvalue formulation.- 4.3.1 Surface moisture boundary condition.- 4.3.2 Surface temperature boundary conditions.- 4.3.3 Comparison with exact solution.- 4.4 Finite element hygrothermal stress formulation.- 4.4.1 Stress and strain relation.- 4.4.2 Strain and displacement expressions.- 4.5 Sudden localized heating of semi-infinite solid.- 4.5.1 Moisture and temperature distribution.- 4.5.2 Hygrothermal stresses.- 4.6 Concentration of diffusion and stresses around a circular cavity.- 4.6.1 Finite element grid pattern.- 4.6.2 Change of surface moisture.- 4.6.3 Change of surface temperature.- 4.6.4 Radial, circumferential and transverse normal stresses.- 4.7 Redistribution of hygrothermal stresses around an elliptical opening.- 4.7.1 Grid pattern for region with elliptical hole.- 4.7.2 Moisture boundary condition.- 4.7.3 Temperature boundary condition.- 4.7.4 Transient hygrothermal stresses.- 4.8 Appendix A: Variational procedure.- 4.9 Appendix B: Derivation of ?TI and ?CI.- 4.10 Appendix C: Modal decomposition.- References.- 5 Coupled theory of heat, moisture and deformation.- 5.1 Introduction.- 5.2 General information.- 5.2.1 Irreversible thermodynamics.- 5.2.2 Coupled linear elastic deformation.- 5.3 Plane hygrothermoelasticity.- 5.3.1 Plane stress.- 5.3.2 Plane strain.- 5.4 Method of hygrothermoelastic potential.- 5.5 Physical constants in deformation coupled theory.- 5.5.1 Moisture boundary conditions.- 5.5.2 Temperature boundary conditions.- 5.6 Uncoupled theories.- References.- 6 Complex variable formulation of hygrothermoelasticity problems.- 6.1 Introduction.- 6.2 Stress function.- 6.3 Complex formulation.- 6.4 Conformai transformation.- 6.4.1 Mapping function.- 6.4.2 Curvilinear coordinates.- 6.5 Circular region subjected to diffusion and deformation.- 6.5.1 Coupled solution.- 6.5.2 Displacement potential.- 6.5.3 Uniform compression.- 6.5.4 Suddenly applied compression.- 6.6 Remote extension of region with cavity.- 6.6.1 Superposition scheme.- 6.6.2 Circular cavity in infinite domain.- References.- 7 Numerical analysis of coupled diffusion and deformation problems.- 7.1 Introduction.- 7.2 Basic formulation.- 7.3 Smooth slab subjected to sudden moisture change.- 7.4 Smooth slab subjected to sudden temperature change.- 7.5 Diffusion and stress boundary conditions applied to body with circular cavity.- 7.5.1 Sudden moisture rise on cavity.- 7.5.2 Sudden temperature rise on cavity.- 7.6 Hygrothermal stresses around narrow elliptical cavity.- 7.6.1 Sudden moisture change on elliptical cavity.- 7.6.2 Sudden temperature change in elliptical cavity.- 7.6.3 Coupled thermal stresses around ellipse.- References.- 8 The strain energy density function.- 8.1 Introduction.- 8.2 Energy per unit volume.- 8.2.1 Isothermal and constant moisture.- 8.2.2 Non-isothermal and moisture change.- 8.3 Energy density decay near a crack.- 8.3.1 Moisture rise on crack.- 8.3.2 Temperature rise on crack.- 8.3.3 Coupled thermoelasticity.- 8.4 Failure criterion.- 8.4.1 Stationary values.- 8.4.2 Failure interpretation.- 8.4.3 Irreversibility.- References.- Author index.

ISBN: 9789024733569
ISBN-10: 9024733561
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 260
Published: 30th September 1986
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 29.7 x 21.0  x 1.7
Weight (kg): 1.25