Micromechanics of defects in solids

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Bibliographic Information

Micromechanics of defects in solids

Toshio Mura

（Mechanics of elastic and inelastic solids, 3）

M. Nijhoff , Kluwer Academic Publishers [Distributors for USA & Canada], 1987

2nd, rev. ed

  • : hbk
  • : pbk

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Note

Incledes bibliographical references (p. 513-571) and indexes

Previous ed. 1982: Published by M. Nijhoff (The Hague ; Boston ; London), and distributors for the U.S. and Canada by Kluwer Boston (Higham, Mass.)

"Reprinted with minor corrections 1991" -- on t.p. verso of 1998 reprinted

Description and Table of Contents

Volume

: pbk ISBN 9789024732562

Description

This book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and re searchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materi als: plasticity, fracture and fatigue, constitutive equations, composite materi als, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method. ' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.

Table of Contents

1. General theory of eigenstrains.- 1. Definition of eigenstrains.- 2. Fundamental equations of elasticity.- Hooke's law.- Equilibrium conditions.- Compatibility conditions.- 3. General expressions of elastic fields for given eigenstrain distributions.- Periodic solutions.- Method of Fourier series and Fourier integrals.- Method of Green's functions.- Isotropic materials.- Cubic crystals.- Hexagonal crystals (transversely isotropic).- 4. Exercises of general formulae.- A straight screw dislocation.- A straight edge dislocation.- Periodic distribution of cuboidal precipitates.- 5. Static Green's functions.- Isotropic materials.- Anisotropic materials.- Transversely isotropic materials.- Kroener's formula.- Derivatives of Green's functions.- Two-dimensional Green's function.- 6. Inclusions and inhomogeneities.- Inclusions.- Inhomogeneities.- Effect of isotropic elastic moduli on stress.- 7. Dislocations.- Volterra and Mura formulas.- The Indenbom and Orlov formula.- Disclinations.- 8. Dynamic solutions.- Uniformly moving edge dislocation.- Uniformly moving screw dislocation.- 9. Dynamic Green's functions.- Isotropic materials.- Steady State.- 10. Incompatibility.- Riemann-Christoffel curvature tensor.- 2. Isotropic inclusions.- 11. Eshelby's solution.- Interior points.- Sphere.- Elliptic cylinder.- Penny-shape.- Flat ellipsoid.- Oblate spheroid.- Prolate spheroid.- Exterior points.- Thermal expansion with central symmetry.- 12. Ellipsoidal inclusions with polynomial eigenstrains.- The I-integrals.- Sphere.- Elliptic cylinder.- Oblate spheroid.- Prolate spheroid.- Elliptical plate.- The Ferrers and Dyson formula.- 13. Energies of inclusions.- Elastic strain energy.- Interaction energy.- Strain energy due to a spherical inclusion.- Elliptic cylinder.- Penny-shaped flat ellipsoid.- Spheroid.- 14. Cuboidal inclusions.- 15. Inclusions in a half space.- Green's functions.- Ellipsoidal inclusion with a uniform dilatational eigenstrain.- Cuboidal inclusion with uniform eigenstrains.- Periodic distribution of eigenstrains.- Joined half-spaces.- 3. Anisotropic inclusions.- 16. Elastic field of an ellipsoidal inclusion.- 17. Formulae for interior points.- Uniform eigenstrains.- Spheroid.- Cylinder (elliptic inclusion).- Flat ellipsoid.- Eigenstrains with polynomial variation.- Eigenstrains with a periodic form.- 18. Formulae for exterior points.- Examples.- 19. Ellipsoidal inclusions with polynomial eigenstrains in anisotropic media.- Special cases.- 20. Harmonic eigenstrains.- 21. Periodic distribution of spherical inclusions.- 4. Ellipsoidal inhomogeneities.- 22. Equivalent inclusion method.- Isotropic materials.- Sphere.- Penny shape.- Rod.- Anisotropic inhomogeneities in isotropic matrices.- Stress field for exterior points.- 23. Numerical calculations.- Two ellipsoidal inhomogeneities.- 24. Impotent eigenstrains.- 25. Energies of inhomogeneities.- Elastic strain energy.- Interaction energy.- Colunneti's theorem.- Uniform plastic deformation in a matrix.- Energy balance.- 26. Precipitates and martensites.- Isotropic precipitates.- Anistropic precipitates.- Incoherent precipitates.- Martensitic transformation.- Stress orienting precipitation.- 5. Cracks.- 27. Critical stresses of crakes in isotropic media.- Penny-shaped cracks.- Slit-like cracks.- Flat ellipsoidal cracks.- Crack opening displacement.- 28. Critical stresses of cracks in anisotropic media.- Uniform applied stress.- Non-uniform applied stress.- II integrals for a penny-shaped crack.- II integrals for cubic crystals.- II integrals for transversely isotropic materials.- 29. Stress intensity factor for a flat ellipsoidal crack.- Uniform applied stresses.- Non-uniform applied stresses.- 30. Stress intensity factor for a slit-like crack.- Uniform applied stresses.- Non-uniform applied stresses.- Isotropic materials.- 31. Stress concentration factors.- Simple tension.- Pure shear.- 32. Dugdale-Barenblatt cracks.- BCS model.- Penny shaped crack.- 33. Stress intensity factor for an arbitrarily shaped plane crack.- Numerical examples.- 34. Crack growth.- Energy release rate.- The J-integral.- Fatigue.- Dynamic crack growth.- 6. Dislocations.- 35. Displacement fields.- Parallel dislocations.- A straight dislocation.- 36. Stress fields.- Dislocation segments.- Willis' formula.- The Asaro et al. formula.- Dislocation loops.- 37. Dislocation density tensor.- Surface dislocation density.- Impotent distribution of dislocations.- 38. Dislocation flux tensor.- Line integral expression of displacement and plastic distortion fields.- The elastic field of moving dislocationswave equations of tensor potentials.- Wave equations of tensor potentials.- 39. Energies and forces.- Dynamic consideration.- 40. Plasticity.- Mathematical theory of plasticity.- Dislocation theory.- Plane strain problems.- Beams and cylinders.- 41. Dislocation model for fatigue crack initiation.- 7. Material properties and related topics.- 42. Macroscopic average.- Average of internal stresses.- Macroscopic strains.- Tanaka-Mori's theorem.- Image stress.- Random distribution of inclusions-Mori and Tanaka's theory.- 43. Work-hardening of dispersion hardened alloys.- Work-hardening in simple shear.- Dislocations around an inclusion.- Uniformity of plastic deformation.- 44. Diffusional relaxation of internal and external stresses.- Relaxation of the internal stress in a plastically deformed dispersion strenthened alloy.- Diffusional relaxation process, climb rate of an Orowan loop.- Recovery creep of a dispersion strengthened alloy.- Interfacial diffusional relaxation.- 45. Average elastic moduli of composite materials.- The Voigt approximation.- The Reuss approximation.- Hill's theory.- Eshelby's method.- Self-consistent method.- Upper and lower bounds.- Other related works.- 46. Plastic behavior of polycrystalline metals and composites.- Taylor's analysis.- Self-consistent method.- Embedded weakened zone.- 47. Viscoelasticity of composite materials.- Homogeneous inclusions.- Inhomogeneous inclusions.- Waves in an infinite medium.- 48. Elastic wave scattering.- Dynamic equivalent inclusion method.- Green's formula.- 49. Interaction between dislocations and inclusions.- Inclusions and dislocations.- Cracks in two-phase materials.- 50. Eigenstrains in lattice theory.- A uniformly moving screw dislocation.- 51. Sliding inclusions.- Shearing Eigenstrains.- Spheroidol inhomogeneous inclusions.- 52. Recent developments.- Inclusions, precipitates, and composites.- Half-spaces.- Non-elastic matrices.- Cracks and inclusions.- Sliding and debonding inclusions.- Dynamic cases.- Miscellaneous.- Appendix 1.- Einstein summation convention.- Kronecker delta.- Permutation tensor.- Appendix 2.- The elastic moduli for isotropic materials.- Appendix 3.- Fourier series and integrals.- Dirac's delta function and Heaviside's step function.- Laplace transform.- Appendix 4.- Dislocations pile-up.- References.- Author index.
Volume

: hbk ISBN 9789024733439

Description

This book stems from a course on Micromechanics that I started about fifteen years ago at Northwestern University. At that time, micromechanics was a rather unfamiliar subject. Although I repeated the course every year, I was never convinced that my notes have quite developed into a final manuscript because new topics emerged constantly requiring revisions, and additions. I finally came to realize that if this is continued, then I will never complete the book to my total satisfaction. Meanwhile, T. Mori and I had coauthored a book in Japanese, entitled Micromechanics, published by Baifu-kan, Tokyo, in 1975. It received an extremely favorable response from students and re- searchers in Japan. This encouraged me to go ahead and publish my course notes in their latest version, as this book, which contains further development of the subject and is more comprehensive than the one published in Japanese. Micromechanics encompasses mechanics related to microstructures of materials. The method employed is a continuum theory of elasticity yet its applications cover a broad area relating to the mechanical behavior of materi- als: plasticity, fracture and fatigue, constitutive equations, composite materi- als, polycrystals, etc. These subjects are treated in this book by means of a powerful and unified method which is called the 'eigenstrain method. ' In particular, problems relating to inclusions and dislocations are most effectively analyzed by this method, and therefore, special emphasis is placed on these topics.

Table of Contents

1. General theory of eigenstrains.- 1. Definition of eigenstrains.- 2. Fundamental equations of elasticity.- Hooke's law.- Equilibrium conditions.- Compatibility conditions.- 3. General expressions of elastic fields for given eigenstrain distributions.- Periodic solutions.- Method of Fourier series and Fourier integrals.- Method of Green's functions.- Isotropic materials.- Cubic crystals.- Hexagonal crystals (transversely isotropic).- 4. Exercises of general formulae.- A straight screw dislocation.- A straight edge dislocation.- Periodic distribution of cuboidal precipitates.- 5. Static Green's functions.- Isotropic materials.- Anisotropic materials.- Transversely isotropic materials.- Kroner's formula.- Derivatives of Green's functions.- Two-dimensional Green's function.- 6. Inclusions and inhomogeneities.- Inclusions.- Inhomogeneities.- Effect of isotropic elastic moduli on stress.- 7. Dislocations.- Volterra and Mura formulas.- The Indenbom and Orlov formula.- Disclinations.- 8. Dynamic solutions.- Uniformly moving edge dislocation.- Uniformly moving screw dislocation.- 9. Dynamic Green's functions.- Isotropic materials.- Steady State.- 10. Incompatibility.- Riemann-Christoffel curvature tensor.- 2. Isotropic inclusions.- 11. Eshelby's solution.- Interior points.- Sphere.- Elliptic cylinder.- Penny-shape.- Flat ellipsoid.- Oblate spheroid.- Prolate spheroid.- Exterior points.- Thermal expansion with central symmetry.- 12. Ellipsoidal inclusions with polynomial eigenstrains.- The I-integrals.- Sphere.- Elliptic cylinder.- Oblate spheroid.- Prolate spheroid.- Elliptical plate.- The Ferrers and Dyson formula.- 13. Energies of inclusions.- Elastic strain energy.- Interaction energy.- Strain energy due to a spherical inclusion.- Elliptic cylinder.- Penny-shaped flat ellipsoid.- Spheroid.- 14. Cuboidal inclusions.- 15. Inclusions in a half space.- Green's functions.- Ellipsoidal inclusion with a uniform dilatational eigenstrain.- Cuboidal inclusion with uniform eigenstrains.- Periodic distribution of eigenstrains.- Joined half-spaces.- 3. Anisotropic inclusions.- 16. Elastic field of an ellipsoidal inclusion.- 17. Formulae for interior points.- Uniform eigenstrains.- Spheroid.- Cylinder (elliptic inclusion).- Flat ellipsoid.- Eigenstrains with polynomial variation.- Eigenstrains with a periodic form.- 18. Formulae for exterior points.- Examples.- 19. Ellipsoidal inclusions with polynomial eigenstrains in anisotropic media.- Special cases.- 20. Harmonic eigenstrains.- 21. Periodic distribution of spherical inclusions.- 4. Ellipsoidal inhomogeneities.- 22. Equivalent inclusion method.- Isotropic materials.- Sphere.- Penny shape.- Rod.- Anisotropic inhomogeneities in isotropic matrices.- Stress field for exterior points.- 23. Numerical calculations.- Two ellipsoidal inhomogeneities.- 24. Impotent eigenstrains.- 25. Energies of inhomogeneities.- Elastic strain energy.- Interaction energy.- Colunneti's theorem.- Uniform plastic deformation in a matrix.- Energy balance.- 26. Precipitates and martensites.- Isotropic precipitates.- Anistropic precipitates.- Incoherent precipitates.- Martensitic transformation.- Stress orienting precipitation.- 5. Cracks.- 27. Critical stresses of crakes in isotropic media.- Penny-shaped cracks.- Slit-like cracks.- Flat ellipsoidal cracks.- Crack opening displacement.- 28. Critical stresses of cracks in anisotropic media.- Uniform applied stress.- Non-uniform applied stress.- II integrals for a penny-shaped crack.- II integrals for cubic crystals.- II integrals for transversely isotropic materials.- 29. Stress intensity factor for a flat ellipsoidal crack.- Uniform applied stresses.- Non-uniform applied stresses.- 30. Stress intensity factor for a slit-like crack.- Uniform applied stresses.- Non-uniform applied stresses.- Isotropic materials.- 31. Stress concentration factors.- Simple tension.- Pure shear.- 32. Dugdale-Barenblatt cracks.- BCS model.- Penny shaped crack.- 33. Stress intensity factor for an arbitrarily shaped plane crack.- Numerical examples.- 34. Crack growth.- Energy release rate.- The J-integral.- Fatigue.- Dynamic crack growth.- 6. Dislocations.- 35. Displacement fields.- Parallel dislocations.- A straight dislocation.- 36. Stress fields.- Dislocation segments.- Willis' formula.- The Asaro et al. formula.- Dislocation loops.- 37. Dislocation density tensor.- Surface dislocation density.- Impotent distribution of dislocations.- 38. Dislocation flux tensor.- Line integral expression of displacement and plastic distortion fields.- The elastic field of moving dislocationswave equations of tensor potentials.- Wave equations of tensor potentials.- 39. Energies and forces.- Dynamic consideration.- 40. Plasticity.- Mathematical theory of plasticity.- Dislocation theory.- Plane strain problems.- Beams and cylinders.- 41. Dislocation model for fatigue crack initiation.- 7. Material properties and related topics.- 42. Macroscopic average.- Average of internal stresses.- Macroscopic strains.- Tanaka-Mori's theorem.- Image stress.- Random distribution of inclusions-Mori and Tanaka's theory.- 43. Work-hardening of dispersion hardened alloys.- Work-hardening in simple shear.- Dislocations around an inclusion.- Uniformity of plastic deformation.- 44. Diffusional relaxation of internal and external stresses.- Relaxation of the internal stress in a plastically deformed dispersion strenthened alloy.- Diffusional relaxation process, climb rate of an Orowan loop.- Recovery creep of a dispersion strengthened alloy.- Interfacial diffusional relaxation.- 45. Average elastic moduli of composite materials.- The Voigt approximation.- The Reuss approximation.- Hill's theory.- Eshelby's method.- Self-consistent method.- Upper and lower bounds.- Other related works.- 46. Plastic behavior of polycrystalline metals and composites.- Taylor's analysis.- Self-consistent method.- Embedded weakened zone.- 47. Viscoelasticity of composite materials.- Homogeneous inclusions.- Inhomogeneous inclusions.- Waves in an infinite medium.- 48. Elastic wave scattering.- Dynamic equivalent inclusion method.- Green's formula.- 49. Interaction between dislocations and inclusions.- Inclusions and dislocations.- Cracks in two-phase materials.- 50. Eigenstrains in lattice theory.- A uniformly moving screw dislocation.- 51. Sliding inclusions.- Shearing Eigenstrains.- Spheroidol inhomogeneous inclusions.- 52. Recent developments.- Inclusions, precipitates, and composites.- Half-spaces.- Non-elastic matrices.- Cracks and inclusions.- Sliding and debonding inclusions.- Dynamic cases.- Miscellaneous.- Appendix 1.- Einstein summation convention.- Kronecker delta.- Permutation tensor.- Appendix 2.- The elastic moduli for isotropic materials.- Appendix 3.- Fourier series and integrals.- Dirac's delta function and Heaviside's step function.- Laplace transform.- Appendix 4.- Dislocations pile-up.- References.- Author index.

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