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E-raamat: Introduction To Elasticity Theory For Crystal Defects (Second Edition)

(Massachusetts Institute Of Technology, Usa)
  • Formaat: 660 pages
  • Ilmumisaeg: 25-Aug-2016
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814749749
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Introduction To Elasticity Theory For Crystal Defects (Second Edition)Suurem pilt
  • Formaat: 660 pages
  • Ilmumisaeg: 25-Aug-2016
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814749749
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The book presents a unified and self-sufficient and reader-friendly introduction to the anisotropic elasticity theory necessary to model a wide range of point, line, planar and volume type crystal defects (e.g., vacancies, dislocations, interfaces, inhomogeneities and inclusions).The necessary elasticity theory is first developed along with basic methods for obtaining solutions. This is followed by a detailed treatment of each defect type. Included are analyses of their elastic fields and energies, their interactions with imposed stresses and image stresses, and the interactions that occur between them, all employing the basic methods introduced earlier.All results are derived in full with intermediate steps shown, and "it can be shown" is avoided. A particular effort is made to describe and compare different methods of solving important problems. Numerous exercises (with solutions) are provided to strengthen the reader's understanding and extend the immediate text.In the 2nd edition an additional chapter has been added which treats the important topic of the self-forces that are experienced by defects that are extended in more than one dimension. A considerable number of exercises have been added which expand the scope of the book and furnish further insights. Numerous sections of the book have been rewritten to provide additional clarity and scope.The major aim of the book is to provide, in one place, a unique and complete introduction to the anisotropic theory of elasticity for defects written in a manner suitable for both students and professionals.
Preface to First Edition v
Preface to Second Edition ix
Acknowledgements xi
Frequently Used Symbols xiii
Roman xiii
Greek xv
The ± Symbol xvi
Superscripts xvi
1 Introduction
1(6)
1.1 Contents of Book
1(1)
1.2 Sources
2(1)
1.3 Symbols and Conventions
3(1)
1.4 On the Applicability of Linear Elasticity
4(3)
2 Basic Elements of Linear Elasticity
7(50)
2.1 Introduction
7(1)
2.2 Elastic Displacement and Strain Tensor
8(12)
2.2.1 Straining versus rigid body rotation
8(4)
2.2.2 Relationships for strain components
12(8)
2.3 Traction Vector, Stress Tensor and Body Forces
20(6)
2.3.1 Traction vector and components of stress
20(2)
2.3.2 Body forces
22(1)
2.3.3 Relationships for stress components and body forces
23(3)
2.4 Linear Coupling of Stress and Strain
26(13)
2.4.1 Stress as a function of strain
26(5)
2.4.2 Strain as a function of stress
31(2)
2.4.3 "Corresponding" elastic fields
33(2)
2.4.4 Stress-strain relationships and elastic constants for isotropic system
35(4)
2.5 Elastic Strain Energy
39(2)
2.5.1 General relationships
40(1)
2.5.2 Strain energy in isotropic systems
41(1)
2.6 St.-Venant's Principle
41(16)
Exercises
42(15)
3 Methods
57(44)
3.1 Introduction
57(1)
3.2 Basic Field Equation for the Displacement
58(1)
3.3 Fourier Transform Method
59(1)
3.4 Green's Function Method
60(3)
3.5 Sextic and Integral Formalisms for Two-Dimensional Problems
63(21)
3.5.1 Sextic formalism
64(16)
3.5.2 Integral formalism
80(4)
3.6 Elasticity Theory for Systems Containing Transformation Strains
84(6)
3.6.1 Transformation strain formalism
85(3)
3.6.2 Fourier transform solutions
88(1)
3.6.3 Green's function solutions
89(1)
3.7 Stress Function Method for Isotropic Systems
90(1)
3.8 Defects in Regions Bounded by Interfaces --- Method of Image Stresses
91(10)
Exercises
94(7)
4 Green's Functions for Unit Point Force
101(38)
4.1 Introduction
101(1)
4.2 Green's Functions for Unit Point Force
102(16)
4.2.1 In infinite homogeneous region
103(7)
4.2.2 In half-space with planar free surface
110(4)
4.2.3 In half-space joined to an elastically dissimilar half-space along planar interface
114(4)
4.3 Green's Functions for Unit Point Force in Isotropic System
118(21)
4.3.1 In half-space joined to elastically dissimilar half-space along planar interface
119(8)
4.3.2 In infinite homogeneous region
127(1)
4.3.3 In half-space with planar free surface
128(2)
Exercises
130(9)
5 Interactions between Defects and Stress
139(34)
5.1 Introduction
139(1)
5.2 Interaction Energies between a Defect Source of Stress and Various Stresses in Finite Homogeneous Body
140(11)
5.2.1 Interaction energy with imposed internal stress
142(3)
5.2.2 Interaction energy with applied stress
145(3)
5.2.3 Interaction energy with defect image stress
148(2)
5.2.4 Summary
150(1)
5.3 Forces on A Defect Source of Stress in Finite Homogeneous Body
151(13)
5.3.1 General formulation
151(1)
5.3.2 Force obtained from change of the system total energy
152(11)
5.3.3 Force obtained from change of the interaction energy
163(1)
5.3.4 Summary
163(1)
5.4 Interaction Energy and Force Between an Inhomogeneity and Imposed Stress
164(9)
Exercises
165(8)
6 Inclusions in Infinite Homogeneous Regions
173(56)
6.1 Introduction
173(1)
6.2 Characterization of Inclusions
173(1)
6.3 Coherent Inclusions
174(15)
6.3.1 Elastic field of homogeneous inclusion by Fourier transform method
175(10)
6.3.2 Elastic field of inhomogeneous ellipsoidal inclusion
185(3)
6.3.3 Strain energy
188(1)
6.4 Coherent Inclusions in Isotropic Systems
189(23)
6.4.1 Elastic field of homogeneous inclusion by Fourier transform method
189(1)
6.4.2 Elastic field of homogeneous inclusion by Green's function method
190(13)
6.4.3 Elastic field of inhomogeneous ellipsoidal inclusion with uniform ε
203(3)
6.4.4 Strain energy
206(4)
6.4.5 Further results
210(2)
6.5 Coherent → Incoherent Transitions in Isotropic Systems
212(17)
6.5.1 General formulation
212(2)
6.5.2 Inhomogeneous sphere
214(2)
6.5.3 Inhomogeneous thin-disk
216(1)
6.5.4 Inhomogeneous needle
216(1)
Exercises
217(12)
7 Interactions Between Inclusions and Imposed Stress
229(20)
7.1 Introduction
229(1)
7.2 Interactions between Inclusions and Imposed Stress in Isotropic Systems
229(20)
7.2.1 Homogeneous inclusion
229(3)
7.2.2 Inhomogeneous ellipsoidal inclusion
232(7)
Exercises
239(10)
8 Homogeneous Inclusions in Finite and Semi-infinite Regions: Image Effects
249(16)
8.1 Introduction
249(1)
8.2 Homogeneous Inclusions Far From Interfaces in Large Finite Bodies in Isotropic Systems
250(3)
8.2.1 Image stress
250(1)
8.2.2 Volume change of body due to inclusion --- effect of image stress
251(2)
8.3 Homogeneous Inclusion Near Interface in Large Semi-infinite Region
253(1)
8.3.1 Elastic field
253(1)
8.4 Homogeneous Spherical Inclusion Near Surface of Half-space in Isotropic System
254(4)
8.4.1 Elastic field
254(3)
8.4.2 Force imposed by image stress
257(1)
8.5 Strain Energy of Inclusion in Finite Region
258(7)
Exercises
258(7)
9 Inhomogeneities
265(18)
9.1 Introduction
265(1)
9.2 Interaction Between a Uniform Ellipsoidal Inhomogeneity and Imposed Stress
266(9)
9.2.1 Elastic field in body containing inhomogeneity and imposed stress
266(2)
9.2.2 Interaction energy between inhomogeneity and imposed stress
268(3)
9.2.3 Some results for isotropic systems
271(4)
9.3 Interaction Between an Elastically Non-uniform Inhomogeneity and a Non-uniform Imposed Stress
275(8)
Exercises
277(6)
10 Point Defects in Infinite Homogeneous Regions
283(20)
10.1 Introduction
283(1)
10.2 Symmetry of Point Defects
284(2)
10.3 Force Multipole Model
286(12)
10.3.1 Basic model
286(3)
10.3.2 Force multipoles
289(3)
10.3.3 Elastic fields of multipoles in isotropic systems
292(3)
10.3.4 Elastic fields of multipoles in general anisotropic systems
295(1)
10.3.5 The force dipole moment approximation
295(3)
10.4 Small Inclusion Model for Point Defect
298(5)
Exercises
299(4)
11 Interactions between Point Defects and Stress: Point Defects in Finite Regions
303(18)
11.1 Introduction
303(1)
11.2 Interaction Between a Point Defect (Multipole) and Stress
304(1)
11.3 Volume Change of Finite Body Due to Single Point Defect
305(2)
11.4 Statistically Uniform Distributions of Point Defects
307(14)
11.4.1 Defect-induced stress and volume change of finite body
307(4)
11.4.2 The Δ(p) tensor
311(1)
11.4.3 Defect-induced changes in x-ray lattice parameter
312(3)
Exercises
315(6)
12 Dislocations in Infinite Homogeneous Regions
321(92)
12.1 Introduction
321(1)
12.2 Geometrical Features
321(4)
12.3 Infinitely Long Straight Dislocations and Lines of Force
325(9)
12.3.1 Elastic fields
326(6)
12.3.2 Strain energies
332(2)
12.4 Infinitely Long Straight Dislocations in Isotropic Systems
334(6)
12.4.1 Elastic fields
334(5)
12.4.2 Strain energies
339(1)
12.5 Smoothly Curved Dislocation Loops
340(23)
12.5.1 Elastic fields
340(22)
12.5.2 Strain energies
362(1)
12.6 Smoothly Curved Dislocation Loops in Isotropic Systems
363(8)
12.6.1 Elastic fields
363(8)
12.6.2 Strain energies
371(1)
12.7 Segmented Dislocation Structures
371(11)
12.7.1 Elastic fields
372(9)
12.7.2 Strain energies
381(1)
12.8 Segmented Dislocation Structures in Isotropic Systems
382(31)
12.8.1 Elastic fields
382(11)
12.8.2 Strain energies
393(5)
Exercises
398(15)
13 Interactions between Dislocations and Stress: Image Effects
413(46)
13.1 Introduction
413(1)
13.2 Interaction of Dislocation with Imposed Internal or Applied Stress: The Peach-Koehler Force Equation
413(3)
13.3 Interaction of Dislocation with its Image Stress
416(43)
13.3.1 General formulation
416(3)
13.3.2 Straight dislocations parallel to free surfaces
419(10)
13.3.3 Straight dislocation parallel to planar interface between elastically dissimilar half-spaces
429(9)
13.3.4 Straight dislocation impinging on planar free surface of half-space
438(11)
13.3.5 Dislocation loop near planar free surface of half-space
449(2)
13.3.6 Dislocation loop near planar interface between elastically dissimilar half-spaces
451(1)
Exercises
452(7)
14 Interfaces
459(48)
14.1 Introduction
459(1)
14.2 Geometrical Features of Interfaces --- Degrees of Freedom
460(1)
14.3 Iso-elastic Interfaces
461(20)
14.3.1 Geometrical features
461(4)
14.3.2 The Frank--Bilby equation
465(9)
14.3.3 Elastic fields of interfaces consisting of arrays of parallel dislocations
474(3)
14.3.4 Elastic fields of arrays of parallel dislocations in isotropic systems
477(2)
14.3.5 Interfacial strain energies in isotropic systems
479(2)
14.4 Hetero-Elastic Interfaces
481(26)
14.4.1 Geometrical features
481(1)
14.4.2 Elastic fields
482(17)
Exercises
499(8)
15 Interactions between Interfaces and Stress
507(14)
15.1 Introduction
507(1)
15.2 The Energy-Momentum Tensor Force
508(3)
15.3 The Interfacial Dislocation Force
511(10)
15.3.1 Small-angle symmetric tilt interfaces
511(1)
15.3.2 Small-angle asymmetric tilt interfaces
512(2)
15.3.3 Large-angle homophase interfaces
514(1)
15.3.4 Heterophase interfaces
515(1)
Exercises
516(5)
16 Interactions between Defects
521(36)
16.1 Introduction
521(1)
16.2 Point Defect--Point Defect Interactions
521(3)
16.2.1 General formulation
521(2)
16.2.2 Between two point defects in isotropic system
523(1)
16.3 Dislocation--Dislocation Interactions
524(12)
16.3.1 Interaction energies
524(5)
16.3.2 Interaction energies in isotropic systems
529(4)
16.3.3 Interaction forces
533(2)
16.3.4 Interaction forces in isotropic systems
535(1)
16.4 Inclusion--Inclusion Interactions
536(4)
16.4.1 Between two homogeneous inclusions
536(3)
16.4.2 Between two inhomogeneous inclusions
539(1)
16.5 Point Defect--Dislocation Interactions
540(3)
16.5.1 General formulation
540(1)
16.5.2 Between point defect and screw dislocation in isotropic system
541(2)
16.6 Point Defect--Inclusion Interactions
543(1)
16.6.1 General formulation
543(1)
16.6.2 Between point defect and spherical inhomogeneous inclusion with εT/ij = εTδij in isotropic system
544(1)
16.7 Dislocation--Inclusion Interactions
544(13)
16.7.1 General formulation
544(1)
16.7.2 Between dislocation and spherical inhomogeneous inclusion with εT/ij = εTδij in isotropic system
545(1)
Exercises
545(12)
17 Defect Self--interactions and Self-forces
557(32)
17.1 Introduction
557(1)
17.2 Self-force Experienced by a Smoothly Curved Dislocation
557(14)
17.2.1 Circular planar loop
557(11)
17.2.2 General smoothly curved planar loop
568(1)
17.2.3 Some results for isotropic systems
569(2)
17.3 Dislocation Line Tension
571(2)
17.4 Self-force Experienced by Straight Dislocation Segment
573(3)
17.5 Self-force Experienced by Inclusion
576(13)
Exercises
579(10)
Appendix A Relationships Involving the Operator
589(2)
A.1 Cylindrical Orthogonal Curvilinear Coordinates
589(1)
A.2 Spherical Orthogonal Curvilinear Coordinates
590(1)
Appendix B Integral Relationships
591(4)
B.1 Divergence (Gauss's) Theorem
591(1)
B.2 Stokes' Theorem
591(1)
B.3 Another form of Stokes' Theorem
592(3)
Appendix C The Tensor Product of Two Vectors
595(2)
Appendix D Properties of the Delta Function
597(2)
Appendix E The Alternator Operator
599(2)
Appendix F Fourier Transforms
601(2)
Appendix G Equations from the Theory of Isotropic Elasticity
603(4)
G.1 Cylindrical Orthogonal Curvilinear Coordinates
603(2)
G.2 Spherical Orthogonal Curvilinear Coordinates
605(2)
Appendix H Components of the Eshelby Tensor in Isotropic System
607(2)
Appendix I Airy Stress Functions for Plane Strain
609(2)
Appendix J Deviatoric Stress and Strain in Isotropic System
611(2)
References 613(8)
Index 621
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