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E-raamat: Introduction to Elasticity Theory for Crystal Defects

(Massachusetts Institute of Technology)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 22-Jun-2012
  • Kirjastus: Cambridge University Press
  • ISBN-13: 9781139200516
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Introduction to Elasticity Theory for Crystal DefectsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 22-Jun-2012
  • Kirjastus: Cambridge University Press
  • ISBN-13: 9781139200516
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"Self-sufficient and user-friendly, this book provides a complete introduction to the anisotropic elasticity theory necessary to model a wide range of crystal defects. Assuming little prior knowledge of the subject, the reader is first walked through therequired basic mathematical techniques and methods. This is followed by treatments of point, line, planar and volume type defects such as vacancies, dislocations, grain boundaries, inhomogeneities and inclusions. Included are analyses of their elastic fields, interactions with imposed stresses and image stresses, and interactions with other defects, all employing the basic methods introduced earlier. This step by step approach, aided by numerous exercises with solutions provided, strengthens the reader'sunderstanding of the principles involved, extending it well beyond the immediate scope of the book. As the first comprehensive review of anisotropic elasticity theory for crystal defects, this text is ideal for both graduate students and professional researchers"--

Arvustused

'This is a very nice, self-contained and inclusive book. It should provide a foundation for the anisotropic elastic theory of defects and their interactions for years to come.' John Hirth, Ohio State University 'This is a wonderful book on the elastic foundations of point, line and surface defects in crystals. It is well written by a master experimental and theoretical craftsman who has spent a long professional life in this field. The mathematical coverage of crystal defects and their interactions unfolds in classic style.' Johannes Weertman, Northwestern University ' provides a detailed and comprehensive presentation of the elasticity theory of crystal defects in full anisotropic form a full understanding of the ranges of applicability of mechanisms often necessitates the use of anisotropic elasticity employing advanced mathematical methodology. Such methodology is presently available only in scattered journal publications going back many years or in special treatises using advanced mathematical language of a large variety of forms and often involve[ s] frustrating statements of 'it can be shown that'. In his book Balluffi provides detailed and compassionate developments, that skip little detail, permitting the reader to obtain a rare and penetrating view into complex methodology with a uniform mathematical language that is familiar to most advanced students and professionals a standard reference for years to come [ for] physicists, materials scientists and practitioners in applied mechanics.' Ali Argon, Massachusetts Institute of Technology

Muu info

Ideal for graduates and researchers, this book provides a complete introduction to anisotropic elasticity, with exercises and solutions included.
Preface xiii
Acknowledgements xv
List of frequently used symbols
xvi
1 Introduction
1(4)
1.1 Contents of book
1(1)
1.2 Sources
2(1)
1.3 Symbols and conventions
2(1)
1.4 On the applicability of linear elasticity
3(2)
2 Basic elements of linear elasticity
5(27)
2.1 Introduction
5(1)
2.2 Elastic displacement and strain
5(10)
2.2.1 Straining versus rigid body rotation
5(4)
2.2.2 Relationships for strain components
9(6)
2.3 Traction vector, stress tensor, and body forces
15(6)
2.3.1 Traction vector and components of stress
15(3)
2.3.2 Body forces
18(1)
2.3.3 Relationships for stress components and body forces
18(3)
2.4 Linear coupling of stress and strain
21(8)
2.4.1 Stress as a function of strain
21(3)
2.4.2 Strain as a function of stress
24(1)
2.4.3 "Corresponding" elastic fields
25(2)
2.4.4 Stress-strain relationships and elastic constants for isotropic systems
27(2)
2.5 Elastic strain energy
29(2)
2.5.1 General relationships
30(1)
2.5.2 Strain energy in isotropic systems
31(1)
2.6 St.-Venant's principle
31(1)
3 Methods
32(32)
3.1 Introduction
32(1)
3.2 Basic equation for the displacement field
32(2)
3.3 Fourier transform method
34(1)
3.4 Green's function method
34(4)
3.5 Sextic and integral formalisms for two-dimensional problems
38(17)
3.5.1 Sextic formalism
38(14)
3.5.2 Integral formalism
52(3)
3.6 Elasticity theory for systems containing transformation strains
55(5)
3.6.1 Transformation strain formalism
56(3)
3.6.2 Fourier transform solutions
59(1)
3.6.3 Green's function solutions
59(1)
3.7 Stress function method for isotropic systems
60(1)
3.8 Defects in regions bounded by interfaces---method of image stresses
61(3)
Exercise
63(1)
4 Green's functions for unit point force
64(52)
4.1 Introduction
64(1)
4.2 Green's functions for unit point force
64(14)
4.2.1 In infinite homogeneous region
66(6)
4.2.2 In half-space with planar free surface
72(3)
4.2.3 In half-space joined to dissimilar half-space along planar interface
75(3)
4.3 Green's functions for unit point force in isotropic systems
78(15)
4.3.1 In half-space joined to dissimilar half-space along planar interface
78(7)
4.3.2 In infinite homogeneous region
85(1)
4.3.3 In half-space with planar free surface
86(2)
Exercises
88(5)
5 Interactions between defects and stress
93(1)
5.1 Introduction
93(1)
5.2 Interaction energies between defect source of stress and various stresses in homogeneous finite body
94(9)
5.2.1 Interaction energy with imposed internal stress
95(3)
5.2.2 Interaction energy with applied stress
98(2)
5.2.3 Interaction energy with defect image stress
100(3)
5.3 Forces on defect source of stress in homogeneous body
103(10)
5.3.1 General formulation
103(1)
5.3.2 Force obtained from change of the total system energy
103(8)
5.3.3 Force obtained from change of the interaction energy
111(2)
5.4 Interaction energy and force between inhomogeneity and imposed stress
113(3)
Exercises
114(2)
6 Inclusions in infinite homogeneous regions
116(43)
6.1 Introduction
116(1)
6.2 Characterization of inclusions
116(1)
6.3 Coherent inclusions
117(12)
6.3.1 Elastic field of homogeneous inclusion by Fourier transform method
118(8)
6.3.2 Elastic field of inhomogeneous inclusion with ellipsoidal shape
126(2)
6.3.3 Strain energies
128(1)
6.4 Coherent inclusions in isotropic systems
129(18)
6.4.1 Elastic field of homogeneous inclusion by Fourier transform method
129(1)
6.4.2 Elastic field of homogeneous inclusion by Green's function method
130(10)
6.4.3 Elastic field of inhomogeneous ellipsoidal inclusion with uniform εTij
140(2)
6.4.4 Strain energies
142(3)
6.4.5 Further results
145(2)
6.5 Coherent → incoherent transitions in isotropic systems
147(12)
6.5.1 General formulation
147(2)
6.5.2 Inhomogeneous sphere
149(1)
6.5.3 Inhomogeneous thin-disk
150(1)
6.5.4 Inhomogeneous needle
150(1)
Exercises
151(8)
7 Interactions between inclusions and imposed stress
159(12)
7.1 Introduction
159(1)
7.2 Interaction between inclusion and imposed stress
159(12)
7.2.1 Homogeneous inclusion
159(3)
7.2.2 Inhomogeneous ellipsoidal inclusion
162(5)
Exercises
167(4)
8 Inclusions in finite regions - image effects
171(16)
8.1 Introduction
171(1)
8.2 Homogeneous inclusion far from interfaces in large finite body in isotropic system
171(3)
8.2.1 Image stress
171(1)
8.2.2 Volume change due to inclusion - effect of image stress
172(2)
8.3 Homogeneous inclusion near interface in large region
174(3)
8.3.1 Elastic field
174(1)
8.3.2 Force due to image stress
175(2)
8.4 Elastic Field of homogeneous spherical inclusion near surface of hall-space in isotropic system
177(2)
8.5 Strain energy of inclusion in finite region
179(8)
Exercises
180(7)
9 Inhomogeneities
187(14)
9.1 Introduction
187(1)
9.2 Interaction between uniform ellipsoidal inhomogeneity and imposed stress
187(9)
9.2.1 Elastic field in body containing inhomogeneity and imposed stress
188(1)
9.2.2 Interaction energy between inhomogeneity and imposed stress
189(3)
9.2.3 Some results for isotropic system
192(4)
9.3 Interaction between non-uniform inhomogeneity and non-uniform imposed stress
196(5)
Exercises
198(3)
10 Point defects in infinite homogeneous regions
201(14)
10.1 Introduction
201(1)
10.2 Symmetry of point defects
202(1)
10.3 Force multipole model
203(10)
10.3.1 Basic model
203(2)
10.3.2 Force multipoles
205(3)
10.3.3 Elastic fields of multipoles in isotropic systems
208(2)
10.3.4 Elastic fields of multipoles in general anisotropic systems
210(1)
10.3.5 The force dipole moment approximation
210(3)
10.4 Small inhomogeneous inclusion model for point defect
213(2)
Exercises
214(1)
11 Point defects and stress - image effects in finite bodies
215(14)
11.1 Introduction
215(1)
11.2 Interaction between a point defect (multipole) and stress
215(2)
11.3 Volume change of finite body due to single point defect
217(1)
11.4 Statistically uniform distributions of point defects
218(11)
11.4.1 Defect-induced stress and changes in volume of finite body
218(3)
11.4.2 Defect-induced changes in shape of finite body - the λ(p) tensor
221(1)
11.4.3 Defect-induced changes in X-ray lattice parameter
222(2)
Exercises
224(5)
12 Dislocations in infinite homogeneous regions
229(75)
12.1 Introduction
229(1)
12.2 Geometrical features
229(4)
12.3 Infinitely long straight dislocations and lines of force
233(7)
12.3.1 Elastic fields
233(5)
12.3.2 Strain energies
238(2)
12.4 Infinitely long straight dislocations in isotropic system
240(5)
12.4.1 Elastic fields
240(4)
12.4.2 Strain energies
244(1)
12.5 Smoothly curved dislocation loops
245(19)
12.5.1 Elastic fields
245(18)
12.5.2 Strain energies
263(1)
12.6 Smoothly curved dislocation loops in isotropic system
264(6)
12.6.1 Elastic fields
264(6)
12.6.2 Strain energies
270(1)
12.7 Segmented dislocation structures
270(9)
12.7.1 Elastic fields
271(7)
12.7.2 Strain energies
278(1)
12.8 Segmented dislocation structures in isotropic system
279(25)
12.8.1 Elastic fields
279(8)
12.8.2 Strain energies
287(5)
Exercises
292(12)
13 Dislocations and stress - image effects in finite regions
304(36)
13.1 Introduction
304(1)
13.2 Interaction of dislocation with imposed internal or applied stress: the Peach-Koehler force equation
304(3)
13.3 Interaction of dislocation with its image stress
307(33)
13.3.1 General formulation
307(2)
13.3.2 Straight dislocations parallel to free surfaces
309(8)
13.3.3 Straight dislocation parallel to planar interface between dissimilar half-spaces
317(8)
13.3.4 Straight dislocation impinging on planar free surface of half-space
325(8)
13.3.5 Dislocation loop near planar free surface of half-space
333(2)
13.3.6 Dislocation loop near planar interface between dissimilar half-spaces
335(1)
Exercises
335(5)
14 Interfaces
340(37)
14.1 Introduction
340(1)
14.2 Geometrical features of interfaces - degrees of freedom
341(1)
14.3 Iso-elastic interfaces
341(18)
14.3.1 Geometrical features
342(3)
14.3.2 The Frank-Bilby equation
345(8)
14.3.3 Elastic fields of arrays of parallel dislocations
353(2)
14.3.4 Elastic fields of arrays of parallel dislocations in isotropic systems
355(2)
14.3.5 Interfacial strain energies in isotropic systems
357(2)
14.4 Hetero-elastic interfaces
359(18)
14.4.1 Geometrical features
359(1)
14.4.2 Elastic fields
360(13)
Exercises
373(4)
15 Interactions between interfaces and stress
377(9)
15.1 Introduction
377(1)
15.2 The energy-momentum tensor force
378(2)
15.3 The interfacial dislocation force
380(6)
15.3.1 Small-angle symmetric tilt interfaces
380(1)
15.3.2 Small-angle asymmetric tilt interfaces
381(2)
15.3.3 Large-angle homophase interfaces
383(1)
15.3.4 Heterophase interfaces
384(1)
Exercise
385(1)
16 Interactions between defects
386(25)
16.1 Introduction
386(1)
16.2 Point defect point defect interactions
386(2)
16.2.1 General formulation
386(1)
16.2.2 Between two point defects in isotropic system
387(1)
16.3 Dislocation-dislocation interactions
388(11)
16.3.1 Interaction energies
388(5)
16.3.2 Interaction energies in isotropic systems
393(3)
16.3.3 Interaction forces
396(2)
16.3.4 Interaction forces in isotropic systems
398(1)
16.4 Inclusion-inclusion interactions
399(2)
16.4.1 Between two homogeneous inclusions
399(2)
16.4.2 Between two inhomogeneous inclusions
401(1)
16.5 Point defect-dislocation interactions
401(3)
16.5.1 General Formulation
401(1)
16.5.2 Between point defect and screw dislocation in isotropic system
402(2)
16.6 Point defect-inclusion interactions
404(1)
16.6.1 General formulation
404(1)
16.6.2 Between point defect and spherical inhomogeneous inclusion with εTij = εTδij in isotropic system
405(1)
16.7 Dislocation-inclusion interactions
405(6)
16.7.1 General formulation
405(1)
16.7.2 Between dislocation and spherical inhomogeneous inclusion with εTij = εTδij in isotropic system
406(1)
Exercises
406(5)
Appendix A Relationships involving the Δ operator
411(2)
A.1 Cylindrical orthogonal curvilinear coordinates
411(1)
A.2 Spherical orthogonal curvilinear coordinates
411(2)
Appendix B Integral relationships
413(3)
B.1 Divergence (Gauss') theorem
413(1)
B.2 Stokes' theorem
413(1)
B.3 Another form of Stokes' theorem
414(2)
Appendix C The tensor product of two vectors
416(1)
Appendix D Properties of the delta function
417(2)
Appendix E The alternator operator
419(1)
Appendix F Fourier transforms
420(1)
Appendix G Equations from the theory of isotropic elasticity
421(3)
G.1 Cylindrical orthogonal curvilinear coordinates
421(2)
G.2 Spherical orthogonal curvilinear coordinates
423(1)
Appendix H Components of the Eshelby tensor in isotropic system
424(2)
Appendix I Airy stress functions for plane strain
426(1)
Appendix J Deviatoric stress and strain in isotropic system
427(1)
References 428(6)
Index 434
Robert Balluffi is Emeritus Professor of Physical Metallurgy at Massachusetts Institute of Technology. He has previously published two books and more than 200 articles in the field. He is a member of the National Academy of Science and has received numerous awards, including the Von Hippel Award, the highest honour of the Materials Research Society.
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