Physical Basis of Plasticity in Solids

by Toledano, Jean-Claude

• ISBN13: 9789814374057
• ISBN10: 9814374059
• Format: Hardcover
• Copyright: 2012-01-30
• Publisher: World Scientific Pub Co Inc

Summary

This book introduces the physical mechanism of the plastic deformation of solids, which relies essentially on the occurrence and motion of dislocations. These are linear defects, specific of crystalline solids whose motion under external stresses explains the relative ease by which solids (metals in particular) can be deformed in order to give them desired shapes. The objective is to introduce the topic to undergraduate students, restricting to the main ideas and showing their relevance in interpreting phenomena well known to everyone (e.g. why are certain metals harder than others?), and finally training the students in the practice of calculating the simplest properties of dislocations.

Table of Contents

Preface	p. v
Introduction	p. 1
Plasticity	p. 1
Mechanical properties of solids	p. 2
Microscopic mechanisms	p. 4
Organization and contents of the chapters	p. 9
General References	p. 11
The structure of crystalline solids	p. 13
Introduction	p. 13
Crystal geometry	p. 14
Ideal crystal	p. 14
Bravais lattices	p. 16
Definition	p. 16
Properties	p. 17
Unit cells	p. 22
Primitive unit cells	p. 22
Conventional unit cells	p. 22
Classification of the Bravais lattices. Cubic lattices	p. 24
Examples of crystal structures	p. 26
Simple monoatomic structure packings	p. 26
Physical realizations in metals	p. 31
Simple covalent structures	p. 34
Non-crystalline solids	p. 35
Mechanics of deformable solids	p. 39
Introduction	p. 39
Fundamental tensors	p. 39
Strain and stress	p. 39
Stiffness	p. 41
Coordinate changes	p. 42
Stiffness tensor and crystal symmetry	p. 44
General constraints	p. 44
Crystal symmetry	p. 45
Mathematical transformation of tensors	p. 45
Isotropic solids	p. 47
Stiffness tensor	p. 47
Basic equations	p. 48
Vacancies, an example of point defects in crystals	p. 51
Classification of defects in crystals	p. 51
Stability of point-defects in solids	p. 55
Statistical equilibrium	p. 55
Concentration of defects at thermal equilibrium	p. 57
Formation of vacancies	p. 58
Formation energy	p. 59
Random displacement of vacancies, diffusion	p. 64
The geometry of dislocations	p. 73
Introduction	p. 73
Straight edge dislocation	p. 75
Hypothetical procedures of formation	p. 75
Burgers circuit and Burgers vector	p. 78
Edge dislocation loops	p. 82
Other types of dislocations	p. 84
Screw dislocation	p. 84
Mixed dislocation-loops	p. 86
General properties of the Burgers vector	p. 88
Volterra process of formation	p. 89
Edge and screw dislocations	p. 90
General case	p. 93
Observation of dislocations	p. 94
Reflexion of electrons by a crystal	p. 95
How can a dislocation be observed?	p. 97
Lattice planes and reciprocal lattice	p. 99
Diffraction of electron beams	p. 102
Strain field of dislocations	p. 105
Introduction	p. 105
Strain and stress fields	p. 106
Screw dislocation	p. 107
Straight edge dislocation	p. 110
Mixed straight dislocation	p. 113
Elastic energy of a dislocation loop	p. 113
Action of a stress on a dislocation	p. 114
Effective force applied to a dislocation	p. 114
Peach and Koehler formula	p. 115
Line tension of a dislocation	p. 117
Interaction between dislocations	p. 120
Qualitative study	p. 120
Quantitative study	p. 123
Interaction between a dislocation and a vacancy	p. 125
Interactions with the lattice	p. 127
Introduction	p. 127
Core structure of an edge dislocation	p. 128
Lattice planes coordinates	p. 129
Components of the core energy	p. 131
Determination of the core width	p. 134
Peierls-Nabarro stress	p. 136
Gliding of a dislocation	p. 136
Principle of calculation of the Peierls-Nabarro stress	p. 138
Dissociation of the dislocation core	p. 139
Microscopic mechanism of plasticity	p. 143
Introduction	p. 143
Plastic deformation and local shear	p. 145
Amplitude of the slips	p. 145
Resolved shear stress	p. 145
Crystallographic characteristics of the slips	p. 147
Elementary slip and yield strength	p. 149
Edge dislocations	p. 149
Screw dislocations	p. 150
Upper limit of the yield strength	p. 152
Slip assisted by dislocation motion	p. 152
Number of dislocations	p. 153
Dislocation sources	p. 154
Change of configuration of dislocations	p. 154
Frank-Read source	p. 155
Spiral source	p. 158
Dislocation glide and climb	p. 158
Hardening	p. 160
Pinning dislocations	p. 160
Hardening mechanism	p. 166
Unpinning of the motion of dislocations	p. 167
Effect of temperature	p. 169
Deformation rate	p. 172
Orowan formula	p. 172
Dislocation velocity	p. 173
Origin of the diversity of plastic behaviours	p. 174
Easy-glide planes; glide systems	p. 174
Metals with an FCC or HC structure	p. 174
Other solids	p. 177
Exercises	p. 181
Structure of crystalline solids (chap. 2)	p. 181
Dislocations, Burgers vector (chap. 5)	p. 187
Deformations and forces (chap. 6)	p. 193
Core of a dislocation (chap. 7)	p. 199
Mechanism of plasticity (chap. 8)	p. 204
Solutions to Exercises	p. 217
Index	p. 267
Table of Contents provided by Ingram. All Rights Reserved.