Dislocations in Metals, 1954
Dislocations in Metals Dislocations in Metals
J. S. KOEHLER AND F. SEITZ University of Illinois Urbana, Illinois W. T. READ, JR., AND W.SHOCKLEY Bell Telephone Laboratories Murray Hill, New Jersey E. OROWAN Massachusetts Institute of Tcchnology Cambridge, Riassachusetts
Edited by MORRIS COHEN Mass,zchusetts Institute of Technology
Published by THEIXSTITUTE OF R/IET.LLS DIVISION / I THEAMERICAN INSTITUTE OF MINING AND METALLURGICALENGINEERS, INC. 29 LV-EST 39th STREET hT~wYORK, hT. Y. 1954 COPYRIGHT,1954, BY TI-IE AMERICANINSTITUTE OF ~~INING AND METALLURGICALENGINEERS (INCORPORATED)
PRINTED IN THE UNITED STATES OF AMERICA
THE MAPLE PRESS COMPANY, YORE, PENNA. Preface
IT is becoming increasingly evident that dislocation theory must be brought into the teaching-core of physical metallurgy. Deviations from crystalline perfection seem to play a prominent role in the be- havior of metals, and dislocations constitute a most important class of imperfections about which calculations and predictions can be made. At first, the postulation of edge and screw dislocations appeared some- what arbitrary, leaving the metallurgist with the uncomfortable feeling that they lacked reality and merely provided an amusing toy for the mathematician. However, the picture has been broadened consider- ably by the concept of a dislocation loop which comprises varying combinations of edge and screw elements. Thus, if slip spreads along a glide plane, the lattice discontinuity between the slipped and un- slipped regions is inevitably a dislocation, no matter how curvedthe
advancing front may be. .. . Dislocations have proved quite versatile in accounting for many aspects of the mechanical behavior of metals. By the same token, the theory has been criticized as being somewhat too flexible in its ability to fit the facts. During recent years, however,.three striking predictions of dislocation theory have been confirmed by experiment: (a) the role of dislocations in the growth of crystals from the vapor phase and dilute solutions, (b) the calculation of low-angle grain-boundary
,' . energies as a function of the degree of disorientation, and (c) thc movement of low-angle grain boundaries under stress. As a result of these triumphs, dislocation theory is now on such a firm footing that physical metallurgists will find it advantageous, if not essential, to be- come thoroughly conversant with dislocations and their manifestations. As a step in this direction, a Seminar on "Dislocatioils in Metals" was held by the Institute of Metals Division, AIME, at its fall meeting in October 1951. Three outstanding survey lectures were given, by J. S. Koehler,W. T. Read, Jr., and E. Orowan. The presentations were educational in nature, and were purposely not intended totake the form of original papers. The response of the audience of 400 \\.as so enthusiastic that the Executive Committee authorized the publicatioil of the lectures as a separate volume. In the preparation of the manu- scripts, I?. Seitz and W. Shockley joined the authorship. Much addi- v tioilal material has beer1 included that could riot be treated in the origi- nal lectures. A number of new ideas, not previously published, are also contained herein. In Chapter I, Professors Koehler and Seitz discuss the" need" for dislocations, and outline the various phenomena in which they come into play. The geometry, stress-fields, energetics, and interactions of dislocations are reviewed in considerable detail. Chapter 2, by Dr. Read and Dr. Shockley, is devoted'primarily to those aspects of the subject in'\vhich definite predictions of dislocation theory have been subsequently verified by experiment. Emphasis is placed on the problems of crystalgrowth, low-angle grain-boundary energies, and the movement of these boundaries under stress.
The prodigious task of surveying the field of mechanical behavior ' in terms of dislocation theory is handled by Professor Orowail in Chapter 3. The thoroughness and clarity with which he has covered this complex subject will be appreciated by students of metallurgy for many years to come. The Institute of Metals Division is deeply indebted to the five authorities on dislocation theory who have participated in the present undertaking. It is hoped that the reader.response will demonstrate the importance of these IMD Seminar volumes in-which overall perspec- tive, rather than original research, is the keynote. It is also a pleasure to acknowledge the fine cooperation of Dr. Ernest Kirkendall and Miss K. S: Lovell, who helped in many ways to bring this book to the public. MORRISCOHEN, Editor. CABIBRIDGE, MASSACHUSETTS July 15, 1953 Contents
Page v
Chapter 1-The Nature of Dislocations in Ideal Single Crystals . BY J . S . I
Chapter 2-Role of Dislocations in Crystal Growth and ' Grain
~oundaryPhenomena . 1337 131 . T . ~?.F:AD, JR., and W . Saoc1c~sY ...... 37 2.1 ltcccrlt Dcvclopincr~tsin 'I1isloc:~tionTllcory ...... 37 2.2 Crystal Growth ...... 38 2.3 Frank's Thcory of tllc Growth of an Imperfect Crystal . -:30 2.4 Observational 13xaml,les ...... 41 2.5 Gmin Boundaries ...... 42 2.6. Dislocation Modcl of a Silnplc Grain Boundary .... 44 2.7 Derivation of the lzncrgy Formula ...... 4C) 2.8 Predictions from thc Thcory ...... 51 2.9 Cornl)arison with 13xperirnent ...... 54 2.10 Motion of Small-angle Grain Boundary ...... 58 . 2.10a. " Single-typc " Borlndary Motion ...... 59 2.10b. I' Miacd-type" 13locking ...... Gl . . 2.10~.Pt~ri(ication by Slip ...... 61 2.10d. Oblicluc Lattices ...... 63 2.10~.Slip by Diffr~sior~...... G4 2.10j. "Blocking and Cutti~~g"...... 65 2.10~.Parker and Washburn's Experiment ...... GG
. Chapter 3-Dislocations and Rllechanical Properties . By E . Oriowa~...... 69 3.1 I-Tistorical Skbtcli ...... 6!1 3.2 Discrepancy hctwccn 01, scrvcd Valuc of the YicldStress and Its Thcorctical Estin~RtC ...... 52 3.3 Earlier Attempts at Explaining thc Discrepancy .... '77 3.4 Thc Theory of It . Beckcr ...... 78 3.5 Thc Dislocation 13clt Around thc Arca of Local Slip . . 81 V11 cowrI
1.1tdez...... 197 Index , - -
Aluminun~,deformation of single crys- Density of dislocations, in strained tals, 17 metal; 28, 148 Angle of misfit, 45 in well-annealed materials, 20 . Diamond, hardness.determination, 126 Diffusion, movement of markers rclated to dislocations, 4, 34 Beckcr theories, discrepancy, 78, 89 Discrepancies betwecn theory and ob- nucleation, 181 * servation, tensile strength slip, 162 of brittle materials, .77 Beryl crystals, stcp heights in edgcs, 41 yield stress, 72, 77, 89 Brittle materials, discrepancy between Dislocation concept,, usefulness, 1 observed and calculated ten- Dislocation, origin of name;69 sile strcngths, 73 Dislocation line, 9 Burgers circuit, cffcct in crystal, 10 Dislocation mill, definition, 97 Burgers dislocation, formation and double, and bulge extrusion mecha- effect, 6 nism of slip, 97 - explanation of spread of slip Burgers distancc, or vcctor, 9, 14 to other planes, 103 gcncration during slip, 104 Dislocation modcl, 38 43, 70 Dislocation movement, factors facilitat- Cavities, 109 ing, 2 Chemical reaction rate theory, 159 Dislocation rings, 9, 14 Concept of dislocation, useflllness, 1 ~i~l~~~ti~~theory, modern develop- Copper, energy of grain boundaries, 57 ments, 37 ' lattice vacancies, 30 Dislocations, around area of local slip, 81 Creep in crystalline materials, 157, 164 definition, 1 Crystal growth, Frank theory, 38 distribution in crystals, model, 43 from vapor, 39 edge. See Edge nuclei provided by dislocations, 4, energies and interactions, 21 181 half, 13, 15, 16, 154 spirals, 41 mechanical properties, 69 suitable materials for observation, multiplication mechanisms, 95 41 origin, 90 Crystal monolayers, steps in edges, 40 prismatic, 12 197 198 DISLOCATIONS IN METALS
Dislocations, role in crystal growth, 37 Grain boundaries, slnall-angle, 45, 58 screm. See Screw Grain boundary, dislocation model, 42, sessile, 16 44 Shockley, 13, 15 Grain-boundary motion, small-anglc, t\\in, 13, 15, 16, 118 blocking and cutting, 65 Duralumin, prccipitation hardening, 128 mixed-typc blocking, 61 oblique lattices, 63 Parker and .Washburn's experi- mcnt, 66 Edgc dislocations, affinity for im- ' purification by slip, 61 purities, 3, 27 single typc, 59 dcscription, 2, 69 slip by difftlsion, 64 < distribution of stress, 49 Griffith theory, 77 cffects, 6 - Growth. See Crystal Growth formation in disoricnted crystals, 91 generation of slip, 106 role in polygonization, 24 structure, 83 Half dislocations, 13, 15, 16, 154 Z-mills, 110 Hardcning process, precipitation, 128 Elastic field around a dislocation, 143 rolc of stacking faults in cubic face- Energics ant1 interactions of d~sloca- centcrcd crystals, 138 tions, 21 strain, 134 Encrgy, derivation of formula, 46 Herring-Galt experimcnt, 94 of dislocations, elastic, 85 misfit, 88 per unit of lcngth, 87 grain-boundary, measurcn~cnts,sil- Irnpcrfections, interactions, 26 ver, iron, copper, 55 Impurities, affinity for edge disloca- physical mcaning of formula, 51 tions, 3, 27 rclation to dislocations, 5 Interrelations betwccn dislocations and relatioc, measurements, 54 other imperfections, 26 Interstitial atoms, 4, 27, 29, 31 Iodine crystals, gro~vthfrom vapor, 39 Fatigue of mctals, rolc of dislocations, Iron, intergranular cncrgy of boun- 188 darics, 55 Fracture in ductile crystalline materials, upper yicld point in rclation to dis- role of dislocations, 188 locations, 28 Frank theory of crystal growth, 38 Frank and Rcad, doul~lemill, 97 process of producing slip on single atomic plane from singlc Icirkcndall csperiment, ~narkcrmotion, dislocation, 18, 21 4, 34
Grain boundaries, arrays of dislocations, 42, 45, 91 1,attice vacancies. See Vacancics ~ncthodof protlrlcing, 17 Lead, cnergy of grain l~ountlarics,57 INDEX 199
Rfartensitic transformations, forma- Screw dislocations, 6, 24, 31, 40, 69, tion of lamellae of stable 104 phase, 116, 123 Sessile dislocation, 16 hlechanical hysteresis, model explain- Shockley partial dislocation, 13, 15 ing, 70 Silicon carbide, hardness determination, Mercury single crystals, shearing stress 127 with silver as impurity, 3 steps in gro~vth,41 Metals, cold-worked, structural changes, Silver, grain-boundary energy, 55, 57 I75 lattice vacancies. See Vacancics Single crystals, shearing stress, 3 Misfit energy, 88 yield stress, 72 Rfoclel, distril~utionof dislocations, 38, Slip on single atomic plane, 17 43, 44 Slip proccss, critical stable sizc of area, explanation of mcchanical hys- 88 tercsis, 70 cross slip, 105 Movemcnt of dislocations, factors facili- dislocation belt around area, 81 tating, 2 Frank-Rcad double mill, 07 Multiplication inccl~anis~nsof disloca- multiplication mechanisms of dis- tions, 95 locations, 95 procluctior~of latticc in~pcrfections, N 138 Node, definition, 10 spread of slip to othcr planes, Nucleation theories, 181 103 stability conditions, 85 0 twinning, 116 yield-strcss thcories, 165 Origin of dislocations, 90 Slip tracks, 114 Origin of namc dislocation, 69 Small-angle grain boundaries, 45, 58 P Snakes, dislocations, 85 parker ll~~~hb~~~~~experiment, 66 Solid free of dislocations, probable Partial dislocation, Shockley, 13, 15 bchavior, 6 Plastic flow, phenomena accounted for s&cking faults, 138, 150 by dislocation concept, I, 5, Stc~formation, 104 114 Strain aging, causcs, 28 Polygonization, 24, 176 Strain hardening, dislocations cut across Precip~tationhardening, 128 by slip, 146 Prcdiction from dislocation thcory, first elastic ficld around dislocation, 143 dynamic exan~ple,67 stacking faults as cause, 138, 150 Prisn~aticdislocations, 12 thcories, 134 Punching cxperiments in thallium bro- Stress concentrations, 21, 26 mide, 10 R Recovery, 175, 176 Taylor-Orowan dislocation, 2, 6 Recrystallization, 181 Taylor theory of strain hardcning, 126, Ring dislocation, 9, 14 135, 136, 130 DISLOCATIONS IN hlETALS
Thallium bromide, punching experi- ments, 10 Tin crystals, energy of grain boundaries, Yield-point phenomenon, 28, 165 57 Yield stress, definition in contrast to Herring-Galt experiment, 94 yield strength, 72 plastic flow as result of dislocations, discrepancy between observed 5 value and calculated value, . Twin dislocat,ions, 13, 15, 16, 118 89 Twinning in crystals, 20, 107,' 116 discrepancy between observed value and theoretical esti- mate, 72, 77 initial of crystals, 125 Vacancies, 4, 29, 31, 33,,65, 168 -.in precipitation hardening, 134 Volmer nucleation theory, 181, 185 In single crystals, 72 temperature dependence, 157 theories, 165
Warren theory of strain hardening, 138, Z 150 Worms, dislocations, 85 Z-mills, 110, 138, 169