(See also individual Tables of Contents)
Absolute reaction rates, see Rate proc- ess, Viscosity theories
Absorption coefficient, sound excess pressure, 692, 696 magnetic field, 696
thermal relaxation, 694 (10) Abstract rheological concepts, 27, 32 Acceleration, 1, 12
Activated state, flow process, see also Flow
complex, 328 (19), 329 degrees of freedom, 340, 478
Activation energy, activation heat, of flow (see also Flow, Relaxation), 134, 272 (6), 324, 329, 331, 333, 336, 470 (4)
apparent, and weight fraction, 461F., 462F.
argon, 324, 333 average, 345
boundary diffusion, 205
comparison, creep, diffusion, slip, 214 creep, 137, 138, 214, 232
diffusion, 205, 214, 331 dislocation release, 224 for flow, 331
free, 329, 470, 479
grain boundary viscous slip, 214 hole formation, 328, 345 hydrogen-bonded liquids, 343 isobaric (flow), 341
isochoric (flow), 341 jump frequency, 470 molecular weight, 481F.
orientation, 468
precipitation hardening, 229 pressure, effect, 275, 333 self-diffusion, 214, 331 volume diffusion, 214 Activation enthalpy, 609 (100) Activation entropy, 470
Activity coefficient, viscosity, 609 Adherance to the wall, see Boundary con-
ditions, Wall effects
Adiabatic compressibility high frequency, 694 (9), (14) low frequency, 694 (8), (13) Adsorption-magnetic fields, 696 Adsorption on wall, 589 Agency, external, 112F.
Aggregation effects (see also Hydrody- namics, v. Smoluchowski), 582, 589 binary rate, 570
collisions, effect of, 582, 585 osmotic pressure, 587 polystyrene, 585-588 relative viscosity, 584 temperature, influence of, 608 Air
sound velocity, 265 viscosity, 257
Alcohols (see also separate listings; e.g.
Methyl alcohol, Ethyl alcohol, etc.) adiabatic compressibility, 684
sound absorption, 688
viscosity, pressure and molecular weight, 269F.
Alloys
disordered, stress-strain curve, 136F.
impurities, 122 order-disorder, 122
ordered, critical shear-stress of, 135, 136F.
substitutional, as binary resistance, 124
transient creep, 231 (27) Almansi measure (strain), 37, 39
Poynting effect, 39 Aluminum
atomic spacing, 162 bulk modulus, 208 characteristic vector, 162 compression-shear, 307, 308F.
copper alloy, 227
crack at grain boundaries, 236 creep, 213, 236
crystal, friction-temperature, 211, 212F.
crystal, rigidity-temperature, 211, 212F.
715
dislocation, 162 duralumin, 226
internal friction, single and polycrys- talline, 212F.
plastic flow, 238
plastic flow under pressure, 308 pure crystalline, 231
ridigity modulus, 208 slip planes, 227
t u b e s , loading t e s t , 108, 115 t u b e s , thin-walled, 117, 119 viscosity of liquid, 214 (14) Amyl alcohol, see also Alcohols
viscosity a t high pressures, 268 Andrade, 333
creep e q u a t i o n s , t y p e , 222, 231 (26), (27), 233
viscosity equation, 337 (43), 447 (4), 468 (12)
Anelasticity, inelastic behavior, non- elasticity (see also Creep, Friction, internal, Hysteresis, Viscosity), 3, 50,56,128 (45), 208, 209,352
P o y n t i n g and Thomson body, 50, 56 Angular, see also Diffusion, r o t a t i o n a l
distribution, particles, 617 relaxation frequency, 693 velocity, see Velocity Aniline point, 280 (11)
Aniline, viscosity a t high pressures, 268 Anisotropy, 11
intrinsic, 627 molecule, 617 optical, 627 shape, 627 Annealing, 226
Antimony, rhombohedric, 177 Argon
activation energy, 324, 333 liquid, 337
t h e r m a l diffusion, 267 viscosity, 258, 324 Arrhenius
h e a t of flow a c t i v a t i o n , 336 interaction coefficient, 591-594T.
Arsenic, rhombohedric, 177 A.S.M.E., 253,278
aniline point, 280 (11) petroleum densities, 281, 282T.
petroleum oils, 253,278,283,287 petroleum viscosities, 283, 285F.
Asphalt, volume flow, 59 emulsions, viscosity of, 575 Associated dislocations, 156, 157F.
Atomic (lattice) close-packed, 163, 172
distance or spacing, 146, 152, 163, 172 Atoms, force field and migration, 154,
185
Atoms, j u m p s of, 153,167 Atoms, solute, diffusion, 225
A t t e n u a t i o n coefficient (see also D a m p - ing, Friction, i n t e r n a l ) , 422 (125), 686, 691, 695
frequency effects, 691 A u t o f r e t t a g e , 247, 300
Axial ratio (see also Ellipsoids, Diffu- sion, r o t a t i o n a l , Particles), 625, 626
B
Baker, see Viscosity equations B a s a l t , 314
Bauschinger effect (see also H a r d e n i n g ) , 108, 109F., 110F., 301, 309, 311 density decrease, 309
Beam, bending of, 30, 414 (79) Benedict, resistance gauge, 248 Benzene
a c t i v a t i o n energy, 335 birefringence, 622 Maxwell c o n s t a n t , 623T.
ortho dichloro, cross-viscosity, 43 sound absorption, 688
sound velocity, rise with pressure, 684 viscosity, 335, 623T.
viscosity a t high pressures, 268 Beryllium, c r y s t a l , hexagonal close-
packed, 176
Biberstein, s t r a i n servoscanner, 255 Bilby, -Cottrell mechanism, 175
Bingham body, see also Plasticity, Solid, Bingham, Rheological models mobility, 658
number, 95 (76)
plastic, solid, 44, 93, 94F., 96, 657, 658, 659,660,661F., 663, 665, 669
solid, plug flow, 4, 95, 659, 662 solids, b o u n d a r y layers, 96 wall effect, 665
Binnie, plasticity mechanism, 299 Birefringence, see Optical anisotropy
Birefringence a p p a r a t u s , s t r e a m i n g cylinder, 620F.
gradient distribution, 621F.
limitations, 619
optical a r r a n g e m e n t , 620F.
velocity d i s t r i b u t i o n , 621F.
Birefringence, flow, see Birefringence, streaming
Birefringence, solvent influence, 627, 635 acetone, 638F.
benzene, 638F.
brombenzene, 638F.
b r o m e t h y l , 638F.
bromoform, 638F.
b u t y l a c e t a t e , 638F., 639F.
chloroform, 638F.
decalin, 638F.
dichlorethane, 638F.
dioxan, 638F.
ethyl a c e t a t e , 638F.
on nitrocellulose, 639F.
on p o l y m e t h y l m e t h a c r y l a t e , 638F.
on p o l y s t y r e n e , 638F., 641F.
t e t r a l i n , 638F.
toluene, 638F., 641F.
Birefringence, streaming, see also Opti- cal anisotropy
angular distribution function, 621 (17), 633
anisotropy, 616 benzene, 622
b u t y l a c e t a t e , 639, 640 in capillaries, 622
cellulose a c e t a t e , molecular and m i - cellar, 618F.
concentration effects, 639, 640 (40) concentration and coagulation effects,
624, 625
cotton yellow, 617F.
defined, 616 (3)
dependence on gradient, 616, 618 extinction angle (see also E x t i n c t i o n
angle), 616, 628 (20), 639, 640, 642F.
function, 628 (20), 629F.
h e p t y l alcohol, 623
inner viscosity, effect of, 633
intrinsic viscosity relationship, 553 (29), 635
low-molecular-weight liquids, 622 (9) more t h a n proportional increase, 633,
638
necklace model, 633 (28) nitrocellulose, 629, 639F.
optical anisotropy, 635 optical polarization tensor, 618 particle distribution, 626 (18) phase difference, 616
polydispersity, effect of, 633 polyisobutylene 630, 642F.
p o l y m e t h y l m e t h a c r y l a t e , 638 polystyrene, 629
principal axes, 616F.
refractive index influence, 625 relative, 617F.
sign change, 631, 637 sols, 622
solvent influence, see Birefringence, solvent influence
t h e o r y of, 631 undecyl alcohol, 622 Birefringence, stress, 646 (53)
angular distribution function, 651 a p p a r a t u s , 644F.
cellulose gels, 650 crystal orientation, 651 deformation, 643 distortion al, 644
effect of t e m p e r a t u r e , 647 elongation, 650
extension r a t i o s , 645 (49) H o o k e ' s law, 643 hysteresis, 648 inhibition, 651 intrinsic, 651 o r i e n t a t i o n , 645
photoelastic m e t h o d , 644 refractivity, 643, 646 s h a p e , 651
strain-optical coefficient, 643 stress-optical coefficient, 643, 644T.
swelling effects, 650 t h i n sheets, 644 (47)
viscoelastic behavior, s t u d y of, 650 B i s m u t h
compression-shear, 307, 308F.
plastic flow u n d e r pressure, 307, 308 rhombohedric, 177
B i t u m e n (blown) Jeffreys b o d y , 50 Lethersich body, 50 Weissenberg effect, 52 Blankenship, viscometer, 252
Boltzmann superposition principle, 127, 394
Bondi
molecular deformation energy, 340 viscosity of chain molecules, 336 (42) B o u n d a r y conditions (see also Wall ef-
fects), 33, 504, 538, 571, 575 anomalous flow, 660
Couette, 667 pipe flow, 663 suspensions, 529 B o u n d a r y surface, 13
Branching, see Macromolecules Brass
dislocations, 181
grain b o u n d a r y , viscosity, 214 lattice transformation, 178 radiation hardening, 135 Bridgman
dilatometer, 256
flow stress-natural s t r a i n , 305F.
plasticity, physical theory of, 317 plasticity volume changes, 309 pressure chambers, 102, 247, 248 viscometer (horizontal), 251, 257 viscometer (vertical), 250, 290 x-ray strain measurements, 256 Brinkman-Debye-Bueche theory, 561 B r i t t l e fracture, see F r a c t u r e Brown, viscometer, 250
Brownian motion, 495, 496, 503, 511, 512, 515, 519, 535, 548, 617
biased, 411 complete, 544 diffusion, 496, 503 dipoles, 520
distribution function, 496, 632 intramolecular, i n t e r n a l , micro-, 411,
498, 520
Langevin equation, 496 (1), 548 non-Newtonian effects, 511
r o t a r y (as affecting flow and orienta- t i o n ) , 502, 519, 527, 535, 543, 550, 568, 601,604,608,632
streaming birefringence, 617, 623, 632 t e m p e r a t u r e dependence (diffusion),
508, 515, 608, 626 (16) viscoelasticity, 510 viscosity, 512, 527, 551
Buchheim, birefringence optical system, 620F.
Buckingham-Reiner e q u a t i o n , 45 (117) Bueche, A. M .
-Brinkman-Debye t h e o r y , 561 Bueche, F .
cooperative flow, 478
elastic compliance, polymers, 412 molecular flow t h e o r y , 445
non-Newtonian viscosity, 489, 490 (29) Bulge t h e o r y , 88
Bulk modulus, see Modulus Burgers
b o d y , 51
t r a n s i t i o n l a t t i c e t h e o r y , 202
vector, 146, 149, 151, 162, 226, 232, 239 B u t a d i e n e - s t y r e n e , glass t e m p e r a t u r e ,
453
B u t y l a c e t a t e , birefringence, 639, 640 B u t y l a c r y l a t e , 475
Butyl alcohol, see also Alcohols viscosity a t high pressures, 268
C C a d m i u m
axial r a t i o , 177
crystal hexagonal close-packed, 176 t r a n s i e n t flow, 234
Cage (Cell) model (see also Liquids, theo- ries of s t a t e ) , 326, 333, 599
concentration dependence, suspen- sions, 599
i n t e r a c t i o n coefficient, suspensions, 601
for liquids, 328, 684
relative viscosity, suspensions, 599 (90), 600 (91)
C a h n , polygonization, 196 Calcite
dislocations, 182 plastic glide, 184 twinning, 184
Cameron, combined Eyring-Vogel equa- tion, 289 (24)
Capillary flow, see Flow, capillary, Vis- cosimeters
C a p r o l a c t a m sebacate acid chain length-viscosity, 446T.
viscosity, 444F.
Carboloy, fracture, 310 Carbon
in alpha-iron, 127 diamond, 176
diffusion coefficient, 128, 129F.
graphite, 177 Carbon dioxide
Enskog minimum, 263 thermal diffusion, 267 velocity of sound, 266
viscosity, under pressure, 257, 261F., 266F.
Carbontetrachloride, cavitation thresh- o l d , 689
Cascade press, 248 Castor oil
cavitation threshhold, 689 shear elasticity, 687
Cauchy measure deformation, 21 (36), 23 (36), 35 (90), 36, 37 (90), 38 Cavitation, 689
effects, 690
frequency effects, 691 nuclei, 690
streaming, 690 threshhold, 689
Cell-model theory, see Cage theory, Liquids
Cellulose
derivatives, 559, 610 micellar solutions, 630 stress birefringence, gels, 650 swelling ratio, 650
xanthogenate, birefringence, 650 Cellulose acetate, 618F.
birefringence, 618F.
cyclohexanone mixture, 618F., 630 extinction angle, 618F.
Centripetal pump, 42, 52
Chain molecules, see Macromolecules, Molecular flexibility, Particles Chalmers
microplasticity, 225
transition lattice theory, 202 Charron, ballistic viscometer, .257 Clark
lubrication effects, 257
pressure-temperature relationship, 286 Clausius, flow range, 529
Clearage, 313
Climb, of dislocation line, 151
Coaxial cylinders, see Couette, Flow, Vis- cosimeters
Cobalt
crystal, hexagonal close-packed, 176 lattice transformation, 178
Coil, see Macromolecules, Particle shapes Cold-rolling, 312
Cold-working, 300
Collisions, collision effects, see Flow, Ag- gregation effects
Colloidal solutions and suspensions, see also Diffusion, Hydrodynamics, Mac- romolecules, Particles, Viscosity abnormal, 532
activity coefficient, 609 angular velocity, 625 bentonite, flow, 625
birefringence (see also Birefringence, streaming), 624, 630
corresponding states, 602 critical concentration, 533, 595 critical viscosity, 533
crowding factor, 597 diffusion, see Diffusion dilute, 532, 536 (7)
distribution function, 601, 626 doublets, 585
dumbbell model, 577F.
Einstein's viscosity theory, 534, 541 (14), 558, 598 (88)
electro viscous effect, 568 extinction angle, 624 flow enthalpy, 609 immobilization factor, 598
incipient overlap concentration, 602 interaction coefficients, 589, 591-594T.
intrinsic viscosity, general form, 589 kinetic energy, 548
models for (see also Macromolecules), 552, 560, 563, 573, 575, 594T.
non-spherical particles, 542, 546, 551 normal, 532
particle shapes, see Hydrodynamics, Particles
principle dilatations, 575
Schultz molecular weight distribution, 566
solvent flow, 534, 538
solvent flow perturbations, see Hy- drody namics, Perturbation spheres, liquid, 541
spherical particles, 534, 536, 546, 601 superpositions of effects, 534, 538
superpositions of motions, 538 surface tension, 542
t e m p e r a t u r e coefficient, 609 velocity p o t e n t i a l , 548, 549 (24) Colonetti theorem, 149
Comings, viscosity-pressure correlation, 261
Complex modulus (see also Modulus, complex, d y n a m i c ) , 210, 400
Complexity, B r i d g m a n ' s , 269 Compliance, see Elastic compliance Compression, 388, 405, 413 (74) Compression shear a p p a r a t u s , 304 Compressional waves, 684
Concentration, effects, see Solutions Concentric cylinder a p p a r a t u s , see Cou-
e t t e , Flow, r o t a t i o n a l , Viscosimeters Concrete, 10,11
macrorheology, 11
volume changes, stressless, 10 Condensed milks, 52
Cone and plate viscosimeter, see Visco- simeters
Cones, for end correction, 670
Configurations, see also Macromolecules, Relaxation mechanisms, Solvent changes, 411, 425, 632, 687
distribution function, 497 free volume, 480
frozen in glasses, 482 intrinsic, 591 j u m p frequency, 480
liquid s t r u c t u r e , 323, 332, 338 molecular, 424, 480, 555
molecular distribution, 425 (128) nearest neighbors, 472, 480, 595 polymer, 426, 433, 554
probability density, 503 r a n d o m , 433
space of chain molecules, 500 visco-elastic mechanisms, 411, 412 Conservative system, 28, 64, 352 Consistency (flow) curve (see also R h e o -
logical e q u a t i o n s ) , 34, 58 Consistency variables, 34, 45
C o n t i n u i t y e q u a t i o n s , 18, 497, 504, 529, 657
Copper
alloys, critical shear-stress, 229 bulk modulus, 208
compression-shear, 307, 308F.
c o n s t a n t s , 220
decrement-dislocation, 220 in d u r a l u m i n , 226
-gold, disordered, 136 -gold, moduli decrease, 126 -gold, ordered, 136 internal friction, 215 irradiation effects, 135 plastic torsion, 41 p l a s t i c i t y , 309 pure crystalline, 231 rigidity modulus, 208 wire deformation, 137 x-ray detection in alloys, 227
Young's modulus, i n t e r n a l friction, 217 Corners
loading functions, 116 tests for, 116
Correspondance, electrical-mechanical, 398
C o t t o n yellow birefringence, 617F.
extinction angle, 617F.
Cottrell
-Bilby mechanism, 175 dislocation energy, 133
-Jaswon distribution theory, 224 locking, 134
t h e o r y of precipitation hardening, 229 theory of yield point, 133, 221 C o u e t t e (see also Viscosimeters)
birefringence a p p a r a t u s , 59, 620F.
oscillating, 679
r o t a t i o n a l viscosity, a p p a r a t u s , 34, 541 velocity field, 619 (8), 666
volume plasticity, 59
Couette flow (see also F l o w ) , 539, 541, 574, 576, 619
collision effect, 583
components, stress strain r a t e , 667 non-Newtonian, 668, 670
t e m p e r a t u r e effects, 621
velocity of r o t a t i o n (rolling), 583 Coupling constant, chain entanglement,
443, 445, 473, 476F.
Covalent bonds labile, 410
polymer configurations, 410, 554 vulcanization, 424
Crack formation on grain boundaries, 236
Cragoe
pressure coefficient, 284 viscosity function, 284 (16) Creep
Andrade type, 233
anelastic, internal frictional, see pri- mary, Friction, internal
definition of, types, 4, 231 and diffusion, 136
dislocation dependent, 231 exhaustion, 225, 226 experiments, 118, 394 fracture preceding, 231 instantaneous, 231 of glasses, 50
at grain boundaries, activation energy, 211, 213, 214 (14)
logarithmic, 231 (27), 232 long-time, 234
micro, 222, 225
near melting point, 137 plastic, 221, 224, 231, 234
primary, viscoelastic (see also Fric- tion, internal, Voigt body), 47, 209
(5), 210 (10), 214, 390 (6) rate, 232 (28), 234, 235 (38)
rate of limestone under pressure, 310 recovery, elastic after-effect, 47, 61,
391
recovery, rate of, 235, 438
secondary plastico-viscous, plastic (see also Four-parameter model, Max- well body), 50, 137, 138(16), 221, 224, 231, 234, 396(20), 438
steady state, 231, 233, 235(38)
steady state, work-hardening, Orowan, 234
strain relaxation, 213 strains, 233
temperature, 137, 213 tensile viscometry, 434, 438 test, viscoelasticity, 393 and thermal vibrations, 232 time dependence, 231, 391 transient, 231 (26), (27), 233
viscous, high temperature, 137,138 (16) Creep function, 394 (15), 400, 401, 402F.,
416
and relaxation function, 395 tensile, 416, 438
Cross-linking, see Macromolecules, Poly- mers
Crowding factor, 597 Crystal, crystallinity
biaxial, in flow birefringence, 616 cell sizes, 206
dislocation theory of hardening, 227 displacement, 221
elastic deformation, 7, 206
energy density when stressed, 207 excitons, 122
growth on stretching, 649, 650 holes, 122
imperfections, 3,122 lattices, see Lattices
liquid, Maxwell constant, 623 liquid, and order, 684 personality, 192 phonons, 122
structure sensitive properties, 192 thermal vibrations, 122
Cubic body-centered lattice basic vectors, 172
diagonal plane, 172F., 173F.
glide direction, 172
glissile imperfect dislocation, 174 metals, 172
perfect unit dislocation, 172 sessile imperfect dislocation, 174 stacking fault, 174
stacking order, 173 unit cell, 172
Cubic face-centered lattice basic vectors, 163 close-packed, metals, 163 dislocation, perfect unit, 163 stacking order, 164
transformation, 179 twinning, 170 Cubic lattice, 155, 157
mean shift, 162
migration, simple (edge type), 157, 158F.
migration, simple (screw type), 158, 159F.
model for dislocation theory, 152 strain-energy, 156
Cubical dilatation, 23, 38, 57, 59 as invariant, 23, 57
relaxation time, 60 retardation time, 60
Curran, adsorption-magnetic fields, 696 Current density (diffusion), 497 (4), 502,
504
convective, 497 diffusive, 497 Cutting process, 81, 88 Cylinders, thick-walled, 292
anisotropy, 312 collapse pressure, 309
concentric, see Couette, Viscometers deformation, 308, 311
dilation of, 256, 296F.
hysteresis effects, 311 Luder's lines, 298
pressure-stress at yield, 299, 302 rupture under pressure, 296, 303 strain hardening, 308
strain softening, 308 Cylinders, thin-walled
combined stresses, 99F.
flow and work-hardening, 92
Osgood shear-stress variable, 107F., 116
plastic deformation, 101 radial loading, 101 size (grain) effect, 102 strain, loading, 117
stress-increment loading paths, 116F.
for testing, 100
Cylindrical coordinates, 19 D
Damping, see also Attenuation, Friction, internal, Hysteresis
dislocations, 208, 215, 216, 219 (16) macroscopic, 47, 59, 422
Darcy's law, 560 (40)
Dashpot, see Mechanical models Debye
-Brinkman-Bueche theory, 561 dipoles, 535
vibrational frequency, 275 (10) Debye-Bueche treatment, hydrodynamic
effects, 566
Decamethylene adipate, see also Poly- ester
chain length-viscosity, 446T.
solutions, 463F., 465F.
viscosity, 442F., 444F., 450F., 465F.
viscosity relationships, 456T., 458T.
viscosity temperature parameters, 451
Decamethylene sebacate, see also Poly- ester
chain length-viscosity, 446T.
solutions, 463F., 465F.
viscosity, 442F., 444F., 450F., 465F.
viscosity relationships, 456T., 458T.
Decamethylene succinate, see also Poly- ester
chain length-viscosity, 446T.
viscosity relationships, 456T., 458T.
viscosity temperature parameters, 451 Decamethylene sebacate, see also Poly-
ester
chain length-viscosity, 446T.
viscosity relationships, 456T., 458T.
Decamethylene succinate, see also Poly- ester
chain length viscosity, 446T.
viscosity relationships, 456T., 458T.
n-Decane viscosity, 335
viscosity in corresponding states, 270, 271F.
viscosity at high pressures, 268 Decrement, see Attenuation, Damping Deffet, piezometer, 256
Deflection of a beam, 31, 418
Deformations, see also Displacement, Strain
Almansi measure, 37 (110) annular, 378
bending, 30 bulge test, 88
Cauchy measure, 21 (36), 35, 36 (95) conservative and dissipative systems,
64
cubical dilatation, 23 (44), 42, 60, 389 cutting, 81F.
definition, deformation as result of relative displacement, 1, 18, 19, 20, 23, 36, 389
definition (Reiner) as non-recoverable deformation, 10
definition, as relative displacement in progress, 1, 10, 18
deflection, 31 (69)
deviatoric, distortion, 23 (45), 26, 389 (3)
and dislocations, 184 ductility, 97
effect on density, 103
elastic, crystal, 206
elastic sphere macromolecule, 635 equilibrium, 423
extrusion, 82, 83F.
finite, 22, 64, 356
fractional elongation second-order theory, 383
Frenkel-Kontorova theory, 314 grain boundary, 205
Green, 37 (99)
Helmholtz, free energy of, 359 history, 99, 105, 394
homogeneous, 1, 35, 355 Hooke's law, 28, 674
infinitesimal, 18, 22, 26, 57, 64 inhomogeneous, 374
internal (dislocation), 144
irrecoverable, permanent, see also Creep, Flow, 10, 64, 411, 433
irrotational, 417 (95) isothermal, 105
of isotropic material, 353, 359 logarithmic (natural, Henky) measure,
22,26
Mohr's circle, 24F., 25, 106F.
plastic, 64, 81, 101, 108F., 11
plastic, conservative and non-con- servative migration, 149, 150 plastic, contrast to granular materials,
103
plastic, effect on density, 103 plastic, external agency, 112 plastic, of metals, 201
plastic, as succession of shear strains, 103
polymers, 410, 424, 433, 643 principal extensions, 25, 361 prism, 14, 22
pure homogeneous, 355, 365 recoverable, strain, 10, 28 semihomogeneous, 35 shape elasticity, 674 small elastic-plastic, 65 solenoidal, 418 (97)
steel cylinders, see Cylinders stress birefringence, 643 stressless (final), 10 Swainger, 35 (89), 37 (98) surface tractions, 365 tensile plastic, 109, 110F.
tension, 28, 80, 81F.
tensor, 22 (41), 356
theory of elastic, 10, 184, 351 twinning, 312
viscoelastic beam, 415 (80) viscoelastic body, 413 (78) visco-plastic, 93
wedge indentation, 85, 86F.
Degassing temperature, of polymers, 439 Degrees of freedom, internal, molecular (see also Configurations), 7, 426, 497, 500, 508, 520
Degrees of freedom and reaction rate, 328,335, 336, 340, 478, 609
Density
compression, effect of, 11
constancy (see also Incompressibility), 529
defined, 13 force, 560
sound velocity, 685
Density constants, Dow and Fink's equation, 281
Depolarization, 627
Detergent, flow birefringence, 625 Detonation (propellants) pressure, 249,
312
Deutero compounds, 339T.
Deviator, see Tensors Diabase, plasticity, 309
Diamond, lattice imperfections, 177 Dielectric
complex, 521 (55)
constant, polymer solution, 521 (54), 522
loss, 520 polarization, 521
Diethylene adipate, see also Polyester chain length-viscosity, 446T.
viscosity relationships, 456T., 458T.
viscosity temperature parameters, 451 Diffusion constant, see Diffusion, coeffi-
cients
Diffusion, rotational
distribution function, 513, 514, 517 Fick's law, 550
tensor, rotatory, 505, 507 (30), 510 torques, 513, 517, 568
Diffusion, rotational coefficient
gradient interaction, Peterlin and Stuart, 6, 508, 550, 616, 626, 633 reciprocal, as relaxation time, 513, 605,
623
rod-like molecules, 506 (27)
r o t a t o r y , long macromolecules, 507, 508
tensor, 507
and viscosity, 516, 535, 550, 552, 604 Diffusion, t r a n s l a t i o n a l and general, see
also Brownian motion, Self-diffusion.
argon (thermal), 267
center of macromolecular mass, 504 dislocation, 205
distribution function, 496, 509 Fick's law, 225 (22)
fluctuating force, random force, 496, 511, 548
general equation, 503 (16) gradient, 518
grain b o u n d a r y , variation, 205 probability density function, 508, 548 self, and viscosity, 6, 331
solute a t o m s , 225 Stokes resistance, 331 tensor, 497, 506
theory, molecular, and viscosity, 330, 336, 345
vacancies, 138 (16)
volume, grain b o u n d a r i e s , 214 Diffusion, t r a n s l a t i o n a l coefficient, 562,
570
carbon in alpha-iron, 1 8 of chain ends, 633 (30)
coiled molecules, 475, 506 (26), 507 (28) cylinder, 508
Einstein-Smoluchowski, 225 (21), 331 (31), 530
enhanced b y stress, 3, 138 (17) Frenkel, 332 (35)
of rod-like molecules, 506 D i l a t a n c y , 42, 52
D i l a t a t i o n , volume (see also Cubical d i l a t a t i o n ) , 2 3 , 4 2 , 6 0
plastic flow, 44
D i l a t a t i o n a l (deformation) flow com- p o n e n t s , 538, 540, 572, 575
D i l a t o m e t e r , Bridgman, 256
D i m e r particles, pairs, intrinsic viscos- i t y , 585, 590
r a t e of formation, 570
D i m e t h y l siloxane polymer, pressure vis- cosity, 290
Dipoles, dipolar Brownian motion, 520 effects on viscosity, 342 h y d r o d y n a m i c , 544
i n t e r a c t i o n , 230, 410 i n t e r a c t i o n and flow, 340
liquids, energy of vaporization, 343T.
liquids, viscosity, 340 macromolecular, 521
Dislocations, see also Forces, dislocations admissible and inadmissible, 155 anchoring b y foreign a t o m s , 160, 179 arrays of, between mosaic crystals, 143 arrested, 190
back stress, 240 (46) Burgers, 150 Burgers vector, 146 calcite, 182
characteristic vector, 145, 146, 152 climb, 151, 186
closed, 158 closing fault, 151 complete, 146
c o n s t a n t velocity, 225 (23) critical velocity, 225 crystal h a r d e n i n g , 227
decomposition i n t o edge and screw, 167 decrement of v i b r a t i o n s , 219
definition, 144 diffusion in zinc, 215 diffusion velocity, 225 (23) dissociation, 156, 170 (3), (4), 177 distribution of lengths, 219 drift velocity, 225 (21) driving stress, 237, 238 (41) edge, 143, 150, 153, 237 elastic t h e o r y , 184 extended, 170 force on, 218
geometry of, and plastic flow, 221 glissile, 167, 171, 179, 180
glissile, migration of, 175 half, 170, 177
hardening of crystals b y locking, 230 hollow, 147
homogeneous shear, 163 imperfect, 147
i m p u r i t y - a n c h o r e d , 223, 237 interaction in b o u n d a r i e s , 205
i n t e r a c t i o n with imperfections, 126,132 lattice t h e o r y , 142
lattice vector, 151 loop, 131,132, 224, 230 mean shift, 162
migrations, motion, 136, 148, 166, 224, 230F.
migration t h r o u g h obstacles, 230F.
negative, 153 number density, 215
octahedral plane, cut in, 157, 164, 240 oscillating, 218
perfect (complete), 146, 156, 167F., 170 (3)
perfect screw, in hexagonal l a t t i c e , 129 pole, 160
positive, 153
radius of c u r v a t u r e , 130 (6), 228 release of, 232
release energy, yield, 224 ribbon, 171
Shockley ( p a r t i a l ) , 169, 179 screw, Burgers, 132, 133, 150, 155 self energy, 218
sessile, 149, 160, 238, 239, 240 sessile imperfect, 167F., 174 simple p r i s m a t i c , 239 slow moving, 224 spiral, 161F.
spiral p r i s m a t i c , 239 soap bubble analogy, 229 sodium chloride, 181, 182F., 183F.
s t r e n g t h of, 226
stresses, i n t e r n a l , 215, 239 super, 239
sweeping, 160
sweeping, ascent of, 163, 171 sweeping, r o t a t i o n of, 163 T a y l o r (edge), 143, 150 t h e o r y , 142
t h e o r y , grain boundaries, 203, 205 t h e o r y , of m e t a l deformations, 201 t r a p p i n g of, 232
u n i t , 146, 152
universality in n a t u r a l crystals, 192 vortex, analogy t o , 145
work, 149
yield stress, 131 (9), 133, 223 (20) in zinc crystal, 215
Dislocation lines, 130, 145 a r b i t r a r y , 165
ascent, descent, 163
closed circuits around, 151, 158, 159F., 168
crossing, 191, 192F.
kinks, 187
migration, 148, 224, 230F.
migration, conservative, 148, 149, 154F., 158
migration, non-conservative, 148, 149 migration by shifting, 148
migration, simple (edge t y p e ) , 157, 158F.
migration, simple (screw t y p e ) , 158, 159F.
m u l t i p l y connected, 151 nodes, 145, 151, 162, 179 pole, 160, 161
p r e c i p i t a t e d regions, 228 projection of, 149 reflection of, 160 segment, anchored, 160 segment, annihilation, 161 segment, appearance, 160 segment, r o t a t i o n of, 160 segments, 148, 157 in solid solution, 230F.
spiral, 161F.
sweeping, 160, 162
t e m p e r a t u r e , effect of, 195 tension, 187 (7)
yield stress, 131
Displacement (see also Deformation, S t r a i n ) , 1, 18,389
antisymmetrical tensor, 19 atomic, 196
characteristic vector, 162
components of, 19, 20, 21, 354, 356, 391 in crystals, 221
dislocation line, 157, 159F.
fluid, transverse waves, 21, 686 (3) gradients, 21, 24, 361, 368, 369 gradient tensor, 19
grain b o u n d a r y , 204F., 213 (11) infinitesimal, 42
i r r o t a t i o n a l , 417 (95).
normal and t a n g e n t i a l , 155 principal directions, 24, 355
principal extension ratios, 355, 361 sinusoidal, 4, 420, 702
solenoidal, 418 (97) surface, 414
symmetrical tensor, 19, 20 tensor, 389, 391
vectors, 18, 417 Dissipative system, 2, 64
Dissipation, see E n e r g y dissipation Dissipation function, 72, 75
D i s t o r t i o n , deviatoric p a r t of s t r a i n t e n - sor, deformation, see D e f o r m a t i o n , Strain
D i s t r i b u t i o n , distribution function angular, 552, 626 (17), 633 angular density, 617
Brownian motion, general, 498 Cottrell-Jaswon, 224
critical stresses, 4, 229 crystallites, 651
diameters, suspended spheres, 597 diffusion coefficients, 507
effect of dipoles, 340
end-to-end distances, see random-flight energy, 509, 513, 514 (45), 515, 517 flow velocities, 571, 621F., 663, 666-669 fluctuations, 479
Gaussian, 433, 507, 523, 555, 556, 562, 619F.
gradient, 621F.
lengths of dislocations, 219 Maxwellian, of dislocations, 224 molecular configurations, 411, 423, 425
(128), 433, 497
molecular configurations, change in tension, 426
molecular, deformation b y gradient, 323
molecular weight, 442, 457, 566, 619 radial, liquids, 322, 326, 333, 341, 480,
573
radial molecular, p e r t u r b a t i o n by velocity gradient, 323,341,469 radial, suspensions, 548, 601 random-flight, 425, 554 (30), 555, 632 relaxation or r e t a r d a t i o n times, 393,
397, 410, 490, 520, 693
r o t a t i n g anisotropic particles, orienta- tion, 552, 619
segment, see Molecular, Configurations segmental j u m p , 479 (19)
Disulfide links, scission-crosslinking, 410 D o m a i n , 5, 8
Doolittle, free volume viscosity, 483 D o u b l e t s , s e e D i m e r particles Dow
p a r a t o n e and n a p h t h e n i c oil, viscosity 290
viscometer, 250
D r o p s , suspended, in gradients, 635 D u c t i l i t y , 97
curves, 305 of steel, 306
D u m b b e l l model (see also Particles), 547, 577F., 578F.
D u r a l u m i n , hardening, 227
solid solution, s t u d y of, 226
D y n a m i c , complex modulus, see Mod- u l u s , complex, dynamic
D y n a m i c equations (viscoelastic) from corresponding elastic, 418
D y n a m i c gauges, 249
D y n a m i c loss, impedance, 400 E
E a r t h , 10 crust, 51 Jeffreys body, 50 plastic deformation, 103
volume change, stressless, 10, 103 Edsall
birefringence a p p a r a t u s , 620F.
orientation function, 629F.
Egly, viscosity-pressure correlation, 261 Einstein
Brownian motion, 225 (21) diffusion coefficient, 331 (31), 530 dilute suspensions, 529, 530, 534, 542 h y d r o d y n a m i c interaction (perturba-
t i o n ) , 538, 543, 571
hydrodynamical function factor, 561 relative viscosity, 541 (14), 558 (39),
574, 598 (88)
E l a s t i c , also see E l a s t i c i t y balance, equilibrium, 2 b i t u m e n , 32, 50
bodies, see Rheological models completely, solid, 1
fore-effect, 47
limit, 56, 99F., 223, 306
liquid, see E l a s t i c i t y , in liquids macro and micro stress-strain, 207 memory, function of history, super-
position (see B o l t z m a n n ) , 395, 416 second-order effects (cross, lengthen-
ing, s h o r t e n i n g ) , see E l a s t i c i t y t h e o r y
E l a s t i c compliance, reciprocal modulus i n s t a n t a n e o u s , 392, 411
r e t a r d e d , 411, 412
Elastic moduli, constants (see Modulus), 28, 32, 36, 43, 207, 389, 413, 419, 685 complex, d y n a m i c , see Modulus cross, 41
c r y s t a l , 124
i m p u r i t i e s , effect, 124
Lamers, 36
Maxwell element, 48, 410 operators replacing, 413 overall, 43
and relaxation time, 397
relaxed (static), 2, 48, 210, 699, 702 rubber, 427
sound velocity, 417 (96), 684, 685 variation with temperature, single and
poly crystalline, 212F.
Elastic sphere
intrinsic orientation constant, 635 (33) Maxwell constant, 635 (35)
model for elastico-viscous liquid, 675 model for macromolecule, 519 Elasticity, general and theory, 26, 36, 46,
124, 144, 184, 207, 352, 362, 370, 389, 423, 643, 672, 674, 684
anisotropic material, 206, 360, 363 blown bitumen, 32
boundary conditions, 370
configurational, 426, 604, 605, 633, 687 convex loading, 112
cross (modulus), 41
delayed (retarded) (see also Vorgt body), 47, 411
dislocations, 132, 184
dynamic, see Four-parameter model, Maxwell body, Voigt body
energy, work, 28, 64, 186, 207, 358, 674 of a gas, 28
Hooke's law, 2, 28 (56), 36, 699 Hooke solid, ideal, 2, 29, 61 imperfections, 125
instantaneous, see static
isotropic (ideal) material, 353, 388 kinetic (see also Rubber elasticity), 28 in liquids, 48, 410, 433, 571, 671, 674,
675, 677, 687
lengthening (see also Poynting), 379 macromolecules, see Macromolecules,
Rubber elasticity open spring, 32
in oscillation, 210, 400, 413, 678 (52) potential, 28
rubber, see Rubber elasticity second-order, 36, 41, 363, 380, 382, 383 shear, see Modulus rigidity
shortening, 41
static, 29, 48, 210, 352, 364, 392, 413, 685 in steady state flow experiments, 677 strain-energy, 675
temperature dependence, 28, 212 vibrating reed, 418T.
waves, longitudinal, 672 waves, transverse, 672
Elastico-viscous liquids, see also Elas- ticity, Maxwell body, Non-Newton- ian liquids
defined, 348 (129), 396, 675 (48) dielectric behavior, 520
dynamic behavior, see Maxwell body emulsion, 675
flow, 48, 433, 488, 674 (47)
flow between coaxial cylinders, 677 four-parameter model, 408
oscillatory flow, 510, 678, 680F., 681F.
rate-of-shear, 674 relaxation time, 520, 675 rigidity modulus, 674, 687 shear-stress, 674
strength, 56 suspension, 510, 674
Weissenberg effect, 52, 671, 677 yield value, obscure, 674 Elastoplastic state, 44F., 65, 291 Electrical-mechanical analogy, visco-
elasticity, 398T.
dynamic loss, 400 dynamic modulus, 400 Fourier components, 399 (33) frequency, 399
impedance, 399 sinusoidal loading, 399 Voigt element, 399 (32) Electroviscous effect, 568, 631
Ellipsoid, ellipoids, see also Particle shapes, Macromolecules
dielectric relaxation, 521 monodisperse system, 619F.
motion through fluid, 497 optical anisotropy, 627, 628F.
rotation, nonuniform hydrodynamic, 550, 625
rotational, depolarization factors, 627F.
viscosity, suspensions, 515, 551 (27), 552 (28), 582 (70)
Ellipsoid, reciprocal strain, 357 Elongation, see Extension
Energy, see also Configurations, Degrees of Freedom
activation, see Activation energy
balance, elastic-potential, conserved, 2, 28, 64, 124, 352, 699
change (free), segmental j u m p , 479 (13c)
t o deform molecules, 340 density in crystals, 207
dislocation i n t e r a c t i o n , 133 (15) dissipation, see E n e r g y dissipation elastic p o t e n t i a l , 124
elastic strain-, 186, 359, 672 free, see Free energy grain boundaries, 197, 198(8) i n t e r n a l , polymer, 426
kinetic (see also K i n e t i c energy), 583 p o t e n t i a l , see P o t e n t i a l energy p o t e n t i a l , of an alloy, 125 (1) s t r a i n , in cubic l a t t i c e , 156 stored, 2, 699
stresswork, 53 (134), 368, 544, 657, 699 surface, grain orientation, 203F.
surface, new, in imperfections, 148 vaporization, 343T.
work-hardening (see also Work-hard- ening), 111
Energy dissipation (see also D a m p i n g , D y n a m i c loss),2, 54, 511, 532, 544, 657 contribution by suspended particles,
512, 531, 539, 545, 552, 559, 572, 576, 580
diffusion, r o t a t i o n a l , 552 fictitious r a t e of, 73 local, 72, 73
principle of maximum, 72F., 73, 75 segmental, 559
simple shear, 539 (11), 699 of stress, see Energy stresswork t o t a l , 73
v i b r a t i o n a l , 5, 47, 215, 400, 701 Enskog
-Chapman t h e o r y , 267 molecular diameter, 264
T h o r n e , extension of theory, 527 viscosity m i n i m u m , 264(2) E n t a n g l e m e n t , see Macromolecules E n t h a l p y
configurational, 424 flow of polymers, 609 E n t r o p y , 424
activation of flow, 470
change, molecular distribution, 426 (131)
molar, of dilution, 556 order-disorder, 123 rubber elasticity, 424
rate of increase in plastic processes, 318
segmental j u m p , 478
E q u a t i o n s of motion (see also Navier- Stokes), 496 (1), 529, 560, 655 elastic bodies, 370, 418
oscillating dislocations, 219 (15) viscoelastic bodies, 417, 418 Equicohesive t e m p e r a t u r e , 235 Equilibrium, elastic, 2, 12, 47
E t h a n e , viscosity under pressure, 261F.
E t h y l alcohol, see also Alcohols solidifying pressure, 247 viscosity at high pressures, 268 -water, sound velocity, 683 E t h y l e n e
Enskog minimum, 263
viscosity, under pressure, 252, 257, 258, 261F.
viscosity measurements, 252
E t h y l e n e glycol, solidifying pressure, 247 E u l e r ' s angles, 66, 500
Extension, elongation, 21, 28, 38, 40, 361, 371, 382 (65), 426, 427, 632
factor, see Flory
Extinction angle, see also Birefringence, streaming
colloidal systems, 624 concentration influence, 639F.
of cotton yellow, 617F.
function of gradient, 616
monodisperse system, ellipsoids, 619F.
necklace model, 633 (29) non-vanishing, 618 orientation function, 629F.
polydisperse systems, Gaussian, 619F.
rod-like particles, 619 Extrusion, lubricated sheet, 82 Extrusion pressure, 85
E y r i n g
flow t h e o r y , 466, 470, 477
non-Newtonian flow t h e o r y , 488, 489 viscous flow, energy, 470, 487
F
Failure (see also F r a c t u r e , Yielding), 55, 56, 303
Faults, closing, in lattice, 151, 152 Felsing, viscometer, 252
Fibrinogen, 625
Fick's law, see also Diffusion, 225 (22), 550
Fink, density conversion, 281 (12) Flexibility, flexible, see Configurations,
Macromolecule Flory
chain length-viscosity, 446T.
critical miscibility temperature, 556, 591
effect of branching, viscosity, 459 extension factor, 556 (34), 565 (47),
587, 591 free volume, 480
intrinsic viscosity, 565 (47) Flory-Huggins theory, 556
Flow, fluid, viscous, see also Flow, plas- tic, plane, Hydrodynamics absolute reaction rates theory, 327 against centrifugal forces and gravity,
42
around macromolecules, suspended particles, see Hydrodynamics, Macro- molecule
birefringence, see Birefringence, streaming
birefringence apparatus, 619
capillary (see also Flow, Poiseuille), 33, 435, 539, 573, 661F., 663
Clausius range, 529
coaxial cylinder, longitudinal, tele- scopic, 435
coaxial cylinder, rotational, see rota- tional, Couette flow
collisions, molecular, 468, 527 collisions, particles, 570, 582, 585 components, superposition, 538 cooperative, 478
creep (see also Creep), 47, 50, 63 Couette, see also Couette flow, rota-
tional
definition, 10, 64
dilatational, inertia terms, 579 dilatational, principal components in
suspensions, 572
dilatational, unperturbed, 539 (11), 571 (52)
discontinuous shear-, 79 Einstein, 529, 537, 543, 571
elastico-viscous liquids, see Elastico- viscous liquids
energy of activation, see Activation energy
energy dissipation, see Energy dissipa- tion
field, 76
gases, in, 467, 527, 529 hole theory of, 345, 469
hydrodynamic, ultrasonic radiation, 691
instantaneous configuration, relation to, 526
kinetic contribution, 526
laminar (telescopic, rotational), 33, 34, 549, 615(1), 617, 625
longitudinal, 21, 33, 435, 438
mechanism, molecular theory, 6, 71, 323, 327, 467, 472, 527
momentum transfer, 468, 527 by motion of chain ends, 336
Newtonian, 27, 32, 35, 43, 53, 55, 58, 63,93,601,653,660
non-Newtonian (see also Non-Newton- ian liquids), 57,489,515,601,653,656, 659, 660, 664
oscillatory, 679
perturbation, see Einstein, Oseen, and Stokes
porous beds, through, 560
plane (see also Flow, plane plastic), 616
plastic, see Flow, plastic
Poiseuille (see also Flow, capillary), 34,251,549,663
rate of, volume (capillary), 34, 663 rectilinear, 657, 660
rotational, coaxial, Couette, 34, 42, 435, 538, 574, 616, 666
shape elasticity, 674
superposition, three flow components, 538
superposition, unperturbed and par- ticle Derturbed, 540, 577
tensor, 20, 21F., 656, 662, 667, 673 transient, 234
turbulent, 606, 607, 620 two-dimensional, 657 unaccelerated, 663
velocity contours, capillary, 661F.
velocity p o t e n t i a l , i r r o t a t i o n a l s t e a d y , 548
viscous (nonrecoverable), 10, 32, 64, 411,432,434,525,659
volume, stressless, 10 wall effect, 659, 661F., 662
Flow, plastic, 3, 4, 44, 64, 81, 82, 83F., 240, 659, 669
anelastic (see also Anelasticity), 127, 209
in aluminum, 238
Bauschinger effect, see Work h a r d e n - ing
Bingham plastico-viscous, visco-plas- tic (see also Bingham solid), 4, 44, 94, 96, 659, 669
Capillary, 45 (117), 665 (27)
condition, yield condition, 43, 55, 59, 67, 68, 72, 76, 77, 88, 104, 105, 292, 293, 297, 299, 665, 669
Couette p a t t e r n , 669
creep (see also Creep), 47,136, 213, 231 criterion, maximum shearing-stress,
293
definition, limitations, 10, 44, 64, 98, 115,129,221,231,291
elastic region, 56, 65, 99F., 223, 659, 669 energy dissipation (see also E n e r g y
dissipation), 4, 64, 67(6), (7), 72 equilibrium, 77
fully, 291, 303
high pressure, 307, 308
high pressure, effect of speed, 308 incremental, 110, 114, 117, 294 initiation under pressure, 304 as in viscid, 64
limited in fracture, 314
mechanism, 3, 71, 93,129,137, 221, 231 melting, local, 317
non-Bingham, 659 p a r t i a l l y , 291
perfectly plastic, ideal, 65, 66, 68, 71, 75, 114
polymers, 412 pseudosteady, 85, 87
rule, 67, 70, 72 (14), 73, 77, 105 rule and energy dissipation, 73 rule, Levy and von Mises, 71, 72 s t e a d y , 85, 662
strain r a t e , 66 (1), 77 (21), 85 as s t r e n g t h limit, 54
streamlines, in extrusion, 85 stresses, 66
visco-, 44, 95, 96, 658, 665 wall effect, 660, 665 wedge i n d e n t a t i o n , 85 Flow, plane plastic, 78, 80, 91
cartesian coordinates, 77 polar coordinates, 78
velocity field, discontinuous, 79 velocity field in extrusion, 82 velocity profile, 79F.
Flow, of polymer, see also Macromole- cules
amorphous linear polymer, 432, 443 p r i m a r y process, 440, 447, 466, 469, 477 short chains, 444, 457, 458T.
Flow stress, maximum, 305, 306 Flow, viscous (see also Flow, fluid, Vis-
cosity), 1 0 , 3 2 , 6 4 , 3 2 3 , 5 2 7 Flowers, viscometer, 250 F l u c t u a t i o n , 224, 479, 496, 548 F l u i d i t y , 3, 32, 658
a p p a r e n t , 665 (28) birefringence, 617
relative, of suspended spheres, 574 F o k k e r - P l a n c k e q u a t i o n , 535, 555, 557 Forces, see also E l a s t i c i t y , Flow, H y d r o -
dynamics, I n t e r a t o m i c , P o t e n t i a l energy, Stress
atomic, 154, 185, 323 (4) a z i m u t h a l , 375
balancing couples, 1 b o d y , 1 4 , 370
Brownian, see Diffusion, F l u c t u a t i o n s compression, shear, 373 (40)
d'Alembert, see I n e r t i a e n t r o p y change, 426 (132) frictional, 44, 114 in glide planes, 188
h y d r o d y n a m i c , 499 (8), 511(39), 512(8) h y d r o d y n a m i c , exchange, 538, 569 h y d r o d y n a m i c , frictional, 473, 499 (6),
547, 560, 580 (66)
h y d r o d y n a m i c , long-range, 569, 570, 573
h y d r o d y n a m i c , short-range (aggrega- tion effects), 582
intermolecular, molecular, 6, 324, 337, 468, 496, 508
normal (see Stress, n o r m a l ) , 29, 364 plastic slip, 188
shear (see also Shear stress), 1, 29, 31 surface, 14, 365, 370 (33), 414
tangential, 364
tension in dislocations, 187 (7) torsion, simple, 30, 375 and traction, 13 (5), (6) as vector, 12
Forces, dislocations, see also Stresses annealing, 196
binding, 223 (19) climb, 189
curved (kinks), 189 dynamic effects, 223 Frank-Read mechanism, 190 image, 189
migration resistance, 187, 223 non-parallel, 190
parallel edge, slip, 189,190F.
parallel screw, 190
shear-stress, law of constant, 188 stable equilibrium, 189, 193
tension along dislocation line, 187 (7) yielding, and binding, 223 (20) Four-parameter model (see also Rheo-
logical models), 209 (5), 408F., 411 Fourier transforms, impedance, 399 (34),
404
Fracture, failure brittle, 7, 54, 314 classification, 313
cleavage type velocity of, 314 conditions for, 55, 312 crystallography of, 221 cup and cone, 56 distribution, 313 effects of pressure, 310 incipient, as shear failure, 314 intergranular, 235, 236 and latent heat, 317 natural strain at, 310 plasticity, relation to, 312 pressure effect, 103, 303, 317 propagation, velocity, 314 rupture, 7, 314
strain energy and latent heat, 317 transgranular, 235
Frank
imperfect and sessile dislocation, 167F.
partial dislocation, 168 Frank-Read
back stress, 240 (46)
generating stress, 239, 240 generator, 239
mechanism, 159, 182, 183F., 238 source, 160,161,232,233,238,239 Free energy
activation, 329, 470 configurational, 508 deformational, 425, 427, 525 mixing, 346
segmental jump, 479 (13c) Free volume
temperature dependence of segment jumps, 448
and viscosity, 332, 447, 469, 481, 482, 483, 596
Frenkel
defects (interstitial atoms), 123 deformation, theory of, 315 diffusion, 331 (30), 345 viscosity, 345 (49)
Frequency, see also Jump frequency acoustic, 686, 691
characteristic natural, 434, 489, 520 equivalence with rate of shear, 492 molecular, fundamental, 328, 470 molecular, in shear, 489, 515, 605 sinusoidal (viscoelastic dependence
on), 4, 399, 420,489 spectrum, 519 thermal vibration, 232 vibrations, 419, 420 Friction
anelastic, see Friction, internal cavitation, 690
fluid, Newton's law (see also Flow), 32, 546, 549, 655
in cold work, internal, hysteresis, 209 plastic, see Flow, plastic
and plasticity, difference, 115, 116F.
St.Venant,44 Friction, hydrodynamic
constant (coefficient), 325, 496, 498, 499 (6), 503, 513, 527, 558, 561, 564 596, 632, 655
of effective group, 473, 513, 632 forces, 496, 560, 580 (66) forces, by chain on fluid, 499 (8) segmental sliding, 474
suspensions, 544, 547 tensor, 503, 504 (17)
Friction, internal, see also D a m p i n g , Vis- coelasticity, Voigt model
anelasticity, as, 128, 208
forces from e n t a n g l e m e n t , 473, 474 i n t e r n a l (see also Viscosity), 128 (4),
208, 210 (10), 213, 215, 392, 498, 657 (8), 700
i n t e r n a l , a m p l i t u d e dependence, 215 i n t e r n a l , crystals, 215
i n t e r n a l , of m e t a l single crystals, 218 i n t e r n a l , peak b y i n t e r s t i t i a l s , 128 i n t e r n a l , polycrystalline and single
aluminum crystals, 212F.
i n t e r n a l , relaxation t i m e , 128, 210 plastic action, difference, 115,116F.
t e m p e r a t u r e dependence in a l u m i n u m , 211
Frictional resistance, 545, 654 Frictional t h e o r y , definition, 44, 115 F r i t z , viscometer, 250
G
G a d d , orientation function, 629F.
Gases, 257, 527 K n u d s o n range, 529
G a u s s ' t h e o r e m , 540, 541, 545, 572 Gaussian distribution, 433, 507, 523, 555,
556, 562, 619F., 645 distorted, 556
Gaussian d i s t r i b u t i o n , non-, birefrin- gence, 648
Gel sponges sol, t r a n s i t i o n , 47 suspended, 47,
Gelatin, stress-optical coefficient, 644T.
Germanium
c r y s t a l , diamond, 176
grain b o u n d a r y displacement, 197 Glass
glass forming liquids, 484 plasticity, 310
P o y n t i n g and Thomson body, 50 s t a t e , 3, 411
stress-optical coefficient, 644T.
Glass t e m p e r a t u r e , 452, 453T., 454 (9), 455T., 462, 481F.
Glide lamalla, 221
Glide planes, see also Slip planes law of c o n s t a n t shear stress, 188 Glucose, molecular radius, 530 Glycerine, solidifying pressure, 247
Gold
density, 11
wire deformation, 137 Gold-copper alloy
bulk modulus, 208 dislocations, 182 moduli decrease, 126 ordered, disordered, 136 rigidity modulus, 208
Goldstein, birefringence a p p a r a t u s , 620F.
Gonikberg, viscometer, 252 Goranson
deformation t h e o r y , 317 pressure chambers, 247 G r a d i e n t , see Shear r a t e Grain b o u n d a r y
activation energy, 204, 214 amorphous layer, 201 angle, large, 201 angle, small, 201
a r r a y of dislocations, 202, 204 cracks, 235, 236
creep, 205
critical shear stress, 204 diffusion, 205
dislocation collecting in channels, 205 dislocation i n t e r a c t i o n s , 205
dislocation t h e o r y , 202, 205 energy, dependence on angle, 203 i n t e r g r a n u l a r fracture, 235,236 lineage, 205
K i n g and Chalmers, 202 M o t t ' s island model, 203
m o v e m e n t , critical shear stress, 204 m o v e m e n t , r a t e of, 204
relaxation, 210 slip, 213
slip, activation energy, 214 slip, relaxation effect, 214 s t r e n g t h of, 235
s u b s t r u c t u r e , 205
t r a n s i t i o n lattice t h e o r y , 202 viscosity, activation energy, 214 viscous creep, 138
viscous n a t u r e , 211, 213, 235 viscous slip, a c t i v a t i o n energy, 214 viscous slip and diffusion, 214 zinc c r y s t a l , 204
Green, H . S.
radial distribution in a liquid, 322
t h e o r y , liquid flow, 45, 323, 344 viscosity, 323 (8), 324 (11) Green, J . W., pressure chambers, 247 Green measure (strain), 37, 39, 52 G R S , intrinsic viscosity and solvent, 569 Guinier, precipitation hardening t h e o r y ,
227 G u t h
molecular shape effects, 581 -Simha-Gold t h e o r y , 573 wall effect, C o u e t t e flow, 541
H
Hagen-Poiseuille e q u a t i o n , 34 (82) Halides, alkali
electrolytic c o n d u c t i v i t y , 123 p h t h a l i u m , dislocations, 181 radiation hardening, 135 silver, dislocations, 181 vacancies, 123
H a m i l t o n i a n coordinates, 548
Hardening, Hardness, see also Strain-, Work-hardening
annealing, 226 of crystals, 230 definitions, 7, 90 of duralumin, 227
external agency, 111, 112F.
homothetic work-, 91 i r r a d i a t i o n , 135 isotropic, 90 o r t h o t r o p i c , 90 parabolic law, 239 release, 232
short-range order, 136 of solid solutions, 222, 227 s t a t e of, 90
s t r a i n , see Strain-hardening stress, see Stress-hardening t h e o r y , T a y l o r , 237, 239 work, see Work-hardening
H e a t of activation, see Activation energy H e a t capacity, polymers, 479
H e a t of mixing, 610 Hencky
equations, 292 flow condition, 55, 59
measure, logarithmic, n a t u r a l , 22 (40), 24, 27, 57
yield condition, 103 Herzfeld 's theorem, 295
H e p t y l alcohol birefringence, 622 Maxwell c o n s t a n t , 623T.
viscosity, 623T.
Herring, theory of viscous creep, 137, 138 (16)
Hersey
viscometer (ball), 250 viscometer ( t u b e ) , 252, 289
Hess, interaction coefficients, 591-594T.
Hexagonal, close-packed lattice axial r a t i o , 177
dissociation of dislocation, 177 face-centered cubic l a t t i c e , relation of,
177
half dislocation, 177 lattice distances, 177 m e t a l s , 176
stacking order, 177, 178F.
t r a n s f o r m a t i o n , 179 Hill
bulge t h e o r y , 88
crystal grain, stress-strain, 206 H o m o m o r p h effects, 349
H o m o t h e t i c work-hardening, 91 Hooke
body, 43, 47 elastic solid, 63
law, 28 (56), 220, 390, 644, 674 solid, 29, 32, 39
H u b e r , yield condition, 103
H u g g i n s ' interaction c o n s t a n t s , 576, 579, 581, 590 (81)
H y d e , viscometers, 251 Hydrocarbon mixtures, 346T.
H y d r o d y n a m i c s , see also Flow, Macro- molecules, P e r t u r b a t i o n
Arrhenius dependence, 587
b o u n d a r y conditions, see B o u n d a r y conditions
and Brownian motion, see Brownian motion
c a v i t a t i o n , 690 collision, effects, 582
concentrated suspensions, cage model, 533, 587, 599
d i l a t a t i o n p e r t u r b e d , 539, 572 dilute suspensions, 529, 534, 544, 571 dipoles, 544, 606
dissipation of energy, see E n e r g y dis- sipation
dumbbell model, 543, 549, 577F.
Einstein method, 534, 543
equations, see Equations of motion, Navier-Stokes
exchange forces, reflections, 538, 569, 571
flow, ultrasonic radiations, 691 forces, long-range (see also Interac-
tion), 569, 570, 573, 574, 589 forces, short-range (aggregation ef-
fects), 582, 589
friction, factor, see Friction, hydro- dynamic
geometric relations, dumbbells and flow, 577F., 578F.
interaction between chain elements, 498, 499, 560, 605
interaction coefficients, 576 (61), 579, 581, 586, 589, 594F.
interaction, diffusion, friction, 504, 505 interaction, inter- and intra-molecu-
lar, 546
interaction, long-range, 574, 580 interaction, long-range (of aggre-
gates), 584,585 Kramers' method, 547
macromolecular, support for, 531 macromolecular systems, 531, 558 models, see Macromolecules
non-Newtonian viscosity, see Non- Newtonian liquids
ordering effect, 601
orientation (see also Birefringence, streaming, Euler's angles), 507, 512, 535, 550, 616, 618F.
Oseen-Burgers method, 498, 531, 546 osmotic pressure, 587
perturbation, see Einsteiri, Oseen, Stokes
porous swarm hypothesis, 559 shielding, 601
solvent flow, 538, 539 (11), 543, 550, 560, 569
Stokes approximation, 531 Stokes method, law, see Stokes superposition, linear, of perturbations,
546, 571
superposition of motions, 538
superposition, Stokes' flow, 547, 577, 579
surface tension, 542
Hydrogen
molecular radius, 530 thermal diffusion, 267 viscosity, 258
viscosity under pressure, 247 Hydrogen bonds, 410
viscosity, effect on, 341 Hydrostatic pressure (stress), 101
effect on ductility, 103, 306 effect on elasticity, 306 effect on shearing, 103
effect on yield point, Bridgman, 102 as isotropic tensor, 17, 388
Hydroxy undecanoate
chain length-viscosity, 446T.
viscosity relationships, 456T., 458T.
Hysteresis, see also Damping, Friction, Energy dissipation, Impedance atomic rearrangement, 127
general property of plastic state, 302 internal friction, cold work, 3, 209 under high pressure, 309, 311
I
Ideal bodies as standards, 27 Impact, detonation, 312, 313F., 315 Impurity atoms (see also Solid), 122
binding field of, 219 break from dislocation, 223 diffused, 132
effect on elastic behavior, 125 precipitation hardening, 131, 135, 226,
228, 229 yield point, 133
Impedance, viscoelastic, 399 complex, 422
function of frequency, 399 plane transverse waves, 421
transformation to operator equation, 404
Incompressibility, 29, 66, 293, 354, 529, 656
Indentation vertical force, 87 wedge, 85 Indium
in copper alloys, 229
crystal body-centered, tetragonal, 176 Inelastic behavior, see Anelasticity Inertia (d'Alembert force), 12
terms, 521, 536, 537, 542, 573
Interaction (see Hydrodynamics), 498, 573, 576
Interaction coefficients, colloidal sus- pensions, 506,581,590 (81), 591-594T.
Interatomic, intermolecular, see also Ag- gregation, Hydrodynamics, Interac- tion, Macromolecule, Solution forces, 125, 322
hydrogen bond, 341, 695
imperfections, effect of, 125, 219, 223 ions, 343
isomerization, 349 mixtures, 344
potential energy, 125, 264, 273, 323, 338, 342, 468, 479, 496
relaxation mechanisms, 410 solvent-solute contacts, 565, 610 volume effect, 554
Interchange reaction, sulfide, 410 Internal (see under noun)
Interstitial atoms distribution, 127, 224 effect on moduli, 126 effect on yielding, 224 as Maxwellian gas, 224
Interstitial carbon, diffusion of, 128 Intrinsic orientation constant, 628 (22),
635 (33)
Intrinsic viscosity (see also Macromole - cules, Particles, Viscosity) aggregation effects, 584 (73) birefringence relation, 553(29) branched polymer, 567 dense coils, 558, 565 (47) dimer, 590
dumbbells, 547
effective, 586, 587(79), 593, 601, 602 exponent, 557 (37), 561, 563, 564, 565 Flory constant, 565
general form, 589
molecular weight relation, 512-517, 533, 536, 545, 553, 557, 558, 561-566, 636, 637 (39)
osmotic virial coefficient, 565 (46) polydispersity, 566
real part of complex, 512 and rotational diffusion, 553 and shape, 515, 540, 542, 553, 563, 567 shear dependence, 515, 550, 604 solvent (see also Solvent), 554, 556,
557, 564, 565, 590
stiffness, 515, 543, 563, 634, 636 temperature, 515, 556, 610 Invariants, 23, 55, 57, 358
shear rate tensor, 673 (46) strain, 358 (6), 361 stress-strain rate, 656,657
Inviscid, plastic, flow, see also Flow, plastic
Ionic motion, 342, 343T.
activation energy, 343T.
attractive potential, 343T.
electrolytic dissociation, 344T.
energy of vaporization, 343T.
viscosity, 344T.
Irany, pi function, 270 Iron
alpha-crystal, 127 cast, plasticity, 309 dislocations, twinning, 176 dislocation, yield constant, 223 grain boundary-viscosity, 214 hysteresis, 309
-nickel transformation, 178 Norway, plasticity, 309
Irreversible processes, reference to the- ory of, 522,527,548
Isobaric activation energies, 341T.
Isobutane, viscosity, 257
Isochoric activation energies, 341T., 343T.
hydrogen bonded liquids, 343T.
Isochoric viscosity, temperature func- tion, 336
Isomerization and viscosity, 349 Isopentane, viscosity at high pressures,
268
Isopropyl alcohol, viscosity at high pres- sures, 268
Isotropie
ideal elastic materials, 388 plastic material, 98,105
pressure (hydrostatic, mean normal), 17, 66,103, 246, 303, 388, 656, 663, 677 pressure, Poynting effect, 38
(quasi) materials, 11 Isotropie strength
in compression, 55 in tension, 55 Isotropy
crystal deformation, 208 defined, 11
quasi-, transformation, to anisotropy (aeolotropic), 11
transverse, 360
J
J2 theory, Mises, 114,119 Jeffreys body, 50
Johnson, pressure chambers, 247 piston gauge, 249
Jump frequency (see also Flow mecha- nism, Flow polymer, Viscosity), 440
(1)
absolute reaction rates, 470 (13), 477 activation energy, 470
concentration effect, 460, 461, 481 cooperative, 478
degrees of freedom, 478 distribution function, 479 (19) entropy of activation, 478 flow assumption, 485 free energy change, 479 (13c) non-Newtonian viscosity, 488 paraffin, 487T.
polyisobutylene, 487T.
polystyrene, 487T.
segmental, 441 (1), 447 (lc), 470, 478, 488
segmental friction, 476 (18c) temperature dependence, 460, 461 transmission coefficient, 470 variation, free volume, 481
K
Kelvin body, see Voigt body Kelvin effect, 38
Kerosene, solidifying pressure, 247 Kinetic energy, see also Equations of
motion, Inertia inertia neglect, 531 suspensions, 548, 583 relative motion, 539
King, transition lattice theory, 202 Kirkwood
friction constant, 496 momentum transport, 325 Kirkwood-Riseman theory, 562, 566 Knudsen number, 529
Clausius range, 529
Koiter, slip theory, loading, 115 Konterova, theory of deformation, 315 Krafft, strain servoscanner, 255
Kratsky, crystallites theory, 651 Krishnan, static orientation theory, 624
(12)
Kronecker's delta, 36, 657
Kuhn, intrinsic viscosity, theory, 557 (37)
Kuhn and Kuhn
macromolecule model, 519, 631 Kuss, viscometer, 250
L
Lacey, viscometer, 250
Laidler, pair potential barriers, 327 Lambda factor, 77, 78
Lamers (elasticity) modulus, 36 Langevin equation, 496 (1), 548
Latex, viscosity concentration function, 574, 600, 601
Lattice vacancies, see Vacancies Lattices
body-centered cubic, see Cubic, body- centered lattice
body-centered tetragonal (indium), 176
cubic, see Cubic lattice diamond, 176
face-centered cubic, see Cubic, face- centered lattice
healthy, 147
hexagonal (graphite), 176
hexagonal, see Hexagonal, close - packed lattice
liquid, for polymer configurations, 554 liquid, quasi-crystalline, 275
rhombic, 177 rhombohedral, 177 tetragonal (tin), 176 transformations of, 178, 179
twinning depending on structure, 171 unhealthy, 147
unit cell, close-packed, 163 Lead
grain orientation, surface energy, 203F.
internal friction, 215 plastic torsion, 41 transient flow, 234
wire, Trouton and Rankine body, 50 Lennard-Jones potential, 264, 323 (4),
329, 333 Lethersich body, 50
Levy-von Mises flow rule, 71 (11) Limestone, Solenhafen, plasticity, 310 Liquids, see also Flow
absorption coefficient of sound, 688 distribution function, molecular ra-
dial, 323, 469
dynamical equation of state, 692 elastic-inelastic, distinction (see Elas-
tico-viscous liquids), 677
elastico-viscous, 49, 53, 396, 433, 510, 674
inelastic, 681F.
intermolecular forces, 324, 337,468, 508 Maxwell body, 48, 396
metals, viscosity, 337
mixtures, 267, 344, 346T., 527, 686 models, 322, 327, 469, 684
molecular jumps, 275, 327, 411, 447, 466, 470
Newtonian (see Newtonian liquid) non-Newtonran (see Non-Newionian
liquid) porosity of, 273
potential function, 264, 322, 327, 333, 339, 448, 470, 477
self-diffusion, 2, 273, 330 standard, difficulties of, 286 tensile strength, 689 viscous, definition, 64 Liquid crystals, see Crystal
Liquid, theories of state and viscosity Andrade, 333, 447, 526
Barrer, 335
Born and Green, 324
Eyring, 274, 326, 447, 469, 609 Frenkel, 273, 331, 345, 695 Green, 322, 526
Kirkwood, 324, 468 Thorne, 527 Loading
Bauschinger, 109F.
convex surface, 112F.
convex surface, proof of, 113 curve, 108
elastic beam, 31F., 416 (81) equilibrium, 29
function, 108F., 109F.
high pressure, 246 path of, 99, 105, 110 plastic strain vector, 113 radial, 101, 102F., 105, 106
rod in tension, 416 sinusoidal, 219, 399
stress-increment in, accuracy, 16 surfaces, successive, 108
viscoelastic beam, 414F., 415 (80) and yield function, 105
Lode, variables, 106F.
London, dispersion forces, 324 Lorentz field, 521(56)
Lüder's lines, 298F.
Lui, loading function, Bauschinger ef- fect, 109F.
M Maass, viscometer, 252
MacCoull-Walther equation, 285 (21) Sanderson's extension, 286 (22) Macromolecules, macromolecular, 519
branching, effect of, 456T., 459,567,592 branching, effect on network, 459 coiled, 7,433,507,631, 634,636,645 coil swelling, 556
compact coils, 558 (39), 565 (47) coil shrinkage, 586, 588 (80) configurations, see Configurations critical chain length, 44
crystalline-amorphous, 645, 649 deformation, by shear rate, 490, 604 deformation, under stress, 8, 426 degrees of freedom, 500
diffusion, 507 dipole movement, 521 disentanglement, 589 disturbance of flow field, 511
end-to-end distance, 473, 554, 555, 632 entanglement, 433, 440, 445, 464, 465,
472, 473, 475, 687
expended radius, 555 (33), 556, 565 (47) free-draining, 473, 558, 605, 636 frequency, natural, 434
Gaussian distribution distorted, 556 hampered flow (interaction), 499, 564,
636
hindered rotation, 559,632 inner viscosity, 7, 519, 604, 633, 700 interaction, 581
interaction between elements (seg- ments), 499, 546, 561, 563, 587, 687 law of flow, 445, 446T.
mass center, 504, 512 Maxwell constant, 634
