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Home , Firn, Ice Ic, Ice Ih, Ice II, Ice III, Ice V

Cambridge University Press 978-0-521-80620-6 - Creep and Fracture of Ice Erland M. Schulson and Paul Duval Index More information

Index

100-year wave force, 336 friction and fracture, 289, 376 60° dislocations, 17, 82, 88 indentation failure, 345 microstructure, 45, 70, 237, 255, 273 abrasion, 337 multiscale fracture and frictional accommodation processes of basal slip, 165 sliding, 386 acoustic emission, 78, 90, 108 nested envelopes, 377 across-column cleavage cracks, 278 pressure–area relationship, 349, 352 across-column confinement, 282 S2 growth texture, 246, 273 across-column cracks, 282, 306, SHEBA faults, 371 across-column loading, 275 SHEBA stress states, 377 across-column strength, 246, 249, 275 Arctic Ocean, 1, 45, 190, 361 activation energy, 71, 84, 95, 111, 118, 131 aspect ratio, 344 activation volume, 114, 182 atmospheric ice, 219, 221, 241, 243 activity of pyramidal slip systems, 158 atmospheric icing, 31 activity of slip systems, 168 atmospheric impurities, 113 adiabatic heating, 291, 348 atomic packing factor, 9 adiabatic softening, 291 audible report, 240 affine self-consistent model, 160 avalanches, 206 air bubbles, 38 air-hydrate crystals, 37 bands, 89 albedo, 363 basal activity, 162 aligned first-year sea ice, 246 basal dislocations, 77 along-column confinement, 282 basal planes, 214, along-column confining stress, 282, basal screw dislocations, 77, 87 along-column strength, 244, 275 basal shear bands, 163 ammonia dihydrate, 181 basal slip, 18, 77, 127, 228 ammonia–water system, 186 basal slip lines, 77 amorphous forms of ice, 5 bend strength, 213, 224 Andrade creep, 108 bend test, 213 Andrade law, 104, 107 Bernal–Fowler ice rules, 9 anisotropic ice, 129, 153, 154, 156, 172, biaxial compressive strength, 270 apparent activation energy, 342 biaxial loading, 270, 274 apparent contact area, 349 paths, 274 apparent fracture toughness, 204, 341 Bjerrum defects, 15, 82, 88, applied stress tensor, 280 blowout, 297 arctic and antarctic sea ice blue zone, 347, 348 aligned first-year sea ice, 246 boundary diffusion, 126 brine-drainage channels, 43, 223 Brazil test, 213, brine pockets, 43, 62, 217, 223, brine drainage channels, 43, 224, 231 224, 249 ductile–brittle transition, 118, 119 brine pockets, 43, 62, 217, 224, 231 failure envelope, 275, 278, 376 brittle behavior, 240

391

392 Index

brittle compressive failure, 237 columnar-shaped grains, 31, 41 brittle compressive strength of confined ice comb cracks, 266, 296, 297, 366 biaxial loading, 270, 274 mechanism, 300, biaxial loading paths, 274 compact tensile specimens, 198 comb-crack mechanism, 300, compliance, 157 confinement strengthening, 276 matrix, 60 confinement weakening, 276, 280 compliant brush platens, 238 Coulombic faults, 272, 278, 282, 314 compressibility, 55 failure envelope, 275, 278, 376 compressive shear faults, 236, 372 failure surfaces, 286 compressive strength fracture and friction, 289 compliant brush platens, 238 plastic faults, 272, 282, 292, 308, 314 failure process, 251 post-terminal failure, 267 length-to-diameter ratio, 238 pressure-cell method, 267 loading platens, 238 proportional loading, 267 longitudinal split, 251 triaxial test, 267 multiple splitting, 240 true triaxial loading, 268 parallelism of ends, 238 wing cracks and comb cracks, 294 specimen shape, 238 brittle failure modes, 342 stiffness of loading frame, 237 blue zone, 347, 356 vs. cyclic loading, 249 continuous, 337 vs. damage, 249 high-pressure zone, 348, 356 vs. grain size, 247 local loads, 349 vs. growth texture, 246 non-simultaneous failure, 349 vs. porosity/salinity, 247 pressure–area curve, 351 vs. size and boundary conditions, 250 strain-rate softening, 240, 243, 338 vs. strain rate, 243 transition strain rate, 239, 309, 331 vs. temperature, 245 transition velocity, 341 wing-crack mechanics, 261 brittle failure surface, 288 concentric cracks, 356 brittle fracture mode confined single crystals, 237 Coulombic faulting, 282, 348 confinement, 242, 266, 328, 344, 375 intergranular, 320 strengthening, 276 spalling, 278, 304, 343 weakening, 276, 280 splitting, 327 confining pressure, 116, 267, 269 transgranular, 216 conjugate fracture, 365 brittle-like failure mode conjugate sets, 272 plastic faulting, 292, 308, 348 constitutional super-cooling, 43 brittle-to-ductile transition, 226,242, 320, 337, 386 constriction of partial dislocations, 89 bubbly ice, 30, 37 contact area, 350 buckling, 306 contact zone, 266, 292, 336, 347, 355 stress, 369 continuous indentation, 337 bulk modulus, 58 continuous recrystallization, 128 Burgers’ vector b, 16, 89 convective flow, 186 Coulombic faults, 272, 278, 282, 314 c-axis alignment, 45 shear fault, 276, 282, 303, 373 calving of icebergs, 1, 212 Coulombic material, 237 cellular material, 207 Coulomb’s failure criterion, 259, 310 ceramics, 247 covalent bonds, 7, 188 chemical compounds, 34 cracked/damaged polycrystals, 64 circumferential cracking, 343 cracks ,68 circumferentially notched tensile bars, 198 cleavage, 216 cleavage, 214, 216 comb, 266, 294, 296, 297, 366 climb, 16 critical crack, 229 basal dislocations, 122 density, 249 dislocations, 125 extension force, 192 CO2 hydrate, 180 frictional sliding, 68, 237, 247, 261, 278, 282, 289, cohesion, 289, 290, 311 302, 375, 376 cohesive strength, 228, 260, 311, growth, 40, 196 coincident site lattice, 22 horsetail, 299 collective dislocation motion, 91, 94 interaction, 258 columnar ice, 162, 219, 246, 273 intergranular, 320

Index 393

cracks (cont.) ice Ih, 5 micro-plates, 297, 300 radial isotropy, 9, 14 most dangerous flaw, 352 cyclic bending tests, 250 nucleation, 39, 212, 229 cyclic hardening, 250 control, 229 cyclic loading, 83, 205, 249 parent, 252, primary, 251, 294 D-type Bjerrum defect, 11 propagation, 228, 231 damage, 66, 68, 203, 222, 249, 262, 266, 294, control, 228 328, 347 secondary, 251, 255, 266, 282, 296, 324, 366 theory, 64 splay, 299 threshold, 249 systems, 194, 195 damage-dependent elastic stiffness constants, 66 tip creep, 197 debris-laden ice, 113, tip stress state, 193 decohesions, 231 transgranular, 216 deformation gradients, 79, 96, 155 velocities, 231 deformation matrix, 66 wing, 252, 258, 294, 361, 366, 372 deformation textures, 139 crater dimensions, 356 deformation twins, 22 cratering, 355 delayed elastic strain, 103 creep densification, 37, 160 activation energy, 71, 84, 95, 111, 118, 131 density, 8, 207 Andrade creep, 109 destabilization, 297, 304 behavior at low stresses, 109 deviatoric stresses, 109 diffusion creep, 103, 125, 126 diamond anvil cell, 182 effect of confining pressure, 114 diamond-shaped patterns, 362 effect of grain size, 107, 112 differential stress, 270 effect of liquid phase, 127 diffusion effect of particles and impurities, 113 dislocation climb, 90, 95, 125 glide-controlled mechanism, 124 self-diffusion, 70, 123 Harper–Dorn creep, 125, volume diffusion coefficient, 122 melt-free pure ice, 111 diffusion of acids, 72 primary creep, 103, 104, 161 diffusion coefficient, 70, 71 rate-controlling processes, 95, 122, 124 diffusion creep, 103, 125, 126 recovery creep, 115 diffusion of gases, 70, 72 secondary creep, 103, 109, 111, 112, 113, dimensional analysis, 352, 356 122, 311 directional viscosity, 154 stress exponent, 109, 116, 128, 160, 179, 187 direct tensile test, 214 superplastic flow, 112, 125 dirty ice, 330 tertiary creep, 103, 115, 129 dislocation motion creep damage, 250 avalanches, 78, 90, 92, 94, 107, 108, 230 creep relaxation, 258 basal slip, 18, 77, 127, 228 creep zone, 324 climb, 90, 95 crevasses, 212, collective motion, 91, 94 critical cracks, 229 cross-slip, 16, 18, 77, 89, 95, 123 critical flaw, 231 dislocation mobility, 82, 87, critical grain size, 221, 222, dislocation velocity, 87, 88 critical loading rate, 197, glide-controlled mechanism, 124 critical nucleus, 39 mobile dislocations, 78, 82, 95 critical size, 228 Orowan equation, 92, 124 critical strain rate, 320 prismatic slip, 161, 243 critical stress for crack propagation, 192 dislocations , 12, 70, 73 cross-slip, 16, 18, 77, 89, 95, 123 60° dislocations, 17, 82, 88 crushing, 343, 345 avalanches, 78, 90, 92, 94, 107, 108, 230 force, 354 basal dislocations, 77 crystalline forms of ice, 5 basal screw dislocations, 77, 87 crystals, 125 climb, 90, 95 growth, 40 density, 15, 21 plasticity, 362 dissociation, 18, 89 structure of ice Ih, 6 edge, 13, 86, 88, 164 crystal structure excess dislocations, 95, 143 ice Ic, 5 interstitial prismatic loop, 14

394 Index

dislocations (cont.) effect of temperature, 111 jogs, 123 effective shear stress, 260, 266 kinetics, 213 elastic anisotropy, 58, 64 line energy, 16 elastic buckling, 297, 369 line (strain) energy, 16 elastic compliance constants, 52, 54 loops, 71 elastic constants, 66 mixed, 14 elastic energy, 137, 191 mobility, 82, 87, elastic limit, 323 multiplication, 24, 79, 89, 94, 96 elastic mismatch, 229, non-basal edge dislocations, 20, 77 elastic moduli, 54 partial dislocations, 18, 22, 89 elastic stiffness constants, 52 pile-ups, 229, elastically isotropic, 58 prismatic loop, 14, 18 elasto-viscoplastic, 160 screw, 14, 89 electron back-scatter diffraction, 144 slip system, 17, 122, 123, 155, 157, 160, 174 elongation, 226, sources, 79, 85 Enceladus , 51 statistical dislocations, 95, 143 end constraint, 238, 245 vacancy prismatic loop, 9, 14 energy release rate, 300, 301 velocity, 87, 88 engineered ceramics, 226 displacement field, 194 enhancement factor, 129, 172, 173 double-cantilever beams, 198 entrapped brine, 43 double subscript notation, 274 equilibrium, 191 driving force, 131, 136 equilibrium melting point, 269, 286 ductile behavior, 239 equivalent stress, 114 ductile–brittle analysis, 353 etch pitting, 21 ductile failure of columnar S2 ice, 119 Euler, 306 ductile failure surface, 286 Euler buckling, 238, 279, 306 ductile-to-brittle transition, 118, 119, 190, 226, 239, Europa, 1, 51, 190, 212, 236, 237, 241, 293, 321 eutectic, 217 arctic sea ice, 63 evolution of Coulombic faults, 294 competition between creep and fracture, 321 excess dislocations, 95, 143 critical strain rate, 320 critical strain rate compression, 320 fabric, 41, 45 critical strain rate tension, 226 failure envelope, 275, 278, 376 ice–structure interaction, 114 biaxial loading, 270, 274 inelastic zone, 196, 323 columnar ice, 162, 219, 246, 273 micromechanical model, 321 faulted ice, 309, vs. confinement, 328, 344, 375 granular ice, 200, 218, 254, 297 vs. damage, 249, 262, 266, 294, 328 nested envelopes, 379 vs. grain size, 326, 327 post-terminal, 267, 308, 310 vs. size, 329 sea ice, 31, 43, 62, 200, 204, 224, 225, 231, 278, 297, vs. temperature, 328 301, 302, 309 ductility, 223, 226 sea ice cover, 236, 361 dynamic compressive strength, 243 failure process, 251 dynamic constants, 54 failure surfaces, 286 dynamic failure, 232 columnar ice, 162, 219, 246, 273 dynamic instability, 291 granular ice, 200, 218, 254, 297 dynamic loading, 231 fast crack propagation, 212 dynamic recrystallization, 62, 118, 129, 130, 142, fast Fourier transform, 154, 159, 162 175, 183 fatigue of ice, 250 dynamic strength, 231, 244 fatigue sharpening, 198 dynamic Young’s modulus, 63 faulting-to-spalling transition, 278 dynamics of dislocations, 86, 96 faults conjugate sets, 272 edge dislocations, 13, 86, 88, 164 Coulombic, 272, 278, 282, 314 edge-loaded plates, 342 diamond-shaped patterns, 362 effect of confining pressure, 114 healing, 290, 310, 311, 376 effect of grain size, 107, 112 leads, 361 effect of impurities, 80 left-lateral lineaments, 368 effect of liquid phase 127 oriented features, 361 effect of particles and impurities, 113 plastic, 272, 282, 292, 308, 314

Index 395

faults (cont.) fragmentation, 238 rhomboidal-shaped openings, 364 pattern, 387 right-lateral lineaments, 368 fragments, 353 SHEBA, 369, 377 friction, 258, 347 stacking, 18, 22, 90 and fracture, 376 strike-slip, 368, 374 coefficient, 311, 322, 325, 380 structural defects, 373, 375 frictional crack sliding, 262, 266, 278 feather cracks, 299 frictional drag, 297, 300 fibers, 202 frictional heating, 313 Fick’s law, 70 frictional melting, 70 field fluctuations, 175 frictional sliding, 68, 237, 247, 261, 278, 282, 289, 302, field study, 203 375, 376 finely grained ice, 109, 125, 183 full-field approach, 153 firn, 30, 207 formulation, 162 and bubbly ice, 160 model, 159 first cracks, 344 solutions, 175 flexural strength, 213 fundamental elastic constants, 52, 57 floating ice cover, 205, 237 floating ice sheet, 30 gas hydrates, 180 flow law for basal slip, 84 geometric selection, 40 flow of ice II, 182 geometrical analysis, 352 flow parameters, 184 geometrical factor, 194 fluid cushions, 238 geometrically necessary dislocations, 143 Fourier points, 162 geometry, 204 fractal analysis, 353 girdle texture, 141 fractal dimension, 353 glacier flow modeling, 111 fractal hierarchy, 354 glacier ice, 102, 111, 113, 139, 198, 271 fracture and friction, 289 glacier icefalls and crevasses, 1 fracture mechanics glaciers, 30, 175 circumferentially notched tensile bars, 198 crevasses, 212, compact tensile specimens, 198 densification, 37, 160 crack-extension force, 192 glacier flow modeling, 111 crack-tip stress state, 193 ice cores, 139, 171 double-cantilever beam, 198 ice-sheet flow model, 172, 175 fracture toughness, 190, 195, 228, 375 microstructure, 30, 32, 70, 206, 225, 231, 237, Griffith energy balance concept, 255, 273 190, 191 polar ice sheets, 23, 30, 104, 116, 125, 127, 130, 136, linear elastic, 190, 207, 212 154, 171 modes of crack propagation, 193 temperate glacier, 111, 139, 140, 143 notched beams, 198 texture, 34, 45, 62, 201 notch-tip acuity, 198 textures in polar ice sheets, 171 pyramidal and conical indentations, 198 glass, 356 resistance to growth, 196 glaze, 31 ring test, 198, 213, Glen’s law, 122 short rods with chevron notches, 198 glide-controlled mechanism, 124 strain energy release rate, 193, 194 glide set, 18, stress intensity factor, 194, 229, 323 global climate, 1, 376 toughness, 190, 195, 228, 375 global loads, 236, 349 fracture path, 207 gouge-like material, 276 fracture toughness (KIc) 190, 195, grain boundaries, 22, 68, 70, 108, 323 228, 375 boundary diffusion, 126 snow, 64, 206 bulging, 138 vs. cyclic loading, 83, 205, 249 cracks, 321, 369 vs. damage, 203, diffusivity, 72 vs. external water, 203 energy, 23 vs. grain size, 200 migration, 127 vs. growth texture, 201, 204 rate, 128, 134 vs. particulates and fibers, 386 mobility, 132 vs. porosity, 201, sliding, 23, 102, 112, 115, 119, 123, 125, 226, 229, vs. size, 203, 230, 304 vs. temperature, 199 superplastic flow, 112, 125

396 Index

grain growth, 23, 128, 130, 131, 132, 136, 171 covers, 250 and recrystallization, 30 films, 72 in glacial ice, 132 forces, 190, 241 grains, 90 ice Ic, 5 anisotropy, 175 ice Ih, 5 nucleation, 130 ice II, 179, 182 refinement, 201, 240 ice III, 179, 182 size, 183 ice V and VI, 184 granular ice, 200, 218, 254, 297 ice-infested waters, 236 granular material, 270 ice loading, 336 Griffith, 258 ice-sheet flow model, 172, 175 Griffith’s energy balance concept, 190, 191 ice sheets, 175 GRIP ice core, 167 ice shelves, 212 growth, 40 ice–structure interaction, 114 texture, 31, 40, 58, 204, 222 ice thickness distribution, 236 twins, 22 ice–water interfacial energy, 23 icebergs, 190, 202, 225, 342, 347 hailstones, 31 icy satellites, 91, 179 Hall–Petch form, 219 Enceladus , 51 Hall–Petch law, 108 Europa, 190, 212, 236, 237, Hall–Petch strengthening, 219, 222 Triton , 51 hard particles, 24 impact Harper–Dorn creep, 125, 126 crater dimensions, 356 healing, 290, 310, 311, 376 cratering, 355 Hertzian-like cone-shaped cracks, 356 indentation, 355 Hertzian stresses, 299 impurities, 32, 33 hexagonal unit cell, 25 indentation, 269 Hibernia, 236 failure, 336 hierarchy of events, 353 transition strain rate, 340 hierarchy theory of complexity, 387 velocity, 337 high-angle boundary, 22 indented walls, 345 high-density ice, 5 inelastic deformation, 206, 219, 239 high-pressure ices, 179 inelastic zone, 196, 323 ammonia–water system, 186 inhomogeneous deformation, 369 effect of grain size in creep, 107, 112 interaction tensor, 157 flow parameters, 184 interference colors, 32 ice II, 179, 182 intergranular cracks, 320 ice III, 179, 182 interlocking of asperities, 313 ice V and VI, 184 intermediate principal stress, 272, 276 methane hydrates, 185 intermittency, 379 planetary ices, 7, 188 internal friction, 23, 82, 279, 289 rheology, 184 coefficient, 290, 379 stress exponent, 109, 116, 124, 128, 160, 179, 183, 187 internal stress field, 77, 79, 89, high-pressure zones, 348, 349 123, 164 high-speed photography, 252 interstitial, 10–11, 71 higher-confinement faults, 272, interstitial prismatic loop, 14 Hill’s criterion, 120, 274, 286 intracrystalline dislocation glide, 102, 125 Hill’s method, 58 intracrystalline fields, 162 homogeneous equivalent medium (HEM), 156, 159 intragranular field fluctuations, 154, 159 homogenization, 155 intragranular stresses, 172 Hooke’s law, 52, 53, 66 ionic and Bjerrum defects, 11 horsetail cracks, 299 isotropic hardening, 107 hot spots, 348 Hurst exponent, 381 jogs, 123 hydrate crystals, 30, 38 hydrogen bonds, 7, 208 KIc vs. cyclic loading, 205 hydrostatic axis, 286, KIc vs. damage, 203 KIc vs. external water, 203 ice, 164 KIc vs. grain size, 200 breaking, 212 KIc vs. growth texture, 201 cores, 139, 171 KIc vs. particulates and fibers, 202

Index 397

KIc vs. porosity, 201 microsimilar samples, 293 KIc vs. size, 203 microstructure, 30, 32, 70, 206, 225, 231, 237, KIc vs. temperature, 199 255, 273 kaolinite, 202 migration recrystallization, 115, 116, 135, 137, 142 kinematic hardening, 95, 115, 124 minerals, 272 kinetic coefficient of friction, 67, 68, 261 mixed dislocation, 14 kink bands, 163 mixed-mode loading, 198 mobile dislocations, 78, 82, 95 L-type Bjerrum defect, 11 mode-I, 193 lattice friction, 92, 93 stress intensity factor, 266, 270 stress, 87 mode-II, 193 lattice parameters, 7 mode-III, 193 lattice preferred orientations, 154 modeling ductile behavior lattice rotation, 139, 168 affine self-consistent model, 160 leads, 361 enhancement factor, 129, 172, 173 left-lateral displacement, 364 fast Fourier transform, 154, 162 left-lateral lineaments, 368 full-field approach, 153 left-lateral sliding, 370 intragranular field fluctuations, 154 length-to-diameter ratio, 238 micro-macro model, 153, 165 lineaments, 361 multiscale approach, 386 linear elastic fracture mechanics, 190, second-order self-consistent method, 159 207, 212 static approximation, 155 linear kinematic features, 362 tangent approximation, 154 liquid-like layer, 113 Taylor model, 155, 168, 169 load-drops, 240 viscoplastic self-consistent (VPSC) model, loading platens, 238 154, 158 loading rate, 197, 199, 204, 261, 324 model of Riedel and Rice, 197, 324 local and global climate, 236 models of ice cover , 376 local and global failure, 236 modes of crack propagation, 193 localization, 386 molecular ices, 5 of plastic flow, 292 molecular stacking, 7 localized melting, 313 Molikpaq, 236, 337 localized prismatic slip, 243 mortar and concrete, 238 local loads, 349 multi-axial loading, 238, 274 longitudinal split, 251 multi-fractal analysis, 386 long-range dislocations interaction, 91 multi-maxima texture, 62, 144 long-range internal stress, 95, 107 multiple/cyclic loads, 204 field, 127, 143 multiple loadings, 204 low-density ice, 5 multiple splitting, 240, 252 lower-confinement faults, 272, multi-pole textures, 140 multiscale approach, 153 macroscopic faults, 237 fracture and frictional sliding, 386 shear fault, 294 multi-year hummock, 236 macrostructure, 43 Mars, 212 nested failure envelopes, 377 material collapse, 251, 261 neutral axis, 207 maximum principal strain, 372 NH3, 180 maximum principal stress, 276, 368 non-basal dislocations, 87, 123 measurement of KIc, 196 non-basal edge dislocations, 20, 77 mechanical anisotropy of S2 ice, 276 non-basal glide, 20 mechanical energy, 191 non-basal slip, 83, 96, 158 mechanical fields, 153 non-basal slip systems, 168 mechanical instability, 254 non-linear friction, 313 melt-free pure ice, 111 non-simultaneity, 349 melting temperature, 101 non-simultaneous failure, 349 metals and alloys, 291 non-uniform sliding, 299 methane hydrates, 185 notched beams, 198 method of linear intercepts, 219, notch-tip acuity, 198 micro-macro model, 153, 165 nucleation, 39 micromechanical model, 321 theory, 39 micro-plates, 297, 300 numerical values of fundamental constants, 54

398 Index

oceanic salt budget, 236 pressure melting, 269 off-shore structures, 236 pressure ridges, 31, 212 optical microscopy, 32 pre-straining, 203, 226 orientation distribution function, 165, 172 primary creep, 103, 104, 161 orientation gradients, 137, 143 principal directions, 287 orientation tensor, 166 principal strains, 53, 55 oriented features, 361 principal stresses, 53, 267, 274, 289, 321, 345, 381 Orowan equation, 92, 124 direction, 374 Orowan form, 219 prismatic activity, 169 Orowan strengthening, 219, 222 prismatic glide, 77 orthotropic material, 172 prismatic loop, 14, 18 orthotropic symmetry, 58 prismatic planes, 214 Ostwald ripening, 38 prismatic slip systems, 161 outer Solar System, 46, 180 process zone, 297 outward bending, 260 proportional loading, 267 proton disorder, 22, 88 pack ice, 363 protonic defects, 10, 11 paleoclimatology, 1 protonic rearrangement, 16 pancake ice, 212 pykrete, 202 parallelism of ends, 238 pyramidal activity, 169 partial dislocations, 18, 22, 89 pyramidal and conical indentation, 198 particle-stimulated nucleation, 138 pyramidal slip, 97, 161 passive proportional loading, 267, path independence, 275 quasi-liquid layer, 24 Peierls barrier, 87, 88 quasi-static failure, 237 penny-shaped flaws, 228 physical characteristics, 9 radial cracking, 343 pinning pressure, 132, radial isotropy, 9, planes, 26, 82 rafting, 31 plane strain, 195, 205, 229, 371 Raman spectroscopy, 34 fracture toughness, 195 randomly oriented polycrystals, 58 plane stress, 194 rate-controlling processes, 95, 122, 124 plastic anisotropy, 156 rate of unloading, 250 plastic faults, 272, 282, 292, 308, 314 recovery creep, 115 plastic strain, 239 recovery processes, 127, 143 plastic work, 204 recrystallization, 34, 68, 104, 243, 292, 348 plastically orthotropic material, 274 continuous, 128 plasticity, 376 dynamic, 62, 118, 129, 130, 142, 175, 183 point defects, 71, 82 energy, 130 Poisson’s ratio, 55, 61, 62, 63, 64, 66, 191 grain boundary bulging, 138 polar ice sheets, 23, 30, 104, 116, 125, 127, 130, 136, grain boundary migration, 127 154, 171 grain nucleation, 130 polycrystal grains, 226, 272, 282, 347 anisotropy, 154 microstructure, 291 compliances, 60 migration, 115, 116, 135, 137, 142 deformation and recrystallation textures, 62 particle-stimulated nucleation, 138 growth textures, 58 rotation, 134, 135, 171, 172 polygonization, 134 static, 130, 144 polynomial flow law, 160 textures, 115, 129, 139, 171 porosity, 63, 200, 201, 224, 225, 247, 249 reference resolved shear stress, 157 post-terminal envelope, 310 reference stresses, 160 post-terminal failure, 267, 308 relative shear displacement, 364 potential energy, 191 representative volume element (RVE), 155 power-law creep, 124 resistance to growth, 196 precursors, 229 Reuss’ method, 58 preferred crystal orientation, 30,103 rheology of high-pressure ices, 184 pre-melting, 231 rheology of planetary ices, 7, 188 pressure–area relationship, 349, 351, 352 rhomboidal-shaped openings, 364 pressure-cell method, 267 right-lateral lineaments, 368 pressure hardening, 271, 272 rime, 31 pressure-induced plasticity, 243, 286 ring test, 198, 213,

Index 399

rocks and minerals, 247, 256, 267, 272, 290, 291, 297, sheets of cracks, 306 303, 331 shock resistance, 202 Ronne Ice Shelf, 201 short rods with chevron notches, 198 rotation recrystallization, 134, 135, 171, 172 shuffle set, 18 roughness, 313, 381 single crystals, 214, 227, 241 singular stress field, 322 S1 ice, 45 sintering, 36, 37 growth texture, 247 and densification, 30 S2 ice, 45, 119, 273, 274, 275 size, 203, 207, 225, 250, 329 growth texture, 246 size distribution, 353 S3 ice, 45, 273 size effect, 204 growth texture, 246 slabs, 270, saline ice, 119, 224 slenderness, 369 salinity, 62, 217, 223, 246, 249, 262 sliding lineaments, 373 salt-water ice, 197, 249, 326 slip, 129 saw-cuts, 314 activity, 161 scale, 386 bands, 89, 92, 94 scale effect, 3 direction, 77 scale independence, 387 line, 15, 18, 92, 362, scale independent fracture physics, 387 system, 17, 122, 123, 155, 157, 160, 174 scale invariance, 91, 92, 93, 94, 162, 354 slip-stick behavior, 67, 68 scaling laws, 384 snow, 64, 206 scanning electron microscopy, 32 elastic properties, 64 Schmid factor, 172 fracture toughness, 190, 195, 204, 341, 375 Schmid law, 80 microstructure, 32, 70, 206, 225, 237, 255, 273 Schmid tensor, 157 porosity, 63, 200, 201, 224, 225, 247, 249 Schmidt projection, 166 transition to firn, 64 screw dislocation, 14, 89 snow and firn, 64 sea ice, 31, 43, 62, 200, 204, 224, 225, 231, 278, 297, solidification, 30 301, 302, 309 solubility of foreign species, 11 bend strength, 213, 224 solutes, 11 compressive strength, 243, 270 space group, 7 Coulombic faults, 272, 278, 282, 314 spallation, 278, 304, 343, 355 cover, 236, 361 specimen shape, 238 ductility, 223, 226 splay cracks, 299 failure envelope, 275, 278, 376 split Hopkinson pressure bar, 244 fracture toughness, 190, 195, 204, 341, 375 splitting, 327 growth, 41 stable growth, 195, 196 linear kinematic features, 362 stable vs. unstable crack propagation, 195 microstructure, 30, 32, 70, 206, 225, 231, 237, 255, stacking fault, 18, 22, 90 273, 291 static approximation, 155 nested failure envelopes, 377 static recrystallization, 130, 144 scaling laws, 384 static and Taylor models, 168 tensile strength, 213, statistical analysis, 352 thermal gradient, 336 statistical dislocations, 95, 143 viscous flow, 382, 384 stiffness constants, 66 sea salts, 39 stiffness of loading frame, 237 second moments, 159 stiff systems, 237 second-order model, 154, 173 stored energy, 130 second-order self-consistent method, 159 strain second-phases, 202 deformation gradients, 79, 96, 155 secondary creep, 103, 109, 111, 112, 113, 122, 311 delayed elastic strain, 103 self-consistent approach, 122, 155, 175 inhomogeneities, 172 self-diffusion, 70, 123 plane strain, 195, 205, 229, 371 shards, 255, 270 principal, 53, 55 shear crevasses, 193 strain-rate tensor, 372 shear faults, 240, 266, 272 strain accommodation, 174 shear modulus, 230 strain energy release rate, 193, 194 SHEBA, 369, 377 strain hardening, 291 faults, 371 strain-induced textures, 153 stress states, 377, 379 strain-rate fields, 159

400 Index

strain-rate fluctuations, 172 critical cracks, 229 strain-rate hardening, 218, 239, 291 critical grain size, 221, 222, strain-rate softening, 240, 243, 338 decohesions, 231 strain vectors, 287, direct tensile test, 214 strength of ceramics, 247 dislocation avalanches, 78, 90, 92, 94, 107, 108 strength of ice V, 184 dislocation pile-ups, 229, strength of ice VI, 184 dynamic strength, 231, 244 strength of methane hydrate, 185 elastic mismatch, 229, stress, 108, 126 grain boundary sliding, 23, 102, 115, 119, 123, 125, concentration, 190 226, 229, 230, 304 deviatoric stress, 109 mechanisms, 227, 261 differential stress, 270 ring test, 198, 213, effective shear stress, 260, 266 Stroh’s analysis, 230 elastic limit, 323 thermal expansion mismatch, 229 equivalent stress, 114 vs. brine content, 223 hydrostatic axis, 286, vs. damage, 323 intensity factor, 194, 229, 323 vs. grain size, 218 internal stress field, 77, 79, 89, 123, 164 vs. growth texture, 222 intragranular stress, 172 vs. pre-strain, 226 lattice friction stress, 87 vs. size, 225 plane stress, 194 vs. strain rate, 217 principal stresses, 53, 267, 274, 289, 321, 345, 381 vs. temperature, 216 reference resolved shear stress, 157 Zener’s analysis, 230 relaxation, 324 tension and compression textures, 139 stress components, 194 terminal failure, 240, 242, 269, 282, 308, 311, 345 stress concentrators, 243, 379 stress, 240, 251, 261 stress exponent, 109, 116, 124, 128, 160, 179, 183, 187 tertiary creep, 103, 115, 129 stress–strain curve, 239, 240, 252 texture, 34, 45, 62, 201 stress tensor, 194 anisotropic ice, 129, 153, 154, 156, 172, yield stress, 79 deformation textures, 139 strike-slip faults, 368, 374 development, 154 Stroh’s analysis, 230 enhancement factor, 129, 172, 173 structural defects, 373, 375 glaciers, 139 sub-boundaries, 22, 72, 228, growth texture, 58, 94, 201, 204, 222, 246, 247 sub-critical crack growth, 212 ices, 158, 169, 172 sublimation, 33 multi-pole textures, 140 substructure, 43 orientation distribution function, 165, 172 super-cooling, 39 orientation tensor, 166 superplastic flow, 112, 125 polar ice sheets, 171 superplasticity, 226 preferred crystal orientation, 103 surface defects, 73 recrystallization textures, 115, 129, 139, 171 surface diffusion coefficient, 73 strain-induced textures, 153 surface energy, 23, 191, 206 strength, 166 surface roughness, 313 temperate glacier, 111, 139, 140, 143 surfaces, 23, 73, 228 tension and compression textures, 139 energy, 23, 191, 206 thermal cracks, 212, 369 roughness, 313 thermal expansion, 8 coefficient, 8 tangent approach, 156, 158 mismatch, 229 tangent approximation, 154 thermal gradient, 336 tangent model, 158, 173 thermal mismatch, 229 tangent modulus, 56 thermal shocking, 196 Taylor model, 155, 169 thermal softening, 239, 291 Taylor orientation factor, 230 thermal super-cooling, 43 temperate glacier, 111, 139, 140, 143 thermodynamics, 191 temperature, 328 thrust faults within glaciers, 292 tensile strength, 213, tilt boundary, 22, 134 bend test, 213 tilt sub-boundaries, 90 Brazil test, 213, Titanic, 349 crack-nucleation control, 229 topography of Coulombic faults, 381 crack-propagation control, 228 torsional modulus, 56, 57,

Index 401

toughness, 195 viscoplastic self-consistent (VPSC) model, 154 transformation matrix, 56 viscosity, 383 transient creep, 160 viscous flow, 382, 384 transitional behavior, 214 viscous-plastic mechanics, 376 transition strain rate, 239, 309, 331, 339 Voigt’s method, 58 under compression, 324 volume, 114 vs. fresh-water and salt-water ice, 325 volume diffusion coefficient, 122 transition velocity, 341 volumetric defects, 24 transmission electron microscopy, 21, 32 von Mises criterion, 286 transmission X-ray diffraction, 21 vorticity, 371 transverse isotropy, 65 VPSC model, 129, 158, 168 triaxial compressive strength, 280, 282 triaxial high-pressure apparatus, 181 warm ice, 203 triaxial loading, 267, 270, 280 water, 203, 313 triaxial state of stress, 245, 267 water ice, 1–2, 5 triaxial strength, 270, 282, 286 Weibull’s theory, 352 triaxial test, 267 wing cracks, 196, 251, 252, 258, 294, 361, triaxial yield stress, 121 366, 372 Triton, 51 and comb cracks, 294 true triaxial loading, 268, growth, 259 twist boundary, 22, 134 mechanics, 261 mechanism, 274 unconfined ice, 237 unidirectional solidification, 41, X-ray microanalysis, 32 uniform strain-rate approximation, 155 X-ray microtomography, 32 unit cell, 6 X-ray topography, 21, 22, 31, 77, 92, 93 unloading, 115 unstable growth, 196 yield drop, 78 yield stress, 79 vacancy, 10 Young’s modulus, 56, 57, 64, 191, 207 vacancy prismatic loop, 9, 14 vibration of compliant structure, 337 Zener’s analysis, 230 viscoplastic anisotropy, 153 zero-point entropy, 9