Fracture Processes of Concrete. Assessment of Material Parameters for Fracture Models
Jan G. M. van Mier
1997 г.
В книге представлены основы механики разрушения бетона при растяжении, в том числе зарождения, образования и раскрытия трещин на основе результатов теоретических и экспериментальных исследований параметров нисходящий ветви (tension-softening) диаграммы состояния бетона в условиях растяжения .Книга будет полезна аспирантам и работникам научно-исследовательских организаций, в том числе специалистам, занимающимся симуляцией поведения под нагрузкой железобетонных конструкций с учетом физической нелинейности материалов с использованием таких пакетов конечно-элементного анализа как ANSYS, ABAQUS, DIANA и др.
Оглавление
TABLE OF CONTENTS
1. INTRODUCTION: SETTING THE STAGE
1 . 1 Cracking in concrete and concrete structures . ................. .............. 1
1 .2 Limit theories of materials and structures ...... . ....... ................... ..... 3
1 .3 Different levels of observation ... ..... ............... . . .......... . ............ ....... 5
1 .4 Experiments and (numerical) simulations .................... .......... ........ 7
1 .5 Organisation of the book ....................... .............................. ......... 11
PART 1. STRUCTURE AND MECHANICAL
BEHAVIOUR
2. STRUCTURE OF CEMENT AND CONCRETE
2. 1 Structure of cement ...... . .. . ....... . .. ................................................... 17
2. 1 . l Raw materials and clinkers ........ .......... .. . . ................... . ....... 18
2. 1 .2 Hydration of cement ..................... .............. ........ .... . . ........... 21
2. 1 .3 Water-cement ratio and porosity ...... . .... ........................ ...... 27
2. 1 .4 Structural models for hardened cement paste . ... ... .. ... ......... 30
2.2 Structure of concrete . .......... .......... .. ............. ........ ........ ............ ..... 3 3
2.2. 1 Aggregates, types and properties, particle
distributions ....................... ....... ........... .............. . . . .......... ..... 3 3
2.2.2 Interface between aggregates and cement matrix ............... 3 8
2.2.3 Interface properties: strength and fracture energy ...... . .... ... 46
2.3 Final remarks ......... .. . . . ............... .. . ............ . ........ . ..................... . .... . 52
3 . MECHANICAL BEHAVIOUR O F CONCRETE
3 . 1 Introduction ................................................................................... 55
3 .2 Uniaxial compression ... ......................... ................... .. ... . . . ............. 56
3 . 2. 1 Initial stiffness .... . . . ....... . . .................................. ......... .......... 56
3 . 2.2 Microcracking and micromechanisms .............. ..... . ............. 60
3.2.3 Stress-deformation response ....... .. . ..... . ................................ 68
3 .2.4 Post-peak behaviour and localization of deformations ....... 70
3.2.5 Effect of material composition ...... .......... .................... . ....... 80
3 .2.6 Loading rate and load cycling ............................... ..... . ........ 83
3.2.6. 1 Effect o f loading rate .... ........ ....................... ....... .... 84
3.2.6.2 Cyclic loading .. ...... ............... . . . ................. .... . . ........ 85
3 . 3 Uniaxial tension (Mode I ) ........... ........ ........ ...... .... . . ............ ...... . .. 88
3 .3 . 1 Microcracking and micromechanisms in tension .... . . ...... ... 89
3.3 . 1 .1 Impregnation ..... .... ........ ......... .... ... ............. . ...... ...... 92
3.3. 1 .2 Optical microscopy .. ............. ....... . .... ..... ............. . ... 97
3 . 3 .2 Effect of material structure on tensile softening .............. 102
3 . 3 .2. 1 Effect of particle size and particle type ............... 102
3 .3.2.2 Effect of water-cement ratio and porosity ........... 106
3.3.2.3 Effect of curing conditions ................. .................. 107
3.3.3 Effect of load-cycling, fatigue and impact ....................... 110
3.4 Shear (mode II, III and mixed modes) ....................................... 114
3.4.1 Different approaches to shear fracture ................... ........... 115
3 .4.1.1 Linear fracture mechanics approach .................... 116
3.4.1.2 Mixed-mode I and II fracture energy? ................. 119
3.4.1.3 Extension of the fictitious crack model for
shear ...................................................................... 120
3.4.2 Does mode II fracture in concrete exist ? ......................... 128
3.4.3 Short note on mode III fracture ........................................ 131
3.5 Multiaxial states of stress ............ ............................................... 132
3.5.1 Micromechanisms .............................................................. 133
3.5.2 Failure contours ................................................................. 134
3.5.2.1 Biaxial failure contours ........................................ 134
3.5.2.2 Triaxial failure contours ....................................... 136
3.5.2.3 Bounding surfaces from constant
displacement-ratio tests ...... . . ................................ 141
3.5.3 Stress-strain behaviour ..................................................... 143
3.5.4 Failure under multiaxial stress .......................................... 150
3.6 Final remarks ............................................................................... 154
PART 2. EXPERIMENTAL AND MODELLING TOOLS
4 EXPERIMENTAL TOOLS
4.1 Loading equipment ..................................................................... 157
4.1.1 Load- versus displacement-controlled testing ............. .... 158
4.1.2 Selecting the control variable ............................................ 162
4.1.2.1 General set-up of a stable fracture experiment. ... 162
4.1.2.2 Examples of advanced fracture experiments ....... 166
a. Four-point-shear experiments ........................... 166
b. Hydraulic fracture tests ............. ....................... 171
c. Multiaxial compression experiments ................ 173
4.1.3 The importance of boundary conditions ........................... 177
4.1.3.1 Frictional restraint ................................................. 178
a. Uniaxial compression experiments ................... 178
b. Beam experiments ............................................ 188
4.1.3 .2 Boundary rotations ............................................... 189
a. Boundary rotations in uniaxial tensile
experiments ....................................................... 190
b. Maintaining uniformity of deformations
in a three-jack system .......................... ............. 199
4.1.3.3 Platen interactions ............................................... . . 200
4.2 Specimen selection ...................................................................... 202
4.2.1 Specimen surface ...... ......................................................... 204
4.2.2 About notches .. ................................... ............................... 205
4.2.3 Size and scale of specimens and materials ....................... 207
4.2.4 Specimen shape . .......... . . .. .......................... ................ . . .... . . 210
4.3 Data acquisition ......... ............ . ..................................................... 212
4.4 Crack detection techniques . . . ................................................ ...... 215
4.4.1 Local surface deformation measurements .................. ..... .. 216
4.4.2 Full-field surface deformation measurement techniques .. 220
4.4.2. 1 Photo-elastic coating techniques ................... ..... .. 221
4.4.2.2 Interferometry techniques ......... . ....... ............. ..... . . 222
4.4.2. 3 Stereo-photogrammertry ............ .............. .... ...... .. . 223
4.4.3 Microscopy, impregnation and image analysis .......... . .... . . 224
4.4.4 Acoustic techniques .......... .......................................... ...... . 230
4.4.5 Other techniques ........................... ........... ....... .. ......... . ..... . . 233
4.4.6 Concluding remarks .......................... . .. . ... . . ................ . .. .... . 235
4.5 Theory of experimental designs ................ ....... . ......................... 235
4.6 The need for standard testing ................ ........ . .................... ........ 241
4.6. 1 Fracture energy and tensile softening . . ......... ................ ... . 243
4.6.2 Compressive strength and softening ........ .. ....................... 250
5. MODELLING AS A TOOL FOR TEST INTERPRETATION
5 .1 Introduction ................................................................................. 253
5.2 Representing the material ..................... ......................... ... .......... 255
5.2.1 Continuum or lattice ... .... . .. ... . .. . . ..... ............... ..... ........... . . .. 255
5.2.2 Mapping the material structure ....... .... ................. .... ....... .. 259
5 .3 Fracture laws for continuum based models .... ... ................ ......... 264
5.3.1 Classical Strength of materials law: brittle failure .. ........ . 265
5.3.2 Linear elastic fracture mechanics .............. ... ... .. ... .... . . .... ... 272
5.3 .2. 1 Irwin's model ........... ... ...... ....... .......... . . .. .... . . . ........ 275
5.3.2.2 Griffith theory .. . ......... . ....... . . ... .. .......... . ....... . ......... 279
5.3 .2.3 Example of crack growth analysis . ...... ... ..... . ...... . 281
5.3 .2.4 Application of LEFM at the meso-level ..... ......... 284
5.3.3 The Dugdale-Barenblatt plastic crack tip .. . .. . ........... ........ 290
5 . 3 .4 Fictitious crack model ............... .. .. . .. ... ..... .... ................. .... 291
5.3 .4. 1 Principle of the model ......... . .. . .. .. . ........................ 292
5.3.4.2 Stability considerations .... ... ... .......... ..................... 295
5.3.4.3 Crack-band width ..... .......... . .................... ....... ...... 298
5.3.4.4 Mixed fracture modes ..... ................ ................ ...... 299
5 . 3.5 Summary of the basic models .................. ..... .................... 30 1
5.4 Fracture laws for lattice type models ..... ............... ............... ... ... 30 1
5 .4.1 An atomic view on fracture ....... . ......................... .. . . . .... . . .. 302
5 .4.2 Fracture laws for beam models ................ ... .............. .... .... 306
PART 3. SYNTHESIS
6. VALIDATION OF MODEL PARAMETERS
6. 1 Introduction .... . ............................................ ...... ... . ..... ... . .. .. .. ....... 315
6.2 Fictitious crack model ................................................................. 315
6.3 Lattice model ............................................................................... 320
6.3. l Parameters related to the elastic lattice properties ............321
6.3.2 Fracture parameters ........................................................... 324
6.3.3 Small particle effect, porosity and 30-effect .................... 328
6.3.3.1 Omitting small particles ....................................... 328
6.3.3.2 Including porosity ................................................. 330
6.3.3.3 3D-effects .............................................................. 332
7. NUMERICAL SIMULATION OF PLAIN CONCRETE
FRACTURE EXPERIMENTS
7.1 Introduction ................................................................................. 337
7.2 Uniaxial tension .......................................................................... 339
7.2.1 Crack face bridging ........................................................... 339
7 .2.2 Effect of boundary rotations on tensile softening ............ 344
7.2.3 Non-uniform opening: comparing different approaches .. 348
7 .3 Combined tension and shear ....................................................... 350
7.3.1 "Shear" in a four-point-shear beam? ................................ 350
7.3.2 Boundary effects in biaxial tension/shear experiments .... 354
7.4 UniaxiaJ compression .................................................................. 357
7.4.1 Lattice model analyses ...................................................... 357
7.4.2 Continuum particle models ............................................... 358
7.5 Failure contours ........................................................................... 361
8. FRACTURE MECHANICS FOR STRUCTURAL ANALYSIS
8. 1 Introduction ................................................................................. 367
8.2 Analysis of bond-slip between steel and concrete ..................... 368
8.3 Analysis of anchor puU-out ........................................................ 375
8.4 Evaluation of brittleness of structures ........................................ 384
Appendix: Principal stresses and invariants . . . . .. ....... . . . ................ 389
References ........................................................................................ 397
Index ... ....... .... . . . . . . . ... . . . .......... ...................... . . . .... . .......... 423
1. INTRODUCTION: SETTING THE STAGE
1 . 1 Cracking in concrete and concrete structures . ................. .............. 1
1 .2 Limit theories of materials and structures ...... . ....... ................... ..... 3
1 .3 Different levels of observation ... ..... ............... . . .......... . ............ ....... 5
1 .4 Experiments and (numerical) simulations .................... .......... ........ 7
1 .5 Organisation of the book ....................... .............................. ......... 11
PART 1. STRUCTURE AND MECHANICAL
BEHAVIOUR
2. STRUCTURE OF CEMENT AND CONCRETE
2. 1 Structure of cement ...... . .. . ....... . .. ................................................... 17
2. 1 . l Raw materials and clinkers ........ .......... .. . . ................... . ....... 18
2. 1 .2 Hydration of cement ..................... .............. ........ .... . . ........... 21
2. 1 .3 Water-cement ratio and porosity ...... . .... ........................ ...... 27
2. 1 .4 Structural models for hardened cement paste . ... ... .. ... ......... 30
2.2 Structure of concrete . .......... .......... .. ............. ........ ........ ............ ..... 3 3
2.2. 1 Aggregates, types and properties, particle
distributions ....................... ....... ........... .............. . . . .......... ..... 3 3
2.2.2 Interface between aggregates and cement matrix ............... 3 8
2.2.3 Interface properties: strength and fracture energy ...... . .... ... 46
2.3 Final remarks ......... .. . . . ............... .. . ............ . ........ . ..................... . .... . 52
3 . MECHANICAL BEHAVIOUR O F CONCRETE
3 . 1 Introduction ................................................................................... 55
3 .2 Uniaxial compression ... ......................... ................... .. ... . . . ............. 56
3 . 2. 1 Initial stiffness .... . . . ....... . . .................................. ......... .......... 56
3 . 2.2 Microcracking and micromechanisms .............. ..... . ............. 60
3.2.3 Stress-deformation response ....... .. . ..... . ................................ 68
3 .2.4 Post-peak behaviour and localization of deformations ....... 70
3.2.5 Effect of material composition ...... .......... .................... . ....... 80
3 .2.6 Loading rate and load cycling ............................... ..... . ........ 83
3.2.6. 1 Effect o f loading rate .... ........ ....................... ....... .... 84
3.2.6.2 Cyclic loading .. ...... ............... . . . ................. .... . . ........ 85
3 . 3 Uniaxial tension (Mode I ) ........... ........ ........ ...... .... . . ............ ...... . .. 88
3 .3 . 1 Microcracking and micromechanisms in tension .... . . ...... ... 89
3.3 . 1 .1 Impregnation ..... .... ........ ......... .... ... ............. . ...... ...... 92
3.3. 1 .2 Optical microscopy .. ............. ....... . .... ..... ............. . ... 97
3 . 3 .2 Effect of material structure on tensile softening .............. 102
3 . 3 .2. 1 Effect of particle size and particle type ............... 102
3 .3.2.2 Effect of water-cement ratio and porosity ........... 106
3.3.2.3 Effect of curing conditions ................. .................. 107
3.3.3 Effect of load-cycling, fatigue and impact ....................... 110
3.4 Shear (mode II, III and mixed modes) ....................................... 114
3.4.1 Different approaches to shear fracture ................... ........... 115
3 .4.1.1 Linear fracture mechanics approach .................... 116
3.4.1.2 Mixed-mode I and II fracture energy? ................. 119
3.4.1.3 Extension of the fictitious crack model for
shear ...................................................................... 120
3.4.2 Does mode II fracture in concrete exist ? ......................... 128
3.4.3 Short note on mode III fracture ........................................ 131
3.5 Multiaxial states of stress ............ ............................................... 132
3.5.1 Micromechanisms .............................................................. 133
3.5.2 Failure contours ................................................................. 134
3.5.2.1 Biaxial failure contours ........................................ 134
3.5.2.2 Triaxial failure contours ....................................... 136
3.5.2.3 Bounding surfaces from constant
displacement-ratio tests ...... . . ................................ 141
3.5.3 Stress-strain behaviour ..................................................... 143
3.5.4 Failure under multiaxial stress .......................................... 150
3.6 Final remarks ............................................................................... 154
PART 2. EXPERIMENTAL AND MODELLING TOOLS
4 EXPERIMENTAL TOOLS
4.1 Loading equipment ..................................................................... 157
4.1.1 Load- versus displacement-controlled testing ............. .... 158
4.1.2 Selecting the control variable ............................................ 162
4.1.2.1 General set-up of a stable fracture experiment. ... 162
4.1.2.2 Examples of advanced fracture experiments ....... 166
a. Four-point-shear experiments ........................... 166
b. Hydraulic fracture tests ............. ....................... 171
c. Multiaxial compression experiments ................ 173
4.1.3 The importance of boundary conditions ........................... 177
4.1.3.1 Frictional restraint ................................................. 178
a. Uniaxial compression experiments ................... 178
b. Beam experiments ............................................ 188
4.1.3 .2 Boundary rotations ............................................... 189
a. Boundary rotations in uniaxial tensile
experiments ....................................................... 190
b. Maintaining uniformity of deformations
in a three-jack system .......................... ............. 199
4.1.3.3 Platen interactions ............................................... . . 200
4.2 Specimen selection ...................................................................... 202
4.2.1 Specimen surface ...... ......................................................... 204
4.2.2 About notches .. ................................... ............................... 205
4.2.3 Size and scale of specimens and materials ....................... 207
4.2.4 Specimen shape . .......... . . .. .......................... ................ . . .... . . 210
4.3 Data acquisition ......... ............ . ..................................................... 212
4.4 Crack detection techniques . . . ................................................ ...... 215
4.4.1 Local surface deformation measurements .................. ..... .. 216
4.4.2 Full-field surface deformation measurement techniques .. 220
4.4.2. 1 Photo-elastic coating techniques ................... ..... .. 221
4.4.2.2 Interferometry techniques ......... . ....... ............. ..... . . 222
4.4.2. 3 Stereo-photogrammertry ............ .............. .... ...... .. . 223
4.4.3 Microscopy, impregnation and image analysis .......... . .... . . 224
4.4.4 Acoustic techniques .......... .......................................... ...... . 230
4.4.5 Other techniques ........................... ........... ....... .. ......... . ..... . . 233
4.4.6 Concluding remarks .......................... . .. . ... . . ................ . .. .... . 235
4.5 Theory of experimental designs ................ ....... . ......................... 235
4.6 The need for standard testing ................ ........ . .................... ........ 241
4.6. 1 Fracture energy and tensile softening . . ......... ................ ... . 243
4.6.2 Compressive strength and softening ........ .. ....................... 250
5. MODELLING AS A TOOL FOR TEST INTERPRETATION
5 .1 Introduction ................................................................................. 253
5.2 Representing the material ..................... ......................... ... .......... 255
5.2.1 Continuum or lattice ... .... . .. ... . .. . . ..... ............... ..... ........... . . .. 255
5.2.2 Mapping the material structure ....... .... ................. .... ....... .. 259
5 .3 Fracture laws for continuum based models .... ... ................ ......... 264
5.3.1 Classical Strength of materials law: brittle failure .. ........ . 265
5.3.2 Linear elastic fracture mechanics .............. ... ... .. ... .... . . .... ... 272
5.3 .2. 1 Irwin's model ........... ... ...... ....... .......... . . .. .... . . . ........ 275
5.3.2.2 Griffith theory .. . ......... . ....... . . ... .. .......... . ....... . ......... 279
5.3 .2.3 Example of crack growth analysis . ...... ... ..... . ...... . 281
5.3 .2.4 Application of LEFM at the meso-level ..... ......... 284
5.3.3 The Dugdale-Barenblatt plastic crack tip .. . .. . ........... ........ 290
5 . 3 .4 Fictitious crack model ............... .. .. . .. ... ..... .... ................. .... 291
5.3 .4. 1 Principle of the model ......... . .. . .. .. . ........................ 292
5.3.4.2 Stability considerations .... ... ... .......... ..................... 295
5.3.4.3 Crack-band width ..... .......... . .................... ....... ...... 298
5.3.4.4 Mixed fracture modes ..... ................ ................ ...... 299
5 . 3.5 Summary of the basic models .................. ..... .................... 30 1
5.4 Fracture laws for lattice type models ..... ............... ............... ... ... 30 1
5 .4.1 An atomic view on fracture ....... . ......................... .. . . . .... . . .. 302
5 .4.2 Fracture laws for beam models ................ ... .............. .... .... 306
PART 3. SYNTHESIS
6. VALIDATION OF MODEL PARAMETERS
6. 1 Introduction .... . ............................................ ...... ... . ..... ... . .. .. .. ....... 315
6.2 Fictitious crack model ................................................................. 315
6.3 Lattice model ............................................................................... 320
6.3. l Parameters related to the elastic lattice properties ............321
6.3.2 Fracture parameters ........................................................... 324
6.3.3 Small particle effect, porosity and 30-effect .................... 328
6.3.3.1 Omitting small particles ....................................... 328
6.3.3.2 Including porosity ................................................. 330
6.3.3.3 3D-effects .............................................................. 332
7. NUMERICAL SIMULATION OF PLAIN CONCRETE
FRACTURE EXPERIMENTS
7.1 Introduction ................................................................................. 337
7.2 Uniaxial tension .......................................................................... 339
7.2.1 Crack face bridging ........................................................... 339
7 .2.2 Effect of boundary rotations on tensile softening ............ 344
7.2.3 Non-uniform opening: comparing different approaches .. 348
7 .3 Combined tension and shear ....................................................... 350
7.3.1 "Shear" in a four-point-shear beam? ................................ 350
7.3.2 Boundary effects in biaxial tension/shear experiments .... 354
7.4 UniaxiaJ compression .................................................................. 357
7.4.1 Lattice model analyses ...................................................... 357
7.4.2 Continuum particle models ............................................... 358
7.5 Failure contours ........................................................................... 361
8. FRACTURE MECHANICS FOR STRUCTURAL ANALYSIS
8. 1 Introduction ................................................................................. 367
8.2 Analysis of bond-slip between steel and concrete ..................... 368
8.3 Analysis of anchor puU-out ........................................................ 375
8.4 Evaluation of brittleness of structures ........................................ 384
Appendix: Principal stresses and invariants . . . . .. ....... . . . ................ 389
References ........................................................................................ 397
Index ... ....... .... . . . . . . . ... . . . .......... ...................... . . . .... . .......... 423
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