简介
This book serves both as a textbook and a scientific work. As a textbook, the work gives a clear, thorough and systematic presentation of the fundamental postulates, theorems and principles and their applications of the classical mathematical theories of plasticity and creep. In addition to the mathematical theories, the physical theory of plasticity, the book presents the Budiansky concept of slip and its modification by M. Leonov. Special attention is given to the analysis of the advantages and shortcomings of the classical theories. In its main part, the book presents the synthetic theory of irreversible deformations, which is based on the mathematical Sanders flow plasticity theory and the physical theory, the Budiansky concept of slip. The main peculiarity of the synthetic theory is that the formulae for both plastic and creep deformation, as well their interrelations, can be derived from the single constitutive equation. Furthermore, the synthetic theory, as physical one, can take into account the real processes that take place in solids at irreversible deformation. This widens considerably the potential of the synthetic theory. In the framework of the synthetic theory such problems as creep delay, the Hazen-Kelly effect, the deformation at the break of the load trajectory, the influence of the rate of loading on the stress-strain diagram, creep at the changes of load, creep at unloading and reversed creep, have been analytically described. In the last chapter, the book shows the solution of some contemporary problems of plasticity and creep: Creep deformation at cyclic abrupt changes of temperature, The influence of irradiation on the plastic and creep deformation, Peculiarities of deformation at the phase transformation of some metals.
目录
Title 1
Contents 4
Classical Theories of Plasticity 8
Definition of Subject 8
Hencky\u2013Nadai Deformation Theory 10
Hencky Relations 17
Infinite Thin Plate with a Circular Hole: Comparison of Three Solutions 20
Ilyushin\u2019s Theorems 27
Prager Deformation Theory 39
Ilyushin\u2019s Space 42
Isotropy Postulate 46
Loading Surface 51
Drucker\u2019s Postulate 54
Analysis of the Hencky\u2013Nadai Theory 57
Boundaries of the Applicability of the Hencky\u2013Nadai Relations 62
Flow Plasticity Theories: Isotropic Hardening Rule 67
Flow Theory for Elastic-Perfectly Plastic Materials 75
More Complicated Flow Plasticity Theories 80
Flow Plasticity Theory with Kinematic Hardening 82
Lode-Nadai Variable 87
Experimental Check of the Laws of Plasticity at Combined Loading 88
Flow Plasticity Theory with a Singular Loading Surface 100
Conclusions 106
The Concept of Slip 108
One- and Two-Level Models of Deformation 108
Some Basic Knowledge in the Physics of Metals 109
The Batdorf-Budiansky Theory of Slip 115
Uniaxial Strain Pure Shear 120
The Cicala Formula 123
The Cicala Surface 125
Analysis of the Budiansky Theory 131
Generalization of Yield Criterion 134
The Leonov Theory of Slip 137
Shear Strength 140
Rehabilitation of the Concept of Slip 142
Peculiarities of Plastic Straining under Proportional Loading 146
Drucker\u2019s Postulate and the Concept of Slip 150
Analysis of the Leonov Theory 153
Plastic Strain under Combined Loading 154
Two Problems 157
Rearranging in Differential Equations 161
Computer-Aided Calculations 165
The Concept of Slip and the Isotropy Postulate 166
Loading Surface 168
The Bauschinger Effect 171
Alternating Loading in Tension-Compression 173
Loading Surface at Alternating Loading in Tension-Compression 176
Conclusions Relative to Shear Strength 178
Leonov-Shvajko Model 179
Comparison of Two Models 182
Discrete Scheme of Slips 184
Synthetic Theory of Plasticity 188
Introductory Remarks 188
Partial Cases of the Tresca Yield Surface 188
Tresca Yield Surface in Five-Dimensional Stress Deviator Space 191
Koiter\u2019s Result 194
Introduction of New Variables 196
Modification of Yield Criterion 199
Modified Yield Surface 201
Tangential Planes and Their Traces 202
Basic Equations 203
Pure Shear 207
Proportional Loading 210
Cicala Formula 212
Two-Segment Loading Trajectory 215
Plastic Strain at Two-Segment Loading Path 221
Partial Cases 225
Loading Surface 228
Another Variant of the Deformation Anisotropy 233
Alternating Torsion 235
Proportional Alternating Loading 240
Discussion 241
The Creep Theory 244
General Remarks 244
Non-homogenous Distribution of Strains and Stresses of the Second Kind 247
Local Peak Stresses 251
Elastic Area 255
Mathematical Measure of Local Peak Stresses 256
Properties of the Integral of Non-homogeneity 260
Account of Loading Rate 262
The Creep and Yield Limit 264
Influence of Loading Rate on Stress-Strain Diagram in Pure Shear 269
Sudden Increase in Loading Rate 271
Proportional Loading 273
Stress-Strain Diagram at Elevated Temperatures 274
The Integral of Non-homogeneity in Alternating Torsion 276
Cyclic Properties of Material 279
Peculiarities of Irreversible Straining in Alternate Loading 280
Deformation in Alternating Torsion 283
Instantaneous Plastic and Creep Deformation 287
Classical Creep Theories in Uniaxial Tension 289
Creep Potential 295
Experimental Verification of Creep Laws 301
On the Advantages of the Physical Theories of Plasticity and Creep 303
Physics of Unsteady-State Creep 306
Unsteady Creep in Pure Shear 307
Generalization to an Arbitrary State of Stress 310
Creep Delay 311
Haazen-Kelly's Effect 312
Creep with Variable Loading 315
Generalization of the Cicala Formula 318
Analysis of the Generalized Cicala Formula 322
Intermediate Discussion 324
Physics of Steady-State Creep 326
Generalized Synthetic Theory of Irreversible Deformation 327
Irreversible Deformation in Pure Shear 334
Creep Deformation in Pure Shear 336
Creep in a State of Complex Stress 339
Definition of Function K 342
Definition of Function K: Continuation 345
Creep with Different Plastic Pre-strains 346
Creep with Different Plastic Pre-strains: Continuation 352
Reverse Creep 355
Duration of Creep Delay and Reverse Creep 358
Discussion 367
Light Alloys Creep 368
Conclusions to the Chapter 4 370
New Problems of Plasticity and Creep 372
Temperature After-Effect Strain 372
Physical Nature of Temperature After-Effect 375
Modeling of Temperature After-Effect 376
Temperature After-Effect in Pure Shear 378
Temperature After-Effect at Cooling 384
Temperature Strengthening 388
Influence of Atomic Irradiation Upon Plastic and Creep Deformation of Metals 391
Mathematical Theory of the Irreversible Deformation in Irradiation 394
Creep and Yield Criteria 398
Plastic Deformation in Radiation 401
Creep Deformation in Radiation 403
The Determination of Function K 406
Phase Transformations 407
Stress-Strain Diagram under Phase Transformations 411
Effective Temperature 414
Mathematical Model of Deformation under Phase Transformations 416
PT-Deformation under Heating or Cooling 420
Mathematical Description of Pseudo-elasticity 422
Modeling of Pseudo-elasticity at Unloading 425
Modeling of Transformation Plasticity 428
Conclusions 430
Conclusions 431
References 434
Contents 4
Classical Theories of Plasticity 8
Definition of Subject 8
Hencky\u2013Nadai Deformation Theory 10
Hencky Relations 17
Infinite Thin Plate with a Circular Hole: Comparison of Three Solutions 20
Ilyushin\u2019s Theorems 27
Prager Deformation Theory 39
Ilyushin\u2019s Space 42
Isotropy Postulate 46
Loading Surface 51
Drucker\u2019s Postulate 54
Analysis of the Hencky\u2013Nadai Theory 57
Boundaries of the Applicability of the Hencky\u2013Nadai Relations 62
Flow Plasticity Theories: Isotropic Hardening Rule 67
Flow Theory for Elastic-Perfectly Plastic Materials 75
More Complicated Flow Plasticity Theories 80
Flow Plasticity Theory with Kinematic Hardening 82
Lode-Nadai Variable 87
Experimental Check of the Laws of Plasticity at Combined Loading 88
Flow Plasticity Theory with a Singular Loading Surface 100
Conclusions 106
The Concept of Slip 108
One- and Two-Level Models of Deformation 108
Some Basic Knowledge in the Physics of Metals 109
The Batdorf-Budiansky Theory of Slip 115
Uniaxial Strain Pure Shear 120
The Cicala Formula 123
The Cicala Surface 125
Analysis of the Budiansky Theory 131
Generalization of Yield Criterion 134
The Leonov Theory of Slip 137
Shear Strength 140
Rehabilitation of the Concept of Slip 142
Peculiarities of Plastic Straining under Proportional Loading 146
Drucker\u2019s Postulate and the Concept of Slip 150
Analysis of the Leonov Theory 153
Plastic Strain under Combined Loading 154
Two Problems 157
Rearranging in Differential Equations 161
Computer-Aided Calculations 165
The Concept of Slip and the Isotropy Postulate 166
Loading Surface 168
The Bauschinger Effect 171
Alternating Loading in Tension-Compression 173
Loading Surface at Alternating Loading in Tension-Compression 176
Conclusions Relative to Shear Strength 178
Leonov-Shvajko Model 179
Comparison of Two Models 182
Discrete Scheme of Slips 184
Synthetic Theory of Plasticity 188
Introductory Remarks 188
Partial Cases of the Tresca Yield Surface 188
Tresca Yield Surface in Five-Dimensional Stress Deviator Space 191
Koiter\u2019s Result 194
Introduction of New Variables 196
Modification of Yield Criterion 199
Modified Yield Surface 201
Tangential Planes and Their Traces 202
Basic Equations 203
Pure Shear 207
Proportional Loading 210
Cicala Formula 212
Two-Segment Loading Trajectory 215
Plastic Strain at Two-Segment Loading Path 221
Partial Cases 225
Loading Surface 228
Another Variant of the Deformation Anisotropy 233
Alternating Torsion 235
Proportional Alternating Loading 240
Discussion 241
The Creep Theory 244
General Remarks 244
Non-homogenous Distribution of Strains and Stresses of the Second Kind 247
Local Peak Stresses 251
Elastic Area 255
Mathematical Measure of Local Peak Stresses 256
Properties of the Integral of Non-homogeneity 260
Account of Loading Rate 262
The Creep and Yield Limit 264
Influence of Loading Rate on Stress-Strain Diagram in Pure Shear 269
Sudden Increase in Loading Rate 271
Proportional Loading 273
Stress-Strain Diagram at Elevated Temperatures 274
The Integral of Non-homogeneity in Alternating Torsion 276
Cyclic Properties of Material 279
Peculiarities of Irreversible Straining in Alternate Loading 280
Deformation in Alternating Torsion 283
Instantaneous Plastic and Creep Deformation 287
Classical Creep Theories in Uniaxial Tension 289
Creep Potential 295
Experimental Verification of Creep Laws 301
On the Advantages of the Physical Theories of Plasticity and Creep 303
Physics of Unsteady-State Creep 306
Unsteady Creep in Pure Shear 307
Generalization to an Arbitrary State of Stress 310
Creep Delay 311
Haazen-Kelly's Effect 312
Creep with Variable Loading 315
Generalization of the Cicala Formula 318
Analysis of the Generalized Cicala Formula 322
Intermediate Discussion 324
Physics of Steady-State Creep 326
Generalized Synthetic Theory of Irreversible Deformation 327
Irreversible Deformation in Pure Shear 334
Creep Deformation in Pure Shear 336
Creep in a State of Complex Stress 339
Definition of Function K 342
Definition of Function K: Continuation 345
Creep with Different Plastic Pre-strains 346
Creep with Different Plastic Pre-strains: Continuation 352
Reverse Creep 355
Duration of Creep Delay and Reverse Creep 358
Discussion 367
Light Alloys Creep 368
Conclusions to the Chapter 4 370
New Problems of Plasticity and Creep 372
Temperature After-Effect Strain 372
Physical Nature of Temperature After-Effect 375
Modeling of Temperature After-Effect 376
Temperature After-Effect in Pure Shear 378
Temperature After-Effect at Cooling 384
Temperature Strengthening 388
Influence of Atomic Irradiation Upon Plastic and Creep Deformation of Metals 391
Mathematical Theory of the Irreversible Deformation in Irradiation 394
Creep and Yield Criteria 398
Plastic Deformation in Radiation 401
Creep Deformation in Radiation 403
The Determination of Function K 406
Phase Transformations 407
Stress-Strain Diagram under Phase Transformations 411
Effective Temperature 414
Mathematical Model of Deformation under Phase Transformations 416
PT-Deformation under Heating or Cooling 420
Mathematical Description of Pseudo-elasticity 422
Modeling of Pseudo-elasticity at Unloading 425
Modeling of Transformation Plasticity 428
Conclusions 430
Conclusions 431
References 434
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