Many components in conventional and nuclear power stations, chemical plants, airplane engines, manufacturing processes such as super plastic forming, and soon operate at combinations of temperature and stress that are high enough for creep and creep fracture to occur. In order to satisfy the desire to increase efficiency while reducing emissions, there is a continuous drive to increase the temperatures of and load levels applied to high-temperature components, while still ensuring that they operate safely and economically.
In order to achieve the required higher and higher temperatures and stresses, there have been major developments in alloys and the processes used to manufacture and heat-treat the components produced using the improved materials. Major improvements have also been achieved in the stress analysis techniques used by the designers and operators of high-temperature equipment. In addition, developments in inspection techniques used for crack and damage detection and of small scoop or boat sample removal techniques have resulted in improvements in design, maintenance, and remaining life assessment methods. Various novel small creep specimens can be machined from the scoop or boat samples in order to obtain bulk material creep properties for steam pipes or pipe bends, for example.
Creep mechanics is concerned with the use of creep material behavior models in conjunction with stress/deformation analysis methods to predict the creep behavior of components. The material behavior models are based on data obtained from creep testing. It is clear that, to a greater or lesser extent, the creep behavior of materials and components is of interest to a wide range of students and specialists, including metallurgists, materials scientists, designers, stress analysts, researchers, and students(undergraduate and postgraduate)of engineering, solid mechanics, mathematics, and materials-related courses.
This book is intended for a wide audience. Those just beginning to study creep will find Chaps. 2 and 4 of help because they place creep mechanics in the broader context of solid mechanics; the use of complicated mathematics is minimized. Chapter 3 contains descriptions of various creep and creep damage constitutive equations and outlines the test types and data processing used to establish the material constants. Chapter 5 describes the basis of the reference stress method and of other simplified, but extremely powerful, creep mechanics methods. By the completion of Chap. 5, the types of creep constitutive equations commonly used and the types of analytical methods used for the analysis of single-material(homogeneous) components will be fully described. Chapter 7 introduces the finite element method as it applies to single-material components, and the results of finite element analyses are used to verify the simplified methods described in Chap. 5.
Less widely known applications are covered in the remainder of the book. These are the analytical solutions for the creep of multi material(heterogeneous)components in Chap. 6, the creep of welded components(which can be regarded as a particular case of heterogeneous structure)in Chap. 8, the creep of notched and cracked components(using fracture mechanics and damage-mechanics methods)in Chaps. 9 and 10, and the use of small-specimen creep testing to obtain "bulk"creep data in Chap. 11.
The authors have attempted to include in a single volume a book that contains an up-to-date account of applied creep mechanics, covering the basic material, in the broad context of solid mechanics, as well as advanced topics, such as creep of welded components, creep of cracked components, and small-specimen creep testing.
Much of the book is based on research work carried out in the group to which the authors belong. However, references are provided for many other authors in relation to specific topics in creep mechanics, but it is acknowledged that there will be unintentional omissions, and we apologize for that. However, creep is avast topic, and at some point, the writing of a book has to stop. The authors acknowledge the considerable contributions made by the many research students who have worked with them and those made by their colleagues.
Note: Several of the figures are available in color for download at www. mhprofessional. com/hyde(Figs. 7. 10, 8. 11, 8. 13, 8. 34, 8. 36, 8. 38, 8. 49, 8. 52, 10. 14, 10. 16, 10. 19, 10. 20 and 10. 21).

Preface xii

1 Introduction 1

Notation 8

References 8

2 General Solid Mechanics Background 9

2.1 Material Behavior When Subjected to a Uniaxial State of Stress.to a Uniaxial State of Stress 9

      2.1.1 Elastic Behavior of Materials 9

      2.1.2 Elastic-Plastic Behavior of Materials 10

      2.1.3. Creep Behavior of Materials 14

2.2 Material Behavior When Subjected to a Multiaxial State of Stress 18

      2.2.1 Elastic Behavior of Materials 18

      2.2.2 Elastic-Plastic Behavior of Materials 20

      2.2.3 Creep Behavior of Materials 23

2.3 Structural Analysis of Linear-Elastic Components 27

      2.3.1 Description of Broad Problem Types 27

      2.3.2 Linear-Elastic Bending of Beams 30

      2.3.3 Linear-Elastic Behavior of Internally Pressurized Thick Tubes 32

      2.3.4 Application of an Energy-Based Method to Linear-Elastic Components 35

2.4 Elastic-Plastic Analysis of Components 39

      2.4.1 Elastic-Plastic Bending of Beams 39

      2.4.2 Elastic-Plastic Behavior of Internally Pressurized Tubes 40

      2.4.3 Notch Stresses and Strains 41

2.5 Fatigue and Fracture Mechanics 43

      2.5.1 Basic Phenomena 43

      2.5.2 Fatigue Data 44

      2.5.3 Effect of Mean Stress 45

      2.5.4 Effect of Stress Concentrations 46

      2.5.5Linear-Elastic Fracture Mechanics 47

      2.5.6 Fatigue Crack Growth 52

2.6 The Finite Element Method 54

Notation 55

References 56

3 Material Behavior Models For Creep Analysis 59

3.1 Introduction 59

3.2 Norton's Creep Law for Secondary Creep 61

      3.2.1 The Model 61

      3.2.2 Estimating the Material Constants 61

3.3 Damage Mechanics Models 62

      3.3.1 Single-Damage Parameter Equations 62

      3.3.2 Two-Damage Parameter Equations 74

3.4 Unified Viscoplasticity Model 78

      3.4.1 The Basic Model 78

      3.4.2 Estimating the Material Constants for the Chaboche Unified Viscoplasticity Model 81

3.5 Optimization of Material Constants for the Visco plasticity Model 95

      3.5.1 Basis of the Optimization Process 95

      3.5.2 The Optimization Procedure 98

3.6 Other Models 104

Notation 106

References 107

4 Stationary State Creep of Single-Material, Uncracked Components 111

4.1General Behavior of Components Under Creep Conditions 111

4.2 Statistically Determinate Problems 115

      4.2.1 Axially Loaded Tapered Bar 116

      4.2.2 Axially Loaded Stepped Bar 117

      4.2.3 Internally Pressurized Thin Cylinder with Closed Ends 118

      4.2.4 Internally Pressurized Thin Sphere 120

4.3 Statistically Indeterminate Problems 121

      4.3.1 Beams Subjected to Pure Bending 121

      4.3.2 Deflections of Beam-Type Structures 123

      4.3.3 Pure Torsion of a Circular Bar 131

      4.3.4 Internally Pressurized Thick Cylinder 132

      4.3.5 Internally Pressurized Thick Sphere 138

      4.3.6 Two-Bar Structure 143

Notation 144

Reference 145

5 Inferences from Single-Material, Un cracked, Stationary-State Creep Analyses 147

5.1 Stationary-State Deformation Rates 147

5.2 Stationary-State Stress Distributions 155

5.3 Maximum Stationary-State Stresses 159

Notation 163

Reference 164

6 Stationary-State Creep Of Multimaterial Uncracked Components

6.1 Multi bar Structures 170

      6.1.1 Two-Bar Structure 170

      6.1.2 Three-Bar Structure 172

6.2 Multi material "Sandwich" Beam Components 173

      6.2.1 Two-Material "Sandwich" Beam Components 173

      6.2.2 Three-Material "Sandwich" Beam Components 177

6.3 Multi material Compound Internally Pressurized Thin Spheres 181

6.3.1 Two-Material Compound Spheres 181

6.3.2 Three-Material Compound Spheres 183

6.4 Multi material Compound Internally Pressurized Thin Tubes 184

      6.4.1 Two-Material Compound Cylinders 184

      6.4.2 Three-Material Compound Cylinders 187

6.5 Multi material Compound Internally Pressurized Thick Cylinders 189

      6.5.1 Two-Material Thick Cylinders 189

      6.5.2 Three-Material Thick Cylinders 191

6.6 General Form of the Solutions for Stresses in Multi material Components 193

6.7 General Form of the Solutions for Deformation in Multi material Components 198

Notation 199

References 200

7 Applications Of The Finite Element Method For Single-Material Components

7.1 Introduction 201

7.2 The Example Geometries and Loading Modes 202

7.3 Finite Element Meshes and Boundary Conditions 205

7.4 Material Behavior Models 207

      7.4.1 Initial Linear-Elastic Properties 207

      7.4.2 Norton Power-Law Properties 207

      7.4.3 Continuum-Damage Material Properties 208

7.5 Linear-Elastic Behavior 208

      7.5.1 Notched Bar 208

      7.5.2 Internally Pressurized Thick Pipe 208

      7.5.3 Internally Pressurized Pipe Bend 208

7.6 Stationary-State Creep Behavior 210

      7.6.1 Notched Bar 210

      7.6.2 Internally Pressurized Thick Pipes 213

      7.6.3 Internally Pressurized Pipe Bend 214

7.7 Continuum Damage Behavior 215

      7.7.1 Notched Bar 215

      7.7.2 Internally Pressurized Thick Pipe 215

      7.7.3 Internally Pressurized Toroid 216

7.8 General Observation of Component Behavior 218

Notations 219

References 219

8 Creep of Welded Components 221

8.1 Introduction 221

8.2 The Creep of Longitudinal and Transverse Uniaxial Specimens 226

      8.2.1 Columnar and Equiaxed Compositions 226

      8.2.2 Typical Experimental Behavior 226

      8.2.3 Finite Element Modeling of Weld Metal 227

8.3 Creep of Cross-Weld Specimens 237

      8.3.1 Geometry and Loading 237

      8.3.2 Stationary-State Creep of Two-Material Cross-Weld Specimens with Norton

      Creep Models 238

      8.3.3 Stress Singularity in Cross-Weld Creep Test Specimens under Steady-State Conditions 245

      8.3.4 The Effect of Including Damage on the Predicted Behavior of Cross-Weld Test Specimens 252

8.4 Creep of Circumferentially Welded Straight Pipes 258

      8.4.1 Geometry and Loading 258

      8.4.2 Stationary-State Creep of Circumferentially Welded Straight Pipes 260

      8.4.3 The Effect of Including Damage on the Predicted Behavior of Circumferentially Welded Straight Pipes 269

Notation 280

References 281

9 Creep Of Notched Components 285

9.1 Introduction 285

9.2 Elastic-Creep Behavior 285

9.3 Elastic-Plastic Creep Behavior 288

9.4 Comparison of the Techniques for Predicting Notch Stresses and Strains 90

9.5 Use of the Neuber Method in Conjunction with a Time-Stepping Integration Method 291

9.6 Determination of Principal Stresses and Strains 295

Notation 298

References 299

10 Creep of Cracked Components 301

10.1 Introduction 301

10.2 The Creep Fracture Mechanics Approach 303

      10.2.1 Stationary Cracks 303

      10.2.2 Growing Crack 307

      10.2.3 Crack Growth Predictions Using the C*Parameter 308

10.3 The Damage-Mechanics Approach 311

      10.3.1 The General Approach 311

      10.3.2 Determination of the Multiaxial Stress-State Parameter a That Is Suitable for Crack Growth Predictions 313

      10.3.3 Prediction of Crack Front Shape for CT Specimens 317

      10.3.4 Prediction of Crack Growth and Crack Shape for a Rectangular Bar with a Thumbnail Crack 317

Notation 324

References 324

11 Small Specimen Creep Testing 327

11.1 Introduction 327

11.2 Sub size Conventional Specimens and Creep Testing 329

11.3 Impression Creep Test Specimens and Testing 330

      11.3.1 Background 330

      11.3.2 Interpretation of Impression Creep Test Data 331

      11.3.3 Inverse Reference Stress Method 332

      11.3.4 Use of a Rectangular Indenter 332

      11.3.5 Typical Results and Practical Limitations 334

11.4 Small Punch Test Specimens and Testing 340

      11.4.1 Background 340

      11.4.2 Interpretation of Small Punch Creep Test Data 342

      11.4.3 Typical Results and Practical Limitations 344

11.5 Small Ring—Type Test Specimens and Testing 344

      11.5.1 Background 344

      11.5.2 Typical Results and Practical Limitations 346

11.6 Two-Bar Test Specimens and Testing 349

      11.6.1 Background 349

      11.6.2 Interpretation of Two-Bar Creep Test Data 349

      11.6.3 Typical Results and Practical Limitations 350

11.7 General Observations 352

Notation 353

References 353

Index 357

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