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List of Contributors xv
Preface xvii
1 Overview of Residual Stresses and Their Measurement 1Gary S. Schajer and Clayton O. Ruud
1.1 Introduction 1
1.1.1 Character and Origin of Residual Stresses 1
1.1.2 Effects of Residual Stresses 3
1.1.3 Residual Stress Gradients 4
1.1.4 Deformation Effects of Residual Stresses 5
1.1.5 Challenges of Measuring Residual Stresses 6
1.1.6 Contribution of Modern Measurement Technologies 7
1.2 Relaxation Measurement Methods 7
1.2.1 Operating Principle 7
1.3 Diffraction Methods 13
1.3.1 Measurement Concept 13
1.3.2 X-ray Diffraction 14
1.3.3 Synchrotron X-ray 15
1.3.4 Neutron Diffraction 15
1.4 Other Methods 16
1.4.1 Magnetic 16
1.4.2 Ultrasonic 17
1.4.3 Thermoelastic 17
1.4.4 Photoelastic 18
1.4.5 Indentation 18
1.5 Performance and Limitations of Methods 18
1.5.1 General Considerations 18
1.5.2 Performance and Limitations of Methods 19
1.6 Strategies for Measurement Method Choice 19
1.6.1 Factors to be Considered 19
1.6.2 Characteristics of Methods 24
References 24
2 Hole Drilling and Ring Coring 29Gary S. Schajer and Philip S. Whitehead
2.1 Introduction 29
2.1.1 Introduction and Context 29
2.1.2 History 30
2.1.3 Deep Hole Drilling 31
2.2 Data Acquisition Methods 31
2.2.1 Strain Gages 31
2.2.2 Optical Measurement Techniques 33
2.3 Specimen Preparation 35
2.3.1 Specimen Geometry and Strain Gage Selection 35
2.3.2 Surface Preparation 38
2.3.3 Strain Gage Installation 40
2.3.4 Strain Gage Wiring 40
2.3.5 Instrumentation and Data Acquisition 41
2.4 Hole Drilling Procedure 42
2.4.1 Drilling Cutter Selection 42
2.4.2 Drilling Machines 43
2.4.3 Orbital Drilling 44
2.4.4 Incremental Measurements 45
2.4.5 Post-drilling Examination of Hole and Cutter 46
2.5 Computation of Uniform Stresses 47
2.5.1 Mathematical Background 47
2.5.2 Data Averaging 49
2.5.3 Plasticity Effects 50
2.5.4 Ring Core Measurements 50
2.5.5 Optical Measurements 50
2.5.6 Orthotropic Materials 50
2.6 Computation of Profile Stresses 51
2.6.1 Mathematical Background 51
2.7 Example Applications 54
2.7.1 Shot-peened Alloy Steel Plate - Application of the Integral Method 54
2.7.2 Nickel Alloy Disc - Fine Increment Drilling 54
2.7.3 Titanium Test-pieces - Surface Processes 56
2.7.4 Coated Cylinder Bore - Adaptation of the Integral Method 57
2.8 Performance and Limitations of Methods 57
2.8.1 Practical Considerations 57
2.8.2 Common Uncertainty Sources 58
2.8.3 Typical Measurement Uncertainties 59
References 61
3 Deep Hole Drilling 65David J. Smith
3.1 Introduction and Background 65
3.2 Basic Principles 68
3.2.1 Elastic Analysis 68
3.2.2 Effects of Plasticity 71
3.3 Experimental Technique 72
3.4 Validation of DHD Methods 75
3.4.1 Tensile Loading 75
3.4.2 Shrink Fitted Assembly 77
3.4.3 Prior Elastic-plastic Bending 78
3.4.4 Quenched Solid Cylinder 79
3.5 Case Studies 80
3.5.1 Welded Nuclear Components 80
3.5.2 Components for the Steel Rolling Industry 82
3.5.3 Fibre Composites 82
3.6 Summary and Future Developments 83
Acknowledgments 84
References 85
4 The Slitting Method 89Michael R. Hill
4.1 Measurement Principle 89
4.2 Residual Stress Profile Calculation 90
4.3 Stress Intensity Factor Determination 96
4.4 Practical Measurement Procedures 96
4.5 Example Applications 99
4.6 Performance and Limitations of Method 101
4.7 Summary 106
References 106
5 The Contour Method 109Michael B. Prime and Adrian T. DeWald
5.1 Introduction 109
5.1.1 Contour Method Overview 109
5.1.2 Bueckner's Principle 110
5.2 Measurement Principle 110
5.2.1 Ideal Theoretical Implementation 110
5.2.2 Practical Implementation 110
5.2.3 Assumptions and Approximations 112
5.3 Practical Measurement Procedures 114
5.3.1 Planning the Measurement 114
5.3.2 Fixturing 114
5.3.3 Cutting the Part 115
5.3.4 Measuring the Surfaces 116
5.4 Residual Stress Evaluation 117
5.4.1 Basic Data Processing 117
5.4.2 Additional Issues 120
5.5 Example Applications 121
5.5.1 Experimental Validation and Verification 121
5.5.2 Unique Measurements 127
5.6 Performance and Limitations of Methods 130
5.6.1 Near Surface (Edge) Uncertainties 130
5.6.2 Size Dependence 131
5.6.3 Systematic Errors 131
5.7 Further Reading On Advanced Contour Method Topics 133
5.7.1 Superposition For Additional Stresses 133
5.7.2 Cylindrical Parts 134
5.7.3 Miscellaneous 134
5.7.4 Patent 134
Acknowledgments 134
References 135
6 Applied and Residual Stress Determination Using X-ray Diffraction 139Conal E. Murray and I. Cevdet Noyan
6.1 Introduction 139
6.2 Measurement of Lattice Strain 141
6.3 Analysis of Regular df¿ vs. sin2¿ Data 143
6.3.1 D¿olle-Hauk Method 143
6.3.2 Winholtz-Cohen Least-squares Analysis 143
6.4 Calculation of Stresses 145
6.5 Effect of Sample Microstructure 146
6.6 X-ray Elastic Constants (XEC) 149
6.6.1 Constitutive Equation 150
6.6.2 Grain Interaction 151
6.7 Examples 153
6.7.1 Isotropic, Biaxial Stress 153
6.7.2 Triaxial Stress 154
6.7.3 Single-crystal Strain 156
6.8 Experimental Considerations 159
6.8.1 Instrumental Errors 159
6.8.2 Errors Due to Counting Statistics and Peak-fitting 159
6.8.3 Errors Due to Sampling Statistics 159
6.9 Summary 160
Acknowledgments 160
References 160
7 Synchrotron X-ray Diffraction 163Philip Withers
7.1 Basic Concepts and Considerations 163
7.1.1 Introduction 163
7.1.2 Production of X-rays; Undulators, Wigglers, and Bending Magnets 166
7.1.3 The Historical Development of Synchrotron Sources 167
7.1.4 Penetrating Capability of Synchrotron X-rays 169
7.2 Practical Measurement Procedures and Considerations 169
7.2.1 Defining the Strain Measurement Volume and Measurement Spacing 170
7.2.2 From Diffraction Peak to Lattice Spacing 173
7.2.3 From Lattice Spacing to Elastic Strain 173
7.2.4 From Elastic Strain to Stress 178
7.2.5 The Precision of Diffraction Peak Measurement 179
7.2.6 Reliability, Systematic Errors and Standardization 180
7.3 Angle-dispersive Diffraction 184
7.3.1 Experimental Set-up, Detectors, and Data Analysis 184
7.3.2 Exemplar: Mapping Stresses Around Foreign Object Damage 186
7.3.3 Exemplar: Fast Strain Measurements 187
7.4 Energy-dispersive Diffraction 188
7.4.1 Experimental Set-up, Detectors, and Data Analysis 189
7.4.2 Exemplar: Crack Tip Strain Mapping at High Spatial Resolution 189
7.4.3 Exemplar: Mapping Stresses in Thin Coatings and Surface Layers 190
7.5 New Directions 191
7.6 Concluding Remarks 192
References 193
8 Neutron Diffraction 195Thomas M. Holden
8.1 Introduction 195
8.1.1 Measurement Concept 195
8.1.2 Neutron Technique 196
8.1.3 Neutron Diffraction 196
8.1.4 3-Dimensional Stresses 198
8.1.5 Neutron Path Length 198
8.2 Formulation 199
8.2.1 Determination of the Elastic Strains from the Lattice Spacings 199
8.2.2 Relationship between the Measured Macroscopic Strain in a given Direction and the Elements of the Strain Tensor 199
8.2.3 Relationship between the Stress si,j and Strain ei,j Tensors 200
8.3 Neutron Diffraction 201
8.3.1 Properties of the Neutron 201
8.3.2 The Strength of the Diffracted Intensity 202
8.3.3 Cross Sections for the Elements 203
8.3.4 Alloys 204
8.3.5 Differences with Respect to X-rays 205
8.3.6 Calculation of Transmission 205
8.4 Neutron Diffractometers 206
8.4.1 Elements of an Engineering Diffractometer 206
8.4.2 Monochromatic Beam Diffraction 206
8.4.3 Time-of-flight Diffractometers 209
8.5 Setting up an Experiment 210
8.5.1 Choosing the Beam-defining Slits or Radial Collimators 210
8.5.2 Calibration of the Wavelength and Effective Zero of the Angle Scale, 2¿0 210
8.5.3 Calibration of a Time-of-flight Diffractometer 210
8.5.4 Positioning the Sample on the Table 211
8.5.5 Measuring Reference Samples 211
8.6 Analysis of Data 211
8.6.1 Monochromatic Beam Diffraction 211
8.6.2 Analysis of Time-of-flight Diffraction 212
8.6.3 Precision of the Measurements 213
8.7 Systematic Errors in Strain Measurements 213
8.7.1 Partly Filled Gage Volumes 213
8.7.2 Large Grain Effects 214
8.7.3 Incorrect Use of Slits 214
8.7.4 Intergranular Effects 215
8.8 Test Cases 215
8.8.1 Stresses in Indented Discs; Neutrons, Contour Method and Finite Element Modeling 215
8.8.2 Residual Stress in a Three-pass Bead-in-slot Weld 218
Acknowledgments 221
References 221
9 Magnetic Methods 225David J. Buttle
9.1 Principles 225
9.1.1 Introduction 225
9.1.2 Ferromagnetism 226
9.1.3 Magnetostriction 226
9.1.4 Magnetostatic and Magneto-elastic Energy 227
9.1.5 The Hysteresis Loop 228
9.1.6 An Introduction to Magnetic Measurement Methods 228
9.2 Magnetic Barkhausen Noise (MBN) and Acoustic Barkhausen Emission (ABE) 229
9.2.1 Introduction 229
9.2.2 Measurement Depth and Spatial Resolution 230
9.2.3 Measurement 232
9.2.4 Measurement Probes and Positioning 233
9.2.5 Calibration 233
9.3 The MAPS Technique 235
9.3.1 Introduction 235
9.3.2 Measurement Depth and Spatial Resolution 237
9.3.3 MAPS Measurement 238
9.3.4 Measurement Probes and Positioning 239
9.3.5 Calibration 240
9.4 Access and Geometry 243
9.4.1 Space 243
9.4.2 Edges, Abutments and Small Samples 244
9.4.3 Weld Caps 244
9.4.4 Stranded Wires 244
9.5 Surface Condition and Coatings 244
9.6 Issues of Accuracy and Reliability 245
9.6.1 Magnetic and Stress History 245
9.6.2 Materials and Microstructure 246
9.6.3 Magnetic Field Variability 248
9.6.4 Probe Stand-off and Tilt 248
9.6.5 Temperature 249
9.6.6 Electric Currents 250
9.7 Examples of Measurement Accuracy 250
9.8 Example Measurement Approaches for MAPS 252
9.8.1 Pipes and Small Positive and Negative Radii Curvatures 252
9.8.2 Rapid Measurement from Vehicles 252
9.8.3 Dealing with 'Poor' Surfaces in the Field 253
9.9 Example Applications with ABE and MAPS 253
9.9.1 Residual Stress in a Welded Plate 253
9.9.2 Residual Stress Evolution During Fatigue in Rails 253
9.9.3 Depth Profiling in Laser Peened Spring Steel 254
9.9.4 Profiling and Mapping in Ring and Plug Test Sample 254
9.9.5 Measuring Multi-stranded Structure for Wire Integrity 255
9.10 Summary and Conclusions 256
References 257
10 Ultrasonics 259Don E. Bray
10.1 Principles of Ultrasonic Stress Measurement 259
10.2 History 264
10.3 Sources of Uncertainty in Travel-time Measurements 265
10.3.1 Surface Roughness 265
10.3.2 Couplant 265
10.3.3 Material Variations 265
10.3.4 Temperature 265
10.4 Instrumentation 266
10.5 Methods for Collecting Travel-time 266
10.5.1 Fixed Probes with Viscous Couplant 267
10.5.2 Fixed Probes with Immersion 267
10.5.3 Fixed Probes with Pressurization 270
10.5.4 Contact with Freely Rotating Probes 270
10.6 System Uncertainties in Stress Measurement 270
10.7 Typical Applications 271
10.7.1 Weld Stresses 271
10.7.2 Measure Stresses in Pressure Vessels and Other Structures 272
10.7.3 Stresses in Ductile Cast Iron 273
10.7.4 Evaluate Stress Induced by Peening 273
10.7.5 Measuring Stress Gradient 273
10.7.6 Detecting Reversible Hydrogen Attack 273
10.8 Challenges and Opportunities for Future Application 274
10.8.1 Personnel Qualifications 274
10.8.2 Establish Acoustoelastic Coefficients (L11) for Wider Range of Materials 274
10.8.3 Develop Automated Integrated Data Collecting and Analyzing System 274
10.8.4 Develop Calibration Standard 274
10.8.5 Opportunities for LCR Applications in Engineering Structures 274
References 275
11 Optical Methods 279Drew V. Nelson
11.1 Holographic and Electronic Speckle Interferometric Methods 279
11.1.1 Holographic Interferometry and ESPI Overview 279
11.1.2 Hole Drilling 282
11.1.3 Deflection 285
11.1.4 Micro-ESPI and Holographic Interferometry 286
11.2 Moiré Interferometry 286
11.2.1 Moiré Interferometry Overview 286
11.2.2 Hole Drilling 287
11.2.3 Other Approaches 289
11.2.4 Micro-Moiré 289
11.3 Digital Image Correlation 290
11.3.1 Digital Image Correlation Overview 290
11.3.2 Hole Drilling 291
11.3.3 Micro/Nano-DIC Slotting, Hole Drilling and Ring Coring 292
11.3.4 Deflection 293
11.4 Other Interferometric Approaches 294
11.4.1 Shearography 294
11.4.2 Interferometric Strain Rosette 294
11.5 Photoelasticity 294
11.6 Examples and Applications 295
11.7 Performance and Limitations 295
References 298
Further Reading 302
Index 303
Gary S. Schajer1 and Philip S. Whitehead2
1University of British Columbia, Vancouver, Canada
2Stresscraft Ltd., Shepshed, Leicestershire, UK
The hole-drilling method is the most widely used general-purpose technique for measuring residual stresses in materials. It is convenient to use, has standardized procedures and it has good accuracy and reliability. The test procedure involves some damage to the specimen but the damage is often tolerable or repairable. For this reason, the method is sometimes called “semi-destructive.”
The hole-drilling method involves drilling a small hole in the test specimen at the place where the residual stresses are to be evaluated. This removal of stressed material causes a redistribution of the residual stresses in the remaining material around the hole and associated localized deformations. Figure 2.1 schematically illustrates the deformations around a hole drilled into material with tensile residual stresses. The consequent stress release causes elastic springback that slightly expands the hole edge, with a small local surface rise due to Poisson strain. The reverse happens with compressive stresses. For experimental evaluations, strain gage or optical techniques are available to quantify the surface deformations of the surrounding material, from which the residual stresses originally existing within the hole can be determined.
Figure 2.1 Schematic cross-sections around a hole drilled into tensile residual stresses. (a) Before hole drilling and (b) after hole drilling
The ring-core method is an “inside-out” variant of the hole-drilling method, where the measurement area is in the middle and the “hole” takes the form of a surrounding annular groove. Figure 2.2 compares the geometry of the hole drilling and ring-core methods. The two methods are identical mathematically, and differ only in the numerical constants used for the residual stress evaluations. The ring-core method has the advantage of producing larger relieved strains and has superior capability to measure very large residual stresses close to the material yield stress. However, the hole-drilling method is the more commonly used procedure because of its much greater ease of use and lesser specimen damage.
Figure 2.2 Residual stress measurement methods. (a) Hole drilling and (b) ring-core. Reproduced with permission from [13], Copyright 2010 Springer
The hole-drilling method derives from the pioneering work of Mathar in the 1930s [1]. Since that time, the method has grown and developed remarkably, with contributions from many researchers. The hole-drilling method is now well-established, with an ASTM Standard Test Procedure [2] and extensive instructional literature [3–6]. It is a tribute to the fertility of Mathar's original concept that, after over 75 years, interest in hole drilling continues to grow, with frequent new developments.
From an early stage, the mechanical extensometer used by Mathar was recognized as a major factor limiting the accuracy and reliability of hole-drilling residual stress measurements. The development of strain gages in the 1940s provided an opportunity for substantial improvements in deformation measurement quality. In 1950, Soete [7] introduced the use of strain gages for hole-drilling measurements, greatly improving measurement accuracy and reliability, and allowing smaller holes to be used. The use of strain gages was further investigated by Kelsey who explored the incremental drilling technique to estimate stress vs. depth profile [8]. In the same period, Milbradt [14] introduced the ring-core method, with subsequent developments by Gunnert [15] and Hast [16].
The modern application of the strain gage hole-drilling method dates from the work of Rendler and Vigness [9] in 1966. They established a standardized strain gage geometry for residual stress measurements and developed the hole-drilling method into a systematic and repeatable procedure. Their work provided the basis for the establishment of ASTM Standard Test Method E837 in 1981, updated several times since then [2]. Early hole-drilling measurements were used to identify uniform stresses, then approximate methods were used to identify stress profile with depth [8]. The later availability of finite element calculations enabled accurate stress profile measurements to be achieved [10, 11], and the procedure has now been standardized in E837. A large literature on strain gage hole-drilling measurements has also developed, with descriptive information [4, 5], a good practice guide [3], and measurement accuracy analysis [6].
A further variant approach is the deep-hole method, described in detail in Chapter 3. It is useful for determining the residual stresses within the deep interior of large specimens. The method was initially developed as a means of measuring geological stresses within large rock masses [17], and was later extended to the measurement of residual stresses in large metal components such as castings [18, 19]. The method involves drilling a deep hole into the test material and then measuring the change in diameter as the surrounding material is overcored. The method combines some mechanical elements of the hole drilling and ring-core methods, but it differs significantly in that the measurements are made in the interior of the hole rather than at the surface. This is an important feature because the location of the measurements controls the location of the measured stresses. Conventional hole drilling and ring coring involve measurements at the surface, so they are mostly sensitive to the residual stresses at the surface, with some diminishing sensitivity to stresses within a depth approximately equal to the hole radius. In contrast, deep-hole measurements indicate the residual stresses in the deep interior.
Strain gages have, over an extended period, proven to be a robust and reliable means for measuring the surface deformations that occur during hole-drilling residual stress measurements. Following the work of Rendler and Vigness in the 1960s, specialized strain gage rosettes have been manufactured commercially for hole-drilling measurements. The design of these rosettes takes advantage of the photographic production method of strain gages to ensure that the individual gages of the rosettes are accurately oriented in space. This feature significantly reduces alignment error sources and greatly enhances the quality of the measured data. Hole-drilling rosettes typically contain three radial strain gages arranged in rectangular format (0° −135° −270° or 0° −45° −90°) to identify the three in-plane stress components and .
Modern strain gages and associated electronic instrumentation can make very accurate and stable strain measurements, which is an essential feature because hole-drilling strains tend to be small, typically low hundreds of microstrain, sometimes less than one hundred. The compact and portable character of strain gage equipment enables effective field use. This ability to make successful hole-drilling measurements within a wide range of outside-lab measurement environments is a major factor in the wide acceptance of the strain gage hole drilling method.
A further important advantage of standardizing hole-drilling rosette geometry is that the calibration constants that relate the measured strains to the residual stress results also become standardized. This feature greatly simplifies the stress computations and allows documents such as ASTM E837 to give explicit stress calculation instructions.
E837 describes the use of three different rosette types to suit a range of measurement needs. Figure 2.3 illustrates the rosette geometries. Type A, which follows the Rendler and Vigness geometry, is a general-purpose design appropriate for most measurement needs. Type B has all three strain gages placed on the same side of the hole location and is useful for making measurements adjacent to obstacles. However, this rosette pattern should be used only for this purpose because the single-sided geometry increases its sensitivity to hole eccentricity errors.
Figure 2.3 Standardized hole-drilling strain gage rosettes. Reprinted with permission from ASTM E837-08 [2]
The Type C rosette is a specialized design suited to measurement of small residual stresses and to measurements on materials with low thermal conductivity such as plastics. The design comprises three radial strain gages and three circumferential gages, connected in three half-bridge circuits. This arrangement increases the effective strain sensitivity of the rosette and also provides compensation for thermal strains, both very useful features when measuring small strains. The thermal strain compensation also greatly stabilizes measurements on low-conductivity materials that do not provide adequate heat dissipation for strain gages when connected within quarter-bridges. Again, this rosette pattern should be used only for these purposes because the half-bridges are costly and time-consuming to assemble.
Starting in the 1980s and 1990s, several optical techniques have been introduced as alternative surface deformation measurement techniques when evaluating residual stresses by the hole-drilling method. Chapter 11 describes these techniques in detail. Camera-based optical...
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