Practical Residual Stress Measurement Methods

Gary S. Schajer is Professor of Mechanical Engineering at the University of British Columbia, Vancouver, Canada.  He received his doctorate from the University of California, at Berkeley and worked as a senior research engineer in industry before returning to academia. His research interests include hole-drilling measurements of residual stress and related inverse solutions, and he has been the recipient of numerous awards for teaching and research. Professor Schajer has written extensively in related journals and conference proceedings, and is currently the Associate Technical Editor of Experimental Mechanics.

• List of Contributors xvPreface xvii1 Overview of Residual Stresses and Their Measurement 1Gary S. Schajer and Clayton O. Ruud1.1 Introduction 11.1.1 Character and Origin of Residual Stresses 11.1.2 Effects of Residual Stresses 31.1.3 Residual Stress Gradients 41.1.4 Deformation Effects of Residual Stresses 51.1.5 Challenges of Measuring Residual Stresses 61.1.6 Contribution of Modern Measurement Technologies 71.2 Relaxation Measurement Methods 71.2.1 Operating Principle 71.3 Diffraction Methods 131.3.1 Measurement Concept 131.3.2 X-ray Diffraction 141.3.3 Synchrotron X-ray 151.3.4 Neutron Diffraction 151.4 Other Methods 161.4.1 Magnetic 161.4.2 Ultrasonic 171.4.3 Thermoelastic 171.4.4 Photoelastic 181.4.5 Indentation 181.5 Performance and Limitations of Methods 181.5.1 General Considerations 181.5.2 Performance and Limitations of Methods 191.6 Strategies for Measurement Method Choice 191.6.1 Factors to be Considered 191.6.2 Characteristics of Methods 24References 242 Hole Drilling and Ring Coring 29Gary S. Schajer and Philip S. Whitehead2.1 Introduction 292.1.1 Introduction and Context 292.1.2 History 302.1.3 Deep Hole Drilling 312.2 Data Acquisition Methods 312.2.1 Strain Gages 312.2.2 Optical Measurement Techniques 332.3 Specimen Preparation 352.3.1 Specimen Geometry and Strain Gage Selection 352.3.2 Surface Preparation 382.3.3 Strain Gage Installation 402.3.4 Strain Gage Wiring 402.3.5 Instrumentation and Data Acquisition 412.4 Hole Drilling Procedure 422.4.1 Drilling Cutter Selection 422.4.2 Drilling Machines 432.4.3 Orbital Drilling 442.4.4 Incremental Measurements 452.4.5 Post-drilling Examination of Hole and Cutter 462.5 Computation of Uniform Stresses 472.5.1 Mathematical Background 472.5.2 Data Averaging 492.5.3 Plasticity Effects 502.5.4 Ring Core Measurements 502.5.5 Optical Measurements 502.5.6 Orthotropic Materials 502.6 Computation of Profile Stresses 512.6.1 Mathematical Background 512.7 Example Applications 542.7.1 Shot-peened Alloy Steel Plate – Application of the Integral Method 542.7.2 Nickel Alloy Disc – Fine Increment Drilling 542.7.3 Titanium Test-pieces – Surface Processes 562.7.4 Coated Cylinder Bore – Adaptation of the Integral Method 572.8 Performance and Limitations of Methods 572.8.1 Practical Considerations 572.8.2 Common Uncertainty Sources 582.8.3 Typical Measurement Uncertainties 59References 613 Deep Hole Drilling 65David J. Smith3.1 Introduction and Background 653.2 Basic Principles 683.2.1 Elastic Analysis 683.2.2 Effects of Plasticity 713.3 Experimental Technique 723.4 Validation of DHD Methods 753.4.1 Tensile Loading 753.4.2 Shrink Fitted Assembly 773.4.3 Prior Elastic–plastic Bending 783.4.4 Quenched Solid Cylinder 793.5 Case Studies 803.5.1 Welded Nuclear Components 803.5.2 Components for the Steel Rolling Industry 823.5.3 Fibre Composites 823.6 Summary and Future Developments 83Acknowledgments 84References 854 The Slitting Method 89Michael R. Hill4.1 Measurement Principle 894.2 Residual Stress Profile Calculation 904.3 Stress Intensity Factor Determination 964.4 Practical Measurement Procedures 964.5 Example Applications 994.6 Performance and Limitations of Method 1014.7 Summary 106References 1065 The Contour Method 109Michael B. Prime and Adrian T. DeWald5.1 Introduction 1095.1.1 Contour Method Overview 1095.1.2 Bueckner’s Principle 1105.2 Measurement Principle 1105.2.1 Ideal Theoretical Implementation 1105.2.2 Practical Implementation 1105.2.3 Assumptions and Approximations 1125.3 Practical Measurement Procedures 1145.3.1 Planning the Measurement 1145.3.2 Fixturing 1145.3.3 Cutting the Part 1155.3.4 Measuring the Surfaces 1165.4 Residual Stress Evaluation 1175.4.1 Basic Data Processing 1175.4.2 Additional Issues 1205.5 Example Applications 1215.5.1 Experimental Validation and Verification 1215.5.2 Unique Measurements 1275.6 Performance and Limitations of Methods 1305.6.1 Near Surface (Edge) Uncertainties 1305.6.2 Size Dependence 1315.6.3 Systematic Errors 1315.7 Further Reading On Advanced Contour Method Topics 1335.7.1 Superposition For Additional Stresses 1335.7.2 Cylindrical Parts 1345.7.3 Miscellaneous 1345.7.4 Patent 134Acknowledgments 134References 1356 Applied and Residual Stress Determination Using X-ray Diffraction 139Conal E. Murray and I. Cevdet Noyan6.1 Introduction 1396.2 Measurement of Lattice Strain 1416.3 Analysis of Regular dφψ vs. sin2ψ Data 1436.3.1 D¨olle-Hauk Method 1436.3.2 Winholtz-Cohen Least-squares Analysis 1436.4 Calculation of Stresses 1456.5 Effect of Sample Microstructure 1466.6 X-ray Elastic Constants (XEC) 1496.6.1 Constitutive Equation 1506.6.2 Grain Interaction 1516.7 Examples 1536.7.1 Isotropic, Biaxial Stress 1536.7.2 Triaxial Stress 1546.7.3 Single-crystal Strain 1566.8 Experimental Considerations 1596.8.1 Instrumental Errors 1596.8.2 Errors Due to Counting Statistics and Peak-fitting 1596.8.3 Errors Due to Sampling Statistics 1596.9 Summary 160Acknowledgments 160References 1607 Synchrotron X-ray Diffraction 163Philip Withers7.1 Basic Concepts and Considerations 1637.1.1 Introduction 1637.1.2 Production of X-rays; Undulators, Wigglers, and Bending Magnets 1667.1.3 The Historical Development of Synchrotron Sources 1677.1.4 Penetrating Capability of Synchrotron X-rays 1697.2 Practical Measurement Procedures and Considerations 1697.2.1 Defining the Strain Measurement Volume and Measurement Spacing 1707.2.2 From Diffraction Peak to Lattice Spacing 1737.2.3 From Lattice Spacing to Elastic Strain 1737.2.4 From Elastic Strain to Stress 1787.2.5 The Precision of Diffraction Peak Measurement 1797.2.6 Reliability, Systematic Errors and Standardization 1807.3 Angle-dispersive Diffraction 1847.3.1 Experimental Set-up, Detectors, and Data Analysis 1847.3.2 Exemplar: Mapping Stresses Around Foreign Object Damage 1867.3.3 Exemplar: Fast Strain Measurements 1877.4 Energy-dispersive Diffraction 1887.4.1 Experimental Set-up, Detectors, and Data Analysis 1897.4.2 Exemplar: Crack Tip Strain Mapping at High Spatial Resolution 1897.4.3 Exemplar: Mapping Stresses in Thin Coatings and Surface Layers 1907.5 New Directions 1917.6 Concluding Remarks 192References 1938 Neutron Diffraction 195Thomas M. Holden8.1 Introduction 1958.1.1 Measurement Concept 1958.1.2 Neutron Technique 1968.1.3 Neutron Diffraction 1968.1.4 3-Dimensional Stresses 1988.1.5 Neutron Path Length 1988.2 Formulation 1998.2.1 Determination of the Elastic Strains from the Lattice Spacings 1998.2.2 Relationship between the Measured Macroscopic Strain in a given Direction and the Elements of the Strain Tensor 1998.2.3 Relationship between the Stress σi,j and Strain εi,j Tensors 2008.3 Neutron Diffraction 2018.3.1 Properties of the Neutron 2018.3.2 The Strength of the Diffracted Intensity 2028.3.3 Cross Sections for the Elements 2038.3.4 Alloys 2048.3.5 Differences with Respect to X-rays 2058.3.6 Calculation of Transmission 2058.4 Neutron Diffractometers 2068.4.1 Elements of an Engineering Diffractometer 2068.4.2 Monochromatic Beam Diffraction 2068.4.3 Time-of-flight Diffractometers 2098.5 Setting up an Experiment 2108.5.1 Choosing the Beam-defining Slits or Radial Collimators 2108.5.2 Calibration of the Wavelength and Effective Zero of the Angle Scale, 2θ0 2108.5.3 Calibration of a Time-of-flight Diffractometer 2108.5.4 Positioning the Sample on the Table 2118.5.5 Measuring Reference Samples 2118.6 Analysis of Data 2118.6.1 Monochromatic Beam Diffraction 2118.6.2 Analysis of Time-of-flight Diffraction 2128.6.3 Precision of the Measurements 2138.7 Systematic Errors in Strain Measurements 2138.7.1 Partly Filled Gage Volumes 2138.7.2 Large Grain Effects 2148.7.3 Incorrect Use of Slits 2148.7.4 Intergranular Effects 2158.8 Test Cases 2158.8.1 Stresses in Indented Discs; Neutrons, Contour Method and Finite Element Modeling 2158.8.2 Residual Stress in a Three-pass Bead-in-slot Weld 218Acknowledgments 221References 2219 Magnetic Methods 225David J. Buttle9.1 Principles 2259.1.1 Introduction 2259.1.2 Ferromagnetism 2269.1.3 Magnetostriction 2269.1.4 Magnetostatic and Magneto-elastic Energy 2279.1.5 The Hysteresis Loop 2289.1.6 An Introduction to Magnetic Measurement Methods 2289.2 Magnetic Barkhausen Noise (MBN) and Acoustic Barkhausen Emission (ABE) 2299.2.1 Introduction 2299.2.2 Measurement Depth and Spatial Resolution 2309.2.3 Measurement 2329.2.4 Measurement Probes and Positioning 2339.2.5 Calibration 2339.3 The MAPS Technique 2359.3.1 Introduction 2359.3.2 Measurement Depth and Spatial Resolution 2379.3.3 MAPS Measurement 2389.3.4 Measurement Probes and Positioning 2399.3.5 Calibration 2409.4 Access and Geometry 2439.4.1 Space 2439.4.2 Edges, Abutments and Small Samples 2449.4.3 Weld Caps 2449.4.4 Stranded Wires 2449.5 Surface Condition and Coatings 2449.6 Issues of Accuracy and Reliability 2459.6.1 Magnetic and Stress History 2459.6.2 Materials and Microstructure 2469.6.3 Magnetic Field Variability 2489.6.4 Probe Stand-off and Tilt 2489.6.5 Temperature 2499.6.6 Electric Currents 2509.7 Examples of Measurement Accuracy 2509.8 Example Measurement Approaches for MAPS 2529.8.1 Pipes and Small Positive and Negative Radii Curvatures 2529.8.2 Rapid Measurement from Vehicles 2529.8.3 Dealing with ‘Poor’ Surfaces in the Field 2539.9 Example Applications with ABE and MAPS 2539.9.1 Residual Stress in α Welded Plate 2539.9.2 Residual Stress Evolution During Fatigue in Rails 2539.9.3 Depth Profiling in Laser Peened Spring Steel 2549.9.4 Profiling and Mapping in Ring and Plug Test Sample 2549.9.5 Measuring Multi-stranded Structure for Wire Integrity 2559.10 Summary and Conclusions 256References 25710 Ultrasonics 259Don E. Bray10.1 Principles of Ultrasonic Stress Measurement 25910.2 History 26410.3 Sources of Uncertainty in Travel-time Measurements 26510.3.1 Surface Roughness 26510.3.2 Couplant 26510.3.3 Material Variations 26510.3.4 Temperature 26510.4 Instrumentation 26610.5 Methods for Collecting Travel-time 26610.5.1 Fixed Probes with Viscous Couplant 26710.5.2 Fixed Probes with Immersion 26710.5.3 Fixed Probes with Pressurization 27010.5.4 Contact with Freely Rotating Probes 27010.6 System Uncertainties in Stress Measurement 27010.7 Typical Applications 27110.7.1 Weld Stresses 27110.7.2 Measure Stresses in Pressure Vessels and Other Structures 27210.7.3 Stresses in Ductile Cast Iron 27310.7.4 Evaluate Stress Induced by Peening 27310.7.5 Measuring Stress Gradient 27310.7.6 Detecting Reversible Hydrogen Attack 27310.8 Challenges and Opportunities for Future Application 27410.8.1 Personnel Qualifications 27410.8.2 Establish Acoustoelastic Coefficients (L11) for Wider Range of Materials 27410.8.3 Develop Automated Integrated Data Collecting and Analyzing System 27410.8.4 Develop Calibration Standard 27410.8.5 Opportunities for LCR Applications in Engineering Structures 274References 27511 Optical Methods 279Drew V. Nelson11.1 Holographic and Electronic Speckle Interferometric Methods 27911.1.1 Holographic Interferometry and ESPI Overview 27911.1.2 Hole Drilling 28211.1.3 Deflection 28511.1.4 Micro-ESPI and Holographic Interferometry 28611.2 Moiré Interferometry 28611.2.1 Moiré Interferometry Overview 28611.2.2 Hole Drilling 28711.2.3 Other Approaches 28911.2.4 Micro-Moiré 28911.3 Digital Image Correlation 29011.3.1 Digital Image Correlation Overview 29011.3.2 Hole Drilling 29111.3.3 Micro/Nano-DIC Slotting, Hole Drilling and Ring Coring 29211.3.4 Deflection 29311.4 Other Interferometric Approaches 29411.4.1 Shearography 29411.4.2 Interferometric Strain Rosette 29411.5 Photoelasticity 29411.6 Examples and Applications 29511.7 Performance and Limitations 295References 298Further Reading 302Index 303