Residual Stress: Measurement by Diffraction and Interpretation

ISBN-13: 9781461395713 / Niemiecki / Miękka / 2012 / 276 str.

Ismail C. Noyan; Jerome B. Cohen

Opis

As industries find that the market for their goods and services is often as closely connected to their quality as to their price, they become more interested in inspection and quality control. Non-destructive testing is one aspect of this topic; the subject of this book is a sub-field of this domain. The techniques for measuring residual stresses have a long history for a technological subject. Yet, in the last decade or so there has been renewed and vigorous interest, and, as a result of this, there has been considerable progress in our understanding and in our methods. It seemed a proper time to bring the new material together in an organized form suitable for a course or for self-teaching, hence this book. After an initial introduction to the qualitative ideas concerning the origin, role, and measurement of residual stresses, we follow with chapters on classical elasticity and the relatively new subject of microplasticity. These are primarily introductory or review in nature, and the reader will find it important to consider further the quoted references if he is to be involved in a continuing basis in this area. There follows a chapter on diffraction theory, and then we fuse these subjects with a chapter on diffraction techniques for measuring stresses and strains which at present is our most general tool for non-destructive evaluation in this area.

Spis treści

1 Introduction.- 1.1 The Origin of Stresses.- 1.2 Methods of Measuring Residual Stresses.- 1.3 Some Examples of Residual Stresses.- References.- 2 Fundamental Concepts in Stress Analysis.- 2.1 Introduction.- 2.2 Definitions.- 2.3 Stress and Strain.- 2.4 Forces and Stresses.- 2.5 Displacements and Strains.- 2.6 Transformation of Axes and Tensor Notation.- 2.7 Elastic Stress-Strain Relations for Isotropic Materials.- 2.8 Structure of Single Crystals.- 2.9 Elastic Stress-Strain Relations in Single Crystals.- 2.10 Equations of Equilibrium.- 2.11 Conditions of Compatibility.- 2.12 Basic Definitions in Plastic Deformation.- 2.13 Plastic Deformation of Single Crystals.- 2.14 Deformation and Yielding in Inhomogeneous Materials.- Problems.- 3 Analysis of Residual Stress Fields Using Linear Elasticity Theory.- 3.1 Introduction.- 3.2 Macroresidual Stresses.- 3.3 Equations of Equilibrium for Macrostresses.- 3.4 Microstresses.- 3.5 Equations of Equilibrium for Micro- and Pseudo-Macrostresses.- 3.6 Calculation of Micro- and PM Stresses.- 3.7 The Total Stress State in Surface Deformed Multiphase Materials.- 3.8 Macroscopic Averages of Single Crystal Elastic Constants.- 3.9 The Voigt Average.- 3.10 The Reuss Average.- 3.11 Other Approaches to Elastic Constant Determination.- 3.12 Average Diffraction Elastic Constants.- Summary.- References.- 4 Fundamental Concepts in X-ray Diffraction.- 4.1 Introduction.- 4.2 Fundamentals of X-rays.- 4.3 Short-wavelength Limit and the Continuous Spectrum.- 4.4 Characteristic Radiation Lines.- 4.5 X-ray Sources.- 4.6 Absorption of X-rays.- 4.7 Filtering of X-rays.- 4.8 Scattering of X-rays.- 4.9 Scattering from Planes of Atoms.- 4.10 The Structure Factor of a Unit Cell.- 4.11 Experimental Utilization of Bragg’s Law.- 4.12 Monochromators.- 4.13 Collimators and Slits.- 4.14 Diffraction Patterns from Single Crystals.- 4.15 Diffraction Patterns from Polycrystalline Specimens.- 4.16 Basic Diffractometer Geometry.- 4.17 Intensity of Diffracted Lines for Polycrystals.- 4.18 Multiplicity.- 4.19 Lorentz Factor.- 4.20 Absorption Factor.- 4.21 Temperature Factor.- 4.22 X-ray Detectors.- 4.23 Deadtime Correction for Detection Systems.- 4.24 Total Diffracted Intensity at a Given Angle 20.- 4.25 Depth of Penetration of X-rays.- 4.26 Fundamental Concepts in Neutron Diffraction.- 4.27 Scattering and Absorption of Neutrons.- Problems.- Bibliography and References.- 5 Determination of Strain and Stress Fields by Diffraction Methods.- 5.1 Introduction.- 5.2 Fundamental Equations of X-ray Strain Determination.- 5.3 Analysis of Regular “d” vs. sin2? Data.- 5.4 Determination of Stresses from Diffraction Data.- 5.5 Biaxial Stress Analysis.- 5.6 Triaxial Stress Analysis.- 5.7 Determination of the Unstressed Lattice Spacing.- 5.8 Effect of Homogeneity of the Strain Distribution and Specimen Anisotropy.- 5.9 Average Strain Data from Single Crystal Specimens.- 5.10 Interpretation of the Average X-ray Strain Data Measured from Polycrystalline Specimens.- 5.11 Interpretation of Average Stress States in Polycrystalline Specimens.- 5.12 Effect of Stress Gradients Normal to the Surface on d vs. sin2? Data.- 5.13 Experimental Determination of X-ray Elastic Constants.- 5.14 Determination of Stresses from Oscillatory Data.- 5.15 Stress Measurements with Neutron Diffraction.- 5.16 Effect of Composition Gradients with Depth.- 5.17 X-ray Determination of Yielding.- 5.18 Summary.- Problem.- References.- 6 Experimental Errors Associated with the X-ray Measurement of Residual Stress.- 6.1 Introduction.- 6.2 Selection of the Diffraction Peak for Stress Measurements.- 6.3 Peak Location.- 6.3.1 Half-Value Breadth and Centroid Methods.- 6.3.2 Functional Representations of X-ray Peaks.- 6.3.3 Peak Determination by Fitting a Parabola.- 6.3.4 Determination of Peak Shift.- 6.4 Determination of Peak Position for Asymmetric Peaks.- 6.5 Statistical Errors Associated with the X-ray Measurement of Line Profiles.- 6.6 Statistical Errors in Stress.- 6.6.1 The sin2? Technique.- 6.6.2 Two-Tilt Technique.- 6.6.3 Triaxial Stress Analysis.- 6.6.4 Statistical Errors in X-ray Elastic Constants.- 6.7 Instrumental Errors in Residual Stress Analysis.- 6.7.1 Variation of the Focal Point with ? and ?.- 6.7.2 Effect of Horizontal Divergence on Focusing.- 6.7.3 Effect of Vertical Beam Divergence.- 6.7.4 Effect of Specimen Displacement.- 6.7.5 Effect of ?-axis not Corresponding to the 2?-axis.- 6.7.6 Error Equations for the ?-Goniometer.- 6.7.7 Effect of Errors in the True Zero Position of the ?-axis.- 6.7.8 Alignment Procedures.- 6.8 Corrections for Macrostress Gradients.- 6.9 Corrections for Layer Removal.- 6.10 Summary.- Problems.- References.- 7 The Practical Use of X-ray Techniques.- 7.1 Introduction.- 7.2 The Use of Ordinary Diffractometers.- 7.3 Software and Hardware Requirements.- 7.4 Available Instruments.- 7.5 Selected Applications of a Portable X-ray Residual Stress Unit (By W. P. Evans).- Reference.- 8 The Shape of Diffraction Peaks — X-ray Line Broadening.- 8.1 Introduction.- 8.2 Slit Corrections.- 8.3 Fourier Analysis of Peak Broadening.- Problem.- References.- Appendix A: Solutions to Problems.- Appendix B.- B.1 Introduction.- B.2 The Marion-Cohen Method.- B.3 Dölle-Hauk Method (Oscillation-free Reflections).- B.4 Methods of Peiter and Lode.- B.5 Use of High Multiplicity Peaks.- References.- Appendix C: Fourier Analysis.- Appendix D: Location of Useful Information in “International Tables for Crystallography”.- Appendix F: A Compilation of X-ray Elastic Constants (By Dr. M. James).- References.