Showing papers on "Residual stress published in 1987"

Residual Stress: Measurement by Diffraction and Interpretation

Abstract: 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 Dolle-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.

Microfabricated structures for the in situ measurement of residual stress, Young’s modulus, and ultimate strain of thin films

Abstract: Two microfabricated structures for the in situ measurement of mechanical properties of thin films, a suspended membrane, and an asymmetric ‘‘released structure,’’ are reported. For a polyimide film on silicon dioxide, the membrane measurements yield a residual tensile stress of 30 MPa and a Young’s modulus of 3 GPa. The released structures measure the ratio of residual stress to Young’s modulus, and yield 0.011 at strains comparable to the suspended membranes, and 0.015 at larger strains. The ultimate strain as measured by both structures is approximately 4%.

Coupled temperature, stress, phase transformation calculation

Abstract: The quenching of steels involves thermal, mechanical, and structural phenomena and their couplings. In this paper, a coupled thermal, phase transformation, internal stresses calculation model is presented. Especially, the stress-phase transformation interactions (transformation plasticity and kinetics modifications through internal stresses) are taken into account in this model, not only for martensitic transformation but also for diffusion dependent transformation. Using a specific case, the cooling of a cylinder made of eutectoid carbon steel, an analysis of how the stress phase transformation interactions affect the internal stresses, and plastic strain evolutions during cooling are performed. The calculated results show that internal stresses have an important effect on the kinetics of pearlitic transformation. These changes in transformation kinetics modify the levels of the internal stresses themselves and the residual stresses.

Towards an acoustoelastic theory for measurement of residual stress

Abstract: The rudiments of an acoustoelastic theory is developed within the framework of linear elasticity with initial stress. Since no assumption is made about the origin of the initial stress, our acoustoelastic theory will be applicable to evaluation of stress in plastically deformed bodies, provided that the superimposed ultrasonic waves be hyperelastic. New universal relations are deduced. An approach to evaluation of stress which does not use calibration specimens and makes full use of universal relations in our acoustoelastic theory is advocated. Examples are given which illustrate application of our theory to evaluate residual stress in plates. Preliminary corroborations of our theory are provided by the recent experiments of King & Fortunko and Thompson et al.

Quench factor analysis of aluminium alloys

Abstract: A model was developed almost 20 years ago which described how precipitation during the quench affected the development of properties of aluminium alloys during subsequent aging treatment. This model was the basis for an analytical process, known as quench factor analysis, that was used to predict the effects of quench path on corrosion characteristics and strength. The purpose of this paper is to provide a theoretical basis for the model and to review how quench factor analysis has been used in solving industrial problems. Several investigators have confirmed that quench factor analysis is an effective predictive method for all quenching conditions save one. The exception is when material has been quenched below the knee of the C-curve and subsequently reheated above the knee before the quench is complete. Applications include the design of quench systems, the development of quench practices which optimize combinations of high strength and low residual stress and distortion, and predictions of the...

Role of x-ray diffraction analysis in surface engineering: investigation of microstructure of nitrided iron and steels

Abstract: X-ray diffraction analysis can be very usefully applied in the field of surface engineering, since a depth of a few micrometres only is usually probed. This paper provides an overview of current X-ray diffraction methods for the analysis of surface layers. The treatment is illustrated by examples taken from recent work on nitrided iron and steels. Distinct ways to characterize the effective depth and layer thickness probed are presented. Composition-depth profiles can be measured accurately by tracing the lattice parameter (taking into account the possible presence of stresses) as a function of depth below the surface by successive sublayer removals. A correction for the penetration effect is required and methods for that are presented and demonstrated. The basis of the determination of (macro) stress (the sin2ψ method) is indicated. Attention is paid to the determination of the strain free lattice spacing and (diffraction) elastic constants, to the effect of a concentration-depth profile, and to ...

Novel microstructures for the in situ measurement of mechanical properties of thin films

Abstract: This paper discusses microfabricated structures designed for the in situ measurement of the mechanical properties of thin films under residual tensile stress. The film is deposited and patterned on a (100) silicon substrate in which 5‐μm‐thick diaphragms have been fabricated. When the silicon diaphragm is etched from the backside in an SF6 plasma, the microstructures are released and deform under the residual tension. Measurement of this deformation in conjunction with appropriate mechanical models determines the mechanical properties of interest. We have used these structures to study benzophenonetetracarboxylicdianhidride‐oxydianiline/metaphenylene‐diamine polyimide films. Typical value for the residual stress to modulus ratio in this case was determined to be 0.011±0.001 while the ultimate strain at break was found to be 4.5% for 5.5‐μm‐thick films. For thicker films (8.5 μm), the film did not fail until 8% strain was reached.

Stress Buildup and Relaxation During Ion Exchange Strengthening of Glass

Abstract: A soda-lime-silica glass was subjected to an ordinary ion exchange treatment in molten potassium nitrate at temperatures near and substantially below the strain point of the glass. Stress profiles were measured as a function of exchange temperature and time. At all temperatures, the measurements showed rapid relaxation of the surface stress and the development of a pronounced compression maximum in a short period. A simple viscoelastic model with composition-independent parameters was used to analyze the stress profiles. Neither Maxwell's nor Michelson's relaxation expression could satisfy both characteristics of the residual stress development. Reasons for discrepancies are discussed.

The effect of residual stresses induced by shot‐peening on fatigue crack propagation in two high strength aluminium alloys

Abstract: — The crack initiation lives of peened specimens of aluminium alloys 7010 and 8090 are shorter than those of unpeened specimens. This is caused by the acceleration of crack initiation due to stress concentration in the rough peened surface, especially at fold-like defects. The crack growth rate in peened specimens is significantly reduced with increasing ΔK, i.e. with increasing crack length. At a crack length of approximately 0.3 mm this trend is reversed and the crack growth rate rapidly increases and attains the same level of crack growth rate as that in unpeened specimens. The point of smallest crack growth rate roughly corresponds to the point of maximum residual stress. The crack growth rate in a peened specimen has been modelled by assuming the effect of residual stress reduces to the equivalent stress ratio. The predicted results agree well with the experimental data.

Transformation Toughening of Ceramics

Abstract: Ceramic materials can be considerably toughened by utilizing the phase transformation of Zr02 particles. The transformation is nucleation-controlled and invariably stress-assisted. Three main toughening mechanisms are operative: stress-induced transformation, microcracking and crack deflection. Some toughened ceramics with low critical transformational stress “exhibit transformation plasticity and memory effects analogous to martensitic metal alloys. Micro- structural features of the three Zr02 toughened ceramic (ZTC) groups are presented: Partially — stabilized Zr02 (PSZ), tetragonal Zr02 polycrystals (TZP) and dispersion -toughened ceramics, e.g. ZT-AI2O3, ZT-mullite, etc. The mechanical properties of some ZTC are compared with predicted values. Since ZTC generally exhibit a disappointing high-temperature behavior, some strategies are outlined to overcome the characteristic deficiencies.

The measurement of subsurface residual stress and cold work distributions in nickel base alloys

Abstract: A method of determining the diffraction peak width accurately and rapidly in conjunction with x-ray diffraction residual stress measurement using Pearson VII function profile analysis is described. An empirical relationship between the (420) diffraction peak width and the degree of cold work is developed for four nickel base alloys. The peak width produced was found to be independent of the method of deformation. Examples of the concurrent determination of subsurface residual stress and cold work distributions are presented for samples of abraded and shot peened Inconel 718 and ground Inconel 600. X-RAY DIFFRACTION TECHNIQUES can be used to determine both macroscopic and microscopic residual stresses. Macrostresses, which extend over ranges large compared to the dimensions of the crystals in the material, are determined from the shift in the position of the diffraction peak. Microstresses, which extend over distances on the order of the unit cell, cannot be directly measured individually but can be quantified in the aggregate from the broadening of the diffraction peak which they produce. Macrostresses are tensor properties measurable by mechanical means which are additive to applied stresses. The average magnitude of the microstress in a sample can be treated as a scalar property and is related to the hardness or degree of cold work of the material. As a metal is cold worked, the dislocation density increases, thereby reducing the size of the perfectly crystalline regions or crystallites (coherent diffracting domains) and increasing the average (root mean square) microstrain in the crystal lattice. The reduced crystallite size and increased microstrain both produce broadening of diffraction peaks which can be conveniently measured as a means of quantifying the degree to which the material has been cold worked. A number of practical difficulties are encountered in determining the diffraction peak width in conjunction with macroscopic residual stress measurement. First, the Kα radiation generally used for residual stress measurement produces two overlapping diffraction peaks. The Kα doublet (consisting of peaks produced by the Kα 1 and Kα 2 radiations) can be separated to determine the width of the stronger Kα 1 peak using the Rachinger correction.

Relaxation of residual stresses by annealing or mechanical treatment

Abstract: The current knowledge of the relaxation of residual stresses is presented in a condensed and, as far as possible, systematic form. During subjection to thermal or mechanical energy at not too high temperatures the residual stress relaxation is caused by an oriented slip of dislocations which transforms elastic residual strains into microplastic strains. Relaxation will be found as soon as residual stresses − possibly superimposed with external stresses of the same orientation -locally exceed the resistance for onset of plastic deformation. The effect of characteristic properties on the onset and rate of relaxation of residual stresses by annealing, uniaxial and cyclic deformation will be verified by typical examples of experimental results. Possible formulae which can be used to quantify residual stress relaxation are considered and the underlying mechanisms are discussed.

Effect of Joint Thickness and Residual Stresses on the Properties of Ceramic Adhesive Joints: I, Finite Element Analysis of Stresses in Joints

Abstract: The finite element method was used to determine the stress distributions in adhesive joints prepared using alumina adher-ends and silicate glass adhesives with varying thicknesses and thermal expansion coefficients. These analyses, together with the results of literature analyses for joints subjected to externally applied loads, aided in interpreting the experimental observations which are described in Part II of the paper.

Determination of Strain and Stress Fields by Diffraction Methods

Abstract: Up to this point the mechanical and micromechanical behavior of solids and basic concepts of x-ray and neutron scattering from crystalline solids have been presented. In this chapter these concepts are combined in the derivation of the basic equations of residual stress determination with diffraction. The fundamental assumptions inherent in these derivations and the limits they impose on the applicability of the stress measurement will also be discussed. Various problems in an actual stress measurement, such as the effect of stress gradients, the separation of micro and macrostresses, determination of stresses in thin films and single crystals, etc., are also considered, with special emphasis on the interpretation of the data within the limitations of the theory.

Thermally Induced Stresses and Deformations in Angle-Ply Composite Tubes

Abstract: Cure-induced uniform temperature change effects on the stresses, axial expansion, and thermally-induced twist of four specific angle-ply tube designs are discussed with a view to the tubes' use as major space structure components. The stresses and deformations in the tubes are studied as a function of the four designs, the off-axis angle, and the single-material and hybrid reinforcing-material construction used. It is found that tube design has a minor influence on the stresses, axial stiffness, and axial thermal expansion characteristics, which are more directly a function of off-axis angle and material selection; tube design is, however, the primary influence in the definition of thermally-induced twist and torsional stiffness characteristics. None of the designs is free of thermally induced twist.

Kinetics of Crack Tip Blunting of Glasses

Abstract: When abraded or indented glasses are annealed, a strength increase of 20% to 30% is observed. Crack tip blunting and removal of tensile residual stress near the crack tip have both been proposed to explain this phenomenon. In order to resolve which is the more likely mechanism, the kinetics of strength increase of soda-lime, borosilicate, and high-silica glasses were measured as a function of heat-treatment temperature and atmosphere. The sinusoidal profile decay of corrugated glass surfaces of the soda-lime glass was also investigated at similar temperatures and atmospheres. From these two complementary measurements, it was concluded that the observed strength increase of glasses upon annealing is caused by crack tip blunting, most likely due to viscous flow assisted by water diffused from the atmosphere.

Measurement of residual stress distribution by the incremental hole-drilling method

Abstract: The hole-drilling method is widely used to measure residual stresses in mechanical components. Recent developments have shown that strains measured on the surface during an incremental drilling can be related to residual-stress distribution. Researchers throughout the world have proposed different calibration methods which lead to more or less accurate results.

Mean stress dependence of the thermoelastic constant

Abstract: The SPATE 8000 thermoelastic stress analyser has been used to demonstrate the mean stress dependence of the thermoelastic constant. This dependence has potential application in the measurement of residual stress provided the material has not yielded.

Analysis of residual stress effects in piles

Abstract: A simple method is outlined for analyzing the residual stresses in a single pile following driving or jacking and for determining the subsequent axial load-deformation behavior. It is found that the stiffness of the pile head response is generally less for tensile loading than for compression loading. The most significant effects occur for piles in sand; piles in soft clay are not significantly influenced by the presence of residual stresses. The cyclic response of piles in sand may also be affected adversely by residual stresses. Comparisons with field and laboratory test data suggest that the theory incorporating residual stress effects can give reasonable estimates of axial pile behavior.