Standard Deviations in X-Ray Stress and Elastic Constants Due to Counting Statistics

1988 ◽  
Vol 32 ◽  
pp. 377-388 ◽  
Author(s):  
Masanori Kurita
Keyword(s):  
Elastic Constants ◽  
Stress Measurement ◽  
Steel Specimen ◽  
Polycrystalline Materials ◽  
X Rays ◽  
Confidence Limits ◽  
X Ray Diffraction ◽  
X Ray ◽  
Standard Deviations ◽  
Counting Statistics

AbstractX-ray diffraction can be used to nondestructively measure residual stress of polycrystalline materials. In x-ray stress measurement, it is important to determine a stress constant experimentally in order to measure the stress accurately. However, every value measured by x-ray diffraction has statistical errors arising from counting statistics. The equations for calculating the standard deviations of the stress constant and elastic constants measured by x-rays are derived analytically in order to ascertain the reproducibility of the measured values. These standard deviations represent the size of the variability caused by counting statistics, and can be calculated from a single set of measurements by using these equations. These equations can apply Lu any meuhud for x-ray stress ifiesuremenL. The variances of the x-ray stress and elastic constants are expressed in terms of the linear combinations of the variances of the peak position. The confidence limits of these constants of a quenched and tempered steel specimen were determined by the Gaussian curve method. The 95% confidence limits of the stress constant were -314 ± 25 MFa/deg.

Residual Stress Measurement of Silicon Nitride and Silicon Carbide by X-Ray Diffraction Using Gaussian Curve Method

1988 ◽  
Vol 32 ◽  
pp. 459-469 ◽  
Author(s):  
Masanori Kurita ◽  
Ikuo Ihara ◽  
Nobuyuki Ono
Keyword(s):  
Residual Stress ◽  
Single Crystal ◽  
Elastic Constants ◽  
Stress Measurement ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
X Ray ◽  
Small Areas ◽  
Curve Method ◽  
The Continuum

The residual stress induced by grinding or some thermal treatment has a large effect on the strength of ceramics. The X-ray technique can be used to nondestructively measure the residual stress in small areas on the surface of polycrystalline materials. The X-ray stress measurement is based on. the continuum mechanics for macroscopically isotropic polycrystalline materials. In this method, the stress value is calculated selectively from strains of a particular diffraction plane in the grains which are favorably oriented for the diffraction. In general, however, the elastic constants of a single crystal depend on the plane of the lattice, since a single crystal is anisotropic, The behavior of the deformation of individual crystals in the aggregate of polycrystalline materials under applied stress has not yet been solved successfully. Therefore, the stress constant and elastic constants for a particular diffracting plane should be determined experimentally in order to determine the residual stress accurately by X-ray diffraction.

New methods for diffraction stress measurement: a critical evaluation of new and existing methods

2000 ◽  
Vol 33 (4) ◽  
pp. 1059-1066 ◽  
Author(s):  
J.-D. Kamminga ◽  
Th. H. de Keijser ◽  
E. J. Mittemeijer ◽  
R. Delhez
Keyword(s):  
Stress Analysis ◽  
Elastic Constants ◽  
Stress Measurement ◽  
Critical Evaluation ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
X Ray ◽  
New Methods

New methods of diffraction stress analysis of polycrystalline materials, consisting of cubic elastically anisotropic crystallites, are proposed and compared with existing methods. Whereas for the existing methods knowledge of the diffraction elastic constants is presupposed, three new methods are presented that require only knowledge of the (macroscopic) mechanical elastic constants. The stress values obtained with these new methods on the basis of the mechanical elastic constants are more reliable than those obtained with the methods on the basis of the diffraction elastic constants. New and existing methods are illustrated by means of measurements of X-ray diffraction from a magnetron-sputtered TiN layer.

Micro Diffraction Imaging of Bulk Polycrystalline Materials

2006 ◽  
Vol 524-525 ◽  
pp. 273-278
Author(s):  
Thomas Wroblewski ◽  
A. Bjeoumikhov ◽  
Bernd Hasse
Keyword(s):  
High Spatial Resolution ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Short Sample ◽  
X Ray ◽  
Detector Distance ◽  
Transmission Geometry ◽  
Diffraction Imaging ◽  
Position Sensitive

X-ray diffraction imaging applies an array of parallel capillaries in front of a position sensitive detector. Conventional micro channel plates of a few millimetre thickness have successfully been used as collimator arrays but require short sample to detector distances to achieve high spatial resolution. Furthermore, their limited absorption restricts their applications to low energy X-rays of around 10 keV. Progress in the fabrication of long polycapillaries allows an increase in the sample to detector distance without decreasing resolution and the use of high X-ray energies enables bulk investigations in transmission geometry.

2D real space visualization of d values in polycrystalline bulk materials of different hardness

2021 ◽  
Vol 54 (2) ◽  
pp. 597-603
Author(s):  
Mari Mizusawa ◽  
Kenji Sakurai
Keyword(s):  
Lattice Distortion ◽  
Structural Information ◽  
Hardness Test ◽  
Real Space ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Diffraction Imaging ◽  
D Values

Conventional X-ray diffraction measurements provide some average structural information, mainly on the crystal structure of the whole area of the given specimen, which might not be very uniform and may include different crystal structures, such as co-existing crystal phases and/or lattice distortion. The way in which the lattice plane changes due to strain also might depend on the position in the sample, and the average information might have some limits. Therefore, it is important to analyse the sample with good lateral spatial resolution in real space. Although various techniques for diffraction topography have been developed for single crystals, it has not always been easy to image polycrystalline materials. Since the late 1990s, imaging technology for fluorescent X-rays and X-ray absorption fine structure has been developed via a method that does not scan either a sample or an X-ray beam. X-ray diffraction imaging can be performed when this technique is applied to a synchrotron radiation beamline with a variable wavelength. The present paper reports the application of X-ray diffraction imaging to bulk steel materials with varying hardness. In this study, the distribution of lattice distortion of hardness test blocks with different hardness was examined. Via this 2D visualization method, the grains of the crystals with low hardness are large enough to be observed by X-ray diffraction contrast in real space. The change of the d value in the vicinity of the Vickers mark has also been quantitatively evaluated.

X-Ray Diffraction

2021 ◽  
pp. 408-480
Author(s):  
Kannan M. Krishnan
Keyword(s):  
Point Group ◽  
Polycrystalline Materials ◽  
X Rays ◽  
X Ray Diffraction ◽  
Symmetry Point Group ◽  
X Ray ◽  
Atomic Scattering ◽  
Scattering Factor ◽  
Diffraction Patterns ◽  
Lattice Planes

X-rays diffraction is fundamental to understanding the structure and crystallography of biological, geological, or technological materials. X-rays scatter predominantly by the electrons in solids, and have an elastic (coherent, Thompson) and an inelastic (incoherent, Compton) component. The atomic scattering factor is largest (= Z) for forward scattering, and decreases with increasing scattering angle and decreasing wavelength. The amplitude of the diffracted wave is the structure factor, F hkl, and its square gives the intensity. In practice, intensities are modified by temperature (Debye-Waller), absorption, Lorentz-polarization, and the multiplicity of the lattice planes involved in diffraction. Diffraction patterns reflect the symmetry (point group) of the crystal; however, they are centrosymmetric (Friedel law) even if the crystal is not. Systematic absences of reflections in diffraction result from glide planes and screw axes. In polycrystalline materials, the diffracted beam is affected by the lattice strain or grain size (Scherrer equation). Diffraction conditions (Bragg Law) for a given lattice spacing can be satisfied by varying θ or λ — for study of single crystals θ is fixed and λ is varied (Laue), or λ is fixed and θ varied to study powders (Debye-Scherrer), polycrystalline materials (diffractometry), and thin films (reflectivity). X-ray diffraction is widely applied.

scholarly journals Influence of Layer Removal Methods in Residual Stress Profiling of a Shot Peened Steel Using X-Ray Diffraction

2014 ◽  
Vol 996 ◽  
pp. 175-180 ◽  
Author(s):  
Rasha Alkaisee ◽  
Ru Lin Peng
Keyword(s):  
Residual Stress ◽  
Chemical Etching ◽  
Stress Measurement ◽  
Diffraction Measurement ◽  
X Rays ◽  
X Ray Diffraction ◽  
X Ray ◽  
Layer Removal ◽  
Compressive Stresses ◽  
The Difference

For X-Ray Diffraction Measurement of Depth Profiles of Residual Stress, Step-Wise Removal of Materials has to be Done to Expose the Underneath Layers to the X-Rays. this Paper Investigates the Influence of Layer Removal Methods, Including Electro-Polishing in Two Different Electrolytes and Chemical Etching, on the Accuracy of Residual Stress Measurement. Measurements on Two Shot-Peened Steels Revealed Large Discrepancy in Subsurface Distributions of Residual Stress Obtained with the Respective Methods. Especially, the Chemical Etching Yielded much Lower Subsurface Compressive Stresses than the Electro-Polishing Using a so Called AII Electrolyte. the Difference was Explained by the Influence of the Different Layer Removal Methods on the Microscopic Roughness.

Measuring Residual and Applied Stress using X-Ray Diffraction on Materials with Preferred Orientation and Large Grain Size

1992 ◽  
Vol 36 ◽  
pp. 585-593
Author(s):  
James Pineault ◽  
Michael Brauss
Keyword(s):  
Grain Size ◽  
Stress Measurement ◽  
Preferred Orientation ◽  
Polycrystalline Materials ◽  
X Ray Diffraction ◽  
X Ray ◽  
Common Solution ◽  
Virtual Window ◽  
The Common ◽  
Comparison Of The Results

AbstractOne of the most difficult tasks in applied and residual stress measurement of polycrystalline materials using x-ray diffraction is dealing with preferred orientation and large grain size.A common solution to large grain size problems has been to choose a larger aperture, but in certain cases this is undesirable and/or impossible. When preferred orientation has been identified as the problem, the common approach has been to choose another diffraction plane or oscillate the x-ray diffraction head during data collection. Remedies such as these can distort the peak breadth and are often not sufficient to totally negate the grain size and preferred orientation effects.A technique described as the “step scan with virtual window” has been developed jointly at MTL (formerly Canmet) and Proto Mfg. Ltd. to deal specifically with the aforementioned effects of grain size and preferred orientation.This paper highlights some of the problems that arise in stress analysis of materials exhibiting preferred orientation and large grain size. Subsequently a comparison of the results obtained using standard diffraction technique, oscillation and the “step scan with virtual window” is made.

Errors in Residual Stress Measurements due to Random Counting Statistics

1970 ◽  
Vol 14 ◽  
pp. 377-388 ◽  
Author(s):  
C. J. Kelly ◽  
M. A. Short
Keyword(s):  
Residual Stress ◽  
Standard Deviation ◽  
Stress Measurement ◽  
Mathematical Expression ◽  
X Ray Diffraction ◽  
Intensity Maximum ◽  
X Ray ◽  
Diffraction Angle ◽  
Data Points ◽  
Counting Statistics

AbstractThe measurement of residual stress, using X-ray diffraction techniques, is based on the change in diffraction angle determined for the Intensity maximum of some suitable reflection from the sample when this is placed consecutively with its surface at two different angles to the diffracting planes. These diffraction angles may be obtained in a variety of ways, but are most often calculated from measurements of three X-ray diffraction intensities at angles selected in the immediate vicinity of the peak maximum at each sample angle and fitting each set of data to a parabolic curve. A simple mathematical expression may be derived relating the diffraction angles, and hence the residual stress, to the measured X-ray intensities; there will, however, be statistical errors in the calculated diffraction angles due to random counting errors in the measurement of the X-ray diffraction intensities. From the expression relating the residual stress to the X-ray intensities an equation has been derived giving the standard deviation in the residual stress due to random counting errors. In addition, a simple approximation has been obtained from this equation showing that the standard deviation is decreased by increasing the number of counts accumulated for each X-ray intensity measurement and by increasing the size of the angular increments between the data points. It will also be shown that, using the approximation, it is possible to estimate in advance the number of accumulated counts at each point necessary to attain a desired standard deviation in a residual stress measurement.

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