Properties and general use of the X-ray elastic factors

2007 ◽  
Vol 22 (2) ◽  
pp. 103-107 ◽  
Author(s):  
Balder Ortner
Keyword(s):  
Plastic Deformation ◽  
Stress Measurement ◽  
Measured Data ◽  
Least Square ◽  
Data Evaluation ◽  
X Ray ◽  
Rank Tensor ◽  
The Matrix ◽  
Hooke's Law ◽  
Linear Regressions

The equation ε(φ, ψ, hkl)=Fij(φ, ψ, hkl)σij can be directly deduced from Hooke’s law. It is shown that the matrix Fij(φ, ψ, hkl) which is usually called X-ray elastic factors, behaves as a second rank tensor. Since this behaviour is the only criterion for the question of whether or not it is a tensor, the F-matrix must be regarded as a second rank tensor. This allows us to make some statements about the structure of the F-matrix on the basis of Neumann’s principle, to find relationships among F-matrices in different measurement directions, and to apply the methods and strategies for the measurement of a second rank tensor. All this is shown in a few examples. It is further shown that a consistent use of the F-matrix can replace all methods for data evaluation which makes use of linear regressions and, in addition, avoids all difficulties and disadvantages of these methods. One of these disadvantages is that the sin2 ψ-method, as well as its derivatives, is generally not correct least square fits of the measured data. This is also shown in an example. The more complicated cases with stress or constitution gradients in the range of the probed volume or stress measurement after plastic deformation are not discussed.

The Matrix Method for Data Evaluation and its Advantages in Comparison to the Sin2ψ and Similar Methods

2011 ◽  
Vol 681 ◽  
pp. 7-12 ◽  
Author(s):  
Balder Ortner
Keyword(s):  
Matrix Method ◽  
Stress Measurement ◽  
Data Evaluation ◽  
Traditional Methods ◽  
X Ray ◽  
Data Treatment ◽  
The Matrix

This article gives an overview of different methods for data treatment in x-ray stress measurement, and how these methods should be replaced with the matrix method, which in general is more versatile, more accurate and, in most cases, also easier to handle. It also shows how much the accuracy could be improved by replacing the traditional methods with the matrix method.

Residual Stress Measurement of Industrial Polymers by X-Ray Diffraction

2015 ◽  
Vol 1110 ◽  
pp. 100-103
Author(s):  
Doi Taisei ◽  
Masayuki Nishida ◽  
Ozaki Junichi
Keyword(s):  
Residual Stresses ◽  
Measurement Accuracy ◽  
Stress Measurement ◽  
Regression Line ◽  
Polymeric Materials ◽  
Measured Data ◽  
Diffraction Peak ◽  
X Ray Diffraction ◽  
Transmission Method ◽  
X Ray

In this study, residual stresses in polyamide (PA) materials were measured by the x-ray stress measurement technique. X-ray stress measurement is widely used to measure residual stresses, however, this measurement is not many used in polymeric materials. There are two problems for measuring residual stresses in polymer. Firstly, the diffraction peak from the polymer appears at the low 2θangle region. Thus the measurement accuracy for strains reduces. Secondly, the low 2θangle region is very difficult to use the sin2ψmethod. In this study,Ω-diffractometer with transmission method was used to resolve these problems. The measured data was plotted in thed-sin2ψdiagram, and it was coincident with the linear regression line clearly. X-ray elastic constant (XEC) of PA was estimated from these results.

In Situ X-Ray Stress Measurement in Electrodeposited Cu Foils under Tensile and Fatigue Loading

2007 ◽  
Vol 353-358 ◽  
pp. 2395-2398 ◽  
Author(s):  
Yoshiaki Akiniwa ◽  
Tsuyoshi Suzuki ◽  
K. Tanaka
Keyword(s):  
Plastic Deformation ◽  
Deformation Behavior ◽  
Stress Measurement ◽  
Fatigue Loading ◽  
The Other ◽  
Full Width ◽  
Half Maximum ◽  
X Ray ◽  
The Difference

Monotonic and cyclic loadings were subjected to electrodeposited copper foils (thickness is 8 and 20 μm), and the deformation behavior was observed. In-situ X-ray stress measurement was carried out under monotonic loading. The tensile strength of 8 μm foil was higher than that of 20 μm foil. On the other hand, the elongation of 8 μm foil was smaller. When the plastic deformation occurred, difference between the X-ray stress and the applied stress became large. The difference of 20 μm foil was larger than that of 8 μm foil. Fatigue strength of 8 μm foil was also higher than that of 20 μm foil. The value of the full width at half maximum, FWHM, increased dramatically at the first cycle, and then the value became nearly constant. Just before fracture, the value increased again. The change in FWHM corresponded to the change in the accumulated ratchet strain.

X-Ray Stress Measurement by the Single-Exposure Technique

1967 ◽  
Vol 11 ◽  
pp. 401-410 ◽  
Author(s):  
John T. Norton
Keyword(s):  
Stress Measurement ◽  
Practical Method ◽  
Least Square ◽  
Single Exposure ◽  
X Ray ◽  
Tension And Compression ◽  
Diffraction Patterns ◽  
Time Required ◽  
Exposure Technique

AbstractX-ray techniques employing film recording continue to play an important role in the routine determination of residual stresses in metals, particularly where heavy and bulky specimens are involved. The single-exposure technique in which the two diffraction patterns required are obtained simultaneously in a single X-ray exposure has several practical advantages over the more conventional two-exposure technique for many routine applications. Details of the method are discussed and an analysis is made of the factors influencing the reliability of the stress determination. An apparatus for stress measurement having some unique features is described and a practical application presented, illustrating the use of the single-exposure technique for the determination of the stress constant of a specimen of hardened steel. The specimen was subjected to a series of known stresses in bending, both in tension and compression. The measured diffraction-line displacements were plotted against the applied stress, and a line was fitted to the points by a least-squares calculation. From its slope, the stress constant was determined. The standard deviation of individual stress determinations from the “true” values given by the least-square line was calculated and was in excellent agreement with the value calculated from the errors of measurement. It is concluded that the single-exposure technique with its reduced time required for measurement and less demanding requirement of precise instrumental adjustment provides a reliable and practical method for many routine stress measurement applications.

Two-Dimensional X-Ray Diffraction for Structure and Stress Analysis

2005 ◽  
Vol 490-491 ◽  
pp. 1-6 ◽  
Author(s):  
Bob B. He ◽  
Ke Wei Xu ◽  
Fei Wang ◽  
Ping Huang
Keyword(s):  
Stress Analysis ◽  
Stress Measurement ◽  
Unit Vector ◽  
Sample Space ◽  
Matrix Transformation ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Texture Measurement ◽  
X Ray ◽  
The Matrix

This paper introduces the recent progress in two-dimensional X-ray diffraction as well as its applications in microstructure and residual stress analysis. Based on the matrix transformation between diffraction space, detector space and sample space, the unit vector of the diffraction vector can be expressed in the sample space corresponding to all the geometric parameters and Bragg conditions. The same transformation matrix can be used for texture and stress analysis. The fundamental equations for both stress measurement and texture measurement are developed with the matrix transformation defined for the two-dimensional diffraction. Stress measurement using twodimensional detector is based on a direct relationship between the stress tensor and the diffraction cone distortion. The two-dimensional detector collects texture data and background values simultaneously for multiple poles and multiple directions.

The generalized sin2ψ method: An advanced solution for X-ray stress analysis in textured materials

2014 ◽  
Vol 29 (2) ◽  
pp. 133-136 ◽  
Author(s):  
A. Haase ◽  
M. Klatt ◽  
A. Schafmeister ◽  
R. Stabenow ◽  
B. Ortner
Keyword(s):  
Residual Stress ◽  
Stress Analysis ◽  
Special Form ◽  
Measured Data ◽  
Data Evaluation ◽  
One Dimensional ◽  
X Ray ◽  
Stress Measurements ◽  
Pole Figures ◽  
Textured Materials

Residual stress measurements on strongly textured materials using the standard sin2ψ evaluation show significant non-linearities. According to EN 15305 there is currently no existing solution for this problem. A method is presented that solves this problem. It is based on two tools. (i) The use of a one-dimensional detector having a large capture angle that yields the full diffraction profiles at each point of the pole figures. Therefore, some hundreds of d-values can be used for the stress calculation. (ii) Data evaluation with the recently developed generalized sin2ψ method. This has the advantage of being based on a flawless theory (Hooke's law in the special form of Dölle–Hauk's equation) and being able to handle any distribution of measurement directions and any number of measured data. The method was successfully tried out at a sheet of brass with significant texture.

scholarly journals Matrix Method for X-Ray Stress Measurement in Single Crystals, and the Rational Planning of the Measurements

2014 ◽  
Vol 996 ◽  
pp. 58-63
Author(s):  
Balder Ortner
Keyword(s):  
Single Crystals ◽  
Matrix Method ◽  
Stress Measurement ◽  
X Ray Diffraction ◽  
X Ray ◽  
Stress Calculation ◽  
Rational Planning ◽  
The Matrix ◽  
Experimental Effort

With the so-called matrix method stress calculation from x-ray diffraction measurements is much easier than it used to be with older methods. The matrix method is also well suited to optimize the choice of reflections (hkl) to be measured in order to obtain the best results with least experimental effort. Pseudocodes for the stress calculation are given.

Reliability Analysis on Errors of Measuring Residual Stress in 7050 Aluminum Alloy with X-Ray Diffraction

2011 ◽  
Vol 105-107 ◽  
pp. 1867-1871
Author(s):  
Ai Xin Feng ◽  
Bin Li ◽  
Chuan Chao Xu ◽  
Jun Wei Wang ◽  
Zhen Chun Han ◽  
...  
Keyword(s):  
Residual Stress ◽  
Aluminum Alloy ◽  
Stress Measurement ◽  
Residual Stress Distribution ◽  
Least Square ◽  
Residual Stress Measurement ◽  
Material Surface ◽  
X Ray Diffraction ◽  
X Ray ◽  
7050 Aluminum Alloy

The error distribution of residual stress tested by X-ray diffraction on 7050 aluminum alloy was studied. In this paper, residual stress was measured, independently and repeatedly, many times on 7050 aluminum alloy with X-ray diffraction, then the errors about 50 stress values within the range of 30MPa were analyzed by the hypothesis testing. The results indicate that the errors of the residual stress measurement on 7050 aluminum alloy were followed the law of normal distribution about and the errors can be estimated by the least square calculator. The research lays the foundation to subsequent researches on the inherent law of the residual stress measurement with X-ray diffraction and the residual stress distribution and accuracy of stress of material surface.

Dependence of Stress Constant on Microstructure of Quenched and Tempered Steels in X-Ray Stress Measurement

1991 ◽  
Vol 35 (A) ◽  
pp. 519-525
Author(s):  
Masanori Kurita ◽  
Akira Saito
Keyword(s):  
Residual Stress ◽  
Stress Measurement ◽  
Practical Importance ◽  
Carbon Steels ◽  
X Ray Diffraction ◽  
Tempered Martensite ◽  
Tempering Temperature ◽  
X Ray ◽  
The Matrix ◽  
High Residual Stress

AbstractThe residual stress measurement of quenched and tempered steels is of practical importance because the quenching can sometimes induce the high residual stress which affects the strength of materials. The stress constants of carbon steels quenched and tempered at various temperatures were measured in order to determine the residual stress of steels by x-ray diffraction. The stress constant increased slowly with increasing tempering temperatures below 500°C; it increased rapidly with tempering temperatures above about 500°C, This rapid increase in the stress constant is closely related to the change in microstructure of the steels in tempering; above the tempering temperature of around 500°C, the tempered martensite recrystallized and transformed to ferritic iron and fine cementite particles dispersed in the matrix; these coalesced and grew to be speroidized cementites and finally laminar cementite plates.

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