Papers by Keyword: X-Ray Stress Measurement

Abstract: Conventionally, the sin²ψ method has been used as X-ray stress measurement. However, in recent years, the XRD² method and the cos α method have been put into practical use and spreading. In addition, the Fourier analysis method that shares the same measurement principle of the cos α method has been developed and is attracting attention. Therefore, in this paper, the Fourier analysis method is examined from the measurement theory and the measurement accuracy is investigated. It is reviewed that the basic equation is a finite Fourier series, and that stress can be determined from the Fourier coefficients by using coordinate transformations. Then, while comparing it with the multiple regression analysis, the accuracy of the Fourier analysis method is discussed by using numerical calculations.

Abstract: The X-ray stress measurements by the sin²ψ method, the cos α method and the XRD² method are basically composed of the fundamental equations based on diffraction vectors and the calculation for determining X-ray stress. The fundamental equations are expressed differently, which are due to the fact that the measurement systems associated with the incident X-ray control device and the diffracted X-ray detector are different. Although the dependent variable that is the measured quantity is the same diffraction angle theta in the fundamental equations, the main independent variable is different like the tilt angle ψ in the sin² ψ method and the central angle α, γ of the Debye-Scherrer ring in the cos α method, the XRD² method, respectively. Therefore, the stress determination method has been devised based on each the fundamental equation. By clarifying the differences between each X-ray stress measurement method and making a relationship, a unified representation for the fundamental equations is formalized. Therefore, a comparison of each X-ray stress measurement method is expressed in the same Euler space, and a conversion method for each X-ray stress measurement method is presented.

Abstract: Currently, the sin²ψ method is established as an effective technique as how to measure the residual stress state of metal materials non-destructively by X-ray diffraction. In recent years, new X-ray stress measurements with two-dimensional detector are developed and spreading in the world. There is the cosα method as one of the new techniques. However, the research about the statistical errors in the method continues. The measurement theory of the cos α method is reviewed on the triaxial stress state. The triaxial stress analysis by the method is examined and discussed from a viewpoint of the derived errors for the determination.

Abstract: The sin² ψ method [1] is conventionally used well as how to measure non-destructively the residual strain and stress states of polycrystalline materials by X-ray diffraction. In the conventional method, there are Dölle-Hauk method [2] and Winholz-Cohen least squares analysis [3] as the determinations of the strain and stress states for limiting the influence of measurement errors. Many researches are made about the statistical error in those methods. In recent years, use of the X-ray stress measurements with two-dimensional detector from the conventional method is spreading. One of the measurements is called the cos α method. The measurement errors have attracted a great deal of attention for users as the spreads. Therefore, the basic equations and determinations of the strain and stress states are examined. The confidence intervals of measured stress by the cos α method. The research and development is performed for the the cos α method which took the influence of measurement errors into consideration.

Abstract: Research of residual stresses in steel at different depths from its surface is presented in this paper. The material used for research was AISI 310S heat resistant steel (containing approx. 0.2%C, 25%Cr and 20%Ni) in form of a rolled steel sheet with a thickness of 2mm. Stress measurements were conducted with the use of K_αCo radiation by the sin²ψ method in three directions, including the direction of the sheet's rolling (φ = 0°). For the purpose of measuring stresses at different depths from the surface, the steel underwent the process of electropolishing in electrolyte based on perchloric acid at 32 V for various durations (every 1-5 s) to the maximum depth of 35 μm. The set residual stress distributions vary depending on the direction of the test. The strongest stresses are on the steel's surface, and stresses have the widest range (from compressing to streching ones) in the area under the surface, which occurred in the rolling direction, and the narrowest range in its transverse direction. A correlation was discovered in the distribution of compression stresses and microhardness in the outer layer of the steel to a depth of 10 μm, where the role of plastic deformation in shaping the qualities of the steel outweighs the influence of structure content. This was proven using polar figures.

Abstract: It is shown that the knowledge of standard deviations (Δσ_ij ) of the components of a stress tensor (σ_ij) is not sufficient to calculate also standard deviations of quantities derived from the stress tensor, as principal stresses (σ_I, σ_II, σ_III), von Mises stress, Tresca stress, and the components of the deviatoric stress tensor σ'_ij. For such a calculation one needs all information about the measurement and the method for the calculation of σ_ij. This information is: the accuracy of each measured lattice plane distance and the x-ray elastic factors F_ij(φ,ψ,hkl) of each measured point. Equations are given for the calculation of the standard deviations of all the mentioned quantities. For special cases of measurement strategy the wanted calculations become easier. This is also given.

Abstract: 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.

Abstract: This paper shows X-ray residual stress analysis of stainless steel using 2-dimensional detection method. The 2-dimensional detection method of X-ray stress measurement will determine stress by conducting a 2-dimensional detecting of a Debye ring and analyzing the image data. The basic of typical austenitic stainless steel (JIS SUS304) was studied in this study, considering the fact that, at certain power plants, maintenance takes place to prevent stress corrosion cracking by adding compressive residual stress to the structure..

Abstract: The tungsten fiber reinforced titanium composite (W/Ti) was produced by the spot welding method. This manufacturing method used only a simple spot welding system, and it did not need a vacuum chamber and a high temperature furnace such as existing common methods. The arranged tungsten fibers were held between titanium plates (thickness 0.5mm) and fixed by spot welding. Therefore, this W/Ti composite produced by spot welding did not join at all positions between the tungsten fiber and the titanium matrix because of the partial welding in the spot welding point. The coverage, a rate of welding area to the whole plate area, became 150% for the sample in this study, because it should make up for the partial welding by this method. From the microscopic observation in the cross section of the W/Ti composite, it was conformed the good jointing in the whole position between the tungsten fiber and the titanium matrix. ON the other hand, the alteration of thermal residual stress under the thermal cycling was measured by the in-situ x-ray stress measurement technique. These results were discussed from the viewpoint of the thermal expansion coefficient between fiber and matrix.

Abstract: Microscopic residual stresses developed in a copper bi-crystal and in an aluminum tri-crystal after plastic deformation were investigated by X-ray and neutron diffraction. The copper bi-crystal tensile specimen was prepared so as to have a grain boundary along the tensile axis. The aluminum tri-crystal compressive specimen had a triple point and one of the grain boundaries was parallel to the compressive axis. The present study revealed that (1) residual micro-stresses are inhomogeneous within a crystal, (2) average residual stress in each crystal is different from each other, and (3) the direction of principal stress varies from grain to grain. Furthermore, the compatibility of residual stresses existing in both sides of a grain boundary was confirmed in a microscopic scale.