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.

A Versatile X-Ray Stress Analyzer Using a Position Sensitive Detector

1980 ◽  
Vol 24 ◽  
pp. 149-153
Author(s):  
Yasuo Yoshioka ◽  
Ken-ichi Hasegawa ◽  
Koh-ichi Mochiki
Keyword(s):  
Residual Stress ◽  
Stress Analysis ◽  
Position Sensitive Detector ◽  
Sensitive Detector ◽  
Counter Method ◽  
X Ray ◽  
Stress Measurements ◽  
Position Sensitive ◽  
Time Required ◽  
Film Method

Instrumentation for X-ray stress analysis has been advanced rapidly in the last few years. Especially, the time required for data accumulation has been remarkably reduced without motion of the detector by using a new X-ray detector called a position sensitive detector (PSD). Applications of PSD to the field of X-ray stress analysis were carried out by James and Cohen, Ruud and Barrett, and the authors. In our laboratory, several position sensitive proportional counters (PSPCs) were designed and manufactured for residual stress measurements. Results show that the PSPC method is a powerful alternative to the conventional counter method or the film method.This paper reports a design of a versatile PSPC X-ray stress analyzer for use in industry and the laboratory.

X-ray residual stress analysis on multilayer systems: an approach for depth-resolved data evaluation

2013 ◽  
Vol 46 (5) ◽  
pp. 1266-1276 ◽  
Author(s):  
Manuela Klaus ◽  
Christoph Genzel
Keyword(s):  
Residual Stress ◽  
Stress Analysis ◽  
Cutting Tools ◽  
Chemical Vapour ◽  
Sample Surface ◽  
Data Evaluation ◽  
Multilayer Systems ◽  
Vector Method ◽  
X Ray ◽  
Diffraction Mode

A data evaluation concept is proposed for the depth-resolved analysis of the residual stress distribution in polycrystalline multilayer systems (MLSs), which consist of alternating sequences of simultaneously diffracting layers of kindBand solely absorbing layers of kindA. This method can be applied to lattice strain data obtained in any diffraction mode used in X-ray stress analysis, such as the sin2ψ method realized in Ω, Ψ and `mixed-mode' geometry, or from measurements performed by means of the scattering vector method. The classical concept used for defining the X-ray information depth τ in the case of bulk materials is shown to lose its physical meaning forA–B–A–B... MLS structures. Starting from the idea of the diffraction power originating from an infinitesimal sublayer below the sample surface, an approach is introduced which weights the contribution of each layerBto the total diffraction signal by the attenuation due to the layer stack above. The formalism introduced in the article is verified by simulations carried out for different MLS geometries. Furthermore, it is applied to sin2ψ measurements performed on surface-blasted hard-coating systems consisting of Al2O3/TiCN layer stacks which were deposited by chemical vapour deposition on cemented carbide cutting tools.

Residual Stress Analysis of Textured Materials by X-Ray Diffraction Method

2012 ◽  
Vol 706-709 ◽  
pp. 1673-1678 ◽  
Author(s):  
Shouichi Ejiri ◽  
Toshihiko Sasaki ◽  
Yukio Hirose
Keyword(s):  
Residual Stress ◽  
Elastic Constant ◽  
Stress Analysis ◽  
Nonlinear Problem ◽  
Elastic Constants ◽  
Lattice Strain ◽  
Stress Measurement ◽  
X Ray Diffraction ◽  
X Ray ◽  
Textured Materials

The residual stress measurement by the conventional X-ray diffraction was formulated on the assumption that a specimen from polycrystalline materials was quasi-isotropic and homogeneous, and the stress was biaxial and almost constant within the X-ray penetration depth. Therefore, it was not available to analyze the stress state of the textured materials by the conventional measurement as a general rule. In resent years, advanced methods have been proposed for the X-ray stress measurement of textured materials. In some methods, it is assumed that the X-ray elastic constant is derived from the crystallite orientation distribution function of textured materials for solving the first anisotropic problem. However, there is a nonlinear problem in the stress analysis from the measured lattice strain. In present study, the X-ray elastic constants were averaged as the expected value around the normal direction of the X-ray diffraction in a similar way. A stress analysis was proposed by differential calculus of the X-ray elastic constant in order to the avoidance of nonlinear problem. The stress analysis was applied to residual stress measurements of a titanium carbide coating film with preferred orientation and a cold-rolled steel with texture. The calculated values of the X-ray elastic constants showed the linearity on some condition for the film. The X-ray stress determination was carried out by the fitting the gradients of the measured lattice strain.

X-Ray Residual Stress Analysis of Nickel Base Alloys

2014 ◽  
Vol 922 ◽  
pp. 274-279 ◽  
Author(s):  
Toshihiko Sasaki ◽  
Toshiyuki Miyazaki ◽  
Hamiru Ito ◽  
Takashi Furukawa ◽  
Tsuyoshi Mihara
Keyword(s):  
Residual Stress ◽  
Stress Analysis ◽  
Nuclear Power ◽  
Power Plants ◽  
Ray Method ◽  
X Ray ◽  
Stress Measurements ◽  
Residual Stress Analysis ◽  
Nickel Base ◽  
Steam Generator Tubes

Nickel based alloys are widely used in steam generator tubes for nuclear power plants. 1-D X-ray stress measurements have been used for these alloys. But 1-D method requires large equipment and it is practically impossible to measure stress in power plants. In order to overcome this problem, we adopted 2-D X-ray method which requires significantly smaller equipment. In this paper we report preliminary results of 2-D X-ray stress measurements of nickel based alloys.

Service Loading Analysis of Wind Turbine Gearbox Rolling Bearings Based on X-Ray Diffraction Residual Stress Measurements

2013 ◽  
Vol 768-769 ◽  
pp. 723-732 ◽  
Author(s):  
Jürgen Gegner ◽  
Wolfgang Nierlich
Keyword(s):  
Residual Stress ◽  
Wind Turbine ◽  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Rolling Contact ◽  
X Ray Diffraction ◽  
Rolling Bearings ◽  
Wind Turbine Gearbox ◽  
X Ray ◽  
Stress Measurements

Rolling bearings in wind turbine gearboxes occasionally fail prematurely by so-called white etching cracks. The appearance of the damage indicates brittle spontaneous tensile stress induced surface cracking followed by corrosion fatigue driven crack growth. An X-ray diffraction based residual stress analysis reveals vibrations in service as the root cause. The occurrence of high local friction coefficients in the rolling contact is described by a tribological model. Depth profiles of the equivalent shear and normal stresses are compared with residual stress patterns and a relevant fracture strength, respectively. White etching crack failures are reproduced on a rolling contact fatigue test rig under increased mixed friction. Causative vibration loading is evident from residual stress measurements. Cold working compressive residual stresses are an effective countermeasure.

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.

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