Using area detectors for stress determination by diffraction methods in a single exposure greatly simplifies the measurement process and permits the design of portable systems without complex sample cradles or moving parts. An additional advantage is the ability to see the entire or a large fraction of the Debye ring and thus determine texture and grain size effects before analysis. The two methods most commonly used to obtain stress from a single Debye ring are the so called cos α and full-ring fitting methods, which employ least-squares procedures to determine the stress from the distortion of a Debye ring by probing a set of scattering vector simultaneously. The widely applied sin 2 ψ method, in contrast, requires sample rotations to probe a different subset of scattering vector orientations. In this paper we first present a description of the different methods under the same formalism and using a unified set of coordinates that are suited to area detectors normal to the incident beam, highlighting the similarities and differences between them. We further characterize these methods by means of in-situ measurements in carbon steel tube samples, using a portable detector in reflection geometry. We show that, in the absence of plastic flow, the different methods yield basically the same results and are equivalent. An analysis of possible sources of errors and their impact in the final stress values is also presented.
Abstract. The original Kompaneets equation fails to describe down-Comptonization, which is the most important radiative transfer process in hard X-ray and γ-ray astronomy, compared with up-Comptonization. In this paper, we improve our previous
The use of portable X-ray stress analyzers, which utilize an area detector along with the newly adopted 'cosα' or full-ring fitting method, has recently attracted increasing interest. In laboratory conditions, these measurements are fast, convenient and precise because they employ a single-exposure technique that does not require sample rotation. In addition, the effects of grain size and orientation can be evaluated from the Debye ring recorded on the area detector prior to data analysis. The accuracy of the measured stress, however, has been questioned because in most cases just a single reflection is analyzed and the sample-to-detector distances are relatively short. This article presents a comprehensive analysis of the uncertainty associated with a state-of-the-art commercial portable X-ray device. Annealed ferrite reference powders were used to quantify the instrument precision, and the accuracy of the stress measurement was tested by in situ tensile loading on 1018 carbon steel and 6061 aluminium alloy bar samples. The results show that the precision and accuracy are sensitive to the instrument (or sample) tilt angle (ψ0) as well as to the selected hkl reflection of the sample. The instrument, sample and data analysis methods all affect the overall uncertainty, and each contribution is described for this specific portable X-ray system. Finally, on the basis of the conclusions reached, desirable measurement/analysis protocols for accurate stress assessments are also presented
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