Stress measurement using area detectors: a theoretical and experimental comparison of different methods in ferritic steel using a portable X-ray apparatus
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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 \(\cos \alpha \) 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 \(\sin ^2\psi \) 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.
KeywordsFerrite Residual Stress Area Detector Residual Stress Measurement Sample Rotation
Loading experiments were performed at the Robert W. Carleton Strength of Materials Laboratory, Columbia University. Dr. A. Brügger’s assistance with the loading setup is gratefully acknowledged. The X-ray portable stress measurement device was kindly supplied by Pulstec Industrial Co., Ltd. The authors would like to thank Toshikazu Suzuki and Yoshinobu Teramoto for installation and technical support. J. Ramirez-Rico gratefully acknowledges the support from the Universidad de Sevilla Research Fund (V Plan Propio).
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Conflict of interest
The authors declare that they have no conflict of interest.
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