Stress measurement using area detectors: a theoretical and experimental comparison of different methods in ferritic steel using a portable X-ray apparatus

Abstract

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.

Precision and accuracy of stress measurement with a portable X-ray machine using an area detector

“…However, only cos is chosen in this study as a representative of two-dimensional methods because the fundamental equation of the XRD 2 method is basically identical to equation 7, and it measures only part of the Debye ring (Miyazaki & Sasaki, 2016), while the cos and full-ring methods use all of the information. We have also shown experimentally that, when using the same dataset, there was no difference between the cos and full-ring fitting methods (Ramirez-Rico et al, 2016).…”

“…1(b). We previously reported that the strain precision of this portable machine is about 9 microstrain (m") with ferrite reference powders (Ling & Lee, 2015), and that in essence the sin 2 and cos methods are theoretically identical (Ramirez-Rico et al, 2016) and yield statistically indistinguishable experimental results (Ramirez-Rico et al, 2016;Ling & Lee, 2015). The mathematical equivalency between sin 2 and cos was also shown very recently (Miyazaki & Sasaki, 2016).…”

“…For the statistical analysis, this whole process was repeated five times (for a total of 540 measurements) at different sample positions. Since equivalency between cos and sin 2 was shown in x3.4 and by other authors (Ling & Lee, 2015;Ramirez-Rico et al, 2016;Miyazaki & Sasaki, 2016) under a homogeneous bi-axial stress state, we used stress values calculated with the instrument software by the cos method. Reference powders were expected to exhibit no stress irrespective of the chosen value for the aforementioned parameters.…”

Precision of the Residual Stress determined by X-ray Diffraction: Summery and Limits

“…Out of this data the residual stress is calculated. Two different methods (sin 2 Ψ-2θ-method [3] and cosα-method [4]) are common. Both methods are compatible and here it is not important difference, which method is used [5;6].…”

Effect of machining-induced residual stress on springback of creep age formed AA2050 plates with asymmetric creep-ageing behaviour

“…Main chemical compositions of AA2050 (wt.%). The surface residual stress results were calculated by cos α method according to strain data determined from the Debye-Scherrer ring[25]. The data were obtained in about 10 µm depth of the surface area.…”