Residual stress analysis of energy-dispersive diffraction data using a two-detector setup: Part I — Theoretical concept

A new goniometer setup for energy-dispersive X-ray diffraction is introduced which is based on simultaneous data acquisition with two detectors D1 and D2, both of them freely movable in a horizontal as well as in a vertical plane. From the multitude of measurement configurations that can be realised with this setup, we figured out three efficient concepts which aim at the fast analysis of residual stress depth profiles by combining the diffraction data gathered with the two detectors. The characteristic feature of the first two configurations consists in the vertical (horizontal) positioning of the first (second) detector, which results in a diffraction geometry where the two scattering vectors span a plane that coincides with the X-circle used for sample tilt. Because each detector does see the sample under another viewing angle, both the positive and the negative $\psi$-branch are covered by just one $\chi$-tilt between 0°and 90°(configuration 1) and 0°and 60°(configuration 2), thus allowing for the simultaneous analysis of the in- and out-of-plane residual stress depth gradients ${\sigma }_{ii}\left(\tau \right)$ and ${\sigma }_{i3}\left(\tau \right)$ ($i=1,2$), respectively, from data sets $d_{D1}^{hkl}\left(\chi \right)$ and $d_{D2}^{hkl}\left(\chi \right)$. The third configuration introduced in this paper is based on a $\varphi$-rotation of the sample under a constant tilt angle $\chi$ and enables a fast and reliable tracing of shear stress fields ${\sigma }_{i3}\left(\tau \right)$ ($i=1$, 2).