Determination of grain-level strain and proposing a new method of strain determination for three dimensional x-ray diffraction (3DXRD)

A new approach for lattice strain determination is proposed for analysis of three dimensional x-ray diffraction (3DXRD) data. Our objective is to establish a correspondence between lattice strain and change of diffraction spot position in $\omega$ ($\omega$ is the rotation angle about the loading axis for 3DXRD experiment), using far-field configuration. The final goal is to apply the same concept to extract subgrain level strain from near-field data (near-field has less resolution in 2$\theta$. $\theta$ is the scattering angle for diffraction). The method is developed using the far-field 3DXRD data obtained from an \textit{in-situ} experiment of a Ti-7Al alloy sample. The experiment is conducted at beamline- 1 ID of the Advanced Photon Source at Argonne National Laboratory. A high-resolution monochromator is used to get high strain resolution. The specimen is subjected to combined bending and uniaxial tensile loads up to yield at highest local stress points. Far-field images are collected in two ways- (a) at each $0.5^o$ rotation about the loading axis from $-180^o$ to $180^o$ (coarse scan),(b) at each $0.05^o$ rotation about the loading axis from $-180^o$ to $0^o$ (fine scan). A near-field data collection is carried out simultaneously. A study of the stress gradient developed in the Ti-7Al sample is performed using lattice strain determination algorithm taking care of the grain precession. A map of grain orientation in the cross-section of the sample is determined through use of the near-field technique. A state of bending with superposed tension is revealed through correlation of the near-field grain map with the far-field strain and center of mass (COM) result. Lattice strain induced changes of $\omega$ are found for all scattering vectors of individual grains. It is plotted against the final $\omega$ positions of the scattering vectors. Such plots are generated for every individual grain indexed by \textit{GrainSpotter}. The theoretically determined values of change of $\omega$ ($\Delta\omega_{model}$) follow a sinusoidal pattern when plotted against the final $\omega$ positions (the effect of grain precession on lattice strain is taken care of in the theoretical calculations). The experimentally found values of change of $\omega$ ($\Delta\omega_{meas}$ or $\Delta\omega_{log}$) may or may not show the similar coorespondence depending on the lattice orientation and lattice strain. The magnitude of the $\Delta\omega_{model}$ is found to be lower than the magnitude of the $\Delta\omega_{meas}$ or $\Delta\omega_{log}$. The fine scan proves to be more informative than the coarse scan for study of shift of $\omega$ position of a diffraction spot with change of load