Determining grain resolved stresses in polycrystalline materials using three-dimensional X-ray diffraction

Abstract

An algorithm is presented for characterization of the grain resolved (type II) stress states in a polycrystalline sample based on monochromatic X‐ray diffraction data. The algorithm is a robust 12‐parameter‐per‐grain fit of the centre‐of‐mass grain positions, orientations and stress tensors including error estimation and outlier rejection. The algorithm is validated by simulations and by two experiments on interstitial free steel. In the first experiment, using only a far‐field detector and a rotation range of 2 × 110°, 96 grains in one layer were monitored during elastic loading and unloading. Very consistent results were obtained, with mean resolutions for each grain of approximately 10 µm in position, 0.05° in orientation, and 8, 20 and 13 × 10−5 in the axial, normal and shear components of the strain, respectively. The corresponding mean deviations in stress are 30, 50 and 15 MPa in the axial, normal and shear components, respectively, though some grains may have larger errors. In the second experiment, where a near‐field detector was added, ∼2000 grains were characterized with a positional accuracy of 3 µm.

Strain tensor determination of compressed individual silica sand particles using high-energy synchrotron diffraction

“…It is based on transmission geometry that can be applied in both layered and bulk materials [23][24][25][26][27]. It allows nondestructive 3D mapping of polycrystalline materials and monitors in situ dynamic processes of the bulk specimens.…”

Measuring the stress field around an evolving crack in tensile deformed Mg AZ31 using three-dimensional X-ray diffraction

“…assign the diffraction spots to oriented grains, in each illuminated layer. The refinement of the centre-of-mass positions, orientations and full elastic strain tensors of the indexed grains was performed as a simultaneous 12-parameter-per-grain fit to the assigned reflections using the FitAllB module of FABLE [25]. The average number of reflections per grain after the built-in outlier rejections and the convergence of the refinement can be seen in Table 2.…”

“…Fig.4. The error bars on the centre-of-mass grain positions, volumes, orientations and strain tensors were estimated by FitAllB as described previously [25]. The average values of these are also summarized in Table 2.…”

“…the sample-to-detector distance, the position of the beam centre on the detector, the tilts of the detector face and of the sample rotation stage, the wavelength of the incident beam and the lattice constants of the undeformed material. All of these parameters were refined using FitAllB on the indexed grains from the data set collected at a macroscopic load of 5 MPa 9 assuming no residual stress as described previously [25]. 5 MPa was chosen as the reference point to ensure that the sample was properly gripped.…”

“…In previous of these so-called grain centre mapping experiments the number of mapped grains were rather limited [20][21][22][23][24], but recent progress has made it possible to map the stress field in a representative volume within the bulk of a polycrystalline sample by using the individual grains as probes [25][26][27]. Notably, the spatial resolution of the stress map is in this case determined by the grain size and the detector resolution (in terms of pixel size and spatial distortions) rather than by the dimensions of the incoming X-ray beam.…”