Three-dimensional reconstruction of intragranular strain and orientation in polycrystals by near-field X-ray diffraction

Abstract

A theoretical framework is proposed for simultaneous reconstruction of the three-dimensional grain shapes, intragranular strain and orientation fields inside polycrystals from near-field X-ray diffraction images, using box beam illumination. The approach, named Iterative Tensor Field (ITF) reconstruction, uses a tensor field representation and a kinematical forward simulation model to reproduce the measured diffraction signal from individual grains. The framework establishes a link between the local deformation components inside the grains and the intensities of the diffraction signal in the measured images by forming a local linear problem. This is solved using a large scale linear optimisation method in every main iteration of the underlying non-linear problem. The optimisation enforces smooth gradients and the objective function may include regularisation constraints of static equilibrium or input from a Crystal Plasticity FEM simulation. The method has modest computational requirements and enables efficient scanning of millimetre or sub-millimetre sized specimens. Results on experimental data measured on a Gum metal specimen are presented, which demonstrate convergence and the feasibility of the approach. The mathematical formulation, data representation and challenges in the reconstruction and validation are discussed. The physical aspects of the contrast phenomenon, the deformation sensitivity of the technique, and potential means of error assessment are described. A number of alternative concepts for a polycrystalline deformation model and potential solvers are also presented.

Imposing equilibrium on experimental 3-D stress fields using Hodge decomposition and FFT-based optimization

“…The proposed method is presented as a post-processing step to the Iterative Tensor Field (ITF) reconstruction method [12] that reconstructs sub-granular elastic strain field from 3DXRD, and then uses this as well as the elastic constants to obtain the experimental stress fields. Since it is a post-processing step, it can be applied to other techniques to experimentally reconstruct voxelized stress field like that of Shen, Liu and Suter (SLS) [13].…”

“…The grainby-grain reconstruction approach is inherently prone to higher errors near grain boundaries. These aspects and potential future improvements of the acquisition and data processing, including the handling of all grains simultaneously and ways to include the local mechanical equilibrium, are described in more detail in [12]. The fit quality in the ITF deformation solver can be monitored through the residual.…”

“…Recently, 3DXRD data inversion methods were improved to provide not only voxelized crystal orientation but also stress fields with intragranular resolution using a variety of experimental procedures, including a microbeam (1D), line beam (2D) or box beam (3D) illumination, each demanding a tailored optimization-based data processing approach [10,11,12,13,14]. However, these types of adopted optimization methods have been exclusively based on imposing diffraction constraints, by minimizing the difference between experimental and simulated detector images obtained by forward-modelling of the diffraction experiment, and retaining as measured fields the orientation and stress fields that produced that minimum.…”

Improved grain mapping by laboratory X-ray diffraction contrast tomography

“…Several techniques have been developed at third-generation synchrotron X-ray facilities for such characterization. These include differential aperture X-ray microscopy (Larson et al, 2002), 3D X-ray diffraction microscopy (Poulsen et al, 2001;Poulsen, 2004Poulsen, , 2012 and its variants like high-energy X-ray diffraction microscopy (Suter et al, 2006), scanning 3D X-ray diffraction microscopy (Hayashi et al, 2015;Henningsson et al, 2020) and diffraction contrast tomography (DCT) (Ludwig et al, 2008;Reischig & Ludwig, 2020), as well as dark-field X-ray microscopy (Simons et al, 2015;Jakobsen et al, 2019;Poulsen, 2020). These methods allow grain mapping at different length scales.…”

Intragranular strain estimation in far-field scanning X-ray diffraction using a Gaussian process

“…Recent advances in diffraction contrast tomography (Reischig & Ludwig, 2020) show promising results for inversion for both orientation and strain fields in three dimensions with intragranular resolution. In scanning 3DXRD where higher angular resolution on scattering vectors is achieved at the cost of diffraction peak resolution (Nervo et al, 2014), multiple proposals for inversion operating solely from scattering vectors have been made.…”