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Bragg-edge strain imaging from energy-resolved neutron transmission measurements poses an interesting tomography problem. The solution to this problem will allow the reconstruction of detailed triaxial stress and strain distributions within polycrystalline solids from sets of Bragg-edge strain images. Work over the last decade has provided some solutions for a limited number of special cases. In this paper, we provide a general approach to reconstruction of an arbitrary system based on a least squares process constrained by equilibrium. This approach is developed in twodimensions before being demonstrated experimentally on two samples using the RADEN instrument at the J-PARC spallation neutron source in Japan. Validation of the resulting reconstructions is provided through a comparison to conventional constant wavelength strain measurements carried out on the KOWARI engineering diffractometer within ANSTO in Australia. The paper concludes with a discussion on the range of problems to be addressed in a three-dimensional implementation.

Technological developments in high resolution time-of-flight neutron detectors have raised the prospect of tomographic reconstruction of elastic strain fields from Bragg-edge strain images. This approach holds the potential to provide a unique window into the full triaxial stress field within solid samples. While general tomographic reconstruction from these images has been shown to be ill-posed, an injective link between measurements and boundary deformations exists for systems subject to in situ applied loads in the absence of residual stress. Recent work has provided an algorithm to achieve tomographic reconstruction for this class of mechanical system. This letter details an experimental proof-of-concept for this algorithm involving the full reconstruction of a biaxial strain field within a non-trivial steel sample. This work was carried out on the RADEN energy resolved neutron imaging instrument within the Japan Proton Accelerator Research Complex, with validation through Digital Image Correlation and constant wavelength neutron strain scans.

Diffraction-based methods have become an invaluable tool for the detailed assessment of residual strain and stress within experimental mechanics. These methods typically measure a component of the average strain within a gauge volume. It is common place to treat these measurements as point measurements and to interpolate and extrapolate their values over the region of interest. Such interpolations are not guaranteed to satisfy the physical properties of equilibrium and applied loading conditions. In this paper, we provide a numerically robust algorithm for inferring two dimensional, biaxial strain fields over a region of interest from diffraction-based measurements that satisfies equilibrium and any known loading conditions. By correctly treating the measurements as gauge volume averages rather than point-wise the algorithm has better performance when large gauge volumes and subsequently shorter beam-times are used. This algorithm is demonstrated on simulation and experimental data and compared to natural neighbour interpolation with linear extrapolation and is shown to provide a more accurate strain field.

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Several recent methods for tomographic reconstruction of stress and strain fields from Bragg-edge neutron strain images have been proposed in the literature. This paper presents an extension of a previously demonstrated approach based on Gaussian process regression that enforces equilibrium in the method. This extension incorporates knowledge of boundary conditions, primarily boundary tractions, into the reconstruction process. This is shown to increase the rate of convergence and is more tolerant of systematic errors that may be present in experimental measurements. An exact expression for a central calculation in this method is also provided which avoids the need for the approximation scheme that was previously used. Convergence of this method for simulated data is compared to existing approaches and a reconstruction from experimental data is provided. Validation of the results to conventional constant wavelength strain measurements and comparison to prior methods show a significant improvement. KEYWORDSBragg-edge neutron imaging, Gaussian process regression, residual stress, strain tomography Strain. 2019;55:e12325.wileyonlinelibrary.com/journal/str

This paper presents the first triaxial reconstruction of strain in three-dimensions from Bragg-edge neutron imaging. Bragg-edge neutron transmission can provide high-resolution tomographic images of strain within a polycrystalline material. This poses an associated rich tomography problem which seeks to reconstruct the full triaxial strain field from these images. Successful techniques to perform this reconstruction could be used to study the residual strain and stress within engineering components. This paper uses a Gaussian process based approach that ensures the reconstruction satisfies equilibrium and known boundary conditions. This approach is demonstrated experimentally on a non-trivial steel sample with use of the RADEN instrument at the Japan Proton Accelerator Research Complex. Validation of the reconstruction is provided by comparison with conventional strain scans from the KOWARI constantwavelength strain diffractometer at the Australian Nuclear Science and Technology Organisation and simulations via finite element analysis.