Tomographic reconstruction of two-dimensional residual strain fields from Bragg-Edge neutron imaging

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 two dimensions before it is demonstrated experimentally on two samples with use of the RADEN instrument at the Japan Proton Accelerator Research Complex spallation neutron source. Validation of the resulting reconstructions is provided through a comparison with conventional constant-wavelength strain measurements performed with the KOWARI engineering diffractometer of the Australian Nuclear Science and Technology Organisation. The paper concludes with a discussion on the range of problems to be addressed in a three-dimensional implementation.