Non-contact stress measurement in granular materials via neutron and X-ray diffraction: theoretical foundations

Abstract

Model validation remains a serious problem within the field of computational granular materials research. In all cases the rigor of the validation process is entirely dependent on the quality and depth of the experimental data that forms the point of comparison. Neutron and X-ray diffraction methods offer the only quantitative non-contact method for determining the spatially resolved triaxial stress field within granular materials under load. Measurements such as this can provide an unprecedented level of detail that will be invaluable in validating many models. In this paper the theoretical foundation underpinning diffraction-based strain measurements, their conversion to local stress in the particles and ultimately into the bulk stress field is developed. Effects such as elastic anisotropy within the particles of the granular material, particle plasticity and locally inhomogeneous stress distribution are shown to not offer any obstacles to the method and a detailed treatment of the calculation of the bulk stresses from the particle stresses is given.