Direct inversion of the Longitudinal Ray Transform for 2D residual elastic strain fields

We examine the problem of Bragg-edge elastic strain tomography from energy resolved neutron transmission imaging. A new approach is developed for two-dimensional plane-stress and plane-strain systems whereby elastic strain can be reconstructed from its Longitudinal Ray Transform (LRT) as two parts of a Helmholtz decomposition based on the concept of an Airy stress potential. The solenoidal component of this decomposition is reconstructed using an inversion formula based on a tensor filtered back projection algorithm whereas the potential part can be recovered using either Hooke's law or a finite element model of the elastic system. The technique is demonstrated for two-dimensional plane-stress systems in both simulation, and on real experimental data. We also demonstrate that application of the standard scalar filtered back projection algorithm to the LRT in these systems recovers the trace of the solenoidal component of strain and we provide physical meaning for this quantity in the case of 2D plane-stress and plane-strain systems.Comment: 30 pages, 9 figure

A laboratory-numerical approach for modelling scale effects in dry granular slides

Granular slides are omnipresent in both natural and industrial contexts. Scale effects are changes in physical behaviour of a phenomenon at different geometric scales, such as between a laboratory experiment and a corresponding larger event observed in nature. These scale effects can be significant and can render models of small size inaccurate by underpredicting key characteristics such as ow velocity or runout distance. Although scale effects are highly relevant to granular slides due to the multiplicity of length and time scales in the flow, they are currently not well understood. A laboratory setup under Froude similarity has been developed, allowing dry granular slides to be investigated at a variety of scales, with a channel width configurable between 0.25-1.00 m. Maximum estimated grain Reynolds numbers, which quantify whether the drag force between a particle and the surrounding air act in a turbulent or viscous manner, are found in the range 102-103. A discrete element method (DEM) simulation has also been developed, validated against an axisymmetric column collapse and a granular slide experiment of Hutter and Koch (1995), before being used to model the present laboratory experiments and to examine a granular slide of significantly larger scale. This article discusses the details of this laboratory-numerical approach, with the main aim of examining scale effects related to the grain Reynolds number. Increasing dust formation with increasing scale may also exert influence on laboratory experiments. Overall, significant scale effects have been identified for characteristics such as ow velocity and runout distance in the physical experiments. While the numerical modelling shows good general agreement at the medium scale, it does not capture differences in behaviour seen at the smaller scale, highlighting the importance of physical models in capturing these scale effects

Stress distribution in iron powder during die compaction

The unique and unusual state of matter represented by granular materials has historically made it very difficult to develop models of stress distributions and was previously not able to be explored experimentally in the required detail. This paper reports the application of the neutron diffraction strain scanning method, originally developed for residual stress measurements within engineering components, to the problem of the stress distribution in granular Fe under a consolidating pressure. Strains were measured in axial, radial, circumferential and an oblique direction using the neutron strain scanning diffractometer KOWARI at ANSTO (Sydney). The full stress tensor as a function of position was able to be extracted for both straight walled, converging and stepped dies. © 2014, Trans Tech Publications

Measurement and analysis of the stress distribution during die compaction using neutron diffraction

The full axisymmetric stress state of a granular material undergoing compaction in a cylindrical die has been measured using a technique based on neutron powder diffraction. This technique allowed the detailed distribution of stress to be measured in situ, deep within a copper powder inside a solid die. Four components of normal strain were measured over a radial cross section. These components consisted of the axial, radial, hoop and an off-axis strain in the axial-radial direction. This allowed for the reconstruction of the full axisymmetric stress tensor as a distribution over the radial cross section. Many interesting features were observed in this distribution, such as exponential decay of the axial stress (described by Janssen in Zeitschrift des Vereines duetscher Ingenieure 39:1045, 1895), and highly localised regions of high shear stress. The potential of this type of data in the validation of numerical models is discussed. © 2012, Springer

Neutron diffraction strain tomography: Demonstration and proof-of-concept

Recently, a number of reconstruction algorithms have been presented for residual strain tomography from Bragg-edge neutron transmission measurements. In this paper, we examine whether strain tomography can also be achieved using diffraction instruments. We outline the proposed method and develop a suitable reconstruction algorithm. This technique is demonstrated in simulation, and a proof-of-concept experiment is carried out, where the strain field in an axisymmetric sample is reconstructed and validated using conventional diffraction strain scans. © 2020 AIP Publishing LLC

Mapping Grain Strains in Sand Under Load Using Neutron Diffraction Scanning

Towards the improvement of the understanding of force/stress distribution in granular media under load, a new experimental approach is suggested. Neutron diffraction, a non-conventional experimental technique, has been successfully used to map the evolution of intragranular strains in sand specimens loaded in a novel plane-strain apparatus. Representative preliminary results from recent experiments are presented, focusing on the correlation between the macro- and micro-scale response of the material, to highlight the potential of the experimental approach