Associate Professor Chris Wensrich

Neutron diffraction techniques are used to measure a series of bulk stress distributions in granular materials undergoing high stress die compaction. Two different granular materials are studied: a ductile material in the form of iron powder and a brittle material in the form of quartz sand. The behaviour of these two materials is examined in terms of the resulting stress distribution within two dies of different geometry: an axisymmetric converging die and a stepped cylindrical die. These measured distributions are examined and discussed to highlight both similarities and differences in the mechanical response of these contrasting materials at high consolidating loads. The potential for neutron diffraction techniques to provide full-field information on the mechanical response and stress within granular samples is demonstrated.

The advent of pixelated detectors for time-of-flight neutron transmission experiments has raised significant interest in terms of the potential for tomographic reconstructions of triaxial strain distributions. A recent publication by Lionheart and Withers [WRB Lionheart and PJ Withers, "Diffraction tomography of strain", Inverse Problems, v31:045005, 2015] has demonstrated that reconstruction is not possible in the general sense; however, various special cases may exist. In this paper, we outline a process by which it is possible to tomographically reconstruct average triaxial elastic strains within individual particles in a granular assembly from a series of Bragg edge strain measurements. This algorithm is tested on simulated data in two and three dimensions and is shown to be capable of rejecting Gaussian measurement noise. Sources of systematic error that may present problems in an experimental implementation are briefly discussed.

An approach for tomographic reconstruction of three-dimensional strain distributions from Bragg-edge neutron transmission strain images is outlined and investigated. This algorithm is based on the link between Bragg-edge strain measurements and the Longitudinal Ray Transform, which has been shown to be sensitive only to boundary displacement. By exploiting this observation we provide a method for reconstructing boundary displacement from sets of Bragg-edge strain images. In the case where these displacements are strictly the result of externally applied tractions, corresponding internal strain fields can then be found through traditional linear-static finite element methods. This approach is tested on synthetic data in two-dimensions, where the rate of convergence in the presence of measurement noise and beam attenuation is examined.

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, Switzerland.

The full triaxial stress state within individual particles in a monodisperse spherical granular assembly has been measured. This was made possible by neutron imaging and computed tomography combined with neutron diffraction strain measurement techniques and associated stress reconstruction. The assembly in question consists of 549 precision steel ball bearings under an applied axial load of 85 MPa in a cylindrical die. Clear evidence of force chains was observed in terms of both the shape of the probability distribution function for normal stresses and the network formed by highly loaded particles. An extensive analysis of the source and magnitude of uncertainty in these measurements is also presented.

The physical nature of contact moments within granular assemblies is reviewed and a new approach is developed for the homogenisation of stress within these materials. This approach revolves around capturing the effects of contact moments through the concept of contact eccentricity. By this method it is possible to calculate an expression for bulk stress that is both symmetric for material in equilibrium and fully consistent with the usual definition of bulk stress as an ensemble average of material stress over a representative volume element. The technique is demonstrated in a simple two dimensional example, as well as a larger scale discrete element modelling simulation of a steady state direct shear experiment. © 2014 Springer-Verlag Berlin Heidelberg.

Expressions for bulk stress within a granular material in a dynamic setting are reviewed and explicitly derived for assemblies of three dimensional arbitrary shaped particles. By employing classical continuum and rigid body mechanics, the mean stress tensor for a single particle is separated into three distinct components; the familiar Love-Webber formula describing the direct effect of contacts, a component due to the net unbalanced moment arising from contact and a symmetric term due to the centripetal acceleration of material within the particle. A case is made that the latter term be ignored without exception when determining bulk stress within an assembly of particles. In the absence of this centripetal term an important observation is made regarding the nature of the symmetry in the stress tensor for certain types of particles; in the case of particles with cubic symmetry, the effects of dynamics on the bulk stress in an assembly is captured by an entirely skew-symmetric tensor. In this situation, it is recognised that the symmetric part of the Love-Webber formula is all that is required for defining the mean stress tensor within an assembly - regardless of the dynamics of the system.

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. © 2013 Springer-Verlag Berlin Heidelberg.