Mapping forces in 3D elastic assembly of grains

Our understanding of the elasticity and rheology of disordered materials, such as granular piles, foams, emulsions or dense suspensions relies on improving experimental tools to characterize their behaviour at the particle scale. While 2D observations are now routinely carried out in laboratories, 3D measurements remain a challenge. In this paper, we use a simple model system, a packing of soft elastic spheres, to illustrate the capability of X-ray microtomography to characterise the internal structure and local behaviour of granular systems. Image analysis techniques can resolve grain positions, shapes and contact areas; this is used to investigate the material's microstructure and its evolution upon strain. In addition to morphological measurements, we develop a technique to quantify contact forces and estimate the internal stress tensor. As will be illustrated in this paper, this opens the door to a broad array of static and dynamical measurements in 3D disordered systems

The effect of surface hardening on the elastic shakedown of elliptical contacts

The effect of varying both the aspect ratio and the coefficient of friction of contacts with elliptical geometry on their elastic shakedown performance has been examined theoretically for surfaces with two types of subsurface hardness or strength profiles. In stepwise hardening the hard layer is of uniform strength while in linear hardening its strength reduces from a maximum at the surface to that of the core at the base of the hardened layer. The shakedown load is expressed as the ratio of the maximum Hertzian pressure to the strength of the core material. As the depth of hardening, expressed as a multiple of the elliptical semi-axis, is increased so the potential shakedown load increases from a level that is appropriate to a uniform half-space of unhardened material to a value reflecting the hardness of the surface and near-surface material. In a step-hardened material, the shakedown limit for a surface 'pummelled' by the passage of a sequence of such loads reaches a cut-off or plateau value, which cannot be exceeded by further increases in hardening depth irrespective of the value of the friction coefficient. For a linear-hardened material the corresponding plateau is approached asymptotically. The work confirms earlier results on the upper bounds on shakedown of both point and line contacts and provides numerical values of shakedown loads for intermediate geometries. In general, the case depth required to achieve a given shakedown limit reduces in moving from a transversely moving nominal line load to an axisymmetric point load.

Effect of elastic stresses on free oscillations in ferroelectric liquid crystals

It is shown experimentally that an elastic mechanical stress in a crystal structure is a necessary factor for the appearance of free oscillations of the director of a ferroelectric liquid crystal. Such a mechanical stress arises as a result of internal textural perturbations in the presence of regions with a different orientation of the director or is produced by external pressure applied to one of the cell plates in the appropriate direction. © 1999 American Institute of Physics.

The effect of dopants on the twist elastic constant and the rotational viscosity coefficient for nematics

The twist elastic constant, K2, and the rotational viscosity coefficient, γ1, are of importance when the response lime for the in-plane switching mode is studied. Since adding dopants is one technique to improve the response characteristics, the effect of dopants on these physical properties is significant. The effect on K2 and γ1 of adding alkyl(alkoxy) phenylcyclopentenones and alkyl(alkoxy) cyanobiphenyls to the base mixture ZLI-4792 together with their temperature dependence have been investigated using different temperature scales. The reduced temperature scale showed the effect of these dopants on K2 is small. On the other hand, the temperature dependence of γ1 depends on both the absolute temperature scale and the reduced temperature scale. Therefore, it is clear that the choice of temperature scale with which to compare γ1 for different systems raises fundamental questions which way not have a unique answer. 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

Viscoelastic properties of bone as a function of hydration state determined by nanoindentation

Spherical indentation creep testing was used to examine the effect of hydration state on bone mechanical properties. Analysis of creep data was based on the elastic-viscoelastic correspondence principle and utilized a direct solution for the finite loading-rate experimental conditions. The zero-time shear modulus was computed from the creep compliance function and compared to the indentation modulus obtained via conventional indentation analysis, based on an elastic unloading response. The method was validated using a well-known polymer material under three different loading conditions. The method was applied to bone samples prepared with different water content by partial exchange with ethanol, where 70% ethanol was considered as the baseline condition. A hydration increase was associated with a 43% decrease in stiffness, while a hydration decrease resulted in a 20% increase in bone tissue stiffness.

Nanoindentation measurements of bone viscoelasticity as a function of hydration state

Bone is an anisotropic material, and its mechanical properties are determined by its microstructure as well as its composition. Mechanical properties of bone are a consequence of the proportions of, and the interactions between, mineral, collagen and water. Water plays an important role in maintaining the mechanical integrity of the composite, but the manner in which water interacts within the ultrastructure is unclear. Dentine being an isotropic two-dimensional structure presents a homogenous composite to examine the dehydration effects. Nanoindentation methods for determining the viscoelastic properties have recently been developed and are a subject of great interest. Here, one method based on elastic-viscoelastic correspondence for 'ramp and hold' creep testing (Oyen, J. Mater. Res., 2005) has been used to analyze viscoelastic behavior of polymeric and biological materials. The method of 'ramp and hold' allows the shear modulus at time zero to be determined from fitting of the displacement during the maximum load hold. Changes in the viscoelastic properties of bone and dentine were examined as the material was systematically dehydrated in a series of water:solvent mixes. Samples of equine dentine were sectioned and cryo-polished. Shear modulus was obtained by nanoindentation using spherical indenters with a maximum load hold of 120s. Samples were tested in different solvent concentrations sequentially, 70% ethanol to 50% ethanol, 70 % ethanol to 100% ethanol, 70% ethanol to 70% methanol to 100% methanol, and 70% ethanol to 100% acetone, after storage in each condition for 24h. By selectively removing and then replacing water from the composite, insights in to the ultrastructure of the tissue can be gained from the corresponding changes in the experimentally determined moduli, as well as an understanding of the complete reversibility of the dehydration process. © 2006 Materials Research Society.

The elastic-plastic indentation response of a columnar thermal barrier coating

Thermal barrier coatings with a columnar microstructure are prone to erosion damage by a mechanism of surface cracking upon impact by small foreign particles. In order to explore this erosion mechanism, the elastic indentation and the elastic-plastic indentation responses of a columnar thermal barrier coating to a spherical indenter were determined by the finite element method and by analytical models. It was shown that the indentation response is intermediate between that of a homogeneous half-space and that given by an elastic-plastic mattress model (with the columns behaving as independent non-linear springs). The sensitivity of the indentation behaviour to geometry and to the material parameters was explored: the diameter of the columns, the gap width between columns, the coefficient of Coulomb friction between columns and the layer height of the thermal barrier coating. The calculations revealed that the level of induced tensile stress is sufficient to lead to cracking of the columns at a depth of about the column radius. It was also demonstrated that the underlying soft bond coat can undergo plastic indentation when the coating comprises parallel columns, but this is less likely for the more realistic case of a random arrangement of tapered columns. © 2009 Elsevier B.V.

Extraction of fibre network architecture by X-ray tomography and prediction of elastic properties using an affine analytical model

This paper proposes a method for extracting reliable architectural characteristics from complex porous structures using micro-computed tomography (μCT) images. The work focuses on a highly porous material composed of a network of fibres bonded together. The segmentation process, allowing separation of the fibres from the remainder of the image, is the most critical step in constructing an accurate representation of the network architecture. Segmentation methods, based on local and global thresholding, were investigated and evaluated by a quantitative comparison of the architectural parameters they yielded, such as the fibre orientation and segment length (sections between joints) distributions and the number of inter-fibre crossings. To improve segmentation accuracy, a deconvolution algorithm was proposed to restore the original images. The efficacy of the proposed method was verified by comparing μCT network architectural characteristics with those obtained using high resolution CT scans (nanoCT). The results indicate that this approach resolves the architecture of these complex networks and produces results approaching the quality of nanoCT scans. The extracted architectural parameters were used in conjunction with an affine analytical model to predict the axial and transverse stiffnesses of the fibre network. Transverse stiffness predictions were compared with experimentally measured values obtained by vibration testing. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.