Mechanical and fracture properties of a self-compacting version of CARDIFRC Mix II

CARDIFRC is the trade name of two main groups of ultra-high performance fibre-reinforced concrete mixes – Mixes I and II – differing primarily in the maximum size of quartz sand used (0.6 mm in Mix I, and 2 mm in Mix II). In this paper, the conversion of CARDIFRC Mix II to a self-compacting and industrially competitive ultra-high performance fibre-reinforced concrete (UHPFRC) is described. A full mechanical and fracture characterisation (i.e. size-independent fracture energy and the corresponding bi-linear stress-crack opening relationship) of this UHPFRC is provided

Conductivities of heterogeneous media with graded anisotropic constituents

Two methods are presented to predict the effective conductivities of heterogeneous media containing discretely suspended particles. The particles have either graded anisotropy or a graded anisotropic interphase. A differential replacement procedure based on an energy equivalency condition is presented first to replace the graded anisotropic constituents by equivalent homogeneous isotropic particles. This allows many approximate schemes to be used to predict the effective conductivities of the heterogeneous media containing graded anisotropic constituents from the conductivity of the equivalent homogeneous particles. Next, the optimized upper and lower bounds on the effective conductivities of these heterogeneous media are presented by introducing comparison materials. It is shown that the DRP predictions are within these bounds for the considered media

Effective conductivities of heterogeneous media containing multiple inclusions with various spatial distributions

A scheme is proposed for predicting the effective conductivities of heterogeneous media containing ellipsoidal inclusions of diverse shapes, spatial distributions, and orientations. This scheme yields explicit expressions for the effective conductivity tensor in terms of three microstructural parameters that characterize the shape, distribution, and orientation of the inclusions. By expanding the effective conductivity tensor in terms of the volume fraction of the inclusions, it is found that the effect of the shape of the distribution ellipsoid on the effective conductivity tensor is of a higher order in the volume fraction than the effect of the shape of the inclusions. The scheme proposed here generalizes the Maxwell formula to heterogeneous media containing multiple inclusions while also taking into account the orientation of the inclusions. Thus, the existing formulas in the literature are special cases of the general formulas given by the present scheme. The predicted effective conductivities of heterogeneous media containing aligned ellipsoidal inclusions, randomly oriented ellipsoidal inclusions, spheroidal inclusions with orientational distributions, and mixtures of cavities and cracks are found to agree well with the experimental results and the results of other schemes

Pattern transformations in periodic cellular solids under external stimuli

The structural patterns of periodic cellular materials play an important role in their properties. Here, we investigate how these patterns transform dramatically under external stimuli in simple periodic cellular structures that include a nanotube bundle and a millimeter-size plastic straw bundle. Under gradual hydrostatic straining up to 20%, the cross-section of the single walled carbon nanotube bundle undergoes several pattern transformations, while an amazing new hexagram pattern is triggered from the circular shape when the strain of 20% is applied suddenly in one step. Similar to the nanotube bundle, the circular plastic straw bundle is transformed into a hexagonal pattern on heating by conduction through a baseplate but into a hexagram pattern when heated by convection. Besides the well-known elastic buckling, we find other mechanisms of pattern transformation at different scales; these include the minimization of the surface energy at the macroscale or of the van der Waals energy at the nanoscale and the competition between the elastic energy of deformation and either the surface energy at the macroscale or the van der Waals energy at the nanoscale. The studies of the pattern transformations of periodic porous materials offer new insights into the fabrication of novel materials and devices with tailored properties

Reorientation of short steel fibres during the flow of self-compacting concrete mix and determination of the fibre orientation factor

A simple method has been developed to assess the orientation and distribution of short steel fibres in self-compacting concrete mixes during flow. The flow of self-compacting fibre reinforced concrete has been simulated using three-dimensional Lagrangian smooth particle hydrodynamics (SPH) which is simpler and more appropriate to use to simulate the flow and to monitor the distribution of fibres and their orientation during the flow. A probability density function (PDF) has been introduced to represent the fibre orientation variables in three dimensions. Moreover, the orientation variables of each individual fibre in an arbitrary two dimensional cross-section have been calculated using the geometrical data obtained from the three dimensional simulations. From these a new definition of the fibre orientation factor has been introduced and a method proposed for its determination from the fibre orientations monitored during the simulations. It is shown that this new definition gives results that are consistent with the expected reorientation of fibres towards the principal direction of flow. A method has also been proposed for its determination from image analysis on cut sections

Theory of elasticity at the nanoscale

We have shown in a series of recent papers that the classical theory of elasticity can be extended to the nanoscale by supplementing the equations of elasticity for the bulk material with the generalized Young-Laplace equations of surface elasticity. This review article shows how this has been done in order to capture the often unusual mechanical and physical properties of nanostructured particulate and porous materials. It begins with a description of the generalized Young-Laplace equations. It then generalizes the classical Eshelby formalism for nano-inhomogeneities; the Eshelby tensor now depends on the size of the inhomogeneity and the location of the material point in it. Then the stress concentration factor of a spherical nanovoid is calculated, as well as the strain fields in quantum dots (QDs) with multi-shell structures and in alloyed QDs induced by the mismatch in the lattice constants of the atomic species. This is followed by a generalization of the micromechanical framework for determining the effective elastic properties and effective coefficients of thermal expansion of heterogeneous solids containing nano-inhomogeneities. It is shown, for example, that the elastic constants of nanochannel-array materials with a large surface area can be made to exceed those of the nonporous matrices through pore surface modification or coating. Finally, the scaling laws governing the properties of nanostructured materials are derived. The underlying cause of the size dependence of these properties at the nanoscale is the competition between surface and bulk energies. These laws provide a yardstick for checking the accuracy of experimentally measured or numerically computed properties of nanostructured materials over a broad size range and can thus help replace repeated and exhaustive testing by one or a few tests