Growth and shape control of disks by bending and extension

Differential growth of thin elastic bodies furnishes a surprisingly simple explanation of the complex and intriguing shapes of many biological systems, such as plant leaves and organs. Similarly, inelastic strains induced by thermal effects or active materials in layered plates are extensively used to control the curvature of thin engineering structures. Such behaviour inspires us to distinguish and to compare two possible modes of differential growth not normally compared to each other, in order to reveal the full range of out-of-plane shapes of an initially flat disk. The first growth mode, frequently employed by engineers, is characterised by direct bending strains through the thickness, and the second mode, mainly apparent in biological systems, is driven by extensional strains of the middle surface. When each mode is considered separately, it is shown that buckling is common to both modes, leading to bistable shapes: growth from bending strains results in a double-curvature limit at buckling, followed by almost developable deformation in which the Gaussian curvature at buckling is conserved; during extensional growth, out-of-plane distortions occur only when the buckling condition is reached, and the Gaussian curvature continues to increase. When both growth modes are present, it is shown that, generally, larger displacements are obtained under in-plane growth when the disk is relatively thick and growth strains are small, and vice versa. It is also shown that shapes can be mono-, bi-, tri- or neutrally stable, depending on the growth strain levels and the material properties: furthermore, it is shown that certain combinations of growth modes result in a free, or natural, response in which the doubly curved shape of disk exactly matches the imposed strains. Such diverse behaviour, in general, may help to realise more effective actuation schemes for engineering structures. © 2012 Elsevier Ltd. All rights reserved.

Measurement of the elastic constants of nanometric films

Carbon coatings of thickness down to 2 nanometers are needed to increase the storage density in magnetic hard disks and reach the 100 Gbit/in2 target. Methods to measure the properties of these ultrathin hard films still have to be developed. We show that combining Surface Brillouin Scattering (SBS) andX-ray reflectivity measurements the elastic constants of such films are accessible. Tetrahedral amorphous carbofilms of thickness down to about 2 nm were deposited on Si by an S bend filtered cathodic vacuum arc, achieving a continuous coverage on large areas free of macroparticles. Film thickness and mass density are measured by X-ray reflectivity: densities above 3 g/cm3 are found, indicating a significant sp3 content. The dispersion relations of surface acoustic waves are measured by SBS. We show that for thicknesses above ∼4 nm these waves can be described by a continuum elastic model based on a single homogeneous equivalent film. The elastic constants can then be obtained by fitting the dispersion relations, computed for given film properties, to the measured dispersion relations. For thicknesses of 3 nm or less qualitative differences among films are well measurable, but quantitative results are less reliable. We have thus shown that we can grow and characterise nanometer size tetrahedral amorphous carbon film, which maintain their high density and peculiar mechanical properties down to around 4 nm thickness, satisfying the requirements set for the hard disk coating material.

Shroud heat transfer measurements from a rotating cavity with an axial throughflow of air

The paper discusses measurements of heat transfer obtained from the inside surface of the peripheral shroud. The experiments were carried out on a rotating cavity, comprising two 0.985-m-dia disks, separated by an axial gap of 0.065 m and bounded at the circumference by a carbon fiber shroud. Tests were conducted with a heated shroud and either unheated or heated disks. When heated, the disks had the same temperature level and surface temperature distribution. Two different temperature distributions were tested; the surface temperature either increased, or decreased with radius. The effects of disk, shroud, and air temperature levels were also studied. Tests were carried out for the range of axial throughflow rates and speeds: 0.0025 ≤ m ≤ 0.2 kg/s and 12.5 ≤ Ω ≤ 125 rad/s, respectively. Measurements were also made of the temperature of the air inside the cavity. The shroud Nusselt numbers are found to depend on a Grashof number, which is defined using the centripetal acceleration. Providing the correct reference temperature is used, the measured Nusselt numbers also show similarity to those predicted by an established correlation for a horizontal plate in air. The heat transfer from the shroud is only weakly affected by the disk surface temperature distribution and temperature level. The heat transfer from the shroud appears to be affected by the Rossby number. A significant enhancement to the rotationally induced free convection occurs in the regions 2 ≤ Ro ≤ 4 and Ro ≥ 20. The first of these corresponds to a region where vortex breakdown has been observed. In the second region, the Rossby number may be sufficiently large for the central throughflow to affect the shroud heat transfer directly. Heating the shroud does not appear to affect the heat transfer from the disks significantly.