Fibre array

In three dimensions a treatment, approaching exactness of the short fibre array was made by Smith and Spencer52 j which hexagonal packing was assumed but the hexagonal unit cell replaced by a composite circular cylinder. Numerical analysis of the cubic lattice of spheres was made by Broutman and Agarwal53 . 

F. Belal and J. L. Anderson, Flow Injection Analysis of Three N-Substi-tuted Phenothiazine Drugs with Amperometric Detection at a Carbon Fibre Array Electrode. Analyst, 110 (1985) 1493. 

Current methods combine at least one of four different principles of allelic discrimination (hybridization, primer extension, ligation, or restriction) with one of four different detection techniques (chemiluminescence/ fluorescence, fluorescence polarization, resonance energy transfer, and mass spectrometry). Assay formats range from (slab)- gel electrophoresis, plates, particles, fibre arrays, and microchip arrays to semi- and homogenous assays that do not require any further sample separation or purification. 

The high fluidity (low viscosity) of the slurry is necessary for adequate penetration of the dense fibre array in the mould. By the addition of fly ash and fine sand, the Portland cement content may be diminished and possible shrinkage cracking reduced. Vibration of pre-placed fibres before and after pouring of cement slurry is often advisable in order to improve the density and distribution of reinforcement. External pressure should also be applied. 

Fig. 2.18 The most important geometries of microelectrodes and microelectrode arrays a microdisk b microring c microdisk array (a composite electrode) d lithographically produced microband array e microband f single fibre (microcylinder) g microsphere h microhemisphere i fibre array j interdigitated array. Image reproduced with permission from Ref. [7], copyright 2000 International Union of Pure and Applied Chemistry...

Bio-inspired fibrillar adhesives of different dimensions, fa, b) Metallic nanowhiskers, (c, d) Hierarchically branching fibre arrays made of epoxy resin, fe, f) Silicone molds of a laser patterned metal surface, (g, h) Carbon nanotubes, (a-d, g, h Original micrographs, a-d, g, h from Gorb 2010. e, f from Peressadko and Gorb 2004a)... 

Laws [4] concluded that the combined efficiency factors, due to both length and orientation, cannot be simply calculated as the product of the length efficiency factor and the orientation efficiency factor. That is, the orientation efficiency factor is also a function of the length in the case of short fibres. For a random, 2D fibre array. Laws [4] derived the following relations ... 

Figure 4.11 Plots of calculated critical fibre volume, Vf(crit) vs. aspect ratio l/d for short fibres (a) composites with different fibre-matrix bond strength tfu, with Omu = 3 MPa and random 2D fibre array and (b) composites of different fibre orientations, with (Xmi = 5 MPa and tifu = 3 MPa.

Figure 4.34 Stress-strain curves of a glass fibre array determined from Eq. 4.82 for various ratios of l/k and td/tfu, assuming aligned short fibres held across a crack. f = 70 GPa, o-fu = 1200 MPa, Vf = 0.05. Failure occurs at F (after Laws [66]).

Equation 4.82 was further modified by Laws to take into account the effect of orientation for a random 2D fibre array ... 

This equation is based on the efficiency factor relationships developed for the case in which the orientation and length effects are combined (Section 4.2.3). Equations 4.82 and 4.83 can then be applied to calculate the strength of the composite from the maximum value ofWf(x) 14 of the fibre array ... 

Misalignment of the two surfaces of the crack, moving laterally as well as longitudinally relative to each other and to the fibre array ... 

---