Fibre uniaxial

As shown in Fig. 3.4 stress-strain tests on uniaxially aligned fibre composites show that their behaviour lies somewhere between that of the fibres and that of the matrix. In regard to the strength of the composite, Ocu, the rule of mixtures has to be modified to relate to the matrix stress, o at the fracture strain of the fibres rather than the ultimate tensile strength, o u for the matrix. 

One of the main methods for improving the mechanical properties of linear polymers is their drawing that can be uniaxial (fibres), biaxial (films), planar symmetrical (films-membranes) etc. As a result of polymer deformation, the system changes into the oriented state fixed by crystallization. 

It was therefore with some confidence in the infra-red and Raman spectroscopic methods that a much more complex investigation was carried out on the molecular orientation in one-way drawn PET films which show uniplanar axial orientation 5). In such films the condition of fibre symmetry is removed in two ways (1). There is no longer uniaxial symmetry of the distribution of chain axes. 

In the uniaxially oriented sheets of PET, it has been concluded that the Young s modulus in the draw direction does not correlate with the amorphous orientation fa or with xa "VP2(0)> 1r as might have been expected on the Prevorsek model37). There is, however, an excellent correlation between the modulus and x,rans,rans as shown in Fig. 15. It has therefore been concluded 29) that the modulus in drawn PET depends primarily on the molecular chains which are in the extended trans conformation, irrespective of whether these chains are in a crystalline or amorphous environment. It appears that in the glassy state such trans sequences could act to reinforce the structure much as fibres in a fibre composite. 

Flow is generally classified as shear flow and extensional flow [2]. Simple shear flow is further divided into two categories Steady and unsteady shear flow. Extensional flow also could be steady and unsteady however, it is very difficult to measure steady extensional flow. Unsteady flow conditions are quite often measured. Extensional flow differs from both steady and unsteady simple shear flows in that it is a shear free flow. In extensional flow, the volume of a fluid element must remain constant. Extensional flow can be visualized as occurring when a material is longitudinally stretched as, for example, in fibre spinning. When extension occurs in a single direction, the related flow is termed uniaxial extensional flow. Extension of polymers or fibers can occur in two directions simultaneously, and hence the flow is referred as biaxial extensional or planar extensional flow. 

This stretching, similar to the drawing of fibres, which promotes orientation and crystallite formation, is called biaxial orientation. It gives the film added strength and gas-barrier properties. In some processes, monoaxial (uniaxial) drawing is employed, e.g., polypropylene, which is then slit into thin strips and fabricated into heavy duty sacks, carpet backing, etc. The stenter process is used to make biaxial oriented poly(vinylidene dichloride) ("ding" film), polyester, polyamide and polypropylene films. 

In analogy with a uniaxially oriented macrocomposite, it is now postulated that the strength of the fibre can be approximated by the expression... 

For, SHG it is desirable to fabricate fibres which allow single mode operation at the fundamental wavelength so that all the launched power is available for conversion. The frequencies for which single mode operation is possible in a step-index uniaxial crystal cored fibre with crystal axis along the fibre axis are given by (30.)... 

At the end of the sixties, Godovsky 64 71> developed a fully automatic deformation microcalorimeter based on the Tiang-Calvet principle for simultaneous recording of thermomechanical behaviour of rubbers and solids (films, fibres) at uniaxial deformation. The device consists of two parts a microcalorimeter and a mechanical loading system with dynamometric assembly. The differential microcalorimeter includes the working and the reference cells. The temperature difference between the... 

The explicit formulae given by Rosen55 are also of value. They are derived from a model consisting of a random assemblage of composite cylinders (Hashin and Rosen56 ) and expressed in terms of the axial Young modulus E, the Poisson ratio for uniaxial stress in the fibre direction v, the transverse plane strain bulk modulus k, the axial shear modulus G and the transverse shear modulus G. ... 

Fig. 17. (a) 2D CSA-DECODER spectrum of polyethyleneterephthalate fibres oriented perpendicular to the rotor axis with a mixing time of 9.6 ms equivalent to a rotation of 125° (b) Simulation of the experimental data using a uniaxial distribution with FWHM = 25°. (Adapted from Lewis et al.260 with permission.)... 

MECHANICAL PROPERTIES OF UNIAXIALLY ORIENTED POLYMERS (FIBRES)... 

Nematic phases are characterised by a uniaxial symmetry of the molecular orientation distribution function f(6), describing the probability density of finding a rod with its orientation between 6 and 6 + d0 around a preferred direction, called the director n (see Fig. 15.49). An important characteristic of the nematic phase is the order parameter (P2), also called the Hermans orientation function (see also the discussion of oriented fibres in Sect. 13.6) ... 

If one assumes fibre symmetry of the sample (like in uniaxial deformation), transverse isotropy for the molecular units (for instance ai U2 = 03), and additivity of polarizabilities, it is easily shown [9] that the difference in macroscopic polarizabilities along and perpendicular to the fibre axis of the sample is simply ... 

The results described in this paper were all obtained from tests on E-glass reinforced composite materials produced by hand lay-up. This is the manufacturing route most frequently used for marine structures. For the majority of the tests reported here the E-glass fibres were either quasi-unidirectional (250 g/m with 1 g/m of polyester fibres bonded in the 90° direction to keep the UD fibres in place) or stitched quadrlaxial (0/45/907-45° 1034 g/m ) cloths. The same uniaxial ply is used in both cloths. The resin is based on DGEBA epoxy (SRI500) with an amine hardener (2505) from Sicomin, France. All epoxy specimens were post-cured at 90°C for 6 hours. Some results are also shown for a woven glass (0/90° 500 g/m ) reinforced isophthalic polyester for comparison, as this is the traditional marine... 

Blackman, B.R.K. and J.G. Williams. On the mode II testing of carbon-fibre polymer composites, in ECFI2 Fracture from Defects. 1998. Sheffield, UK EMAS publishing, Hashemi, S., A.J. Kinloch, and J.G. Williams, The analysis of interlaminar fracture in uniaxial fibre-polymer composites. Proceeding of the Royal Society London, 1990. A427 p. 173-199. 

Fig. 6 Influence of the concentration of fibres and state of fibre/matrix interface on the uniaxial tensile stress-strain curves of fibre-reinforced nylon composites (a) type A interface (b) type B interface.

Table 2 shows a much less extreme example and is for 6 specimens of a uniaxial carbon fibre epoxy material tested in one laboratory. There is some variation in E but much less tnan in the previous example and the mean value is close to the true value of 145 GPa. The miiiimum... 

An elementary carbon fibre is embedded in an epoxy matrix and this model composite is submitted to an uniaxial tensile load in the direction of fibre orientation. 

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