Tensile modulus fibres

In the macrocomposite model it is assumed that the load transfer between the rod and the matrix is brought about by shear stresses in the matrix-fibre interface [35]. When the interfacial shear stress exceeds a critical value r0, the rod debonds from the matrix and the composite fails under tension. The important parameters in this model are the aspect ratio of the rod, the ratio between the shear modulus of the matrix and the tensile modulus of the rod, the volume fraction of rods, and the critical shear stress. As the chains are assumed to have an infinite tensile strength, the tensile fracture of the fibres is not caused by the breaking of the chains, but only by exceeding a critical shear stress. Furthermore, it should be realised that the theory is approximate, because the stress transfer across the chain ends and the stress concentrations are neglected. These effects will be unimportant for an aspect ratio of the rod Lld> 10 [35]. 

Figure 6.10. Glass, aramid and carbon fibre reinforced composites tensile modulus versus tensile strength examples...

Fig. 9. Tensile properties of various high-strength, high-modulus fibres...

Generally it is found that PPT fibres are highly oriented and that those variants with the lowest values of orientation angle exhibit the highest tensile modulus. Indeed the average crystallite orientations derived from azimuthal peak widths at half maximum intensities of the 200 reflections in Kevlar 49 and Kevlar 29 are found to be nine and eleven degrees respectively. 

Fibre type Composition (wt%) Diameter ( tm) Density (gm/cm3) Tensile strength (MPa) Tensile modulus (GPa)... 

Figure 9.16 Increase in tensile modulus as a result of the presence of short glass fibres.

The theoretical treatment of the mechanical properties of fibres is, as a matter of fact, more complicated than that of isotropic polymers. Instead of two elastic parameters, e.g. the tensile modulus and the Poisson ratio, we now need five, because of the anisotropy. 

The following values of the tensile modulus E and rigidity modulus G, expressed in gigapascals, were found for a random co-polyester fibre at two different temperatures E = 125, G = 1.1 and E = 62, G = 0.28. Assuming that equation (12.19) applies, calculate the value of Ej ax and the order parameter S for the fibre. 

The combination with fibres has proved difficult however. Often there are issues with compatibility between bio-resins and fibres (both natural and synthetic), which cause defects in the composite structure and ultimately poorer physical properties. Castor-oil polyurethane was compared with phenolic resins when infused over sisal fibres however, the phenolic resins showed better structural performance when compared with the castor oil-based material [52]. This is not always the case, as some improvements have been made. Soybean oil thermoset polymers were used in a glass/flax hybrid composite resulting in improved mechanical performance [73], Thermoset resins were produced from triglyceride oils with a wide range of properties (tensile modulus 1-2 GPa, glass transition temperature Tg 70-120 °C) and glass- and hemp- fibre composites were manufactured [74,75]. 

Fibre state Technique Solvent Stabilization Treatment Strain to failure (%) UTS (MPa) Tensile modulus (MPa)... 

Care must be mieicised to use the correct fibre modulus Ef in the case of anisotropic fibres such as carbon and Kevlar. In eqn 6.14 it is the axial tensile modulus in eqn 6.20 it is the transverse tensile modulus. 

When strains from eqns 6.19 are substituted in eqn 6.17, an e2q>ression is obtained for the tensile modulus of the composite transverse to the fibres ... 

A composite material consists of 40% (l volume) continuous, uniaxially aligned, glass fibres in a matrix of thermoset polyester. A tensile stress of 100 MPa is to be applied parallel to the fibres. Predict the strains which will result. Take the tensile modulus and Poisson s ratio of glass to be 76 GPa and 0.22, and of thermoset polyester to be 3 GPa and 0.38, respectively. 

The tensile modulus E is obtained by assuming parallel coupling between fibres and matrix, thus (fi om eqn 6.14)... 

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