Fibre Stress-strain Measurements

Riga [1] comments that a TMA has been used as a tool in many diverse projects, such as quality control, verification of standards, failure analysis, and characterisation of polymeric materials. 

Workers at the Institute for Dynamic Materials Testing in Ulm [3] have developed a new method for determining viscoelastic characteristics of thin coatings. Elasticity and damping components of the dynamic shear modulus as a function of temperature or time can be determined from the resonance frequency and damping of the natural vibration of a coated aluminium carrier plate. 

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Figure 15.10 Measurement of fibre stress/strain properties by thermomechanical analysis. Source Author s own files)...

A tentative model has been proposed to relate the interfacial shear strength at the fibre-matrix interface, measured by a fragmentation test on single fibre composites, to the level of adhesion between both materials. This last quantity has been estimated from the surface properties of both the fibre and the matrix and was defined as the sum of dispersive and acid-base interactions. This new model clearly indicates that the micromechanical properties of a composites are mainly determined by the level of physical interactions established at the fibre-matrix interface and, in particular, by electron acceptor-donor interactions. Moreover, to a first approximation, our model is able to explain the stress transfer phenomenon through interfacial layers, such as crystalline interphases in semi-crystalline matrices and interphases of reduced mobility in elastomeric matrices. An estimation of the elastic moduli of these interphases can also be proposed. Furthermore, recent work [21] has shown that the level of interfacial adhesion plays a major role on the final performances (tensile, transverse and compressive strengths and strains) of unidirectional carbon fibre-PEEK composites. 

In addition to giving a measure of the deformation within fibres, the strain-induced band shifts in Raman spectra have been used to follow the micromechanics of fibre reinforcement in model polydiacetylene/epoxy composites (13). The critical length has been measured directly (13) and the effect of resin shrinkage has been examined in detail (14,15). It has also been demonstrated that the technique can be employed to measure fibre strain optically in a high voliine fraction Kevlar 49/epoxy composite (16). In this present paper we demonstrate that Raman microscopy can also be used to measure fibre strain in carbon fibre reinforced PEEK composites (17) and to give a direct measure of residual thermal shrinkage stresses in PEEK matrix composites. 

The problems of making measurements on 10 pm diameter fibres are considerable, one difficulty with brittle fibres being a selection effect due to breaking weaker fibres when mounting them. Work has essentially been confined to the determination of fibre density, modulus, strength and the stress/strain curve. 

Design of experiments methodology was used to determine the maximum variability in viscosity which a poly(vinyl chloride)/wood fibre profile extrusion process was able to tolerate. Fourteen critical dimensions, profile bow, shrinkage, Young s modulus, and stress and strain under maximum load were measured. Quadratic models were created from the dimensional measurements, bow, maximum tensile stress, pressure in the die adaptor and the current drawn by the screw drive, and used to establish the tolerances within which the dimensional and physical specifications were simultaneously achieved. 

This is a very powerful method when applied to oriented materials, since it yields information about the modulus of the crystalline region, i.e. information on a molecular scale. The only drawback is that, whilst the strain can be measured accurately, the stress can only be measured if a basic assumption is made—that the stress is homogeneous. This assumption amounts to the statement that the system can be represented by the series model, in which the strain is inhomogeneous and the stress homogeneous. Evidence for this has been set out in the paper of Holliday and White, and can be regarded as satisfactory for the fibre direction. 

It should be noted that S23 is the compliance relating a strain along the Oy direction to a stress along the Oz direction whilst S32 relates a strain along Oz to a stress along Oy. These two quantities may therefore be obtained in separate experiments on the same material by lateral contraction measurements (width) on samples cut at 0° and 90° to the fibre axis. Similarly 5i3 and 5i2 may be obtained separately firom lateral contraction measurements (thickness) on those two specimens. 

However, as the fibres are supported by a polymer matrix no more stress can be applied to the fibres than the matrix or interfaces will permit and thus other possible failure modes must be accounted for. One of these, for longitudinal compression, is characterised in Figure 4.13. Different cutoffs apply for transverse tension/compression. Therefore by measuring the four characteristic strengths of the lamina, namely longitudinal tension/compression and transverse tension/compression, the complete failure envelope in the strain plane can be constructed. 

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