Failure Fibre

This is because, with brittle fibres, failure of the composite will occur when the fibres reach their fracture strain. At this point the matrix is subjected to the full applied load, which it is unable to sustain. 

Up to this stage we have considered the deformation behaviour of fibre composites. An equally important topic for the designer is avoidance of failure. If the definition of failure is the attainment of a specified deformation then the earlier analysis may be used. However, if the occurrence of yield or fracture is to be predicted as an extra safeguard then it is necessary to use another approach. 

If the fibres are aligned at 15° to the jc-direction, calculate what tensile value of Ox will cause failure according to (i) the Maximum Stress Criterion (ii) the Maximum Strain Criterion and (iii) the Tsai-Hill Criterion. The thickness of the composite is 1 mm. 

Solving this gives X = 169. Hence a stress of Ox = 169 MN/m would cause failure. It is more difficult with the Tsai-Hill criterion to identify the nature of the failure ie tensile, compression or shear. Also, it is generally found that for fibre angles in the regions 5°-15 and 40 -90 , the Tsai-Hill criterion predictions are very close to the other predictions. For angles between 15° and 40° the Tsai-Hill tends to predict more conservative (lower) stresses to cause failure. 

A single ply glass/epoxy composite has the properties Usted below. If the fibres are aligned at 30° to the x-direction, determine the value of in-plane stresses, a, which would cause failure according to (a) the Maximum Stress criterion (b) the Maximum Strain criterion and (c) the Tsai-Hill criterion. 

The concept of a maximum shear strain is supported by the experimental relationship for the lifetime of a polymer fibre. For many polymer fibres the observed lifetime or the time to failure fb is given by... 

An understanding of the mechanism of creep failure of polymer fibres is required for the prediction of lifetimes in technical applications. Coleman has formulated a model yielding a relationship similar to Eq. 104. It is based on the theory of absolute reaction rates as developed by Eyring, which has been applied to a rupture process of intermolecular bonds [54]. Zhurkov has formulated a different version of this theory, which is based on chain fracture [55]. In the preceding sections it has been shown that chain fracture is an unlikely cause for breakage of polymer fibres. 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

Equation 116 was also derived in Sect. 2. It shows that the fibre strength according to the shear failure criterion increases with improved alignment of the chains, and that it is proportional to the shear modulus g. 

Fig. 62 The creep failure curves of a PpPTA fibre with an initial modulus of 91.8 GPa calculated with the same parameters as used in Fig. 61...

Assuming that the fibre breaks due to shear failure, the fracture condition ci3(fb) =j0 is now applied... 

The presented derivations of the load rate and the lifetime relationships applying the shear failure criterion are based on a single orientation angle for the characterisation of the orientation distribution. Therefore these relations give only an approximation of the lifetime of polymer fibres. Yet, they demonstrate quite accurately the effect of the intrinsic structural parameters on the time and the temperature dependence of the fibre strength. 

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