Weibull fibre

Goda, K., Park, J. M. and Netravali, A. N., A new theory to obtain weibull fibre strength parameters from a single-fibre composite test, J. Mater. Sci., 30, 2722 (1995). 

Whereas in the second approach of the size effects it is also assumed that fracture is controlled by defects, the strength is now considered a statistically distributed parameter rather than a physical property characterised by a single value. The statistical distribution of fibre strength is usually described by the Weibull model [22,23]. In this weakest-link model the strength distribution of a series arrangement of units of length L0 is given by... 

Weibull plots of various fibre properties, such as the filament count, modulus, elongation at break and the strength, can provide important information on the quality and performance of the manufacturing process. The results can be used to formulate a strategy for the improvement of the yarn properties. 

Other degradation laws can be combined with a Weibull plot, particularly when a lower threshold of, for example, voltage is anticipated. An example of its application to electrical cable insulation lifetime is given in [9]. As well as service failures Weibull plots have proved useful in assessing the failure of fibres and fibre bundles. 

K. Goda and H. Fukunaga, The evaluation of the strength distribution of silicon carbide and alumina fibres by a muti-modal Weibull distribution, J. Mater. Sci., 21,4475-80 (1986). 

In Equation (9.12), afo is the fibre strength at gauge length 4 and p is the shape parameter of the Weibull distribution for the tensile strength of fibre. 

Patankar SN (1991) Weibull distribution as applied to ceramic fibres. J Mater Sci Lett 10 1176-1181... 

Wu HF, Netravali AN (1992) Weibull analysis of strength-length relationships in single Nicalon SiC fibres. J Mater Sci 27 3318... 

Tedious measurements of the Weibull statistics of single-filament strengths are necessary for the determination of an accurate value of the fibre strength at the critical length afoft). 

Crack Fibre Fibril Fracture Fracture toughness Interfaces Linear elastic fracture mechanics (LEFM) Nanotube Polymer fibre Stress intensity factor Tensile stress Weibull model Whisker... 

The Weibull approach, although useful when comparing fibres, does not take account of the failure mechanism. On the other hand, the deterministic theory of LEFM overcomes some of the limitations of the Weibull method but is applicable only when the initial crack geometry is known. There are intermediate cases where the crack geometry is known but not its precise location, as, for example, inner circular cracks located randomly. In these circumstances, LEFM can provide answers to questions such as what is the maximum rupture stress for a postulated maximum defect size of unknown location ... 

Fig. 13. Influence of the Weibull modulus, m. and of the effective bundle length, 2.x, on tlie tensile strength of a dry fibre bundle a, .

It has been shown that simple modifications of the classical Poisson/Weibull form for ihe strength of single fibres used in oonposites yield a new failure probability function whioh not only may be used to... 

In reality, fibre properties are statistically distributed. This is true for their geometry (length and diameter), but also, especially in the case of ceramic fibres, for their mechanical properties that are distributed according to Weibull statistics (see section 7.3). Non-ceramic fibres are also usually not identical since they may contain surface defects, for instance. Because of this statistical distribution of their properties, not all fibres fail simultaneously even in a homogeneously loaded composite. Instead, the weakest fibre will fail first. Due to the volume effect (see section 7.3.1), the failure probability of a long fibre is greater than that of a short one. 

The slope of the curve is the Weibull scaling parameter m, which indicates the shape of the distribution. Low m-values indicate a large range of surface flaw sizes, while high m-values indicate high surface quality and a close approach to the tensile strength of a flaw-free flbre under normal condition." m-Values for pristine fibres are normally of the order of 80-150. 

Weibull plot of optical fibre with different coating stripping method. — — pristine fibre, — — decoated with acetone, —A— decoated with... 

The hypothesis that the sample data are Weibull distributed by a significance level of a = 5% can t be rejected in case of 79% (for Anderson-Darling) and 93% (for Chi-squared) of the samples. Nevertheless it s important to note, that the amount of data within a sample stays at a low level. An example of Weibull distributed fibres (Table 1, fibre no. 1) is shown in Figure 4. 

Table F.1 Glass fibre strength and step procedure to determine Weibull parameters.

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