Fibres critical length

The maximum value of it will occur when (tensile strength of the fibre, Ofu, and this is defined as the critical fibre length, Ic... 

Example 3.17 Short carbon fibres with a diameter of 10 fim are to be used to reinforce nylon 66. If the design stress for the composite is 300 MN/m and the following data is available on the fibres and nylon, calculate the load transfer length for the fibres and also the critical fibre length. The volume fraction of the fibres is to be 0.3. 

In a short carbon fibre reinforced nylon moulding the volume ffacdon of the fibres is 0.2. Assuming the fibre length is much greater that the critical fibre length, calculate the modulus of the moulding. The modulus values for the fibres and nylon are 230 GN/m and 2.8 GN/m respectively. 

Chen, F. and Jones, F. R Injection moulding of glass fibre reinforced phenolic composites 1. Study of the critical fibre length and the interfacial shear strength, Plast.. Rubber Composites Proc. Appl., 23, 241 (1995). 

The slopes of the two linear branches in the Kc-an diagram and the critical value of the fibre orientation factor (au)c vary from system to system and with the external variables. Just as the critical fibre length, they depend on the combination of internal variables (such as type of matrix, fibre content, fibre dimensions, fibre-matrbc interface) and external variables, i.e. testing and environmental conditions. 

This sharp variation in toughness has been interpreted as a transition between different fracture mechanisms. Matrix fracture and fibre debonding are the prevailing fracture mechanisms at low values of the fibre orientation factor, while at high values the main fracture mechanism is fibre pull-out. Thus, besides a critical fibre length, also a critical fibre angle should be considered. 

The objective of fibre reinforcement is to endow a lightweight matrix with high strength and stiffness. A critical fibre length, 4, is necessary to achieve this ... 

Miwa M, Endo I, Critical fibre length and tensile strength for carbon fiber epoxy composites, J Mater Sci, 29(5), 1174 1178, 1994. 

Whereas qualitative information about the level of interaction between fibre and matrix can be obtained by electron microscopy, various methods are available for quantitative evaluation of fibre-matrix interfacial shear strength in thermoplastics and thermoset polymers [55]. Table 5.3 shows interfacial shear strength and critical fibre length values... 

Table 5.3 Critical fibre length and interfadal shear strength values for glass-fibre reinforced polypropylene compositions determined by a single-fibre fragmentation technique (adapted from [78]) ...

If we aim at a maximum strengthening effect of the fibres, they have to be sufficiently long to be loaded up to their fracture strength With the help of equation (9.8), we can thus define the critical fibre length... 

The load transfer between the crack surfaces results in a maximum of the stress in the part of the fibre that is situated within the crack. This stress has to be transferred to the matrix on both sides, in a region whose size is approximately that of the critical fibre length. If the stress in the fibre in this region exceeds the fracture stress, the fibre breaks. Fracture usually occurs at a defect, for example a surface defect or a local reduction in diameter. Because of this, fibre fracture occurs not always directly at the crack surface, but at an arbitrary position between the stress maximum near the crack surface and the region where the fibre stress has decreased markedly. The size of this region is... 

The crack resistance is the higher, the larger the critical fibre length is. In a ceramic matrix composite, it is thus useful to have a low value of the interfacial shear stress. If fibres are shorter than the critical length, they will not break but will be pulled out on one side of the crack, if they are longer, they will fracture first and be pulled out afterwards. 

A different approach to pull-out and bond testing was developed by Wang etal. [84], in which the critical fibre length was determined, rather than pull-out... 

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