Fracture of fibres

The way of modelling brittle fracture of fibres is paved by LEFM, and good agreement between experimental results has been found. Future refinements will improve the accuracy of the predictions, in particular for anisotropic fibres where cracks propagate in mixed mode. More inputs from fractography and physical aspects of fracture will be helpful in modelling defects able to initiate cracks. 

Additional information on fracture of fibres hierarchically. structured appears in the paper by Viney and in the paper by Hearle ( Fracture of Common Textile Fibres ). 

Blackman B R K, Hadavinia H, Kinloch A J, Williams J G (2003), The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints. International Journal of Fracture, 119, 2546. 

Brittle fractures of fibres in the lower layers of the laminate structure can be also observed as the results of further flexure and bending. This is the same principle to breaching the strength of the whole laminate. Breaking the continuity fibres is unacceptable from the point of view of the further exploitation of the laminate, as a construction material. 

The apparently lov/ value of o for the 0.38 x 38 mm Duoform fibres is due to the fracture of fibres during the failure of the specimen. Since extensive fibre pullout did not occur the analysis is not applicable in this case. The results are shown,... 

S.Mindess, The fracture of fibre reinforced and polymer impregnated concretes a review , in F.H. Wittmann (ed.) Fracture Mechanics of Concrete, Elsevier Science... 

There are less exotic ways of increasing the strength of cement and concrete. One is to impregnate it with a polymer, which fills the pores and increases the fracture toughness a little. Another is by fibre reinforcement (Chapter 25). Steel-reinforced concrete is a sort of fibre-reinforced composite the reinforcement carries tensile loads and, if prestressed, keeps the concrete in compression. Cement can be reinforced with fine steel wire, or with glass fibres. But these refinements, though simple, greatly increase the cost and mean that they are only viable in special applications. Plain Portland cement is probably the world s cheapest and most successful material. 

The word "composites" has a modern ring. But using the high strength of fibres to stiffen and strengthen a cheap matrix material is probably older than the wheel. The Processional Way in ancient Babylon, one of the lesser wonders of the ancient world, was made of bitumen reinforced with plaited straw. Straw and horse hair have been used to reinforce mud bricks (improving their fracture toughness) for at least 5000 years. Paper is a composite so is concrete both were known to the Romans. And almost all natural materials which must bear load - wood, bone, muscle - are composites. 

Its = tensile strength parallel to fibres d] = fracture strength of fibres d = yield strength of matrix. 

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. 

Recently, Oldfield Ellis (1991) have examined the reinforcement of glass-ionomer cement with alumina (Safil) and carbon fibres. The introduction of only small amounts of carbon fibres (5% to 7-5% by volume) into cements based on MP4 and G-338 glasses was found to increase considerably both the elastic modulus and flexural strength. There was an increase in work of fracture attributable to fibre pull-out. A modulus as high as 12-5 GPa has been attained with the addition of 12% by voliune of fibre into MP4 glass (Bailey et al, 1991). Results using alumina fibre were less promising as there was no fibre pull-out because of the brittle nature of alumina fibres which fractured under load. 

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... 

As shown in Fig. 10, the shear strain is proportional to the relative displacement of two parallel aligned adjacent chains. Therefore, it seems plausible to assume that the maximum shear strain value /3=( -8b) at which fracture of the fibre is initiated will be related to a critical overlap length between adjacent... 

Immediately upon fracture the fibre drops from a high-energy state equal to the stored elastic energy to its lowest energy, viz. the unloaded state. Hence, initiation of fracture in the domains in the tail of the orientation distribution p(0) does release most effectively the stored energy of a loaded polymer fibre. So, if there are no impurities and structural irregularities, fracture of the fibre is... 

Fig. 15 Initiation of fibre fracture by a crack oriented parallel to the chain direction in a domain. It is proposed that a circular crack with a radius q releases the strain energy in a sphere around the crack with the same radius. Note that in this two-dimensional drawing only the circular crack is shown in perspective...

In conclusion, the initiation of fracture in a polymer fibre preferably occurs in the domains in the tail of the orientation distribution. The reasons are (1) in these domains the local shear stress will exceed the critical shear stress first, (2) the release of the strain energy is most effectively brought about by fracture of these domains and (3) the Griffith length in these domains adopts its lowest value. 

The ultimate strength, cxLobs, of a conditioned fibre can be estimated using the observed strain energy. The strain energy up to fracture of conditioned cellulose II fibres is 0.058 GJ m-3. From Eqs. 55 and 54 the values g=1.5 and rb=0.42 GPa are derived, respectively. Equation 57 yields ctl=2.6 GPa, which should be compared with 1.7 GPa being the strength measured for Fibre 1 in... 

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]. 

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