Efficiency of fibre reinforcement

The actual composite usually consists of short fibres dispersed in the matrix, of which at least some are at an angle with respect to the load orientation. The contribution of such short, inci i ned fibres to the mechanical properties of the composite is smaller than that of long fibres oriented parallel to the load assumed in Eq. 4.1, that is the efficiency of the short and inclined fibres is less. The efficiency of fibre reinforcement can bejudged on the basis of two criteria the enhancement in strength and the enhancement in toughness of the composite, compared with the brittle matrix. These effects depend upon the fibre length, the orientation of the fibres and the fibre-matrix shear bond strength. These three factors are not independent. 

In many engineering applications, the fibre efficiency is expressed in terms of an efficiency factor, which is a value between 0 and 1, expressing the ratio between the reinforcing effect of the short, inclined fibres and the reinforcement expected from continuous fibres aligned parallel to the load. These factors, t]i and rje for length and orientation efficiency, respectively, can be determined either empirically, or on the basis of analytical calculations. They are frequently used in combination with properties that can be accounted for by the rule of mixtures (Section 4.3). In this section, various analytical treatments to account for efficiency factors will be reviewed, with special emphasis on the effects of bond. The effects of length and orientation will be described separately. 

This relationship is derived from Eqs3.1-3.3. For frictional stress transfer, with a constant interfacial shear stress, xfu, the average stress in the fibre is  

The length efficiency factor in the pre-cracking zone for the frictional stress transfer mechanism can be calculated from Eq. 4.6, and its value is a function of the strain in the composite  

Krenchel [5] and Laws [4] have analysed this zone, assuming that the fibres are intersected by the crack, so that the shorter embedded lengths of each fibre in the matrix are uniformly distributed between 0 and Ijl. At a strain of cW fibres whose shorter embedded length is less than fx/2 will slip, and will not contribute to strength, where fx is given by Eq. 4.7. The probability that a fibre will slip is fx/f and the average stress supported by the fibres at a composite strain of c(- ) is  

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Savage G. Enhancing the exploitation and efficiency of fibre-reinforced composite structures by improvement of interlaminar fracture toughness. Eng Fail Anal 2006 13 198—209. http //dx.doi.Org/10.1016/j.engfailanal.2004.12.047. 

The efficiency of fibre reinforcement is dependent very much upon distribution and orientation of fibres in the matrix. The fibres form an internal structure and various kinds of these structures are described in Section 6.6. 

After automatic calculations of all these parameters from the image of the crack system, its characterization allows the mechanical consequences to be determined, different materials composition to be compared and the efficiency of fibre reinforcement to be estimated. 

The efficiency of fibre reinforcement depends to a large extent on the maximum tensile stress that can be transferred to the fibre. The maximum value would, of course, be the yield strength or tensile strength of the fibre. The shear lag theory (Eqs 3.1-3.3) provides an analytical tool to predict the shear stresses that will develop at the interface in order to achieve this maximum tensile stress. An estimate of the maximum elastic shear stress developed for different levels of... 

George et al. [27] studied stress relaxation behaviour of pineapple fibre-reinforced polyethylene composites. They found stress relaxation to be decreased with an increase of fibre content due to better reinforcing effect It is also reported by George et al. [28] that properties of fibre-reinforced composites depend on many factors like fibre-matrix adhesion, volume fraction of fibre, fibre aspect ratio, fibre orientation as well as stress transfer efficiency of the interface. Luo and Netravah [29] found an increase in the mechanical properties of green composites prepared from PALFs and poly(hydroxybutyrate-co-valerate) resin (a biodegradable polymer) with the fibres in the longitudinal direction. However, the researchers reported a negative effect of the fibres on the properties in the transverse direction. 

It appears from comparison of various theoretical and experimental results that detailed calculations of fibre-reinforced concrete behaviour do not allow reliable data to be obtained without taking into account all influences and factors, such as the precisely determined efficiency coefficient, scale effects, etc. (cf. Bentur and Mindess 2006). 

In particularly complex problems of heavily loaded elements, the application of hybrid reinforcement composed of two or more kinds of different fibres may be considered. In the selection of reinforcement the total cost (materials and execution) should also be taken into account (cf. Chapter 5). The volume of fibres is usually limited by their cost and by the workability of the fresh mix. Also the efficiency of fibres decreases when a high percentage is applied. It is rare in practical cases that a volume fraction of steel fibres higher than 2.5% is used and composites with reinforcement lower than 1% are often applied. This remark does not concern particular cases where higher volume fractions of fibres are purposefully used and where other technologies of placing are applied, for example, SIFCON (cf. Section 13.5). The application of polymer admixtures with fibres may also be foreseen, if the exploitation requirements cannot be satisfied in a less expensive way. 

It is interesting to compare the efficiency of the reinforcement for AS4 fibre in PPS and PEEK. In the former case the values are 92% and 63% for modulus and strength respectively and in the latter 99% and 87% respectively. Modulus uptake is excellent in both cases and strength in the second. The poorer strength result for PPS may be due to reduced compatibility between the fibre surface and matrix. This is supported by the lower ILSS value for PPS carbon fibre composite. Compressive properties are notably lower than tensile ones, while transverse tensile properties are similar to those of thermosetting polymer matrix materials. 

The long-term performance of fibre reinforced cements is of great significance in the development and evaluation of new composites. An important practical tool for this purpose is accelerated testing in the laboratory, where the properties of the composites are determined before and after exposure to the accelerated ageing conditions. In order to develop an efficient test of this kind, it is necessary first to evaluate the physical and chemical processes that may lead to changes in properties in natural exposure, and then devise the means to accelerate them in laboratory-controlled tests. In view of the variety of processes which may lead to ageing, it is difficult to devise a universal test. An illustration of this problem is presented in Table 5.1 and In [33,43], which show that composites which perform well in one type of accelerated test may do poorly in another, and the critical test is different for the different composites. 

Similar trends of the effect of microfibre at 0.5% vol. reinforcement were reported by Yao era/. [125] for carbon microfibre, showing a pseudo-plastic behaviour for system with 0.2% carbon microfibre (7 /nm diameter, 5 mm long) and 0.3% vol. steel (0.5 mm diameter, 30 mm long), with a relatively smooth transition in the load-deflection curve around the matrix cracking stress. Qian and Stroeven [126] demonstrated the enhanced efficiency of hybrid reinforcement of 0.4 w/c ratio concretes, showing that a system of steel macrofibre and polypropylene microfibre could be used to obtain a flexural reinforcing effect at a fibre content of 0.75% vol., similar to that obtained with a higher content (0.9% vol.) of mono-steel macrofibres. 

If the matrix in 3.7 was reinforced with the same volume fraction of glass but in the form of randomly oriented glass fibres rather than continuous filaments, what would be the tensile strength of the composite. The fibres are 15 mm long, have an aspect ratio of 1000 and produce a reinforcement efficiency of 0.25. The fibre strength is 2 GN/m and the shear strength of the interface is 4 MN/m". 

Finally, Figure 4.11(d) shows that glass fibre reinforcement is an efficient means to reach more suitable creep moduli. It should be noted that the modulus scale is four times that of the previous diagrams and that the load is ten times higher. 

In-plane alignment of the fibres Due to the very nature of the technique used for processing the NW composites, inplane alignment of the NWs is a realistic possibility. From the Krenchel theory of short-fibre reinforcements [20], the orientation and length effects can be incorporated using an efficiency factor to evaluate E,... 

As a resnlt of this and further studies by thermogravimetric analysis (TGA), solid-state NMR and electron probe microanalysis, Dabrowski and co-workers [27] conclude that melamine polyphosphate is an efficient flame retardant additive in polyamide-6,6 (glass fibre reinforced or not). The glass fibres are shown to strongly inflnence the fire performance of the intumescent FR material. A reactivity between the additive and the glass fibre and the formation of alumino-phosphates was demonstrated. These species might be responsible for the improvement of the FR behaviour particularly in the conditions of the LOI test. 

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