Straight fibres

Qualitative and quantitativemo6e s have been developed to account for the fibre-matrix stress transfer and crack bridging, by analysing the shear stresses that 

The processes involved in the fibre-matrix interaction take place mainly in a relatively small volume of the matrix surrounding the fibre. The microstructure of the matrix in this zone can be quite different from that of the bulk matrix (Chapter 2), thus invoking effects which are not always predicted by the analytical models which assume a uniform matrix down to the fibre surface. Its influence on the fibre-matrix interaction will be discussed in Section 3.5. 

An understanding of the mechanisms responsible for stress transfer provides the basis for prediction of the stress-strain curve of the composite and its mode of fracture (ductile vs. brittle). Such understanding and quantitative prediction may also serve as a basis for developing composites of improved performance through modification of the fibre-matrix interaction. This might be achieved, for example, through changes in the fibre shape, or treatment of the fibre surface. 

The shear stresses developed parallel to the fibre-matrix interface are of prime importance in control ling the fibre-matrix stress-transfer mechanism, as discussed previously. Yet, one should also consider the effect of strains and stresses that develop normal to the fibre-matrix interface. Such strains and stresses may be the result of the Poisson effect, volume changes, and biaxial ortriaxial loading. They may cause weakening of the interface and premature debonding, and may also induce considerable variations in the resistance to frictional slip, which is sensitive to normal stresses. 

A comprehensive approach to model the stress transfer requires simultaneous treatment of all the above-mentioned effects elastic shear transfer, frictional slip, debonding, and normal stresses and strains. Unfortunately, such a unified approach is complex. Therefore, in this chapter, each of these effects will first be discussed separately, based on models developed for fibres of a simple shape, usually straight fibres with a circular cross section. The stress transfer in uncracked and in cracked composites will also be dealt with separately. 

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Figure 4.1 Sheet structures arising from (a) the random distribution of 970 straight fibres of uniform length, (b) a photomicrograph of a 2.5gmr2 sheet of paper in which the mean fibre length and density correspond to that...

Silk, by contrast, consists of fibroin which does not contain cystine and is a straight fibre. 

Figure 4.9 compares the average thickness of optimum designs obtained using VICONOPT with straight fibre laminates and variable angle tows obtained using either CTS or AFP techniques where the latter assumes shifted (similar) tow paths obtained... 

Figure 4.9 Comparison of average thickness (solid lines) and buckling strains (dashed) for straight fibre optimum designs and variable fibre angle designs obtained using continuous tow shearing and automated fibre placement. In all cases, the panels are 250 mm wide and 750 mm long with simple supports.

Fabric composites have mechanical properties similar to those of laminates made from orthogonal uni-directional layers. However, fibre curvature arising from yarn twist and weave crimp makes fabric reinforcement less efficient than in the case of aligned straight fibres. 

If the bond along a fibre is not sufficient, and usually for plane straight fibres a correct anchorage would require increased length, then hooks or enlarged ends are necessary. The length of a fibre should approximately satisfy a condition /d <100, otherwise the distribution of fibres is difficult. The fibres with improved bond may be much shorter and then their appropriate distribution in the fresh mix is easier. 

The method of evaluation of strength and strain of carbon fibres basing upon stress-strain relationships of straight fibres and dimensions of loops at break is presented. 

Mechanical properties were determined with the use of an Instron tester. Conditions of analysis of straight fibres were as follows ... 

Straight fibres produced by cutting the unraveled wire from scrap or wornout steel cables and wire ropes (S-fibre),which are much cheaper than the other two, the cost of S-fibres is approximately 50% of that of M-fibres or 30% of that of H-fibres. The aspect ratio (length to equivalent diameter) is about 50 for H-fibre and M-fibre,75 for S-fibre. To allow comparison of the properties of SFRC with different types and contents of steel fibres, the matrix of all specimens is the same for each group of tests. 

Figure 3.1 Pull-out of aligned and straight fibres with elastic response and a decaying frictional slip (a) typical pull-out load vs. slip response for steel fibre embedded in cement-based matrix (b) bond shear stress vs. slip relationship with frictional decay (after Bentur et al. [6])...

If the fibre is ductile and of low modulus it will easily bend and a dowel action may be induced leading to additional pull-out resistance. This effect may compensate for the reduced efficiency when considering only the inclination angle in a straight fibre [33,42,53,55-57,59]. If the fibre is brittle and of higher modulus... 

This implies that it is not the length of the fibre which controls its bonding, but rather the number of crimps. Similarly, for hooked steel fibres, it was resolved that the contribution of the hook is independent of fibre length, and it is much greater than the contribution of the interfacial bond of a straight fibre of a similar length [68]. 

Strength also increases with increasing strength of the matrix (35-37). However, for smooth, straight fibres, beyond an aspect ratio of about 100, it is not generally possible to prepare a mix with both sufficient workability and uniform fibre distribution. Therefore, in a typical properly proportioned SFRC, failure is primarily by fibre pull-out, even with the deformed fibres shown in Figure 7.2. 

Thus, different fibre geometries and fibre-matrix interactions can affect the flexural behaviour of SFRC. This is demonstrated in Figure 7.18 [41], which shows the effects of different fibre shapes on the flexural behaviour of steel fibre shotcrete. These data suggest that the aspect ratio (//d) concept, which was developed for smooth, straight fibres, is not really useful when applied to deformed fibres,... 

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