Issue 10

M. Paggi, Frattura ed Integrità Strutturale, 10 (2009) 43-55; DOI: 10.3221/IGF-ESIS.10.06 51 Figure 5 : Determination of the incomplete-self-similarity exponent  3 . As pointed out by Johnston and Zemp [8], the fibre aspect ratio has an important effect on the fatigue behaviour of FRC, whereas the fibre type (smooth wire, surface deformed wire, melt-extract and slit sheet) is of secondary importance. To show this effect in terms of dimensional analysis arguments, let us consider the experimental results by Singh et al. [12]. They tested FRC beams under fatigue loading with different volumetric content of fibres ( 1.0, 1.5 f v  and 2.0% ). However, instead of using a single fibre type as in [8], 50% of their total weight has an aspect ratio of / 20 l d  and the remainder has an aspect ratio of / 40 l d  . Again, as for the previous case, the higher the volumetric content, the higher the fatigue life for a given applied stress range (see Fig. 6). However, now the S-N curves have an average slope equal to 0.030  , corresponding to an exponent 1 33    . This value is significantly higher than 43  found in the case of a higher aspect ratio equal to 6 / 75 l d    . According to dimensional analysis, this difference has to be ascribed to the different value of the aspect ratio and to the fact that the power-law exponent 1  depends on 6  . From the engineering point of view, the use of longer fibres is clearly advantageous, since it increases the fatigue life of the specimen for a given applied stress range, reducing the exponent 1  . Figure 6 : S-N curves of beams tested in flexural fatigue with 50% of fibres with / 20 l d  and the remainder with / 40 l d  (experimental data taken from [12]) . The effect of the crack size Modified Paris’ laws taking into account the effect of the crack size have been proposed both for metals and for quasi- brittle materials. For metals, several researchers have questioned the validity of the similitude hypothesis, which states that