## 5 Fibre Groups Embedded in UHPC
### Cyclic Tensile Loading  
Each test series contained at least three individual tests in terms of cyclic loading. The upper load level was fixed to 70% and the lower load level to 10% of the maximum pullout  
Figure 10: “Breakout cone” of 30”-**(a)**, 60\({}^{\circ}\)-**(b)**, and 90\({}^{\circ}\)-orientated **(c)** steel fibres after monotonic loading.  
Figure 9: Pullout mechanisms of embedded steel fibres under 30\({}^{\circ}\) and 60\({}^{\circ}\).  
resistance obtained in the monotonic tests, leading to a relative stress oscillation width of \(\Delta\sigma_{\text{st}}^{\ell}=0.6\) [-].  
In the VMZ90 series, the test execution stopped unexpectedly after 1000 load cycles due to a defect of the test machine. For the VMZ60 series with an embedded length of \(l_{\text{e}}=6.50\) mm and a fibre angle inclination of \(\alpha=60^{\circ}\), Figure 11 shows the measured pullout displacement \(\delta\) as a function of the applied load cycles \(N\). It can be concluded that the three typical phases of fatigue of concrete also apply to the pullout tests of embedded high-strength micro steel fibres in UHPC:  
* Phase I marks the initial non-linear increase in strain.
* Phase II begins between 5% and 10% of the ultimate load cycle number \(N\) with the transition to a constant, small increase in deformation.
* Phase III is reached at around 95% of the breaking load cycle number \(N\). The total deformations increase rapidly, disproportionately, leading to failure of the concrete.  
High-strength steel fibres should--as described in Section 2--be designed by their geometry and tensile strength to be pulled out under load, i.e., to fail in the bond and thus have a certain deformation capacity. While all test results under monotonic loading show this mechanical behaviour (Table 6), another type of failure could be detected under cyclic loading in VMZ60-2: fibre breakage.  
* This type of failure would actually have been expected with a fibre orientation of 30\({}^{\circ}\), because greater bending stresses occur in the steel fibre compared to an orientation of 60\({}^{\circ}\) (cf. Figure 9). The following explanation can be given for this:
* With a fibre orientation of 30\({}^{\circ}\), no fibre breakage occurs because the \"snubbing effect\" causes a larger concrete breakout, which in turn considerably shortens the bond length. This reduces the bending stresses on the one hand and increases the bond stresses on the other. The latter causes the fatigue damage of the bond zone to progress faster than the material damage. This eventually leads to fibre pullout.
* With 60\({}^{\circ}\)-inclined fibres, on the other hand, the \"snubbing effect\" leads to less concrete breakout and the bond length is reduced less (in comparison to a fibre orientation of 30\({}^{\circ}\)). The relationship between the damage of the bond zone and the fibre material (bending effects) is in an indifferent state, where both fibre pullout (VMZ60-1) and fibre breakage (VMZ60-2) can occur. Both failure modes can also be seen in Figure 12.  
Figure 11: Pullout behaviour of steel fibre from UHPC under cyclic loading.  
For embedded fibres with an orientation of 90\({}^{\circ}\), neither bending effects nor snubbing occur. Damage takes place in the bond zone and progresses until the bond stresses can no longer be transferred between the fibre and the concrete; the fibre pulls out of the concrete matrix.