Comparisons Between Pull-Out Behaviour of Various Hooked-End Fibres in Normal–High Strength Concretes

Three types of commercially available Dramix hooked end steel fibres, namely: 3DH (single bend), 4DH (double bend) and 5DH (triple bend) fibres were used in this study. These fibres have exactly the same length (60 mm), diameter (0.90 mm) and aspect ratio (l_f/d_f = 65) but differ in their hook geometry and tensile strength. The measured geometrical and mechanical properties of these fibres (stacked) are depicted in Fig. 1 and detailed in Table 1. The average stress–strain curves of each fibre is shown in Fig. 2. To investigate the mechanical anchoring effect provided by each fibre hook, straight fibres (3DS, 4DS and 5DS) were obtained from the same hooked end fibres (3DH, 4DH and 5DH) by removing their hook ends.

Pull-out specimens were produced in three different concrete strengths, namely normal (NSC), medium (MSC) and high (HSC). Table 2 summarizes the materials used and mix proportions for all mixtures. Cubic specimens with a side dimension of 100 mm were used for single pull-out tests. Each cube contained three fibres embedded carefully to a depth of a half fibre length i.e. 30 mm. For each mix, five cubic specimens were also prepared for compressive strength tests. During casting, the dry materials (cement, silica fume, sand and crushed granite) were firstly mixed for approximately 1 min before water and superplasticizer (for the HSC) were added. This was then mixed for roughly 11 min. After casting and vibrating, the specimens were covered with a plastic sheet to avoid moisture loss and left for 24 h at room temperature. After that, they were demoulded and left to cure for a further 28 days in a conditioning chamber at 20 ± 2 °C and 96 ± 4% RH.

The pull-out tests were performed using a specially designed grip system, as illustrated in Fig. 3, which was attached to an Instron 5584 universal testing machine. The grips were designed such that the forces applied to the fibre would represent that in a fibre bridging a crack. The body of the gripping system was machined in a lathe using mild steel and had a tapered end to allow the insertion of four M4 grub screws (Fig. 3). These were then tightened around the steel fibre to an equal torque for an even distribution of gripping pressure to minimise the deformation of the fibre ends and avoid breakage at the tip. Two linear variable differential transformer (LVDT) transducers were used to measure the distance travelled by the steel fibre relative to the concrete face during testing (i.e. the pull-out distance). They were held in place using aluminium sleeves on either side of the main grip body (Fig. 3). The LVDT probes had ball bearings at their tips for accuracy in measurements taken from the top datum face. The sample was secured to the Instron base using clamps with riser blocks and M16 studs. The base rested on a round brass disc to retain flatness under test at a displacement rate of 10 µm/s.

The average pull-out-slip curves of (3DS, 4DS and 5DS) straight fibres pulled-out from a NSC, MSC and HSC is shown in Fig. 4a–c. These show that the pull-out behaviour of all straight behaviour is characterized by a rapid increase up to the peak load, followed by a sudden drop in the pull-out load, indicating full debonding of fibre/matrix interface. After that, the pull-out behaviour is controlled entirely by dynamic frictional resistance, where pull-out load gradually decreases with the increase in slip. For the same concrete grade, the maximum pull-out load (P_max) of 3DS, 4DS and 5DS fibres was quite similar, as expected. This is mainly due to the fact that straight fibres (without hooks) have the same geometry, diameter, and embedded length and hence the pull-out behaviour would remain almost the same. On the other hand, Fig. 4a–c show that P_max for all straight fibres increases significantly as the compressive strength of the concrete increase. Compared to the NSC, the percent increase in the P_max in the case of MSC and HSC is 40% and 98%, respectively as shown in Fig. 5.

The experimental pull-out-slip curves of (3DH, 4DH and 5DH) hooked end fibres pulled-out from a NSC, MSC and HSC matrix are presented in Figs. 6, 7 and 8. It can be seen that the initial pull-out response of hooked end fibres is again governed by a combination of two different mechanisms: debonding of the fibre–matrix interface and frictional slip of the fibre. However, in addition to these ‘straight-fibre’ mechanisms, mechanical interlock is introduced by the plastic deformation of the fibre hook. In contrast to a straight fibre, the mechanical anchorage contribution provided by a hooked end fibre increases the pull-out load after de-bonding significantly. It can be observed that P_max for all hook end fibres increases with an increase in matrix strength. It is also evident that an increase in number of hook bends increases P_max dramatically. The 5DH (triple bend) fibres showed considerably higher values of P_max in all concrete matrices (Fig. 9). In addition, the pull-out work of 5DH fibre was significantly higher than that of the 3DH (single bend) and 4DH fibres (double bend). The higher performance for 5DH fibre is due to the high energy needed to deform and straighten the hook bends. However, despite the increased energy consumed during the pull-out, the full straightening of 4DH and 5DH hook bends was not observed (Fig. 10). However, the straightening of the hook increases significantly as the matrix strength increases e.g. a hooked end fibre pulled-out from the HSC showed higher levels of hook straightening that those of the NSC and MSC (Fig. 10). This indicates consistently that concrete matrix with higher strength is needed to ensure the hook bends are almost completely straightened. The benefit of this feature of fibre reinforcement is worth evaluating in the following section.

The plastic zone areas \( \frac{{A_{p} }}{2} \) in the Fig. 12 are in the ratio with the fibre section area \( A_{f} \) as:in which the geometry of Fig. 12 shows:

Hencein which

Therefore,giving an equation between \( R \) and \( \theta_{e} \)

Elastic bending theory applies under the elastic contribution (\( M_{e} \)) to the applied moment (\( M_{ep} \)) shown in Fig. 13.

At the interface position \( r_{f} - h \) between the two zones:which gives an elastic curvature \( \rho_{e} \) for the neutral axis (N.A) as shown:

From Eq. (14)

Equation (15) enables the curvature to be connected to the penetration area ratio. That is, from Eq. (13) \( R = \frac{{A_{p} }}{{A_{f} }} \) is found for a given \( \theta_{e} \).

For example, with \( R = 0.3\left( {30\% } \right) \) and \( r_{f} = 0.9 \) mm, \( \theta_{e} = 35.8^\circ \) is found from Eq. (13) by trial. Then from Eq. (12) \( h = 0.187 \) mm when Eq. (8) gives \( M_{ep} = 0.0792\sigma_{y}. \)

The bend angle (Fig. 14) \( \beta = 45^\circ \) applies to the 3DH fibre. Taking the bend length \( l \) to be a chord of a circle of curvature \( \rho_{e} \) shows:

Hence, for 3D fibres, where \( \beta = 45^\circ \), Eqs. (10) and (11) give: \( \sin \theta_{e} = \frac{{\rho_{e } \sigma_{y} }}{{E_{f} r_{f} }} = \frac{{\sigma_{y} \times l}}{{2E_{f} r_{f} \sin \left( {\frac{\beta }{2}} \right)}} = \frac{1090 \times 2.5}{{2 \times 207 \times 10^{3} \times 0.45 \times \sin \left( {\frac{45}{2}} \right)}} = 0.0382 \) when from Eq. (13) correspondingly, and from Eq. (12)

It appears that this initial estimate reveals too great a spread of plasticity (95.1%) when based solely upon an applied moment. Of course, when the latter is released the curvature \( \rho_{e } \) is altered by a partial recovery of elastic strain i.e. ‘springback’. Therefore the analysis requires an account of springback to provide the residual (initial) wire curvature \( \rho_{R } \) more accurately.

In Fig. 15a the elastic curvature \( \rho_{e} \) under \( M_{ep} \) is that of the N.A within the central elastic zone. When \( M_{ep} \) is released an elastic springback occurs over the whole section for which the residual strain \( \varepsilon_{R} =\varepsilon_{e} -\varepsilon_{E} \) connects to the required curvature \( \rho_{R } \) in a reciprocal relationship \( \varepsilon_{R} = \frac{y}{{\rho_{R} }} \).

Thus at a given depth \( y \) between applying then releasing \( M_{ep} \) in Fig. 15a, b. where the respective elastic–curvatures in Fig. 15a, b are:

Substituting each elastic curvature \( \rho_{e} \) and \( \rho_{E} \) in Eq. (17):

Substituting Eqs. (9) and (11) in to Eq. (18)

Now \( I = I_{E} \) with an elastic recovery across the full section and therefore:

Setting \( y = \frac{{\rho_{R} }}{{\rho_{E} }} \) and \( x = \frac{h}{{r_{f} }} \), Eq. (19) becomes:in which \( \rho_{E} = \frac{{E_{f} r_{f} }}{{\sigma_{y} }} \) giving \( y = \frac{{\rho_{R} \sigma_{y} }}{{E_{f} r_{f} }} \) for \( \rho_{R} = \frac{l}{{2\sin \left( {\frac{\beta }{2}} \right)}} \)

The following seven-steps enable an estimate of the extent of plasticity within the equivalent bend radius of a hooked end fibre.

The \( {\text{P}}_{1} \) value can be predicted using Eq. (28) of straight fibre developed by Naaman et al. (1991a).where \( \uppsi \) is the fibre perimeter, \( \tau_{{fd}} \) (∆) is the frictional shear stress function for a slip ∆, and (l − ∆) is the length of fibre remaining embedded.