the relatively larger crack width bridged by the fibres. The tensile post-cracking behaviour of FRC is related to the mechanisms that arise at matrix/fibre interface such as fibre debonding, matrix fracture/spalling, post-debonding friction between fibre and matrix (fibre pullout), fibre rupture, and fibre yielding, which impact depends on factors such as the quality of cementitious matrix, geometry and fibre material [16, 17]. Thus, for FRC elements a combined effect of aggregate and fibre bridging arises, as illustrated in Figure 3, as the fibre bridging mechanism is gradually activated upon a certain crack width value.
In Figure 3, three distinct zones can be identified, namely, a traction-free zone (with relatively large crack widths), a bridging zone where fibre and aggregate bridging take place and a zone of microcrack growth.
w
E D C B A
traction
free bridging and branching
macro-crack growth
micro-cracking macro-crack
Bridging stress aggregate
bridging
�
C
D fct
A B
E
w FRC
D
E
Elongation, �l bridging and branching macro-crack growth micro-crack growth
Concrete
Figure 3: Schematic representation of the effect of aggregates and fibres in FRC [16].
2.3 Pullout behaviour of steel fibres
The addition of steel fibres to concrete has a major effect in brittleness and crack width control, since the mechanisms that arise after crack initiation, such as crack bridging, dissipate a considerable amount of energy during the fibre pullout process. The crack bridging capacity provided by the fibres is attained as a result of bond-slip mechanisms such as adhesion, friction, mechanical and fibre interlock with the surrounding matrix. In fact, bond mechanism plays a major role in the composite action of FRC [18, 19].
The overall mechanical behaviour of smooth steel fibres results from a combination of adhesion and friction with the surround matrix during the pullout process. The pullout behaviour of an aligned smooth fibre is presented in Figure 4. The first branch of the curve corresponds to a linear force-slip relationship due to the elastic bond originated by the physical and chemical adhesion of the fibre to the surrounding matrix [20]. After reaching point A, the debonding process starts to develop until the peak load is attained at point B and the fibre is fully debonded. After reaching the peak, the load starts to decrease, with the correspondent increase in slip due to the damage propagation at the fibre-matrix interface zone that decreases its frictional resistance. Finally, the C-D branch is governed by the frictional slip of the fibre, until maximum slip is achieved [17].
Figure 4: Typical pullout relationship between end-slip and load for smooth fibre (adapted from Löfgren [16] and Cunha [17]).
The behaviour of an end-hooked fibre is similar to the one of smooth fibre (Figure 4), as it is also composed by a debonding and frictional phase. However, after the debonding process is complete, the frictional phase is complemented with a mechanical bond mechanism originated by the mechanical inter-lock and plastic deformation of the end-hook. A comparison between the pullout behaviour of a smooth and hooked fibre is presented in Figure 5.
� P
o Le
Smooth fibre Hooked-end fibre Deformation of end hook
A B C
D E
F
P
Le
�
A-B partly debonded
P
Le
�
B-C fully debonded
P
Le
�
D-E pullout
P
Le
�
E-F pullout P
Le
�
C-D pullout
Figure 5: Typical pullout relationship between end-slip and load for smooth and end-hooked fibre (adapted from Löfgren [16] and Cunha [17]).
As depicted in Figure 5, the linear branch is very similar in both fibres, however, after the debond process is complete an increase in the pullout load (B-C) is observed, as a result of the contribution of the mechanical anchorage mechanism provided by the hook. As the end-hook becomes progressively deformed, a decrease in the load is observed (D), however, until the fibre does not attain a fully straightened shape, another peak load is observed. Finally, after the fibre is completely straight, the pullout process occurs (E-F) under frictional resistance, similarly to smooth fibres.
The peak pullout force and amount of energy dissipated depends on several factors namely, the mechanical properties and geometry of the fibres, fibre inclination and orientation (see Section 2.4), fibre embedment length and mechanical properties of the matrix.
Currently, all steel fibres have and enhanced bond capacity provided by mechanical “deformations”
(e.g. crimping, indenting, end-hooks/buttons/paddles). As referred previously, a smooth fibre relies mainly on the breakdown of chemical adhesion and friction mechanisms involving the surrounding matrix, however, if a mechanical deformation is induced, the bond effect due to adhesion can be neglected since physical bond has a considerably higher impact on the pullout behaviour [21]. In fact, according to Banthia
2.3. PULLOUT BEHAVIOUR OF STEEL FIBRES
and Trottier [22] and Li and Stang [23], deforming the fibre is the most effective approach to improve bond-slip characteristics of steel fibres in cementitious matrices. Some typical profiles of steel fibres commonly used in FRC are presented in Table 1.
Table 1: Steel fibre profiles [17].
Longitudinal profile Cross section (a) Smooth
Round, flat or any shape (b) Indented/etched/roughened
(c) Flat-ended
Round of flat
(d) Buttons-ended
Round (e) Hooked-ended
(f) Crimped/corrugated
Round, flat or any shape
(g) Polygonal twisted
Polygonal (triangular or rectangular)
Besides fibre geometry, embedment length also constitutes an important parameter in the pullout performance of the fibres. Increasing the embedment length translates into a larger contact surface area with the surrounding matrix, leading to enhanced pullout response, which is specially important when smooth fibres are used [23]. In case of fibres with deformations along its length (e.g. indented, etched, roughened, crimped/corrugated), a better performance is obtained, since the larger embedment length mobilises more mechanical anchorages, as stated in the works of Chanvillard [24] and Groth [25].
However, the use of fibres with mechanical anchorages in its extremities, such as end-hooked fibres, seem to be less affected by larger embedment lengths, since the performance of this kind of fibres is conferred mainly by the grade of mobilisation of the anchorage system and not by the larger bond surface [18, 26].
When fibres are added to concrete, the mixture of aggregates, cement past and fibres are bonded together through the hydration process and development of the matrix microstructure. This results in the formation of the so-called interfacial transition zone (ITZ), which separates the fibre from the bulk cement paste (see Figure 6). From a microscopic point of view, the morphology of this zone is mainly characterised by the existence of a significantly porous layer, and the presence of an increased amount of calcium-hydroxide (CH) crystals, resulting in substantially lower strength when compared to the bulk
cement paste [27, 28]. Thus, matrix properties influence the pullout performance of the fibres, since the bond quality is affected by the microstructure of the ITZ. Several authors state that lower water/binder ratios leads to higher pullout loads, due to the densification of the ITZ and correspondent improved bond strength [22, 25, 29]. However, lower w/b ratios also increases the stiffness and strength of the bulk cement paste which results in lower toughness values [22] and potentially leads to fibre rupture, compro-mising the desired post-cracking performance.
Duplex film
CH Layer Porous layer Bulk paste
Steel Fibre
Figure 6: Schematic representation of the ITZ (adapted from Bentur and Mindess [30]).
When an inclined fibre at an angle,𝜃𝑓, is subjected to a pullout force, a similar behaviour to the case of aligned fibres is observed, however, additional mechanisms are also activated, mainly at the fibre exit point. Firstly, the debonding of the fibre/matrix interface occurs, followed by sliding of the fibre over the debonded interface. However, due to the inclination angle, bending and shearing actions arise, originating local compression and push off of the matrix in the vicinity of the crack faces (Figure 7). The pullout force, N, can be decomposed in two components, 𝑁k and 𝑁⊥. The component 𝑁k is responsible for fibre debonding which is sustained by interfacial stresses,𝑆, whereas 𝑁⊥ originates a bending effect, which is counteracted by the reaction,𝑅, originated by the local compression of the matrix. Hence, the matrix strength is of key importance since a weak matrix is prone to damage in the compressed area, potentially leading to concrete spalling.
�
concrete spalling
N∥
N⟂ R
N S
Before spalling
crack face
(a) (b)
Figure 7: Bending and shearing action of and inclined fibre during the pullout process (a) before and (b) after concrete spalling (adapted from Cunha [17]).
The combination of the aforementioned mechanisms usually results in higher pullout resistance, especially for inclinations ranging between 10 to 30◦[17, 22, 26, 31]. Higher inclination angles originate