*3.3. Flexural Performance*

The flexural behaviour of composites will exhibit deflection-hardening, or softening behaviour after, first, cracking. The first cracking point of the composite is defined as limit of proportionality (LOP), and the maximum equivalent flexural strength point of the composite is defined as modulus of rupture (MOR) [25]. The flexural behaviours of AAFA composites are shown in Figures 8 and 9. The flexural performance of F1 mixture shows a typical form of deflection-softening behaviour; F2 mixture shows quasi-deflection-softening behaviour; and F4 mixture shows deflection-hardening

behaviour. However, for F3 mixture, some of the specimens had complex behaviours, which were deflection-hardening and quasi-deflection-softening behaviours. The maximum loading capacity of F4 mixture was observed to be about 74% greater than that of other mixtures, and the deflection capacity of F4 mixtures was also observed to be greater than that of F1, F2, and F3 mixtures. Similarly, the flexural performance of FS1, FS2, and FS3 mixtures showed typical deflection-softening behaviours, while F4 mixture presented deflection-hardening behaviour. The maximum loading and deflection capacity of F4 mixture were found to be around 65% and 85% greater than the maximum loading and the deflection capacities, respectively, of other mixtures. As the volume fraction ratio of fibre in the AAFA composite increased from 0% to 2.0%, the effects of the fibre volume fraction ratio on the deflection capacities of different mixtures of AAFA composites were plotted in Figure 10. There results show an increasing trend of the deflection capacity at LOP as the linear relationship, and an increasing trend of the deflection capacity at MOR, as the exponential relationship. The improvement of deflection at MOR in Group A was observed to have much higher deflection capacity than that of Group B. Li et al. [6,22,26] reported that adding fine aggregates in OPC composite could improve the pseudo-strain hardening behaviour. In AAFA composite, however, adding fine aggregates (SF) in this case does not improve the flexural deflection and strength capacity. The flexural behaviour of AAFA composite with SF as added fine aggregates shows a decrease in the flexural strength and no improvement in the flexural deflection and strain capacity.

**Figure 6.** Compressive strength developments of Group A (**top**) and Group B (**bottom**).

**Figure 7.** Compressive stress–strain curves of Group A (**top**) and Group B (**bottom**).

**Figure 8.** Flexural behaviour of Group A.

**Figure 9.** Flexural behaviour of Group B.

**Figure 10.** Effect of fibre volume fraction on deflection at limit of proportionality (LOP) (**top**) and modulus of rupture (MOR) (**bottom**).

According to the literature [5,27,28], the tensile and compressive behaviour of a composite material strongly influence the flexural performance. Also, the strain-hardening behaviour in tension leads to a deflection-hardening behaviour when the flexural behaviour of the composites is strongly associated with its tensile characteristic [29]. Thus, the results of the flexural performance obtained in this research could be related with the tensile behaviour of AAFA composites. Based on the theoretical discussions by several researchers [5–7,9,22,26,30], the critical energy release rate *Gc* and the interfacial bond strength *τ* of the composites are important parameters to be considered in a design of the composite's matrix to achieve the strain-hardening behaviour of the composite. In addition, the matrix properties, such as elastic modulus and fracture toughness, which are linked to the composite's critical energy release rate *Gc*, are affected by several parameters [7,22]. Using nanoindentation data, the composite critical energy release rate *Gc* of AAFA matrix was found to be 0.010 kJ/m2. Based on the fracture toughness and the elastic modulus of AAFA matrix [24], the interfacial bond strength of AAFA composite was plotted against the critical fibre volume fraction ratio and the corresponding strain-hardening behaviour with the snubbing coefficient *f* , which is in term of the inclining angle between fibre and matrix, as illustrated in Figure 11. It can be seen that with 2.0% of the fibre volume fraction ratio in the AAFA composites, F4 and FS4 mixtures are in the region of strain-hardening, whereas, with less than 0.5% of the fibre volume fraction ratio, F2 and FS2 are not in the region of strain-hardening. It can also be noticed that with 1.0% of the fibre volume fraction ratio, F3 and FS3 mixtures are partly in the region

of strain-hardening with other parts falling in the region of strain-hardening. This is consistent with F3 mixture, which shows a combination of strain-hardening and quasi-strain-hardening behaviour.

**Figure 11.** Critical volume fraction against interfacial bond strength.
