## 3 Results and Discussion
### Fracture Toughness  
The fracture toughness values (K\({}_{\text{IC}}\)) for all the notch beam specimens are presented in Figure 2B. It can be clearly seen that the addition of PVA fibers increased the fracture toughness value of all the tested specimens. Among all the geopolymer specimens, the GP7 and GP0 showed the highest and lowest values of fracture toughness, respectively. A 7% addition of PVA fibers into a geopolymer specimen increased the fracture toughness strength by 78.29% and 54.88%, with respect to 3% and 5% PVA fiber induced geopolymers. Although 7% incorporation of PVA fibers showed higher fracture toughness, it was difficult to disperse the fibers homogenously into the matrix, and agglomeration of fibers was observed (see Section 3.8). The fracture toughness strength of the GP3, GP5, and GP7 specimens was enhanced by 35.42%, 54.68%, and 139.58%, respectively, in relation to the GP0 specimen, which corresponds to their higher compressive strength values, as shown in Figure 2A. The PVA fibers (8 mm in length) were used in this study. Due to high mechanical strength and enough length, the fibers improved the fracture toughness by bridging numerous micro cracks together. Therefore, the fracture of bridging fibers in the micro cracks was restrained with delayed formation of main cracks. The higher strength is mainly due to the reason that the PVA fibers restrained the crack propagation because of the fiber bridging mechanism. The fiber bridging mechanism in the micro and main cracks efficiently retained the integrity and forms of composites, showing ductile fracture behavior [37]. It was observed that the GP0 specimen exhibited a catastrophic failure, while GP5 specimen showed a ductile failure (Figure 3). This elucidates that cracking occurs at greater values of critical stress in the GP3, GP5, and GP7 specimens than that of the GP0 specimen. The results are in accordance with those published by [PERSON] et al. [10] for fiber reinforced geopolymers. In the present work, the fracture toughness values were in the range of 0.2 to 0.46 MPa m\({}^{1/2}\). [PERSON] et al. [13] also measured the fracture toughness values of geopolymers using different precursors in the range of 0.25-0.65 MPa m\({}^{1/2}\). The higher fracture toughness of the GP3, GP5, and GP7 specimens indicates that crack failure planes are more tortuous, thus consumed more energy, as compared to the GP0 specimen, which is confirmed by visual inspection of rupture surfaces of the geopolymer specimens. Figure 2: Different geopolymer specimens in terms: (**A**) Compressive strength; (**B**) fracture toughness; (**C**) variation of fracture toughness with compressive strength. The fracture toughness value increases with the increase of compressive strength of the geopolymers (Figure 2C). The cracking takes place at critical stress. The higher fracture toughness value reveals that the crack happens at higher critical stress. Therefore, the resistance to crack propagation is higher in PVA fibers reinforced geopolymers. The fracture toughness of composite material is generally affected by the microstructure of the matrix and the size of aggregates. Additionally, in fly ash-based geopolymers the major reaction product formed is an alkaline aluminosilicate gel with a low-ordered crystalline structure. Therefore, the microstructure of the geopolymer matrixes seems to be the most important reason for the different matrix fracture toughness of the specimens, with or without PVA fiber, as the other factors were kept constant. Crack mouth opening displacement (CMOD) was also measured with the help of the clip gauge attached at the bottom of the beam. The maximum load attained by the geopolymer specimens depends upon the fiber concentration. It is clear that load and corresponding CMOD, enhanced with increasing PVA fiber contents in the matrix due to an upsurge in the tensile strain capacity of the matrix, hence resulted in an improved load bearing capacity of the specimen (Figure 4).