# Hybrid Geopolymer Composites Based on Fly Ash Reinforced with Glass and Flax Fibers
## 3 Results and Discussion  
The results of the above-mentioned experiments are presented in the following figures. The mean values are represented by respective symbols according to the used aggregate (circle for river sand and square for glass spheres). The standard deviations are represented by error bars. In some cases, the coefficient of variation was low (under 5%); therefore, it is not possible to see error bars properly. Figure 3 shows the results of non-destructive measurements using the resonance method. The dynamic modulus of elasticity \(E_{\text{dyn}}\) decreased with the addition of fibers in the case of the S composite. The highest decrease was about 18% for FF addition. A slight decrease was also observed for the GS composite containing only single-type fibers, while when the MIX of fibers was used, the value increased by about 10% in comparison with the REF composite. In general, it can be stated that the dynamic modulus of elasticity is significantly lower (less than half) for all GS composites compared to S composites. This relation is connected with a reduction in the density of the materials and the same mechanical properties. Based on the results and their variability, it can be stated that the addition of single-type fibers did not influence the value of the dynamic Poisson ratio \(\
u_{\text{dyn}}\) in the case of S composites. The addition of MIX fibers led to a decrease of about 20%. On the other hand, the increase in the value of the dynamic Poisson ratio for all GS composites with fibers compared to REF was observed. The highest increase of almost 50% was observed for GS with the MIX of fibers. Figure 3: Mean values of dynamic characteristics of investigated geopolymer composites. Figure 4 presents the results of basic physical and mechanical characteristics of investigated geopolymer composites with a standard deviation. In the case where the line of standard deviation is not visible, the values obtained from investigated specimens have very similar values, so the standard deviation was below 5%. The value of bulk density \(\rho\) is almost the same for all S composites, and the difference is less than 3%. In the case of the GS composite, the addition of GF did not affect bulk density; on the other hand, the addition of FF and the MIX of fibers increased the value by about 7%. The bulk density is about 45% lower in the case of GS composites in comparison with S composites. The value of compressive strength of the S composite without fibers is about 46 MPa. It is more than two times higher compared to the GS composite. The addition of fibers caused a decrease in compressive strength in the case of the S composite. A higher decrease of about 17% was observed for S composites with single-type fibers, while when the MIX of fibers was used, the decrease was about 10%. The addition of single-type fibers did not significantly affect the compressive strength of the GS composite. When the MIX of fibers was used, an increase of about 10% was observed. The addition of fibers reduced the maximum force recorded during the fracture tests which led to a decrease of up to 20% in crack strength in the case of S composites. In the case of GS composites, the addition of GF also led to a slight decrease in crack strength. In contrast, the addition of FF and the MIX of fibers led to an increase in the value of crack strength of up to 25% when the MIX of fibers was used. Figure 4: Mean values of basic physical and mechanical characteristics of investigated geopolymer composites. Figure 5 presents the results obtained from the evaluation of the _F-d_ diagrams. The values of the modulus of elasticity show a similar trend as the values of the dynamic modulus of elasticity obtained from the resonance method for both composites. The absolute value of the static modulus of elasticity is about 15-25% higher in comparison with the dynamic one. The addition of fibers led to a decrease of about 15% in the effective fracture toughness in the case of the S composite.