## 3 Results and Discussion
### Fatigue Characteristics  
The results of cyclic fracture tests of specimens in 3 PB at different load levels are summarized in Figure 9a in the form of a Wohler curve (Equation (22)) where the maximum normal stress \(S_{F}\) (in Figure 9 marked as \(y\)) applied during experiments is plotted against the logarithm of the number of cycles to failure \(N\) (in Figure 9 marked as \(x\)). Theoretically, all test specimens are broken after the same number of cycles for one particular stress level. However, the fatigue behavior of a heterogeneous material such as the investigated AAS composite is distant from an optimal case, and the results show variability. It is also connected with the different ages of specimens during the cyclic tests. In this case, the specimens were tested between the age of 140 and 160 days. It is evident that mechanical fracture parameters of the investigated AAS composite significantly change during the specimen's aging (see Figure 8), even after 160 days of hardening. Therefore, the measured data are divided by coefficients determined from the approximation curve of relative compressive strength values to obtain correct values of fatigue characteristics corresponding to the age of specimens at which a particular cyclic test is performed. The measured data are standardized to a particular age of specimens by this procedure. In this case, the compressive strength is chosen because it is the most commonly determined mechanical parameter of quasi-brittle composites, and it is used as an input parameter in the structural design. The compressive strength test is also less time-consuming in comparison with the static fracture test. Nevertheless, the presented procedure can be used with any other mechanical or fracture parameter. The measured values of compressive strength are divided by the average value at the chosen specimen's age. In this case, the compressive strength values at the specimen's age of 28, 90, and 180 days are chosen. The compressive strength at the age of 28 days is usually used as a reference value in the design of cement-based composites. The other two ages of specimens are chosen because the mechanical fracture parameters of the investigated AAS composite significantly change during the specimen's aging. By this procedure, the relative  
Figure 9: The \(S_{F}-N\) curve for the investigated AAS composite plotted for measured data (**a**), the \(S_{F}-N\) curve plotted for standardized data at the specimen’s age 28, 90, and 180 days (**b**); the horizontal axis is plotted in logarithmic scale. compressive strength values for all investigated ages of specimens are obtained. Then, these values are approximated by the selected function:  
\[y=a\cdot\left(1-e^{-b\cdot x^{c}}\right), \tag{24}\]  
where \(x\) is the specimen's age in days, \(y\) is the dimensionless relative compressive strength, \(a\) is the coefficient corresponding with an asymptote to the approximation curve, in other words, the ratio of the theoretical value of the compressive strength at infinitum to the value of compressive strength at the specimen's age of 28, 90, or 180 days, and \(b\), \(c\) are the coefficients corresponding with the size of the time-dependent change of compressive strength, which is generally dependent on the compositions of the used mixture. The approximation is performed using the GTDiPS software [28]. The procedure is based on the non-linear least-square method provided by genetic algorithms, which are implemented in this open-source Java GA package [28]. The approximation curves and coefficients \(a\), \(b\), and \(c\) for relative compressive strength values related to the specimen's age of 28, 90, and 180 days are displayed in Figure 10.  
The Wohler curves for standardized data are introduced in Figure 9b.