# Acoustic Emission-Based Method for IFSS Characterization in Single-Fiber Fragmentation Tests
## 3 Results and Discussion
### Comparison of AE and Optical Microscopy Methods  
Figure 9 shows the number of fragments, average lengths, and IFSS values for the specimens tested with both methods. Figure 9(a1,b1,c1) presents the results obtained by the AE method using \(l_{AE,avg,\ arithmetic}\) and the optical microscope method using \(l_{OP,avg}\). Figure 9(a2,b2,c2) also compares both methods, but in this case, the AE method \(l_{AE,avg,\ fitted}\) is used. Finally, Figure 9(a3,b3,c3) presents the normal distributions corresponding to the results shown in Figure 9(a2,b2,c2). It is important to note that the number of fragments shown in Figure 9(a1,a2) is the same. Figure 9(a1,a2) reveal that the average number of fragments detected with the AE method is 6.82% higher than that obtained with the conventional optical microscopy method, suggesting that the AE sensor detects events caused by phenomena other than fiber fragmentation, such as slippage of the fiber-matrix interface. To determine whether the detected AE-bursts are caused by one or the other phenomenon, conventional indicators were calculated. However, since the tests performed were not focused on characterizing the different types of failure in this type of material, the results obtained were not conclusive for the present investigation but present an interesting topic for future research. Figure 9(b1,b2) show the mean fragment length obtained with both methods. It can be observed that, for the data as a whole, the AE-arithmetic method overestimates the \begin{table}
\begin{tabular}{c c c|c c c} \hline \hline  & \multicolumn{2}{c|}{**AE Method**} & \multicolumn{4}{c}{**AE Method**} \\  & \multicolumn{2}{c|}{**Mean Fragment**} & \multicolumn{2}{c}{**Mean Fragment**} \\  & \multicolumn{2}{c|}{**Length [\%]**} & \multicolumn{2}{c}{**Number of**} & \multicolumn{2}{c}{**Length [\%]**} \\ \cline{2-5}
**Number of** & **Arithmetic** & **Fitted** & **Distribution** & **Number of** & **Arithmetic** & **Fitted** \\  & **Mean** & **Station** & & **Mean** & **Distribution** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 1: Mean fragment lengths obtained using the AE method with different methodologies: arithmetic mean and fitted distribution curve. value by 29.13% concerning the optical method. This is because this methodology assumes a uniform distribution in the fragments, ignoring the real variability in their length. On the other hand, the AE-fitted method offers a more precise estimate, reducing the average difference to 7.69%. Figure 9(c1,c2) show the results of the IFSS calculation for both methods. Since the AE arithmetic method overestimates the fragment length and considers the equation used to calculate the IFSS, this method underestimates the total values by 19.40% concerning the optical method. On the other hand, the AE-fitted method gives results with a difference of 9.67% compared to the optical method. The absolute error of the IFSS obtained by the AE method concerning the optical method is calculated for each sample tested, according to Equation (13), to analyze the results of each sample separately. The average individual error in the calculation of the IFSS with the AE arithmetic method is 22.36% compared to the optical method, while the AE-fitted method has an error of 10.42%. The confidence intervals are shown in Table 2, where it is observed that with the AE-fitted method, 95% of the samples have a maximum error of 14.16%. In contrast, for the same confidence level, the AE arithmetic method  
Figure 9: Results of the calculations using the optical microscopy method and the AE method: (**a**) number of fragments, (**b**) mean fragment length, and (**c**) IFSS. (**1**) Comparison of the results from the AE arithmetic method and the optical method, (**2**) comparison of the results from the AE fitted method and the optical method, and (**3**) normal distribution (line) and histogram (bars) of the results from the AE fitted method and the optical method. has a maximum error of 30.37%.