# Acoustic Emission Analysis of Fracture and Size Effect in Cementitious Mortars
## 4 AE Analysis: Results and Discussion
### AE-Based Fracture Process Zone (FPZ) Analysis  
Several researchers have proposed a method of quantifying the size of FPZ based on the AE technique. According to [PERSON] et al. [9], [PERSON] and [PERSON] [13] and [PERSON] and [PERSON] [15], the energy in the FPZ accounts for 95% of total AE energy. The histogram of located AE events along the direction of interest is used to measure the size of the FPZ. For a splitting crack, this direction of interest is usually perpendicular to the direction of crack propagation (\(x\)-axis). The size of the FPZ is measured at 20% of the maximum magnitude of the histogram. [PERSON] et al. [54] defined the FPZ as the region around the macro-crack  
Figure 9: AE source localization plots at four loading stages of a Brazilian splitting test for the sample sizes, large (**a**), medium (**b**), and small (**c**). Size of the circular marker indicates the AE event amplitude.  
where high-amplitude AE events are located. [PERSON] [12] measured the width of high-energy AE event clusters.  
Here, the width of an FPZ is computed using similar methods to [PERSON] and [PERSON] [13]. This method had previously also been used by [PERSON] et al. [55] to compare the size of the AE-based FPZ for mortars loaded in monotonic and fatigue loads in a Brazilian splitting test. In this method, the circular surface of the sample is divided into 4 mm (the estimated localization error) width of regions. AE events located in each of these regions are counted and connected to give the histogram of the AE events (N) line; see Figure 10. Here, it is assumed that only the AE events that occur after 20% and up to 100% of peak load cause the final fracture, and thus, these are taken for the FPZ analysis. The method and the computed FPZ width for three representative, different-sized samples are shown in Figure 10. As can be seen from Figure 10a-c, the width of FPZ increases with sample size. It was also noticed that most of the located events occur between 80% to 100% of the peak load for the larger sample.  
The width of the FPZ for all of the samples tested in this research is summarized in Figure 10d. This plot shows that FPZ width increases with sample size. However, similar to [PERSON] and [PERSON] [13], the rate of increment was slower than the sample size enlargement. The dependence of FPZ width on sample size is mainly because at macro-scale, strain energy is size-dependent. The stored strain energy increases with sample size.  
Fracture initiates when this stored energy reaches the required fracture energy level at the region where stress concentration occurs (at existing micro-cracks, voids, or pores). As stated before, the FPZ is a region where the fracture energy is released. Hence, for the larger samples, the release of this enormous stored energy at the location of stress concentration results in the broader FPZ. This observation is also supported by the experiments conducted by [PERSON] [12]. The investigation was on a three-point bending test of notched beams. The fracture energy was found to be directly related to the size of the FPZ.  
Figure 10: AE-based calculation of the width of the fracture process zone (\(W_{FPZ}\)) for a Brazilian splitting test for the sample sizes, (**a**) large, (**b**) medium, and (**c**) small, (**d**) the \(W_{FPZ}\) for all the samples in the test series. Size of the circular marker indicates the AE event amplitude.