# Acoustic Emission Analysis of Fracture and Size Effect in Cementitious Mortars
## 4 AE Analysis: Results and Discussion  
### AE Amplitude and Hit Count Analysis  
The cumulative AE hit count for a representative large, medium, and small sample are shown in Figure 6b,d,f respectively. The cumulative AE hit counts are presented for sensors 1 and 3 (referred to as channels Ch-1 and Ch-3), which are positioned on the side of the sample, towards the front and back of the sample, respectively (see also Figure 2b for the sensor locations). These channels are chosen to investigate a possible unsymmetrical nature of the crack propagation (crack initiates on one side and propagates towards the other side of the sample). As there is a small difference observed between the results of both sensors, it can be assumed that there is indeed some asymmetric effect. Hence, the hit-count is captured using these opposite-sided sensors, whichever side the crack initiates. Generally, all samples show a steep rise in AE hit count when reaching the peak load. For the larger sample, there is negligible AE activity until the load approaches the peak load (see Figure 6b). On the other hand, for the medium and the small samples, there are relatively more AE hits occurring early in the test (see Figure 6d,f). From Figure 6a,c,e, it can be seen that these AE hits are low-amplitude hits that can probably be attributed to micro-cracking. Conversely, the AE hits occurring near the peak load have a higher amplitude. There are more of these high-amplitude AE events at the peak load for the larger samples than for the other two sizes. These observations support the theory on size effect due to variations in the release of strain energy. This variation in damage progress can be best explained using the axial bars shown in Figure 7a. The three bars are all made from the same material but have different lengths and cross-sectional areas. When subjected to an axial load, the peak stress and the ductility evolves with sample size (see Figure 7b). Ductility decreases with sample size because the stiffness decreases with length. Hence in the elastic phase, the longer sample deforms more (more elastic energy is stored). The sudden release of this stored energy will cause unstable and more brittle failure. Meanwhile, for the smaller samples, there is no high elastic energy build-up. Instead, there are micro-damages that progressively dampen the energy. Eventually, these micro-damages coalesce to induce failure. Figure 5: Evolution of the experimental tensile splitting strength (\(f_{\text{ct}}\)) computed using [PERSON]’s equation [41] with sample sizes. (**a**) Sample sizes (D = 27, 46, and 106 mm) and boundary conditions (\(\beta=B/D\), where B is the widths of the strips and D is the sample diameter). (**b**) Tensile splitting strength (\(f_{\text{ct}}\)). The mean (\(*\)) and the standard deviation (\(+\)) of the \(f_{\text{ct}}\) value are indicated. Hence, the early occurrence of low-amplitude AE events in the smaller sample can be linked to the sample size. As the sample size decreases, the sample cannot accommodate large elastic deformation. Instead, it starts to form micro-cracks early on in the test (see Figure 6e). The lack of early AE activity on the larger samples indicates the occurrence of more elastic deformation (storage of energy) and less micro-damage (see Figure 6a). The sudden rise of high-amplitude AE in the larger sample indicates a high release of energy  
Figure 6: AE event amplitude versus time (**left**) and cumulative AE hit count versus time (**right**) for the sample sizes, large (**top**), medium (**middle**), and small (**bottom**). Figure 7: Axial bars with varying sizes subjected to an axial tension load (**a**) and axial stress (\(\sigma\)) versus deformation (\(\delta\)) of the three axial bars (**b**). at once (at peak load) for the larger samples. Hence, in quasi-brittle material, the failure becomes more brittle as the sample size increases. Similar results were observed by [PERSON] et al. [10] when investigating the evolution of AE energy on three different sizes of concrete beams.