# The Influence of Sensor Size on Acoustic Emission Waveforms--A Numerical Study
## 4 Discussion
### Experimental Evidence  
Experimentally, the sensor size effect cannot be directly compared between two different sensors, since apart from their possible difference in size or surface contact area, they also possess different frequency response characteristics. In addition, in the specific case studied herein, results between simulations and experiments cannot be directly compared for a number of reasons. First, the damping of the material is not readily known like other parameters (e.g., the elastic modulus) to be imported in the simulation. In addition, although a numerical source can be excited within the material to introduce a pure longitudinal wave, this cannot be realized experimentally as the excitation takes place on the surface forming again stronger Rayleigh waves. Therefore, it is reasonable to compare simulated and experimental waveforms after excitation on the same surface (case of horizontal propagation above) but there is no straightforward quantitative comparison for the case of vertical propagation. However, there is one point of interest which shows the strength of the sensor size effect. As mentioned above, when excitation takes place on the surface, 67% of the energy forms the Rayleigh wave. On the other hand, experimentally, the only amount of energy captured by the sensor standing at the opposite side is the 7% of the longitudinal wave. Therefore, it is expected that the horizontal propagation case will result in stronger waveform than the vertical, also because Rayleigh waves suffer less geometric spreading. Numerically, this is shown when comparing the waveform received by the point sensor coming from the surface excitation (Figure 2, with peak to peak amplitude higher than 0.5) and vertical excitation (Figure 5a, respective amplitude range 0.3). The response to surface excitation is much higher due to the strength of the Rayleigh wave and the reduced geometric spreading of the beam. In this direction, experimental measurements with pencil lead breakage (Hsu-Nielsen source) as acoustic source were conducted (Figure 12). A receiver sensor was positioned at the top surface  
Figure 11: Average coherence up to 2 MHz for different sensor size and angles of propagation relatively to the sensor surface and excitation frequencies (**a**) 1 MHz; (**b**) 500 kHz. of a normal strength concrete sample. The sample had 50 mm thickness. Pencil lead breakages were performed at 50 mm far from the receiver at the top surface and at the bottom side of the sample, just beneath the receiver, as shown in Figure 12.  
The above experimental arrangement was realized using two types of AE sensors. One is the widely used in practice \"R15\" of Mistras Group with a sharp resonant peak at 150 kHz and diameter of 19 mm. The other is the \"Pico\" of the same manufacturer with a broader response and much smaller diameter of 5 mm. A pre-trigger capturing time of 50 us was used. The sampling rate was 2 MHz and the pre-amplification gain was 40 dB. Figure 13 shows several waveforms, each one corresponding to an individual pencil lead break, recorded by vertical (a) and surface horizontal (b) propagation recorded by the Pico (5 mm) sensor. The waveforms are quite repeatable especially at the early part that contains the so-called \"ballistic\" pulse which is not much influenced by scattering [26]. Visually, the waveforms from the surface excitation (Figure 13b) obtain higher amplitude in average than the ones of vertical excitation (Figure 13a). Measuring the peak-to-peak absolute voltage of the highest cycle of the waveforms, the average for the horizontal ones is 0.84 V while for the vertical the average amplitude is 0.54 V. This is verified by the higher peak of the FFT curve of the surface horizontal wave shown in Figure 13c. The FFT curves presented here are obtained by averaging the individual FFTs of waveforms in Figure 13a,b respectively. In contrast, using the longer sensor R15 (19 mm), the waveforms from vertical orientation are higher than surface (Figure 14a,b respectively).