# The Influence of Sensor Size on Acoustic Emission Waveforms--A Numerical Study
## 1 Introduction  
Acoustic Emission (AE) technique is commonly applied for the health monitoring of materials and structures. When the fracture process is of interest, AE offers great sensitivity allowing to detect damage events down to the nano-scale. The number and rate of registered acoustic signals is well related to the damage intensity in different material fields [1; 2; 3]. Source localization can accurately detect in 3D space the AE events emitted in small or large size structures [4; 5; 6]. Traditionally, the focus in AE has mostly been on the sensitivity or the ability to detect low energy signals and not as much on the accurate interpretation of the waveform in terms of the displacement or pressure field, (as in the case of ultrasound). However, the need for control of the structural performance necessitates more information about the failure type or damage mode. For this purpose, the time-domain parameters extracted from the waveform are investigated, as well as the waveform shape that offers valuable and direct information regarding the source's nature. In general, the frequency and the gravity of the waveforms (energy distributed between the early or later part) are well correlated to the corresponding fracture modes in bulk media like concrete or composite plates [7; 8; 9]. Since damage characterization is based on the received waveforms, the performance of the sensors is of utmost importance. Their performance is governed by their piezoelectric element that transforms the disturbance on the surface of the transducer to an electric signal. The piezoelectric elements have certain physical characteristics (stiffness, thickness) thatdefine their frequency response, allowing either resonant or broadband behavior. Although the sensor's response is taken into account in several cases for accurate identification of the source through deconvolution [1; 10; 11; 12; 13], its physical dimensions play a very important role as well. Performance of different sensors can be compared based on calibration curves that are provided by the manufacturer. However, these curves describe mainly the response to elastic waves impinging vertically to the sensor's contact surface [10; 14] with few exceptions dealing with parallel propagation in plates or bars [15; 16; 17]. In the latter studies, it is shown that sensors used for waves propagating on plates or bars (parallel to the sensor's contact surface) exhibit a certain decrease in sensitivity at high frequencies. Still, in the case of different size sensors, it remains difficult to decouple the effect of the sensor's frequency response from the effect of piezoelectric element physical dimension, namely \"aperture\" effect. The latter effect is well masked since the voltage output is derived from the average excitation over the whole surface of the element. Any distortions compared to \"point\" receiver is treated as an error that causes the response to deviate from the ideal behavior [10]. The importance of the aperture effect has been included in numerical studies in plates, coupled with the sensor response function [17]. It was acknowledged that the smaller tip diameter resulted in better match with the reference signal (signal without the presence of the sensor). In a more recent study, it was seen that the sensor sensitivity curves corresponding to bulk, Rayleigh, bar and Lamb waves differ substantially, especially for resonant sensors due to the aperture effect [18]. The present paper is a numerical study that intends to isolate and highlight the effect of sensor physical size on AE measurements, decoupling it from the sensor frequency response. A numeric approach appears to be the only way to evaluate the sensor size effect since experimentally, they exhibit differences in response and that does not allow to individually study the sensor size. Although, sensors with different sizes are commonly available. The numerically simulated sensor measures the average displacement on its length without any resonance effect.