PSI - Issue 18

510 G. Quino et al. / Procedia Structural Integrity 18 (2019) 507–515 G. Quino et. al/ Structural Integrity Procedia 00 (2019) 000–000 Since the tex number is known (provided by supplier) we can estimate the total number of fibres within the bundle � with Equation (4). From microscopic measurements on the fibres, the average diameter was found to be � � 14.63 . Replacing into Equation (4) and considering the density of E-glass fibres � ��� ��� � , � � �6� was obtained. � � �� � � (4) 3.2. Sound measurement technique for fibre bundles Fig. 1 shows the instrumentation required to implement the technique: a microphone and a PC. The sound emitted by the breakage of fibres was acquired by a PC microphone using the software Audacity (The Audacity Team 2017) at a rate of 96 kHz. Since the signal is acquired through the PC audio card, with its own internal pre-amplification, not physical units could be assigned. However, for this study, only the peaks in the signal are relevant hence units are not required. A pre-calibration was needed to set the microphone acquisition gain, to obtain relevant signal levels, and avoid saturation. Post de-noising was performed on the audio signal to reduce the environmental sound and improve the signal to noise ratio (SNR). This was done with the built-in function of Audacity, which makes use of the spectral noising gating (The Audacity Team 2018). The acquired waveform was post-processed in Matlab (MATLAB 2015) to identify the acoustic events and obtain the cumulative number of breaks over time ( � ). An SM event is herein defined as the portion of the signal of 5 ms duration where the signal level reaches a peak above a level threshold. Signals in this study were analysed with a threshold � that is a fraction of the maximum amplitude � of the signal in waveform: � � . � � . Fig. 2 shows a typical experimental data in the time domain: the sound waveform, the history of load during the test � � , and the cumulative number of SM events � . The latter tends to “saturate” to a value of N . When a peak that meets the prescribed criterion is found, the time � of occurrence can be recognised. If � is the total number of fibres in the yarn, and � � � � is the number of broken fibres at time � (when the �� breakage occurred), � � � can be used to find the stress to failure of the breaking fibre. The stress that was needed to break that �� fibre can be calculated from the load � � � acting on the remaining � � � � � � fibres of area � . Thus, the strength TS of the �� fibre can be evaluated as: � � ��� � � �� � �� � �� � ��� � (5) After complete breakage of the bundle ( � � ) it would be expected that � � � � takes the value of the total number of fibres of the bundle � . Nevertheless, that is not the case due to various reasons such as simultaneous breakages, and the arbitrary way the threshold was picked. Instead, � � � � is equal to , depending on the chosen amplitude threshold � . Accordingly, for the reconstruction of the distribution of apparent strengths, it will be assumed that the total number of fibres within the initial bundle are instead of � . The diameter � of the fibres (of area � ) will then have to be re-scaled to � ∗ (for fibres of area �∗ ) to keep the total cross-sectional area of the bundle constant (see Equations (6) and (7)). Thus, the reconstruction of the apparent tensile strengths can be made for the equivalent fibres with Equation (8). �∗ � � � (6) � ∗ � � � � (7) � � � � � � � � � � �� �∗ (8) 4