PSI - Issue 18

G. Quino et al. / Procedia Structural Integrity 18 (2019) 507–515

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G. Quino et. al/ Structural Integrity Procedia 00 (2019) 000–000

The classic approach to study and model the mechanics of fibre bundles consists on randomly generating a distribution of strengths and assign them to each fibre. This distribution can be normal (R’Mili, Godin, and Lamon 2012), or more popularly Weibull (Zhou et al. 2010; Marston, Gabbitas, and Adams 1997; Calard and Lamon 2004). Thus, parallel fibres with no interaction among them, that are pulled in a strain-controlled mode, should break in a stable manner (Calard and Lamon 2004) and have a smooth bell-shaped strain vs. load curve. Acoustic emissions (AE) are now a well-accepted technique to capture failure events. Its work principle is simple: transmitted stress waves are measured by piezoelectric sensors capable to capture frequencies up to 1 MHz. It has been applied to a wide range of material such as metals (Wadley, Scruby, and Speake 1980), granular materials (Caicedo B, Martinez A, and Vallejo L 2011; Mao and Towhata 2015), composites materials (Dahmene, Yaacoubi, and Mountassir 2015), and fibres (Hill and Okoroafor 1995; R’Mili, Moevus, and Godin 2008). Regardless the wide field of applications, there are still some drawbacks. For example, in granular materials the size of the probes can be relatively big when compared to RVE volumes of few millimetres. For application in fibres, probes are attached to the machine near the specimens (Maillet et al. 2014), which are usually fibre bundles glued onto lining plates. Since AE captures transmitted waves, the solids between the event source and the probes can induce noise, attenuation, and alteration of the waves. Therefore, the actual captured signal has characteristics that cannot be intrinsically related to the acoustic phenomenon of the fracture event, but also depends on the properties of the intermediate solids. This may not affect the detection of breaks but may have an impact upon the analysis in the frequency domain. It is proposed that with the aid of the Sound Measurements (SM) (De Cola et al. 2019) – inspired on acoustic emissions (AE) –, we can monitor the progressive failure and find a distribution of strengths for the individual fibres that can lead to an accurate representation of the mechanical behaviour of the bundle. It is assumed that all imperfections will have an effect upon the “apparent strength” of the single fibres within the bundle. The apparent strength is not the real strength of the material, but an effective one, that accounts for the defects such as non parallelism, manufacture, etc. These apparent strengths can be found thanks to the fact that SM is exclusively sensible to fracture (De Cola et al. 2019). Therefore, the number of surviving fibres at a certain load, at any time, can be estimated. In the next section, the mechanics of fibre bundles is discussed, and the Weibull model is described. Later, in Section 3, the details of the experiments are explained, for both the mechanical characterisation, and the SM related work. Section 4 introduces the numerical experiment that was implemented to test the proposed approach and the Weibull one. Results of the tests and the post-process in the time domain of the signals are presented and discussed in Section 5. Finally, some conclusions are drawn, and future directions of research are given.

Nomenclature SM

Sound measurements AE Acoustic emmisions � Fibre strength � Weibull scale factor Weibull shape factor ��� Maximum stress � Strain at maximum load Young’s modulus � Number of fibres in a bundle Applied load � Tensile strength of the �� fibre � Cross sectional area of a single fibre � �� � � Number of broken fibres at the time the �� fibre broke �∗ Re-scaled fibre cross-sectional area � ∗ Re-scaled fibre diameter � Threshold Residual