PSI - Issue 18

G. Quino et al. / Procedia Structural Integrity 18 (2019) 507–515 G. Quino et. al/ Structural Integrity Procedia 00 (2019) 000–000

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Fig. 2. Typical experimental data in time domain: history of load F(t), sound waveform, and cumulative number of peaks.

4. Numerical experiment In this paper, two models are compared: (i) a model that considers Weibull distribution of strengths as described in Section 2, and (ii) a model that makes use of the reconstructed distribution of apparent strengths obtained by SM as presented in Section 3.2. To test these models, a numerical experiment, depicted in Fig. 3, was implemented in Matlab (MATLAB 2015). It considers parallel fibres of the same diameter, pulled uniaxially in a strain controlled manner, in steps of constant strain increments of 0.00001.

Fig. 3. Numerical experiment where non-interacting parallel fibres are pulled. The algorithm, shown in Fig. 4, starts by assigning values of strength to every fibre according to the two cases: (i) a Weibull distribution with prescribed shape and scale factors � and that gives origin to a random set of � strength values � � , or (ii) a reconstructed distribution of apparent strengths � � obtained with the SM technique (Equation (8)). In every strain step, the load within every single fibre is computed. If their strength is reached, the breakage is reproduced by setting the modulus of the individual fibre to zero. The Matlab implementation of the model for the case of fibres with Weibull distribution of strengths is available in the MFibres GitHub repository (Quino 2019). 5. Results and discussion From the experimental curve and Equations (2) and (3), the calculated Weibull parameters were: � � 1.4884 , and � �.� . The Young’s modulus of the material is � � �8 .