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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Strain

2. Weibull description of fibre bundles The simpler analytical models of fibre bundles consider that there is no interaction of any kind between the fibres, and that each of them breaks as soon as its strength is overcome. A Weibull strength distribution for the fibres within the bundle has been found convenient for mathematical simplicity and decent agreement with experimental observations (Z. Wang, Xia, and Yang 1996; Yuanming, Yuan, and Yang 1994). Such Weibull distribution of strengths has a cumulative function as shown in Equation (1). Some modifications to this distribution have been proposed by others to include effects of temperature and strain rate (Z. Wang, Xia, and Yang 1996; Y. Wang and Xia 1999). � � � � 1 � ��� �� � � � � � � � � , (1) where, � is the strength of a single fibre, and � and are the scale and shape factor respectively. These two parameters, and the number of values to generate, are enough to fully describe and produce a non-unique Weibull distribution of strengths. The shape and scale factors can be obtained in several ways from the experimental strain vs. stress curve of a bundle. For instance, Yuanming et. al (Yuanming, Yuan, and Yang 1994) proposed Equations (2), and (3) to compute those parameters. � � ��� � � ��� �� � �� , (2) � � �� � , (3) where ��� is the maximum stress observed in the experimental strain vs. stress curve, � is its corresponding strain, and is the Young’s modulus of the fibres. 3. Experimental 3.1. Material description and mechanical test Experiments with E-glass fibre bundles tex 1200 (weight in grams per 1000 meters of fibre) were performed in the Zwick Z250 universal testing screw-driven machine at a strain rate of 0.001 �� . Specimens with 10 mm gauge length were glued to threaded ends for mounting onto the testing rig (Fig. 1). The load was measured by a 20 kN load cell mounted on the crosshead of the machine. The relative displacement between reflective bands attached to the ends of the specimen was recorded with a laser extensometer EIR-L05 (1 µm resolution).

Fig. 1 Experimental setup and specimen geometry