PSI - Issue 28

M.Z. Sadeghi et al. / Procedia Structural Integrity 28 (2020) 1601–1620 M.Z. Sadeghi et al./ Structural Integrity Procedia 00 (2019) 0 0–000

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Fig. 3. Load distribution and rotation angle in DCB setup. Here, P is the concentrated load applied in the system, θ is the rotation of the point in which load is applied (Fig. 3) and b is the width of the specimen. Later, Sarrado et al. (Sarrado et al., 2015) based on the same procedure, developed a closed-form formula for the determination of J-integral in the MMB tests They implemented their approach in the determination of fracture energy of the delamination process which showed a good agreement with the methods based on LEFM provided by . This model was later implemented successfully for measurement of interlaminar fracture toughness (Zhao et al., 2016). The J-integral formulae for the MMB test offered by Sarrado et al (Sarrado et al., 2015) is as follows: � � P b � L c θ � � � 1 2 � 2 c L � θ � � � 2 c L � 1 2 � θ � � � L c � 1� θ � � (7) where θ A,B,C, D are the points in which the load are applied (Fig. 4), P and b are the applied load and the width of the specimen respectively. In this work, the fracture energy of the DCB and MMB tests were measured using equations (6) and (7). For measuring the rotation at the load introduction points for DCB tests, two inclinometers were mounted on the upper and the lower adherents. For the MMB tests, four inclinometers were used to measure the rotation at the load points A, B, C and D. The effect of the weight of the loading lever is not considered in the formula since the weight of the apparatus lever is less than 3% of the applied loads in any of the MMB tests .

Fig. 4. Load distribution and rotation angle in MMB setup during loading.

2.1.2 Equivalent crack length method (ECLM) Since the classical methods for measuring fracture energies such as Corrected Beam Theory (CBT) or Compliance Calibration Methods (CCM) have some limitations such as the difficulty of detection of the fracture process zone around the crack tip or monitoring the crack growth in the propagation process, de Moura et al. (Moura et al., 2008) proposed a method for determination of the fracture energy for the DCB test. This method, which is based on the equivalent flexural modulus and equivalent crack length are capable of capturing the nonlinear effects in the crack tip and also is independent of monitoring the crack length. In the following, the procedure is briefly explained and then