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) 000–000

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this method is applied for MMB tests and a closed-form formula for measuring fracture energy in MMB test setups has been developed.

Fig. 5. Schematic representation of FPZ and the crack equivalent concept.

2.1.3 DCB specimen Based on Timoshenko beam theory, the compliance C=δ/P of the DCB specimen for an isotropic material is (Moura et al., 2008): C � � E 8 b a h � a � h � � 3�� 5 � �� � (8) in which h is the height of the adherent and half of the adhesive layer, b is the width of the specimen, υ is the poison ratio and a is the crack length. In this equation (8), the effect of bending as well as shear is considered. Considering an adhesively bonded DCB specimen, (Moura et al., 2008) proposed an equivalent modulus of elasticity to consider the couple effects of dissimilarity of the materials between adherents and the adhesive as well as stress concentration ahead of the crack: E �� � 8�a � � �� C � bh � �a � � �� � h � � 3�� 5 � �� � (9) Where a 0 is the initial crack length, C 0 is the initial Compliance and Δ is a crack length correction taking into account the effect of root rotation (Williams, 1989).By the introduction of calculated equivalent modulus of elasticity (equation (9)) into the compliance of the beam, the following equation can be derived which its answer gives the equivalent crack length a e : 8a �� E � bh � � 2��� � ��a � 5E � bh � C � �� (10) By such a procedure, the fracture process zone ahead of the crack tip can be simply considered as it shows it effect on the compliance of the system resultant from the load-displacement curve. By using the Irwin-Kies equation: G � � P � 2b d d C a (11)