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

1609

� � � 3� 4 � L L � � � � � � � L L � � ��

(14)

by this arrangement, the compliance of the system is as follows: C � � 3� 4 � L L � � C � � � � � L L � � C ��

(15)

considering the compliance for mode II (ENF test) based on beam theory (Moura and Morais, 2008): C �� � 3a � � �L � 8Ebh � � 10 3 G L bh by introducing equation (8) and (16) into equation (15), the compliance of the MMB set up can be derived as follows: C � � �� � � � � � � � � � � � � � � � � � � ��� � ��� �� � � �� � � � � � �� � ��� � ���� � � �� � � � �� � . (17) To derive equivalent modulus of the system, the initial condition is introduced to the compliance. These conditions consist of replacing a by (a 0 + ) and a 0 for mode I and II respectively and considering C 0 which is the initial compliance of the load-displacement curve. By this arrangement, the effect of the adherents, stress concentration and the root rotation in the mode-I are considered. Inserting the initial condition into equation (17), the equivalent modulus can be derived as follows: E �� � ��3�0 �a � � �� � � 1�� h � �a � � ���1 � ��� � B�15a �� � 10L � � 40bh � C � ′ (18) where � � � �� � � � � � � B � � �� � � � � C � ′ � C � � 10 3 G B b L h by replacing the elastic modulus in equation (17) by the equivalent modules, one can derive a third order equation, which can be solved for the equivalent crack length as follows: � 8 4 E � � 3B �� bh � ����� � � a �� � �4��1 � �� 5E �� �����b�h � � � a � � BL � 4E �� bh � � C � ��������� � � � 0 (19) the equivalent crack length a � can be calculated by solving the above equation by using the method explained in (Moura et al., 2008): (16)