PSI - Issue 28

1608 M.Z. Sadeghi et al. / Procedia Structural Integrity 28 (2020) 1601–1620 M.Z. Sadeghi et al./ Structural Integrity Procedia 00 (2019) 000–000 The following equation for fracture energy of the DCB tests was proposed which is based on the equivalent crack length (Moura et al., 2008): G � � 12P � E �� b � h � a �� a � � 1 � 5 � � (12) In this work, for calculation of crack length correction (Δ), a procedure was applied as it was recommended in (Moura et al., 2012). A numerical model for a DCB specimen with different initial crack lengths (30mm, 35 mm, 40 mm) was developed using Abaqus. Since there is a linear correlation between the third root of the initial compliance C 0 1/3 and the initial crack length a 0 (based on Euler-Bernoulli beam theory), the crack length correction Δ can be determined by measuring the point where such a linear correlation intersects the abscissa (a 0 ) axis (Fig. 6). Based on the described procedure, Δ was calculated to equal to 3.19 mm.

Fig. 6. Third root of initial compliance over different initial crack lengths.

2.1.4 MMB specimen Using the same approach explained in the previous section (mode I), one can develop a fracture energy formula based on equivalent modulus and consequently equivalent crack length for MMB tests. MMB test setup includes the combination of the DCB (mode I) and ENF (mode II) tests. Since the applied load to the MMB setup is the superposition of the mode I and II, therefore the corresponding loads can be derived as follows (Reeder and Crews, 1990):

Fig. 7. Superposition of the loads in the MMB setup

P � � � �� � � � � � P P �� � � �� � � � P

(13)

One can also divide the total displacement of the setup into two different modes (Reeder, 2003):