PSI - Issue 28

Eda Gok et al. / Procedia Structural Integrity 28 (2020) 2043–2054 Gok et al./ Structural Integrity Procedia 00 (2019) 000–000

2048

6

II G and P can be written using Linear Elastic Fracture Mechanics as follows: 2 , 2 II P dC G B da       

The relation between

(14)

where B is the width, and / C P   is the compliance of the specimen. Analytical solution of ENF problem can be obtained with several theories such as: Corrected Beam Theory (CBT), Simple Beam Theory (SBT) and Compliance Calibration Method. Moura and Morais (2008) stated that CBT gave better results since the mentioned method considers shear and beam rotation at the crack tip. For CBT, expression for compliance C is obtained using Timoshenko beam theory Wang and Williams (1992) and can be calculated as: 3 3 where 11 E is the longitudinal modulus of elasticity, 13 G is the out of plane shear modulus, L is the half length of the specimen and h is the half thickness of the specimen. II  in Eq. (15) denotes the correction factor for Mode II loading due to the beam rotation. In the literature, it is calculated as 0.42 II I    Wang and Williams (1992) where I  is the correction for Mode I and can be calculated as Fernández et al. (2013): 1 1 2 2 2 11 22 11 1.18 E E E              (16) 3 BE h    13 G Bh 11 3( ) 2 3 , L 10 8 II a L C   (15)

    

   

  

3 2 

,

h

 

  

 

 

I

11

G

  

1.18

G

E E



12

12

11 22

where 12 G is the in plane shear modulus, and 22 E is the transverse modulus of elasticity. Substituting Eq. (15) into Eq. (14), fracture toughness for Mode II loading II G might be obtained as: 2 2

(17)

2 B E h   3 11 9 ( 0.42 ) P a 16 I

,

G

F



II

v

where v F represents the correction factor for the large displacement of the end blocks. The value of v F might be calculated using the formulations using large beam deflection theory given in Feito (2012). 3.2. The MMB Test The MMB test is used to determine interlaminar fracture toughness G of continuous fiber reinforced composite materials at various Mode I and Mode II loading ratios ASTM D6671M. The MMB test specimen is a combination of Double Cantilevered Beam (DCB) and ENF specimens as shown in Fig. 5.

Fig. 5. Representation of MMB test.