PSI - Issue 28

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

2047

5

Fig. 3. Peridynamic failure model a) bond force versus stretch b) calculation of energy break bonds per unit area

(9)

s

2

cs



0

  

,

w fds

0

0

2

0

(10)

s

2

1 s cs w fds s s      . 0 1 1 0 ( ) 2

0

Substituting Eq.(9) and Eq.(10) into Eq. (8) w can be calculated as: 0 1 , 2 cs s w  

(11)

where the parameters 0 s and 1 s denotes the critical stretch values at the beginning of softening stage and final failure, respectively. It is possible to link the energy required to break all the bonds per unit area (as given in Fig. 3b) to the macroscopic fracture toughness C G . Therefore, the following relation between the C G and w in can be written as: 1 cos ( / ) 2 2 z    (12) By evaluating the integral in Eq. (12), the fracture toughness can be obtained in terms of 0 s and 1 s as: 5 0 1 . 10 C cs s G   (13) In order to determine 0 s and 1 s , it is assumed that the ratio of 0 f   in Turon et al. (2010) is the same with 1 0 s s in the modified PD material model. 3. Problem Description In the current paper, static solutions of ENF and MMB test specimens are considered by using analytical, PD and FEA method. The ENF and MMB tests are explained and the analytical solutions are found using Corrected Beam Theory (CBT) given in the following subsections. 0 0 0 sin w d d d dz       . C z G      

3.1. The ENF Test

Mode II interlaminar fracture toughness II G can be determined conducting an ENF test ASTM D7905 which is carried out with a simple three-point bending specimen that has an interface crack length a . In ENF test, the specimen is constraint with a pinned support at one end and a roller support at the other end. The load P is applied at the mid span as shown in Fig. 4.

Fig. 4. Representation of ENF test.