PSI - Issue 21

Amir H. Benvidi et al. / Procedia Structural Integrity 21 (2019) 12–20 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

15

4

     

2

(5 8 )(1 ) 4 (5 3 ) 4 K     

K

plane strain

Ic

2

2      2 t Ic

(2)

R



C

plane stress

t

It should be noted that the above equations have established for linear elastic materials with small strain. In fact, the ASED criterion for hyperelastic materials with high strain behavior requires nonlinear analysis. In order to calculate the critical value of , for cracked specimens, Heydari-Meybodi et al. (2018) presented a novel method. This method which is based on the nearly uniaxial state of stress around the crack tip, assumes that the amount of energy required for crack growth is equal to the fracture energy of the dumbbell-shaped specimens under the uniaxial tensile test. Accordingly, the critical value of SED can be calculated after selecting an appropriate hyperelastic material model for target rubber and then, by substitution of the final stretch of the specimen under the uniaxial tensile test ( ) in the selected model. In other words, the following relation can be used for determination of in a cracked rubber: In addition, the critical radius can be obtained by intersection of the graph ̅ (values of SED) in terms of ̅ (different radii of control volume) with the horizontal line of (critical SED). Indeed, as shown schematically in Fig. 1, for an arbitrary sample and in a critical condition (i.e. when the experimental rupture load is applied in the finite element model), different values for radius of control volume ̅ (e.g., R 1 , R 2 , R 3 ) are considered in the finite element simulation and for each case, the corresponding value of ̅ (e. g. , 1 , 2 , 3 ) is obtained. Afterwards, the graph of ̅ versus ̅ is plotted and the point where ̅ meets can be considered as the critical radius . 1 2 3 1 2 3 1 2 3 1 ,      ( , ,    ) ,    , : c Critical values of principal stretches c ten c c ten c c c c c c c W W           (3)

4.5

4

3.5

2 ASED (MJ/m 3 ) 2.5 3

1.5

1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Radius of control volume (mm)

Fig. 1. A schematic representation for determination of the value of R c .