PSI - Issue 13

Lapin V.N. et al. / Procedia Structural Integrity 13 (2018) 1171–1176 Lapin V.N. and Cherny S.G. / Structural Integrity Procedia 00 (2018) 000–000

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Рис. 3. (a) Comparison of the kinking angle at the first step of the fracture propagation obtained by the implicit criterion at fixed ∆ R = 0 . 001 m with the experiment (solid line) and MVK and MVG criteria (dotted and dash-dotted lines): 0 – Experiment, 1 – β = 0 ; 2 – β = 0 . 25 ; 3 – β = 0 . 5 ; 4 – β = 0 . 75 ; (b) Comparison of the kinking angle at the first step obtained at fixed β = 0 . 5 : 1 – ∆ R = 0 . 0005 m ; 2 – ∆ R = 0 . 001 m ; 1 – ∆ R = 0 . 002 m .

Рис. 4. (a) Kinking angle at iterations of the first step; (b) Difference between kinking angle at the current iteration and the last one. Line index coincides with the iteration number.

kink angles obtained from 2DMTS criterion of Erdogan and Sih (1963) here and ones taken from Lazarus et al. (2008) coincide everywhere except the near free surface area. It should be noted that implicit criterion with β = 0 . 5 gives the kinking angle distribution that is close to the experiment ones. To show the influence of the weight parameter β and fracture increment ∆ R the distributions of kinking angle calculated at various β and ∆ R and are shown in Fig. 3 a) and b) correspondingly. One can see that for ∆ R = 0 . 001 m , values β = 0 and 0 . 25 give good agreement with MVK criterion and β = 0 . 5 gives kink angle distribution that is closed to the experiment. But the implicit criterion gives almost linear distribution of kinking angle whereas criteria proposed by Lazarus et al. (2008) demonstrate negative second derivative. It should be subject of the further investigation. The kink angle distributions along the front at iterations for ∆ L = 0 . 001 m , β = 0 . 5 are shown in Fig. 4 a). To show the convergence velocity the difference between the current iteration kinking angle and the final one are shown in Fig. 4 b) also. It is evident that 5-6 iterations are sufficient for the convergence of the iterative process and for determining the fracture front shape.

3.3. Fracture trajectory

Fig. 5 a) shows the shape of the fracture, computed at β = 0 . 5 , ∆ R = 0 . 001 m and the fracture paths obtained from different values of the fracture increment ∆ R . To visualize the trajectory, the intersection line of the crack surface and the sample boundary z = 0 . 01 m is use. It is highlighted in red in Fig. 5 (a). One can