PSI - Issue 5

Behzad V. Farahani et al. / Procedia Structural Integrity 5 (2017) 920–927 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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release rate criterion in the presence of 10 integral contours in front of the crack tip in ABAQUS. All obtained mode I SIF results compared to the ASTM solution in addition to the deviation values are shown on Table 2.

Table 2: Mode I stress intensity factor range for compact tension specimen. a [mm] ∆ [ . 0.5 ] ∆ [ . 0.5 ] ∆ [ . 0.5 ] ∆ [ . 0.5 ] Dev. % DIC & ASTM * 12.98 285.41 277.17 286.53 282.42 -2.89

Dev. % FEM & ASTM **

Dev. % RPIM & ASTM ***

Dev. % FEM & DIC #

Dev. % RPIM & DIC ##

Dev. % RPIM & FEM ###

0.39 -0.61 -1.30 -2.18 -3.05 -2.89 -2.88

-1.05 -1.62 -1.70 -2.94 -2.72 -1.48 -2.40

3.38 1.00 0.97 4.54 -3.56 -0.88 -2.96

1.90 -0.02 0.56 3.73 -3.23 0.56 -2.48

1.45 1.02 0.40 0.78 -0.34 -1.44 -0.50

14.07 15.26 17.01 20.56 21.74 22.48

306.08 330.55 371.27 481.04 529.85 564.95

301.20 323.12 347.40 483.57 519.10 565.39

304.21 326.25 363.18 466.36 514.53 548.65

301.14 324.94 360.36 467.93 522.03 551.39

-1.60 -2.25 -6.43 0.53 -2.03 0.08

* [(∆ − ∆ ) ∆ ⁄ ] ∗ 100 ** [(∆ − ∆ ) ∆ ⁄ ] ∗ 100 *** [(∆ − ∆ ) ∆ ⁄ ] ∗ 100 ### [(∆ − ∆ ) ∆ ⁄ ] ∗ 100 Furthermore, the opening strain variation, , in terms of distance from the crack tip was evolved for different crack growth stages for DIC, FE and RPIM analyses plotted in Fig. 3. Moreover, the opening strain contour obtained for = 21.74 ( ) from DIC, FE and RPIM meshless analyses as shown in Fig. 4. # [(∆ − ∆ ) ∆ ⁄ ] ∗ 100 ## [(∆ − ∆ ) ∆ ⁄ ] ∗ 100

14.07 mm - DIC 17.01 mm - DIC 21.74 mm. DIC

14.07 mm - FEM 17.01 mm - FEM 21.74 mm - FEM

14.07 mm - RPIM 17.01 mm - RPIM 21.74 mm - RPIM

0,008

0,006

0,004

Strain YY

0,002

0

-0,002

12

17

22

27

32

37

Distance to the notch tip [mm]

Fig. 3. Strain variation in front of the crack tip.

(a) (c) Fig. 4. Opening strain, , contours obtained for = 21.74 ( ) ; (a) DIC, (b) FE and (c) RPIM meshless analyses. (b)