PSI - Issue 13

Leonardo Giangiulio Ferreira de Andrade et al. / Procedia Structural Integrity 13 (2018) 1908–1914 Leonardo G. F. Andrade and Gustavo H. B. Donato / Structural Integrity Procedia 00 (2018) 000–000

1912

5

from ASTM can be found in the second line of Tab. 2 – they represent the weights of the five points of measurement (edge, center and three equidistant points) along the crack front. Since the errors observed for high curvature conditions (high T/B ) exceed ASTM limits, a new proposal based on the obtained numerical analyses was developed to compute an adapted equivalent straight crack taking tunneling into account. Once tunneling level T was known from the models, a nonlinear optimization algorithmwas used to determine the best set of weights β that lead to an equivalent crack size representative of the numerically found compliance. All details can be found in Andrade and Donato (2017). Table 2 presents selected results for W/B=2 and W/B=4 , while the grey markers in Figs. 2(c-d) represent the application of such solutions to T = 2, 4 and 6 . It can be realized a remarkable reduction on C DELTA for all presented conditions, which also happened to others studied. Experimental validation is being conducted, but his result has the potential of considering more samples valid for fracture testing, reducing of cost and time.

0.079 0.157 0.236 Relative tunneling level T/B

0.157 0.315 0.472 Relative tunneling level T/B

0

0

-6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 0.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 0.5

-9 -7 -5 -3 -1

(a)

(b)

B=25.4mm W/B=2

B=12.7mm W/B=4

C DELTA

C DELTA

a/W=0.2 a/W=0.5 a/W=0.7 ASTM lim.

a/W=0.2 a/W=0.5 a/W=0.7 ASTM lim.

-15 -13 -11

0

2 6 Tunneling level T ( mm ) 0.079 0.157 0.236 Relative tunneling level T/B 4

0

2 6 Tunneling level T ( mm ) 0.157 0.315 0.472 Relative tunneling level T/B 4

0

0

-9 -7 -5 -3 -1 1

B=25.4mm W/B=2

B=12.7mm W/B=4

(c)

(d)

C DELTA

C DELTA

ASTM

ASTM

Proposal

Proposal

a/W=0.2 a/W=0.5 a/W=0.7 ASTM lim.

a/W=0.2 a/W=0.5 a/W=0.7 ASTM lim.

-15 -13 -11

0

2 6 Tunneling level T ( mm ) 4

0

2 6 Tunneling level T ( mm ) 4

Fig. 2 . C DELTA versus tunneling level for SE(B) specimens with: (a) B = 50.8mm, W/B=2 ; (b) B = 25.4mm, W/B=4. (c) Comparison between the ASTM E1820-2018 and the developed proposal for SE(B) B=25.4 mm W/B=2 and; (d) SE(B) B=12.7 mm W/B=4 . a/W eq.sim. = � /W 1 + � a/W 2 + � a/W 3 + � a/W 4 + � a/W 5 (5) Table. 2. Groups of β coefficients from ASTM (independent on T ) and proposed for the studied SE(B) conditions. Condition (Center) β 1 β 2 β 3 β 4 β 5 (Edge) ASTM statements 0.125 0.250 0.250 0.250 0.125 SE(B) W/B = 2 -0.0051T + 0.1462 -0.0096T + 0.2230 -0.0203T + 0.3227 0.0193T + 0.2139 0.0157T + 0.0943 SE(B) W/B = 4 -0.0106T + 0.1349 -0.0250T + 0.2325 -0.0262T + 0.2826 0.0343T + 0.2415 0.0275T + 0.1085