PSI - Issue 18

B. Marques et al. / Procedia Structural Integrity 18 (2019) 645–650

648

4

B. Marques et al. / Structural Integrity Procedia 00 (2019) 000–000

Figure 3 shows the relation between crack opening and crack closure levels. The crack opening level is higher than the crack closure level and a value of 0.9 was obtained for the ratio between both parameters. It is interesting to notice that the opposite trend is obtained experimentally, i.e., the crack opening level is smaller than the crack closure level. Figure 4 plots plane strain crack closure state versus plane stress crack closure. The crack closure level is quantified by U clos =(F open -F min )/(F max -F min ) which quantifies the portion of the load cycle during which the crack is closed. For values of plane stress crack closure up to 30% there is no crack closure for plane strain. In fact, it is well known that the level of crack closure is significantly higher for plane stress state compared with plane strain state. The stress triaxiality inhibits plastic deformation reducing the crack closure phenomenon. However, above 30%, a linear trend is observed, with a slope higher than 45º, which means that the variation of plane strain closure is faster than the variation of plane stress closure.

100 150 200 250 300 350

60

2050-T8 304L 7050-T6 6082-T6 18Ni300

50

F

40

B

2050-T8 304L 7050-T6 6016-T4 6082-T6 18Ni300

30

U clos (dp)

F open [N]

20

U dp = 1.45 U tp - 47.97

0 50

10

0

0 50 100 150 200 250 300 350

0

10 20 30 40 50 60

F close [N]

U clos (tp)

Fig. 3. Crack opening level versus crack closure level.

Fig. 4. Plane strain closure versus plane stress closure.

The numerical predictions were compared with two literature models. Kujawski proposed that:

(1)

K ) 0.5 K K (K max    

 K + is the positive part of  K, therefore the K K parameter is based on the premise that the negative part of  K does not contribute to crack growth. Figure 5 shows that  K K gives values higher than the numerical predictions of  K eff . The dashed line was obtained multiplying the filled line by a factor of two, and the results are between these two lines. Antunes et al. (2015), using results for the 6016-T4 aluminium alloy, proposed that:

 

eff K 0 ys eff R m( K ) (R )    

(2)

where

K

ys max 

m 47.311(  

) 0.0993

(3)

