PSI - Issue 18

5

Author name / Structural Integrity Procedia 00 (2019) 000–000

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

649

K

ys max

(R )

log( 0.835

) 1.755 

  

(4)

eff K 0



This model is expected to be valid for 0.015

60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

50

40

K K = (K max *ΔK) 0.5

30

2050-T8 2024-T351 304L

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

R eff

20

7050-T6 6016-T4 6082-T6 18Ni300

10

0

0

20

40

60

0

0.2

0.4

0.6

0.8

1

ΔK eff

R eff,model

Fig. 5. Numerical predictions versus Kujawski’s model.

Fig. 6. Numerical predictions versus Antunes’s model (plane stress).

Finally, Figure 7 compares results of CTOD, measured behind crack tip, with stress values predicted immediately ahead of crack tip. When the crack opens at the first node behind crack, the crack tip stress still is in compression (Point A). Below this point there is some variation of stress, which means that there are things happening at the crack above the opening load. However, the rate of variation above point A is significantly higher than below point A, which indicates that crack closure has an effect on crack tip fields. Note that this is not consensual in literature. The stress inversion occurs at point C, for a positive value of CTOD. 4. Conclusions The crack closure level was determined numerically using the finite element method for six materials and different load conditions. The crack closure level was defined 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. 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. For values of plane stress crack closure up to 30% there is no crack closure for plane strain. 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. A comparison was made with literature models. However, these models were not able to fit the numerical predictions, which is explained by the complexity of the crack closure phenomenon.