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

1913

6

3.2. Plasticity effects on elastic unloading compliance C The effects of plasticity on compliance were assessed for all studied materials and geometrical features, including B=50.8mm ( W/B=1 ), B=25.4mm ( W/B=2 ) and B=12.7mm ( W/B=4 ). Since the effects and trends found are very similar, Fig. 3 illustrates the results of C DELTA vs. CMOD for SE(B) 1T , W/B=2 . Table 7 provides additional data, for example, regarding the reference compliances C 0 for the absence of plasticity. All relative crack depths were calculated based on numerical compliance using the fifth order polynomials from ASTM E1820 (2018). Compliance variation due to plasticity stayed within 5.5% for all studied conditions, which means a maximum of 8% deviation in crack size prediction. However, it is worth noting that the impact on C DELTA for a same CMOD yielded a more severe deviation for shallow cracks ( a/W = 0.2 ) and for low hardening materials ( n=10; n=20 ). In addition, a closer look to small CMODs reveals a slight decrease on C DELTA , followed by an increase. Additional modelling is being conducted for clarifications and mentioned phenomena are under experimental validation now. (a) SE(B), B=25.4mm

n5

n10

n20

SE(B), B=25.4mm

-1.0 1.0 3.0 5.0 7.0

n5

n10

n20

a/W = 0.5

-1.0 1.0 3.0 5.0 7.0

a/W = 0.2

C DELTA (%)

C DELTA (%)

0

1

2

3

4

5

0

1

2

3

4

5

CMOD (mm)

(b)

CMOD (mm)

(c)

7 0 SE(B), B=25.4mm

n5

n10

n20

Tab. 7. Plasticity study data for B=25.4mm , W/B=2 .

-1.0 1.0 3.0 5.0 7.0

Highest C DELTA impact (%)

Highest a/W impact (%)

C 0 (mm/N .10 -6 )

a/W = 0.7

Material

a/W

2.56 2.86 2.85 2.06 3.93 5.16 1.35 3.07 4.25

6.79 7.04 7.04 0.75 1.41 1.84 0.25 0.57 0.78

n5

0.2

1.32

n10 n20 n10 n20 n10 n20 n5 n5

C DELTA (%)

0.5

6.56

0.7

23.47

0

1

2

3

4

5

CMOD (mm)

Fig. 9. C DELTA vs. increasing CMOD (and thus plasticity) for the SE(B) B=25.4mm , W/B=2 . All materials and a/W = 0.2, 0.5 and 0.7 . 4. Concluding Remarks  The results allowed describing and understanding the effects of crack tunnelling and plasticity on compliance solutions applicable to SE(B) specimens.  Reduced deviations in compliance ( C DELTA under ± 0.5% ) were observed within ASTM limits, showing that the standardized criterion is robust if its requirements are met. However, once tunneling increases and violates ASTM , deviations increase and errors larger than 13% were observed for high crack tunneling T .  Such scenario can represent loss of samples during real tests or, if not detected, errors in crack size estimations leading to risks for the accuracy of fracture mechanics testing, motivating the development of new proposals.  The proposals to incorporate T on equations to calculate equivalent crack sizes revealed good potential to extend the validity of elastic unloading compliance solutions. However, experimental validation is being conducted.