PSI - Issue 2_A

Xudong Qian et al. / Procedia Structural Integrity 2 (2016) 2046–2053 Author name / Structural Integrity Procedia 00 (2016) 000–000

2050

5

U

A  

(6)

J

avg

net

where net A measures the net intact area of the cracked section and U refers to the strain energy stored in the specimen,

0 2 U Md   

(7)



In Eq. 7, M denotes the applied bending moment on the cracked section of the specimen and θ indicates the rotation of the crack plane, derived from the measured CMOD value,

CMOD   ( ) a d W a

(8)

 





2

where a represents the crack depth, W refers to the specimen height (see Fig. 2) and d equals 0.56 for the SSE(B) specimen, derived from the deformed shape of the crack plane in a large-deformation finite element analysis. The η value in Eq. 6 derives by equating Eq. 6 with the average J value computed from the domain integral solution, or,

N

i U A B    net

B J

i i

(9)

total

where i J denotes the domain integral value computed at individual crack front nodes, i B refers to the length of the individual crack-front segment, and total B corresponds to the length of the entire crack front. The η value thus derived equals 2.97 for the SSE(B) specimen. Substituting Eq. 7 into Eq. 6 allows measurement of the average fracture toughness along the crack front for the SSE(B) specimens from the measured load versus CMOD relationship.

P f

1.0

0.8

0.6

0.4

0.2

T = -90 o C

0

0

300

600 900 1200 1500

(kJ/m 2 ) J avg

Fig. 4. Rank probability of the measured fracture toughness for SSE(B) specimens at -90 o C.

Figure 4 shows the rank probability of the measured fracture toughness for the SSE(B) specimens at -90 o C. The rank probability of the fracture failure follows,

0.3

i



(10)

P



i rank 

0.4

N

