PSI - Issue 2_B

Sabrina Vantadori et al. / Procedia Structural Integrity 2 (2016) 2889–2895 S. Vantadori et al./ Structural Integrity Procedia 00 (2016) 000–000

2891

3

(a)

(b)

L

L



a 2

W

W

a 1

a a 0

a 0

B

B

S

S

Fig. 1. Crack propagates under: (a) pure Mode I; (b) Mixed Mode.

The initial compliance, i C , is used to calculate the elastic modulus, E (Tada et al. (2000)):   C W B E S a V i 2 0 0 6  

(1)

where S , W and B areloading span, depth and thickness of the specimen, respectively, 0 a is the notch length (Fig. 1(a)), i C is the linear elastic compliance. Further, the parameter ( ) 0  V is expressed as follows (Tada et al. (2000)):

W a

0.66

  0 

2

3

0

0.76 2.28

3.87

2.04

with

(2)

V

 

















0

0

0

0

2

1





0

Therefore, if the crack propagates under pure Mode I loading, the effective critical crack length, a , is determined through the following equation, by employing an iterative procedure (Tada et al. (2000)):   C W B E S aV u 2 6   (3) where u C is the unloading compliance, and    V is obtained from Eq.(2) by replacing 0 a with a . Since a stable three-point bend test cannot be performed in some cases, the value u C can approximately be computed by assuming that the unloading path will return to the origin. Finally, the Mode I critical stress-intensity factor, S IC K , is computed by employing the measured value of the peak load, max P , as follows (Tada et al. (2000)):

3

2 W B K P S S IC  2 max

( ) 

(4)

 a f

where:

2

 1 2 1 (1 ) (2.15 3.93 2.70 ) 3/ 2            

W a

 

 ( ) 1 1.99 

with

(5)

f





