PSI - Issue 18

Ivica Čamagić et al. / Procedia Structural Integrity 18 (2019) 205 – 213 Sergio Cicero et al./ Structural Integrity Procedia 00 (2019) 000–000

208

4

ν - Poisson’s ratio and E – Elasticity module. Stress intensity factor Ki for SEB specimens is calculated using the following expression:

 B B W F S i 1 2   





(4)

0 a

K

f

W







i

3 2

N

whereas for CT specimens:

B B W F i  

(5)





i a

K

f

W









i

1/ 2

N

The geometry term f(a0/W), in the case of SEB specimens, is determined as:



  W W W a a    0 0 1



0 a

1,99





   

   





0 a

1 2

3

W









0 a

2

2,15 3,93 

 3 2 2,7

W



(6)





0 a

f

W







0 a

0 a

2 1 2 

1 W W 

and for CT specimens:









i a

i a

   

   

2

0,866 4,64 

13,32

W

W









i a

2

W







 5,6 / a i



i a

3

4

14,72

/

W

W





(7)





i a

f

W





 3 / 2

i a

1

/

W



Plastic component of the J-integral is calculated based on the following expression [15]:      pl i pl i ( 1) ( ) a a  

B A A

  

        1

  

  

  

(8)

1

J

J

i

i

i





i 

( )

 ( 1)

pl i

pl i

b

b

i

N

i

where:

B – specimen thickness; a 0 – initial fatigue crack length; A pl – plastic energy component; S – span between the supports; B N – specimen net width;  i = 2 – SEB specimen coefficient;  i = 2 + 0,522 b i /W – CT specimen coefficient;  i = 1- for SEB specimens and  i = 1 + 0,76 b i /W – for CT specimens.

Based on the obtained data, a J-Δa curve is drawn, and the regression line is then constructed on it, according to standard ASTM E1152 [13]. Critical value of J-integral, J Ic , is then obtained from this regression line. By knowing the values of J Ic , it is possible to calculate the critical stress intensity factor (fracture toughness), K Ic , for plane strain, using the following relation:

2 1     J E K Ic Ic

(9)

Calculated values of critical stress intensity factor are given in table 5, for specimens with the notch in the PM, tested at room temperature and at the elevated temperature of 540°C, [15]. It is important to note that the calculation of fracture toughness for plane strain used different elasticity module values for room temperature (210 GPa) and for elevated temperature (cca 160 GPa for 540°C). Typical F- δ and J -Δ a diagrams for specimens taken out of the parent material, tested at room temperature and the elevated temperature of 540°C are not shown here, due to the scope of this paper [15]. The influence of test temperature