PSI - Issue 23

Sergiy Kotrechko et al. / Procedia Structural Integrity 23 (2019) 413–418 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

417

5

decrease in the magnitude of the shape parameter m . This is in good agreement with the data of Ruggieri (2001). Based on these data, temperature dependences of fracture toughness C K I for the studied steels were plotted (Fig. 3 ( a and b )). The algorithm of calculations of fracture toughness and fracture probabilities is as follows: 1. For each th j stage of loading j K I , the values of equivalent plastic strain i e and normal tensile stresses i YY  in each th i finite element were calculated using the finite elements method (software ABAQUS). 2. Further, the probability of the cleavage initiation in th i element was calculated:

   

   

   m

  

i i

i YY

V V

       1 exp i P

th

(7)

u

0

1

i V 0 is the volume per one crack nucleus (

, value of i  was

i

i V is the finite element volume;



where

i V 0

calculated according to equations (1), (2) and (3)). 3. Then, the total probability of cleavage initiation in specimen can be calculated:   P P n n N n i      1 where N is the number of finite elements falling into the yield region. The step size and the number of loading stages were chosen in such a way as to obtain

(8)

I K values when the

probability of cleavage initiation  P is 5%, 50% and 95%. Figures 3 ( a and b) show the calculated temperature dependences of fracture toughness for RPV and cast steel. Also, here are experimental data for C K I . According to these data, the calculated dependences describe well both the regularities of C K I increase with increasing temperature T and the limits of its scatter at a constant T value. It should be emphasized that in this case, the fact is taken into account that the increase in C K I is not only due to a fall in the yield strength, but also due to a decrease in the rate of generation of the crack nuclei in the vicinity of major crack tip (dependences (3) and (4)). The latter has not been accounted in the conventional concepts of local approach. This usually results in an underestimation of the slope of the C K I temperature dependence. The higher the strength of steel and the higher the temperature for which C K I is determined, the greater the error due to ignoring the temperature dependence of 0 V .

0.5 )

1/2 )

95 %

Cast steel

RPV steel

250

250

50 Fracture toughness, K IC (MPa m 100 150  th = 720 MPa m = 8  u = 3700 MPa 200

50 Fracture toughness, K IC (MPa m  th = 1100 MPa m = 5.4  u = 6835 MPa 100 150 200

50 %

95%

50%

5 %

5%

-160 -140 -120 -100 -80 -60 -40 -20 0 0

-180 -160 -140 -120 -100 -80 -60 -40 0

Temperature, T ( 0 C)

Temperature, T ( 0 C)

Figure 3. The temperature dependences of fracture toughness for RPV steel ( а ) cast low-alloyed manganese steel ( b ): circles designate the experimental evidence; lines are the calculation results.