PSI - Issue 13

Sergiy Kotrechko / Procedia Structural Integrity 13 (2018) 11–21 Sergiy Kotrechko / Structural Integrity Procedia 00 (2018) 000–000

17

7

Weibull approximation. Respectively, we obtain the expression for

f σ :

[

] m 1    

(

)

   

ln

P

1 1

−

f

σ = σ +

(4)

f

th

V

ρ

f

Number of the crack nuclei, forming inside of the volume unit, ρ , depends on temperature T . Data analysis, executed by Kotrechko (2013) and Kotrechko and Mamedov (2016), enables in the first approximation to express this dependence in the form, suitable for practical employment, namely:

th Y ρ ≈ ατ

(5)

where α is the coefficient; th with the conventional one:

Y τ is the thermal component of yield stress Y σ . This dependence may be approximated

1

( ] { C C C e T × − −  ln exp 2 3 1 ) [

th Y τ =

(6)

3

where e  is the rate of local plastic strain within the “process zone”; 1 C , 2 C , 3 C are the constants. For typical RPV steels 1033 1 = C MPa, 0 00698 2 . = С 1 Т − , 000415 0 3 . = С 1 Т − . For irradiated RPV steels the dependence (5) can be used in the temperature range from -140 0 С to + 100 0 С. As follows from the results of computer modeling [Kotrechko et al. (2001)], for typical ferritic steels, the value of m should be ≈ 2. It should be noted that the exponent in the dependence describing the scale effect in the Master of the curve is equal to "4", provided that m = 2. The value f V should depend on the crack front length B , the probability f P and the value of the normalised load at the moment of failure IC Y J σ / (where IC J is the critical value of I J -integral, Y σ is the value of yield stress). Accounting for above mentioned, the expression for f σ may be presented as:

1

λ

  

  

ln th Y

σ = σ + σ

(7)

f

th

u

P

1

−

τ

( ) f u V

2 λ = σ α

where λ is the coefficient ( ), which magnitude depends on the fluence and may be determined applying calibration by the experimental evidence for surveillance specimens at fixed values of B , P and IC Y J σ / . The idea of this calibration procedure is demonstrated in Figure 4. It consists in determining the values of the critical temperatures for the initial unirr c T and irradiated irr c T metal, at which fracture of a specimen with a crack is realised at a fixed value of IC Y J σ / . This condition is satisfied at the points of intersection of the temperature dependences of fracture toughness IC K with a curve ( ) f T K IL = , that is constructed for fixed values of IC Y J σ / :

  

  

J

− ν σ

Y

Y I

= K E IL

×

(8)

2

σ

1

where E is the shear modulus; ν is the Poisson’s ratio.