PSI - Issue 28

Vasilii Gorokhov et al. / Procedia Structural Integrity 28 (2020) 1416–1425 Author name / Structural Integrity Procedia 00 (2019) 000–000

1418

3

To describe the creep strain rate Ф

ij e  the creep model of unirradiated material was used (Kapustin et al. (2015),

Kapustin et al. (2008)) that takes into account the effect of irradiation:

Ф e e F T c c ij ij    

,

( , θ,Ф)

where c ij e  is creep strain rate of unirradiated material (Kapustin et al. (2015), Kapustin et al. (2008)); ( , ,Ф)  F T c is the function which takess into account the effect of the neutron flux Ф on the strain rate of thermal creep; θ is the parameter characterizing the level of stresses at the considered point of the material associated with the deviator of the acting stresses ij σ  the initial ultimate creep of the irradiated material Ф C by the ratio:

2

2 Ф ( ( )) σ σ ( ( )) C T C T ij ij    

.

θ



Ф

The initial ultimate creep Ф C depends on the temperature and neutron flux Ф : ( ,Ф) Ф Ф C C T  . Function ( ,θ,Ф) F T c is determined based on the results of creep experiments on specimens at various parameter values , θ and Ф T . In view of complexity and high labor intensity of such experiments, a simplified approximation of this function is used further in the form: ( ,θ) Ф ( ,θ,Ф) 1    FC T F T c , where ( ,θ) FC T is independent of flux Ф function that takes into account the irradiation effect on strain rate of thermal creep and which can be constructed on the basis of experiments with a fixed value of the flux. The dependence of the initial ultimate creep of irradiated material Ф C on the current values of temperature and neutron flux is also presented in the form of the simplest approximation: ( ,Ф) ( ) ( ,Ф) Ф C T C T FP T c   , where ( ,Ф) FP T is the function that takes into account the effect of irradiation on the radius of the initial ultimate creep, depending on the temperature and the value of neutron flux Ф; ( ) C T c is the radius of the initial creep surface of the unirradiated material. As the variable that determines the damage accumulation process under creep of the irradiated material, a fraction of dissipation energy is used the change of which by the loading step V  is determined by the ratio (Kapustin et al. (2015), Kapustin et al. (2008)):

Ф

σ e V      .

ij

ij

The corresponding change in the damage function ψ  and the measure of damage ω  under creep is taken in the form (Kapustin et al. (2015), Kapustin et al. (2008)):

, ω ω ψ 1       s s s ,

R V V Ф

ψ 

 

where is the ultimate value of the dissipation energy during creep, corresponding to the current stress-strain state (SSS), characterized by the parameter П, effective temperature T and the value of the neutron flux Ф; (T) s s  is material function; ω is accumulated value of the damage measure. The dependence of the function R V Ф on the parameter of the SSS type П, temperature T and the neutron flux Ф, is taken on the basis of relationship: ( , П,Ф) Ф Ф Т V V R R 