PSI - Issue 13

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

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Gb N d × ∆σ = α ν

(1)

where N d × is the product of bulk density of defects on their diameter; G is the shear modulus; b is the Burgers vector; α is the coefficient.

As a rule, α is considered as a parameter, characterizing the barrier effect of defect. However, as it was shown by Kotrechko et al. (2015), the value of α depends not only on the kind of defect (dislocation loops or precipitates), but also on density of these defects. At plastic deformation of irradiated RPV steels, defects of the various types resist simultaneously the movement of dislocations. In general case, a superposition of two components of hardening, namely, dislocation loops and precipitates, can be written as [Chaouadi and Gerrard (2005)]: where the upper script p is the superposition parameter that depends on the obstacle strength, which is a priory unknown. Usually, two limit cases are considered, namely: square-law superposition ( 2 = p , used for obstacles of comparable strength [Thomson (1996); Terentyev and Malerba (2012)]) and the linear superposition ( 1 = p , used for strong obstacles surrounded by high concentration of weak obstacles [Chaouadi and Gerrard (2005)]). An intermediate superposition law is applied if neither linear nor square-law superposition gives acceptable approximation of experimental data. p Y p Y 1 ∆σ = ∆σ + ∆σ ∑ Y p 2 (2)

Fig. 1. The effect of radiation hardening and radiation induced decrease in brittle strength on the shift of temperature of ductile-to-brittle transition, f T ∆ (scheme): unirr Y σ and irr Y σ are the yield stresses in initial and irradiated states, respectively; j is the effective value of overstress factor for crack or notch; unirr f σ and irr f σ are the critical cleavage stresses in initial and irradiated states; h T ∆ and b T ∆ are the temperature shifts due to radiation hardening and decrease in brittle strength.

The density of dislocation loops and precipitates, as well as their size distribution, depend on the chemical composition of RPV steel, fluence, and irradiation conditions. Kotrechko et al. (2015) have exhibited that for RPV steels of type 15Cr2 М oVA and 15Cr2NiMoVA and their welds under irradiation in reactors WWER440 and WWER1000, contribution to the hardening by dislocation loops and precipitates can be described with sufficient accuracy by a linear superposition. However, in general, the problem of selecting supercomposition law has not yet been solved. On the whole, it is necessary to develop advanced model of radiation hardening taking into account both the properties of individual defects, and the collective processes of interaction of a moving dislocation with an array of irradiation-induced defects. Copper content in RPV steels has a key influence on the type and kinetics of formation of precipitates and, accordingly, on the regularities of radiation hardening of these steels. At present, much attention is paid to ascertain the differences in the radiation hardening of steels with high ( 0.4 0.5% C Cu ≈ ÷ ) and low ( 0.05 0.07 % C Cu ≤ ÷ ) content of copper. This is due to the fact that copper is the center of formation of precipitates enriched with Ni, Mg, Si and P. As a result, in most RPV steels with a relatively high Cu content, the main contribution to radiation hardening was provided by CRPs, especially in the early stages of irradiation. A significant lessening in copper content in RPV steels of a new generation has made it possible to reduce their tendency to radiation hardening by decreasing the bulk density of copper-enriched precipitates (CRPs). However, it turned out that in such steels the Mn-Ni-Si rich precipitates (MNPs) form. This gives rise to intensive radiation hardening in the later stages of irradiation. In this connection, Odette and Lucas (1998) hypothesized the existence of so-called "late blooming phases" (LBPs). According to the authors, these phases should be formed at sufficiently