13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- curve as illustrated in Figure 3a where the decrease in σd models increasing neutron fluence. At the same time criterion (2) and the Prometey model may also predict a pure lateral shift of KJC(T) curve to higher temperature range [14]. It may be achieved by an increase of the parameter m0 with increasing neutron fluence F, i.e. an increase of “driving force” eff 1 T nuc m σ ≡σ + ⋅σ ε in condition (2a) (without the decrease in σd). For this case the calculated KJC(T) curves are shown in Figure 4b. It should be noted that the parameter m0, being to some degree sensitive to material microstructure, may depend on the particularities of plastic deformation in steels with radiation defects. It is clear that as a common case, irradiation-induced dislocation loops and precipitates may affect the geometry of dislocation pile-ups arrested by carbides and, hence, the coefficient m0. However, at present, the experimental data are too few to allow an analysis of this effect. Possible trends of this effect have been considered in [14]. In principle, the coefficient m0 may increase as F increases due to decrease of the width and blunting of dislocation pile-up near microcrack initiator that is a result of an increase of the density of radiation defects. Thus, criterion (2) provides a possibility to predict not only a change in KJC(T) curve shape but also pure lateral shift of KJC(T) curve to higher temperature range. It should be emphasize that any models based on the stress controlled criterion (1) predict a variation in the KJC(T) curve shape for any degree of embrittlement. This is because the KJC(T) dependence is determined according to criterion (1) by the σY(T) dependence. These models may predict lateral shift of KJC(T) only if the dependence of SC (or σu in terms of the Beremin model) on temperature and neutron fluence is a priori introduced, for example, as it is made in [21]. Thus, it should be concluded that at present the Prometey model based on criterion (2) is the only model that allows the prediction of lateral shift of KJC(T) curves without additional assumptions. (a) -200 -100 0 100 T, 0C 0 100 200 300 KJC, MPa√m 1 2 3 4 5 MPa ~ MPa ~ MPa ~ MPa ~ MPa ~ d d d d d 4000 5 6000 4 8000 3 12000 2 18000 1 −σ = −σ = −σ = −σ = −σ = (b) -200 -100 0 100 Т, оС 0 100 200 300 KJC, MPa√m m0=0.1 0.2 0.4 0.6 Figure 3. The KJC(T) curves calculated with the Prometey model for decreasing parameter σd and m0 = const (a) and for increasing function m0(F) and σd =const (b). (Specimen thickness is 25 mm and Pf = 0.5.) [14] 4.2. On minimum value of fracture toughness for RPV materials The Master Curve [24]] and Unified Curve [22] methods use the Weibull statistics to describe the scatter in KJC results and the effect of specimen thickness on KJC(T) curve. The fracture probability Pf and KJC is connected by the Weibull distribution function [24] ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − − = − − 4 min 0 min JC f K K K K P 1 exp , (6) where K0 is a scale parameter depending on the test temperature and specimen thickness; deterministic parameter Kmin is the minimum value of fracture toughness.
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