13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- As a common case, Kmin may depend on the test temperature. In [24] it was accepted that Kmin(T) = const and on the basis of large number of experimental data sets for RPV steels over low temperature range (on the lower shelf of KJC(T) curve) it was determined that Kmin= 20 MPa√m. In the present section the results are represented on calculation of Kmin as a function of temperature, Kmin(T), for RPV steels on the basis of local criteria (1) and (2). These results are calculated with the Beremin and Prometey models based on criteria (1) and (2) respectively. To obtain Kmin(T) the following considerations are used. (1) When calculating with the Beremin model the value of Kmin is taken as stress intensity factor KI when conditions (1a) and (1b) are satisfied for the unit cell nearest to the crack tip. (2) When calculating with the Prometey model the value of Kmin is taken as KI when condition (2a) is satisfied for the unit cell nearest to the crack tip. (For cracked specimens from RPV steels brittle fracture is controlled by microcrack nucleation condition (2a).) (3) For both models the unit cell size ρuc is taken to be equal to 50 μm. The dependence σY(T) was taken as obtained in [9] for RPV steel in initial conditions. For the Beremin model two values of the parameter S0 are taken as more typical for RPV steels [9, 10]: S0= 1300 and 1500 MPa. For the Prometey model three values of the controlling parameter σd0 are taken as σd0 = 1300, 1500 and 2000 MPa that corresponds to various estimations of σd0 in [9, 10]. It is important to note that when calculating Kmin(T) the critical parameters are taken as calibrating from specimens without cracks, i.e. from smooth tensile specimens. (4) Stress-and-strain fields near the crack tip are calculated by approximated solution of elastic-plastic problem represented in [9]. The calculation results are shown in Figure 4 for cracked specimens with 50 mm in thickness from RPV steel in initial condition. (Here maximum temperature is restricted by T=100oC as for higher temperatures brittle-to-ductile transition occurs for this steel.) As seen from Figure 4a Kmin(T) decreases over low temperature range and becomes constant at T>0oC for curve 1 and T>-75oC for curve 2. This behavior is caused by different controlling conditions in (1) for these temperature ranges: Eq. (1a) gives decreasing part and Eq. (2) gives const part. As seen from Figure 4b according to the Prometey model Kmin(T) is practically constant or slightly increasing (from 18 to 25 MPa√m for curve 3). (a) -200 -100 0 100 T, oC 0 10 20 30 Kmin, MPa√m 1 2 (b) -200 -100 0 100 T, oC 0 10 20 30 Kmin, MPa√m 1 2 3 Figure 4 The Kmin(T) curves calculated with the Beremin (a) and Prometey (b) models model for RPV steel: (a): 1 - S0=1300; 2 - S0=1500 MPa; (b): 1 - σd0 = 1300; 2 - σd0 =1500; 3 - σd0 =2000 MPa.
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