PSI - Issue 48

Tamás Fekete / Procedia Structural Integrity 48 (2023) 302–309 Fekete / Structural Integrity Procedia 00 (2023) 000 – 000

308

7

The transient starts with an intense cooling phase on the time interval 0 , ... 1900 s; during this period, between 750 ... 1900 s, p increases up to the safety valve opening pressure ( ≈ 95 bar), then the valve opens and closes periodically with fluctuating system p around ≈ 90 – 95 bar. After 1900 s, p drops abruptly to ≈ 40 bar. At this point the coolant starts to heat up, up to T = 158 °C. Between 4400 s and 8000 s, after operator intervention, the coolant T equilibrates at T = 158 °C, p remains stable at p = 35 bar. Then, between 8000 s and 24 400 s, a steady cooling at a rate of 30 °C/h follows, up to T = 20 °C in parallel with a steady pressure relief up to p = 1 bar. Structural Materials Behavior Plastic flow behavior of Structural Materials ( SM s) is given in the form   ,   , based on earlier evaluation of the RPV surveillance program measurements. Data are provided for Cladding , Base Metal and Weld (see Table 1). These data clearly show that RPV SM s form jointly an inhomogeneous system.   ,   ,   0,2 0,2 , FT R FT AR FTT    n p n p n p 

Table 1. Plastic flow behavior of Structural Materials after manufacturing and after 60 OYs Plastic Flow Curve for the material when new ( Mpa )

Plastic Flow Curve for the aged material ( 60 OY ) ( Mpa )

T (°C)

Cladding

Base Metal

Weld

Cladding

Base Metal

Weld

20

σ ' = 420,0+955∙ε p σ ' = 355,1+465∙ε p

σ ' = 550,5+540∙ε p σ ' = 494,5+570∙ε p

σ ' = 469,0+525 ∙ ε p σ ' = 399,0+560∙ε p

σ ' =566,50+955∙ε σ ' =472,50+465∙ε

p σ p σ

' =713,84+540∙ε ' =627,55+570∙ε

p σ p σ

' =633,90+525ε p ' =574,78+560∙ε p

300

Simulations and their selected results The PTS simulations were performed both for the new and the aged RPV . The FE meshes around the crack front were configured in such a way that they could be used to evaluate the CTDF both in the spirit of the original Rice model and according to the NLFTFM model. Due to space limitation, only most relevant results of FM calculations have been selected for presentation. The results apply to point 6 of the crack shown on Fig. 4 . The computed results for the new RPV are shown in Fig. 6 , while simulation results for the aged RPV are reported on Fig. 7 . On the figures, ˆ J is the CTDF , valid for inhomogeneous materials. J stands for the far- tip ‘ J - integral’, defined at a distant path, where path independence was continuously satisfied to a fair approximation during the transient; J is seen as an implementation of Rice's J -integral. Assessing the presented results in Fig. 6 and 7 , both CTDF and J reflect the conditions of the PTS transient. In both RPV states , during uploading, CTDF and J are initially well matched. During the sudden p rise – see Fig. 5 – , there are noticeable differences between behavior of the new and the aged RPV . Most significant differences – both for new and aged RPV – , occur during the unloading phase: during the unloading process, the crack edge stabilizes significantly faster than expected from J , and an inhomogeneous   J r zone is formed around the crack front. Taking the crack-tip driving force to be J , one might expect that the crack edge will be subjected to opening loads throughout the whole transient – like in case of linear elastic FM calculations – . However, this is not the case. An important comment is in order here: during subsequent reloading after the PTS transient, homogeneity of initial conditions cannot be assumed around the crack, but the   J r distribution forms the new initial conditions.

Fig. 6. Evolution of CTDF and Rice's J -integral during the PTS transient, for new RPV , at point 6 of the crack.