Comparison of P-T Limit Curves of OPR-1000 and VVER-1000 RPV based on ASME Code Rule

DOI : 10.17577/IJERTV4IS090342

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Comparison of P-T Limit Curves of OPR-1000 and VVER-1000 RPV based on ASME Code Rule

Ihn Namgung1*, Nguyen Dang Dinh,2 Nuclear Power Plant Engineering Department KEPCO International Nuclear Graduate School Ulsan, South Korea

Abstract The mechanical properties of reactor pressure vessel (RPV) continuously changes after the start of NPP operation mainly due to radiation irradiation. One of the prominent effect is irradiation embrittlement and as time goes by the material becomes more brittle. Because of this embrittlement, the operation of reactor pressure vessel should be carefully maneuvered to avoid brittle fracture. Hence the rate of heatup and cooldown and associated pressure control, which frequently repeated in plant operation, need to follow certain operational guide lines called P-T limit curve. Depending on the temperature of reactor vessel, the internal pressure shall be limited to lower than certain level. For this reason, pressure and temperature during heatup and cooldown processes should follow allowed range of pressure and temperature to prevent brittle fracture. Of all pressure boundary component of primary coolant system of NPP, the welded region of reactor pressure vessel degrade most due to the radiation embrittlement. The P-T limit curves for OPR-1000 and VVER-1000 reactor pressure vessel was investigated and compared. For OPR1000 family of reactors including APR1400 reactor, P-T limit curves were constructed following rules defined in KEPIC code (which is based on the ASME Code) for safe operation NPP, whereas VVER type reactors, it was constructed according to the rules of Russian code. This study compares the P-T limit curves of OPR- 1000 and that of VVER 1000 reactor vessel according to Appendix G of the ASME Boiler and Pressure Vessel Code Section XI. Some of the significant differences are the minimum boltup temperature and lowest service temperature (LST) of OPR-1000 is 21.1°C and 77.8°C and those for VVER-1000 is 16.74°C and 30.6°C respectively. The lowest core critical temperature for OPR-1000 is 77.8°C and that for VVER-1000 is 63.8°C and corresponding maximum allowable pressure for OPR-1000 is 500 psi while that for VVER-1000 1200 psi.

Keywords Radiation embrittlement, Pressure temperature limit curve, prevention of nuclear reactor fracture, Operational limit of pressurized water cooled raector, OPR-1000 reactor P-T limit curve; VVER-1000 ractor P-T limit curve


    At high neutron fluences, material damage on microstructural grain boundary and element transmutation occurs causing swelling and embrittlement. The radiation embrittlement of reactor pressure vessel of great concern in the operation of NPP. Therefore strict guide lines are given for the transient operation of reactor such as heat-up or cool- down [1]. It is usually considered that welded region is more susceptible to radiation embrittlement since the weld material contain more trace element than base metal. Some of the trace element cause adversely to the structural integrity of RPV [2][3][4].


    At low temperature reactor vessel material might exhibit brittle behavior, and in order to prevent such event happening, pressure should be lowered so that the postulated crack at the vessel wall is within the limit of stress intensity value at the temperature. On the other hand too low a pressure may initiate nucleate boiling in the core which is also limiting factor since it also causes inhibit proper heat transfer to coolant and may cause damage to the fuel. Another consideration is that the closure head stud bolts are tightly fastened during operation and the bolting region is in higher stress condition than other part of reactor pressure vessel. So stud and surrounding region is much higher stress state and that is susceptible to low temperature brittle fracture. These are some major considerations in setting up pressure- temperature limit curves [5].

    During startup and shutdown as well as reactor trip, all components in the reactor coolant system (RCS) have to withstand all operating loads of temperature and pressure due to NPP operation mode changes. In order to protect reactor pressure vessel from brittle fracture, pressure – temperature (P

    T) limit curves is constructed to be used as operational guideline of reactor operation and maintain NPP within safe state. During the construction of P-T limit curves for OPR- 1000 and VVER-1000 reactor vessels, the beltline region which is most critical part of reactor vessel due to the susceptibility of brittle fracture. VVER-1000 reactor is manufactured by beltline weld for form RPV. The fabrication step of VVER-1000 reactor is shown in Figure 1. Although OPR-1000 does not have welded part within core region, it is conservatively assumed that the belt-line region of reactor is welded connection of lower head and cylindrical shell [6][7].



      OPR-1000 and VVER-1000 RPV are made from ferritic steels, but their composition, standard designation, and fabrication technique are differential. For example OPR-1000 specified American Society of Mechanical Engineers ASME SA508 for vessel, meanwhile material of VVER pressure vessel is 15KpNMFA [1].

      Figure 1 shows the fabrication process of OPR-1000 reactor vessel and VVER-1000 reactor vessel where the difference of irradiation sensitive core region of the tow reactor is shown. In the figure, the beltline is the region of the reactor vessel that directly surrounds the effective height of

      active core and corresponding to highest neutron fluence region [1].

      Irradiation induced mechanical property changes of SA508 for OPR-1000 and 15KpNMFA in case of VVER- 1000. The property change depends significantly upon the amount of residual elements present in the compositions of material such as copper, phosphorus, and nickel. Table 1 below shows typical value of chemical composition of SA-

      508 and 15KpNMFA. The impurity contents are slightly different from OPR-1000 to VVER-1000 RPV. It is note that the copper and phosphorus are considered in nil ductility temperature (NDT) evaluation and fracture toughness prediction in Russian code whereas US.NRC guide includes copper and nickel.

      1. OPR1000 reactor vessel fabrication process and weld locations

      2. VVER-1000 reactor vessel fabrication process and nozzle locations

      Figure 1. Fabrication and assembly process of OPR1000 and VVER-1000 reactor vessel

      Table 1 – Cu, Ni, and P constituents for OPR-1000 and VVER-1000 reactor vessels



      reactor vessel base metal


      reactor vessel weld metal


      reactor vessel base metal


      reactor vessel

      weld metal

















      The neutron exposure has to be determined from the surveillance specimens. The calculation is focused on the determination of the lead factor, which represents the ratio of exposure of the surveillance specimen to the highest anticipated exposure at the RPV wall. Fluence definition of VVER-1000 and OPR-1000 is different. For VVERs, neutrons with energies greater than 0.5 MeV are consiered to form the fluence that is considered in vessel property change correlations. For PWR this energy boundary is taken to be 1 MeV. Table 2 shows design operating lifetime fluence for light water cooled reactors [8] [9].


      Reactor type

      Flux (n/m2s)

      (E > 1 MeV)

      Lifetime fluence (n/m2)

      (E > 1 MeV)

      VVER-440 core weld


      1.1 ×1024

      VVER-440 maximum






      PWR (OPR)



      PWR (B&W)







    The national regulatory documents in connection with irradiation sensitivity of steels are defined in Regulatory Guide 1.99 Revision 2 in the USA, and OPR-1000 is regulated under similar rule that follows US regulations, and VVER-1000 reactor vessel is regulated under PNAE-G-7- 002-86 in Russia. The main differences in regulatory approaches come from neutron spectrum considered and steel compositions. Russian code identifies copper and phosphorus whereas the US identifies copper and nickel as significant in analysis that will be basic to find chemistry factor for calculation of RTNDT [8][9].

    Neutron fluence and chemical composition are the most relevant factors in radiation embrittlement. The general expression of RTNDT may be reduced to the following [8]:

    RTNDT = CF × FF

    Where CF is the chemical factor, and FF is the fluence factor (n) [8].

    In the US, the fracture toughness curve is used to find equivalent temperature T-RTNDT. RTNDT is the reference temperature for nil ductility transition and is defined in

    ASME code. The increase in RTNDT due to radiation exposure is evaluated according to the Code of Federal Regulations, Title 10, Part 50, Appendix G [8]. The predictive formula is defined in US Regulatory Guide 1.99 Revision 2 [8].

    In VVER reactors, the neutron irradiation effects on mechanical properties are characterized by a shift of critical temperature of . The transition in irradiated condition is determined directly from irradiated Charpy V-notch test results, using the regulatory definition of the transition temperature [9][10].



    For the safe normal operation of RPV, the operation should follow certain operation path call P-T curve. This curve is a result of consideration of material degradation due to radiation exposure of RPV beltline. The most provable failure mode fracture mode I, which is fast fracture failure due to tensile stress. This condition is expressed as follows [11][12]

    intermediate value corresponding to temperatures along the operation shall be estimated proportionally. To do this transient conduction heat transfer calculation is need to find maximum through-wall temperature difference as well as the prorated value temperature difference along the temperature change. Hence KIT is fully defined for input temperatures.

    The is defined by where is given in G- 2214.1 to ASME Sec. III, appendix G as follows, for vessel thickness of 102 mm t 305 mm [10]

    • for an inside axial surface flaw: Mm = 0.0293

    • for an outside axial surface flaw: Mm = 0.0282

    • for an inside or an outside circumferential surface flaw:

      Mm = 0.0140

      With this value, the remaining unknown is , since r is the ID of reactor vessel and t is the thickness of reactor vessel, the pressure is the variable need to be calculated.


    KIC 2KIM + KIT (1)

    Where KIC = Reference critical stress intensity factor specified by Figure G-2210-1 [10]

    KIM = Stress intensity factor for membrane stress due to pressure, and is defined as KIM = mMm

    Mm = Membrane correction factor defined in G- 2214.1 to ASME Sec. XI [10]

    m = (Pr)/t, membrane stress

    P = Internal reactor vessel pressure, psia,

    r = Inside reactor vessel radius, in.,

    t = Reactor vessel wall thickness, in.

    KIT = Stress intensity factor for thermal stress defined in G-2214.3 to ASME Sec III [12].

    The reference critical stress intensity factor is defined by Figure G-2210-1 of ASME Section III App. G and it is expressed in formula as below [11].

    KIC =36.5+22.783e(0.036(T-RTNDT)) (MPam) (2)

    In equation (2), KIC is a function of T of RTNDT. The RTNDT is determined by material chemical composition and accumulated radiation fluence. The right side of eq. (1) consists of the primary membrane stress and secondary membrane stress denoted by KIM and KIT. The KIT is defined as follows

    KIT = 0.579×10-6×CR×t2.5 (MPam) (3-a)

    KIT = 0.458×10-6×HU×t2.5 (MPam) (3-b)

    Where CR is cooldown rate in °C/ hr

    HU is Heatup rate in °C / hr

    t is the thickness of vessel wall in mm

    The KIT defined by eq. (3) corresponds to maximum temperature difference between vessel inner-surface to outer- surface throughout heatup or cooldown operation. Hence the

    Since radiation degradation affects fracture toughness, it need to be properly accounted in the assessment of reference critical stress intensity factor. This critical stress intensity factor is determined from adjusted reference nil ductility transition temperature is defined in Regulatory Guide 1.99 (RG 1.99). The ART values of beltline material for weld metal and base metal at ¼ thickness and ¾ thickness are given by the following expression [11]:

    ART = Initial RTNDT + RTNDT + Margin (4) Where

      • Initial RTNDT is the reference temperature for the unirradiated material.

      • RTNDT is the measure of nil ductility transition temperature change during the reactor operation

      • Margin is to compensate the uncertainties on both initial RTNDT and RTNDT.

    1. The initial reference nil ductility transition temperature, Initial RTNDT

      The initial reference nil ductility transition temperature of

      APR1400 and OPR1000 reactor was determined by actual test of the material. VVER-1000 reactors initial reference nil ductility transition temperature was assumed to be similar to that of OPR-1000 reactor vessel [8].

    2. The shift of initial nil ductility transition temperature

      RTNDT is the mean value of the adjustment in reference temperature caused by irradiation and is calculated as follows:

      RTNDT = (CF)f(0.28-0.10lofg) (5)

      The neutron fluence, f, at any depth in the vessel wall is calculated using methods that conform to the guide lines of RG 1.99 perform as follow [8]:

      f = fsurf(e-0.24x) (6)

      In substituting the radiation fluence in eq. (6), the unit of 1019n/cm2 is used, and the fluence include those of fast neutron range (E>1 MeV). The calculated value of the neutron fluence at the inner wetted surface of the vessel at the location of the postulated defect is used in the calculation.

      In eq. (5), CF stand for chemistry factor is defined RG

      1.99. Base on the material used in reactor vessel beltline, the chemistry factor of copper (Cu) and nickel (Ni) is determined from table if RG 1.99. Since the material composition for reactor vessel and beltline weld are different, the CF for welds and vessel shell be determined separately.

    3. Margin

    According to RG 1.99, margin is quantity in temperature unit, °C, that is to be added to obtain conservative, upper- bound values of ART for the calculations required by Appendix G to 10 CFR Part 50 [8][9][13].

    Margin = (7


    • I is standard deviation for the initial RTNDT.

    • is the standard deviation of RTNDT.


    P-T Limits curves for the core not critical and core critical operating condition apply for both the 1/4t and 3/4t locations. When combine pressure and thermal stress, it is usually necessary to evaluate stresses at the 1/4t location (inside surface flaw) and the 3/4t location (outside surface flaw) [12]. Analysis of heat up and cool-down rate from 10°C/hr to design limit of 100°F/hr intervals are performed by using the Finite Element Method (FEM) for thermal transient simulation, using ANSYS general purpose FEM analysis software. Locations at 1/4t and 3/4t are examined for the heat-up and cooldown transient. The temperature gradient at 1/4 and 3/4t wall depth for heatup and cooldown is obtained. The heat-up and cool-down rates vary from 10°C/hr to design limit of 100°F/hr. An example of thermal analysis result is

    shown in Figure 2 below [14].

    Figure 2. Output results for heatup rate at 37.8°C/hr

    This calculation is necessary to accurately assess the KIT in Eq. (3), where KIT is maximum value. From the temperature transient, the maximum temperature difference between inner to outer surface corresponds to the Thermal Stress Intensity

    Factor given in Eq. (3). Hence at each temperature rise during heatup or temperature down during cooldown, the ratio from the maximum is calculated and corresponding value of Stress Intensity Factor is obtained.


    For the beltline analysis, during normal operations, the following condition is maintained [12]:

    KIC = 2KIm + KIt (8)


    KIm = Mm x Pri/t (9)

    KIt = Max KIt x T/ Max T (10)

    KIC = 36.5 + 22.783e[T-ART] (11)

    Or P= (12)


    KIm: Stress intensity factor for membrane stress due to pressure

    KIt: Stress intensity factor for thermal stress Mm: Membrane correction factor

    P: internal reactor vessel pressure

    r: inside reactor vessel radius t: reactor vessel wall thickness

    T: Maximum steady-state temperature differential across the reactor vessel wall.

    : Function of temperature, T, and adjusted reference temperature, ART, of the material at the crack tip (1/4t or 3/4t)

    In eq. (8), the eq. (1) is modified to calculate the maximum allowable pressure for a given temperature. After substituting all variables, eq. (12) will give maximum allowable pressure. The overall procedure of obtaining P-T limit curve is shown in Figure 3. This calculation should be carried out for heatup and cooldown rate of 100°C, 80°C, 60°C, 40°C, 10°C, etc and hydrostatic test conditions.



    1. Minimum Boltup Temperature of Reactor Vessel Closure Head

      Base on ASME Code, Section III, Division I, Appendix G, Paragraph G-2222, the ASME Code requires that when the flange and adjacent shell region are stressed by the full bolt preload and by pressure shall not exceed 20% of the preoperational system hydrostatic test pressure [8][12].

      This PT limit is a straight vertical line at the minimum boltup temperature (Tmin boltup). The minimum metal temperature in the stressed region must be at least the initial RTNDT plus any effects of irradiation.

      TMIN_BOLTUP = ART + Initial RTNDT

      Since reactor flange where bolt connections is located is away from high radiation, the effect of irradiation embrittlement is negligible and therefore the TMIN_BOLTUP is set to the same as Initial RTNDT

    2. Lowest Service Temperature (LST)

      Determine Adjusted Reference Temperature (ART)

      ART calculation in Section 3.1

      The lowest service temperature (LST) is defined by paragraph NB-2332, Section III of the ASME Code, to be the minimum allowable temperatue at pressures above 20% of the preoperational hydrostatic test pressure. This limit when enveloping all component, a more severe limit need to be applied and that is for clouse NB-2332, and is given by equation as follows [8]:

      Determination KIC Use equation (8)

      LST = RTNDT + 37.8°C (or 100°F)

    3. Minimum Pressure Below Lowest Service Temperature

      Determine temperature distribution (in,¼T, 3/4T,out) Use Ansys in Section 3.2

      Determine KIm Use equation (6)

      Determine Membrane correction factor Mm Use equation into ASME Code, Section III, Division I, G-2214.1

      The minimum allowable pressure below the lowest service temperature is defined by NB-2332, Section III of the ASME Code, to be 20% of the pre-operation hydrostatic test [8].


      • Max KIt(inside)

      • Max KIt(outside)

      Use equation into ASME Code, Section III, G-2124.3

      Determination KIt Use equation (7)

      Figure 3. Process of allowable pressure determination

      Pbelow_LST = 0.2Phydro_test

    4. Core Critical Curve

      The core critical curve is intended to provide additional margins of safety during core operation. The limitation is defined as 40°F above the minimum allowable temperature for heatup or cooldown and nor lower than the minimum temperature allowable for in-service hydrostatic test, in accordance with paragraph IV.A.3 in Appendix G to 10 CFR 50 [10].

    5. Hydrostatic Test Curves

    Determine Allowable Pressure Use equation (9)

    According to G-2400 in Appendix G to Section III of the ASME Code, Hydrostatic curve is to be performed by applying safety factor of 1.5 to the stress intensity factor for membrane stress due to pressure KIm [12].



    1. Pressure-Temperatue Limit Curves of OPR-1000 and VVER-1000 Reactor Vessels

      Determine T from FEM Analysis results

      Construction of pressure-temperature limit curve at beltline of OPR-1000 and VVER-1000 RPV are performed for both heatup and cooldown condition for various temperature gradients. Combined with other temperature limits produces final pressure-temperature limits that should be followed during reactor operation. The results of pressure- temperature limit curve at beltline of OPR-1000 and VVER- 1000 RPV are shown in Figure 4.

    2. Results and Evaluation

      • It showed quite a difference of shape and margin of VVER-1000 and OPR-1000 P-T limit curves. The main differences are come from differences of material, neutron flux, setpoint (hydrostatic test/normal operation pressure), thickness of reactor vessel wall. In order to eliminated computational error and construct accurate P-T limit curves, the time steps were set very small when doing the FEM analysis of temperature distribution through the RPV wall.

    1. P-T Limits Curve of OPR-1000 RPV

    2. P-T Limit Curve of VVER-1000 RPV

    Figure 4. P-T limit curves of OPR-1000 and VVER-1000 RPV

    • The difference of ART and Initial RTNDT values of OPR-1000 and VVER-1000 are also causes difference for minimum boltup temperature and lowest service temperature (LST). Specific margin of minimum boltup temperature and lowest service temperature (LST) of VVER-1000 is 62.14°F and 87°F respectively whereas OPR-1000 is 70°F and 172°F.

    • Hydrostatic pressure of VVER-1000 is less than OPR- 1000 that leads difference of maximum pressure below lowest service temperature, specific value of VVER- 1000 is 713.584 psia and OPR-1000 is 500 psia.

    • Hydrostatic pressure also affect to hydrostatic test curve for both of VVER-1000 and OPR-1000 that have Safety factor of 1.5 is applied to stress intensity factor.

    • The minimum boltup temperature is principally governed by Appendix G to Section III of the ASME code that requires the flange and adjacent shell region are stressed by the full bolt preload. Minimum bltup temperature of two RPV is quite similar, VVER-1000 is 62.14°F and OPR-1000 is 70°F.

    • The Lowest service temperature is minimum allowable temperature at pressure above 20% of the preoperational hydrostatic test pressure. There are significant differences between LST of VVER-1000 (87°F) while LST of OPR-1000 (170°F).

    One of the interesting point is that the lowest core critical temperature for VVER-1000 and OPR-1000 are 146.761°F and 172°F, but the maximum allowable pressure at that temperature is different where for VVER-1000 is 1200 psi and that for OPR-1000 is 500 psi.


Pressure Temperature (P-T) limit curve is generated to control the limit of permissible operating envelope for VVER 1000/320 RPV during reactor operation. P-T limit curves are also used by system designers in evaluating the consequences of transients which challenge reactor vessel integrity. Plant operating procedures guide operators to follow optimum heatup and cooldown curves that do not violate the allowable limits of P-T curve.

The P-T limit curves of the vessel of the belt-line region of VVER-1000 reactor were obtained for a 100°F/hr heatup and cooldown operation. The study was carried out by applying Appendix G of the ASME Boiler and Pressure Vessel Code, Section III, Appendix G to generate P-T limit curves of VVER 1000/320. To determine the adjusted reference temperature (ART) of the 15KpNMFA beltline material of VVER 1000/320, RTNDT was calculated based on Cu and Ni values and neutron fluence. For obtaining temperature through the thickness at inside surface, ¼t and 3/4t and outside surface of beltline region, FEM model of VVER 1000/320 was created and simulated by using transient thermal analysis module of ANSYS software 14.5.

Comparison of P-T limit curve for VVER-1000 and OPR- 1000 was made. It showed that the minimum bolt-up temperature is quite similar but the minimum allowable LST showed significant difference, in which LST for VVER-1000 was 87°F while that for OPR-1000 was 170°F. The lowest core critical temperature also showed some difference where it for VVER-1000 is 146.70°F and it for OPR-1000 is 172°F, but the maximum allowable pressure at that temperature for VVER-1000 is 1200 psi while it for OPR-1000 is 500 psi.


  1. IAEA Nuclear Energy Series, No NP-T-3.11, 2009 Integrity of Reactor Pressure Vessel in Nuclear Power Plant : Assessment of Irradiation Embrittlement Effects in Reactor Pressure Vessel Steel

  2. J.G. Collier, M.R. Hughes and L.M. Davies, 1983 Fracture Assessment of a PWR Pressure Vessel, Vol.75, No.3, pp389-404, Nuclear Engineering and Design

  3. S.B. Fisher and J.T. Buswell, 1987 A Model for PWR Pressure Vessel Embrittlement, Vol 27, No.2, Pp 91-135, International Journal of Pressure Vessels and Piping

  4. R.Ahlstrand, B. Margolin, et al., 2022 TREG 2.01/00 project, Validation of neutron embrittlement for VVER-1000 and 440/213 RPVs with emphasis on integrity assessment, Vol 7, pp52-57,

    Progress in Nuclear Energy

  5. Oya Ozdere Gijlol, Uner Colak, 2003 Comparison of pressure vessel integrity analyses and approaches for VVER-1000 and PWR vessels for PTS condition, Nuclear Engineering and Design 226, pp231-241

  6. Hisming Pan, 1992 The Generation of an Allowable P/T Curve of a Nuclear RPV Using a Display-Oriented System, International Journal of Pressure Vessel and Piping, Vol. 5 No.2, pp. 257-265

  7. Taek-Jin Lee, J.B. Choi, Y.J. Kim, Y.W. Park, 2002 A parametric study on pressure-temperature limit curve using-3D finite element analyses. Nuclear Engineering and Design 214 (2002) pp.73-81

  8. NRC Regulatory Guide 1.99, May 1988 Radiation Embrittlement of Reactor Vessel Materials

  9. V.G. Vasiliev, Yu.V.Kopiev, 2007 WWER pressure vessel life and ageing and management for NPP long term operation in Russia, IAEA-CN-155-056, Second International Symposium on Nuclear Power Plant Life Management

  10. D.Araneo, G. Agresta, F.DAuria, Fracture Mechanical Analysis for VVER1000 Reactor Pressure Vessel, The 7th International Conference on Safety Assurance of NPP with WWER – 2011, Russia, May 17-20, 2011

  11. Appendix G to 10CFR50, Fracture Toughness Requirements, Title 10 Code of Federal Regulations of U.S.A.

  12. ASME Boiler and Pressure Vessel Code 2012 ed. Section XI, Appendix G, Fracture Toughness Criteria for Protection against Failure.

  13. T.L.Dickson, W.J.McAfee, W.E.Penell, and PT Williams (ORNL), Evaluation of Margins in the ASME Rules for defining the P-T Curve for a RPV. USNRC 26th Water Reactor Safety Meeting, Oct 26, 1998

  14. ANSYS V.14.1 General Purpose FEM Analysis Software

  15. KHNP, 2002, Ulchin 5&6 Final Safety Analysis Report

  16. ASME Boiler and Pressure Vessel Code 2012 ed. Section III, Subsection NB Class 1 Components

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