Scholarly article on topic 'Application of the French Codes to the Pressurized Thermal Shocks Assessment'

Application of the French Codes to the Pressurized Thermal Shocks Assessment Academic research paper on "Materials engineering"

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Abstract of research paper on Materials engineering, author of scientific article — Mingya Chen, Guian Qian, Jinhua Shi, Rongshan Wang, Weiwei Yu, et al.

Abstract The integrity of a reactor pressure vessel (RPV) related to pressurized thermal shocks (PTSs) has been extensively studied. This paper introduces an integrity assessment of an RPV subjected to a PTS transient based on the French codes. In the USA, the “screening criterion” for maximum allowable embrittlement of RPV material is developed based on the probabilistic fracture mechanics. However, in the French RCC-M and RSE-M codes, which are developed based on the deterministic fracture mechanics, there is no “screening criterion”. In this paper, the methodology in the RCC-M and RSE-M codes, which are used for PTS analysis, are firstly discussed. The bases of the French codes are compared with ASME and FAVOR codes. A case study is also presented. The results show that the method in the RCC-M code that accounts for the influence of cladding on the stress intensity factor (SIF) may be nonconservative. The SIF almost doubles if the weld residual stress is considered. The approaches included in the codes differ in many aspects, which may result in significant differences in the assessment results. Therefore, homogenization of the codes in the long time operation of nuclear power plants is needed.

Academic research paper on topic "Application of the French Codes to the Pressurized Thermal Shocks Assessment"

Nuclear Engineering and Technology xxx (2016) 1—10

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Original Article

Application of the French Codes to the Pressurized Thermal Shocks Assessment

Mingya Chen a'*, Guian Qian b, Jinhua Shic, Rongshan Wang a, Weiwei Yu a, Feng Lu a, Guodong Zhang a, Fei Xue a, and Zhilin Chen a

a Suzhou Nuclear Power Research Institute, Life Management Center, Xihuan Road, 215004, Suzhou, Jiangsu Province, PR China

b Paul Scherrer Institute, Nuclear Energy and Safety Department, Laboratory for Nuclear Materials, OHSA/06, 5232, Villigen PSI, Switzerland

c Amec Foster Wheeler, Clean Energy Department, 19B Brighouse Court, Barnett Way, Gloucester GL2 4NF, UK

ARTICLE INFO ABSTRACT

Article history: The integrity of a reactor pressure vessel (RPV) related to pressurized thermal shocks (PTSs) Received 17 March 2016 has been extensively studied. This paper introduces an integrity assessment of an RPV Received in revised form subjected to a PTS transient based on the French codes. In the USA, the "screening crite-18 May 2016 rion" for maximum allowable embrittlement of RPV material is developed based on the Accepted 3 June 2016 probabilistic fracture mechanics. However, in the French RCC-M and RSE-M codes, which Available online xxx are developed based on the deterministic fracture mechanics, there is no "screening cri__terion". In this paper, the methodology in the RCC-M and RSE-M codes, which are used for

Keywords: PTS analysis, are firstly discussed. The bases of the French codes are compared with ASME

Pressurized Thermal Shock and FAVOR codes. A case study is also presented. The results show that the method in the

RCC-M RCC-M code that accounts for the influence of cladding on the stress intensity factor (SIF)

Reactor Pressure Vessel may be nonconservative. The SIF almost doubles if the weld residual stress is considered.

RSE-M The approaches included in the codes differ in many aspects, which may result in sig-

Structural Integrity nificant differences in the assessment results. Therefore, homogenization of the codes in

the long time operation of nuclear power plants is needed.

Copyright © 2016, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/

licenses/by-nc-nd/4.0/).

1. Introduction

The reactor pressure vessel (RPV) is a key component of nuclear power plants (NPPs) with regard to safety and lifetime [1]. Although long time operation (LTO) is a main concern, the pressurized thermal shock (PTS) event poses a potentially

significant challenge to the structural integrity of the RPV [2]. Prior to 1978, it was postulated that the most severe PTS event was a large-break loss-of-coolant accident (LOCA). During that type of overcooling transient, low-temperature emergency coolant would rapidly enter and cool the vessel wall which would result in high thermal stresses. In 1978, the occurrence

* Corresponding author. E-mail addresses: chenmingya@cgnpc.com.cn, p134362@163.com (M. Chen). http://dx.doi.org/10.1016/j.net.2016.06.009

1738-5733/Copyright © 2016, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

2 Nuclear Engineering and Technology xxx (2016) 1—10

of an event at the Rancho Seco NPP in the USA showed that rapid cool-down could be accompanied by repressurization during some types of overcooling transients. Following the incident, the USA Nuclear Regulatory Commission (NRC) designated PTS as an unresolved safety issue, and the effects of PTS were extensively analyzed [3]. On the basis of those analyses, the NRC established the Regulatory Guide (RG) 1.154 [4] and 10 Code of Federal Regulation (CFR) 50.61 [5] rules. The 10 CFR 50.61 establishes a "screening criterion" based on the reactor vessel nil-ductility-transition temperature (RTndt). The screening criterion RTndT (called RTpTs in the rule) was selected according to the studies that the risk due to PTS events is acceptable based on the probabilistic fracture mechanics (PFM). In 10 CFR 50.61, the RTpTs is 132°C for plates, forgings, and axial welds, and 149°C for circumferential welds. As long as the limiting temperature is not reached, the risk caused by the PTS events is considered to be acceptable. The PTS issues are widely studied in the USA. However, the technical basis of FAVOR, which is developed by Oak Ridge National Laboratory (ORNL) in Washington, DC and used by the US NRC to perform the PTS analysis [6-8], is not consistent with other codes and standards, such as the ASME [9], RCC-M [10], and RSE-M [11] codes.

Furthermore, no such "screening criterion" exists in the French codes, e.g., RCC-M and RSE-M which were developed based on the deterministic fracture mechanics (DFM). The RPV assessment is mainly based on simplified methods ("engineering approach") instead of the more sophisticated approach in these codes. The criteria of the Level C "exceptional conditions" and Level D "highly improbable conditions", which may be classified as the PTS transients, are lacking clear descriptions. In addition, some fracture mechanics inputs, such as the thermal and stress analyses, have not been revisited since their original design. Therefore, it may be difficult to reassess the safety of the RPV under PTS loadings during the LTO operation according to the RCC-M and RSE-M codes. In fact, there is only a small amount of literature

based on the RCC-M or RSE-M codes to assess RPV integrity, even though the resistance of RPV against fast fracture has been comprehensively studied.

This paper aims to apply the French codes, RCC-M and RSE-M, to perform an RPV integrity assessment, to compare the two codes with the ASME codes, and to discuss the limitations of the three codes. In this paper, the methodology of the Level C and Level D in the French codes, which is classified as the PTS assessment, is firstly discussed. Meanwhile, the methodology is further compared with the fundamental of the FAVOR software. A case study according to the RCC-M and RSE-M codes is presented. Lastly, the limitations of the RCC-M and RSE-M codes, as well as the important factors for the RPV structural assessment, i.e., weld residual stress, cladding influence, and crack arrest assessment criteria, are discussed.

1.1. PTS assessment procedure

The PTS assessment of RPV integrity is based on comparisons of crack driving forces (such as stress intensity factor, SIF Kj) calculated for assessed points along the crack front with its allowable value (such as fracture toughness KIC) for PTS events [12,13]. The flowchart of the PTS analysis is shown in Fig. 1, and the main evaluations are described in the following steps: (1) prediction of material toughness according to the chemical compositions, initial toughness, neutron fluence and material embrittlement; (2) calculation of PTS transients according to thermal-hydraulic analysis; (3) analyses of thermal-mechanical and welding residual stress; (4) definition crack information (position, orientation, size, and type): perform fracture mechanics analysis to calculate the SIF of the postulated cracks; (5) definition failure criteria according to the code (failure model and margin); and (6) assessment: compare SIFs of the postulated cracks with the failure criteria (fracture toughness of the embrittled material).

Fig. 1 - Diagrammatic representation of the PTS analysis. PTS, pressurized thermal shock; SIF, stress intensity factor.

Nuclear Engineering and Technology xxx (2016) 1—10

In the following, the material property, e.g., material toughness and irradiation embrittlement, PTS transient calculation, crack models, and assessment criteria will be discussed.

2. Materials and methods

2.1. Material properties

2.1.1. Material toughness

As described above, material toughness is the critical material property in the PTS study. For ferritic steels, the static fracture toughness KIC (MPa -^m) and the crack arrest toughness KIa(MPa-Vm) are functions of the material temperature T(°C) and RTndt (°C) in the RCC-M and RSE-M codes. In the RSE-M code Version 2007, the toughness is defined as follows:

M code, or calculated according to the Fragilisation par Irradiation Superieure (FIS) equation:

KIC = min{36.5 + 3.1 exp[0.36(T - RTndt + 55.5)], 220}

Kla = minf 29.43 +1.355 exp [0.0261 (T - RTndt + 88.9)], 220} (1b)

It is well known that the weld zone includes the parent, the weld, and the heat affected zone (HAZ). In actual structural assessments, the equation above may be used for all materials, while the RTndt is calculated according to different materials. In the USA, it is recommended and considered adequately conservative to use the equation for steels of minimum yield strengths up to and including 345 MPa [14]. In the early 2000s, it became clear that the irradiation effect on the weld metal of Ringhals 3 and 4 in Swedish reactors was different to that in Westinghouse type RPVs.

As shown in Eq. (1), the upper shelf values of KIC and KIa have no relationship with the neutron fluence. Although the upper shelf value can be taken as 200 MPaVm in [15], 240 MPa Vm is implicitly endorsed by the ASME code [9]. In the USA, Appendix G of 10 CFR 50 [16] requires the upper shelf energy throughout the life of the vessel to be no less than 67.8 J which implicitly endorses that the upper shelf values are related to the fluence. However, there is no description in the RCC-M and RSE-M codes about the relationship between the upper shelf energy and the neutron fluence. This needs further improvement.

2.1.2. Irradiation embrittlement of the RPV RPV material tends to embrittle due to neutron irradiation and the degree of embrittlement is quantified by the change in RTndt in the RCC-M and RSE-M codes. The final RTndt is obtained by adding the shift (DRTndt) to the initial value. The following equation is used in the RCC-M Version 2007, Appendix Z G for the base metal 16MND5:

DRTndt = [22 + 556(%Cu - 0.08) + 2778(%P - 0.008)] f/1019)1/2,

in which, %Cu and %P represents the weight-percent measured values of Cu and P. f represents the fluence expressed in neutrons per cm2, where only neutrons having energy > 1 MeV are considered.

In the RSE-M code Version 2010, the shift of the RTndt due to the embrittlement can be calculated according to the RCC-

ARTndt = 15.4{1 + 35.7max[0; (P - 0.008)]

+ 6.6max[0, (Cu - 0.08)] + 5.8Ni2Cu}f059

in which, P, Cu, and Ni represent the weight-percent measured values of P, Cu, and Ni. f represents the fluence expressed in neutrons per cm2, where only neutrons having energy > 1 MeV are considered.

The FIS equation is based on research by Brillaud, where a series of French surveillance data was analyzed [17]. Compared with the RCC-M code, the influence of Ni composition is considered in the FIS equation. The initial design values of the maximum fluence level from AREVA were between 5.1 and 5.6 x 1019n/cm2 (E > 1MeV) for the design life of 40 years. The reevaluation in 2001 led to 7.2-7.6 x 1019n/cm2 (E > 1 MeV) projected for 40 years. The FIS equation is only applicable up to a maximum neutron fluence of 11.5 x 1019n/cm2 (E > 1 MeV). Thus, during the LTO (operate to 60 years), the fluence will be close to the limit of the equations.

2.2. PTS transient calculation

PTS transients are significant in terms of the stresses which are likely to be induced with associated temperatures, and the temperatures impact on the toughness of the material. The output of the thermal hydraulic analysis, which is input into the fracture mechanics model, is the temporal variation of pressure, temperature, and heat transfer coefficients (HTCs) along the RPV downcomer.

In the design stage, the temporal variation of pressure and temperature at the inlet nozzle of RPVs is given while the focused area is the beltline region in the PTS assessment. The RPV is approximated by a rotationally symmetric two-dimensional model that allows the calculation of axial and circumferential stresses as a function of one-dimensional (along the radial direction) transient temperature distribution [18]. For the simplified analysis in the design stage, the forced convection or free convection of HTCs are often used. In the PTS assessment, some countries adopt the view that the thermal plumes that can occur below the cold legs are of sufficiently small magnitude that they can be neglected, while other countries directly model the effect of these plumes. In the latter case, the pressure, temperature, and HTCs variation along the downcomer takes on both a spatial and a temporal variation [19,20].

In the ASME Code Section XI Appendix E, the pressure and temperature are the temporal variation, and the HTCs should be considered under the event, plant specific flow, and mixing conditions. However, there are few descriptions concerning the thermal-hydraulic calculation in the RCC-M and RSE-M codes.

Crack models

In PTS analysis, it is necessary to demonstrate that the integrity criteria are satisfied for the postulated defects located at the beltline region with high neutron fluence. However, the postulation of a defect is problematic. The inner

Nuclear Engineering and Technology xxx (2016) 1—10

surface of the RPVs is protected with as austenitic cladding to prevent corrosion. Cladding materials are characterized by relatively lower toughness in comparison with the same austenitic material that is not austenized after welding. The cladding is heat treated to remove residual stresses [15]. In the design stage of the RCC-M code, the cladding may be taken into account in determining the temperature and stress fields, but should be neglected for the fracture analyses [10].

In the RCC-M code Version 2010, the conventional reference defect is shown in Fig. 2, and the flaw depth a is defined as follow:

a = min(0.25t, 20mm) t > 40mm

in which, t is the thickness of the vessel, 2b is the flaw length and a/2b = 1/6.

The postulated defects are assumed to be normal to the direction of the maximum principal stresses. For semi-elliptical inner-surface-breaking defects, both the deepest point (DP, point A in Fig. 2) on the crack front and the edge located at the intersurface (IP, point B) should be analyzed. Defects smaller than the reference defect must also be analyzed to ensure that they are no more severe.

The flaw information of the RSE-M code is in accordance with the actual nondestructive examination (NDT) information. The flaw depth a is defined as the sum of the actual crack size and the margin. It is known that no flaws in base metal extended up to the inner surface of the RPV are found in real cladded RPVs [21]. Fracture toughness of the first layer of cladding is important for potential arrest of the underclad crack propagation. If the crack is not arrested there, the second layer of cladding has low fracture toughness and cannot arrest [22,23]. On the basis of these results, a new type of postulated underclad crack for PTS calculations is included in the RSE-M code Version 2007, as shown in Fig. 3 (the first layer is close to the base, and the second layer is close to the inner surface of the RPV). For a circumferential or longitudinal continuous subclad crack of height h = 2a, whose extremity A is located in the cladding and extremity B in the base metal, the equivalent SIF is calculated at the crack tip points A and B, which implicitly endorses that both ends of the defects must be analyzed in the RSE-M code. Thus, the fracture toughness value of the cladding is needed, whereas there is no description in the RSE-M code [23,24].

In the USA, the ASME Code Section XI App. E "Evaluation of Unanticipated Operating Events" [9] provides acceptance

Fig. 3 - Conventional subcladding crack in RSE-M code. r, the thickness of the cladding; SA, ligament between the internal surface of the vessel and extremity A of the crack.

criteria and guidance for performing an engineering evaluation on the effects of PTS on the structural integrity of the RPV beltline region. In App. E which is based on the DFM, a semi-elliptical surface flaw is used, and cladding should be considered in the thermal, stress and fracture mechanics analyses.

The flaw information in FAVOR is in accordance with the actual NDT information. The surface-breaking flaws only exist in the cladding in the FAVOR, which means that there is no embedded flaw propagating through the cladding. This is same in the RSE-M code, but obviously different to the hypothesis in the RCC-M and ASME codes. The models in the RCC-M and ASME codes conservatively postulate that all flaws are inner-surface-breaking flaws. In the reference [12-14,22], the SIF of the subclad crack may be 50% lower than that of the surface breaking crack.

Assessment criteria

Fig. 2 - Conventional reference defect in RCC-M code.

In the RCC-M and RSE-M codes, the information which may be used for PTS assessment, is contained in the Level C "Exceptional conditions" and Level D "Highly improbable conditions". In the RCC-M code Version 2007 and RSE-M code Version 2005, the criteria for Level C and Level D are given in Table 1.

As shown in Table 1, only crack initiation assessment is considered in the transient region (T < RTndt + 60oC), while cracks which initiate in the cool inner region of the vessel may be arrested in a region of the wall where temperature is much higher and neutron fluence is lower [13,15]. Thus, the focusing of RCC-M and RSE-M codes on the beltline region is a conservative assumption. In a ductile tearing analysis for the high temperature range (T > RTNDT + 40oC), the crack shape parameter a/2b is kept at 1/6 in the RCC-M code while the

Nuclear Engineering and Technology xxx (2016) 1—10 5

Table 1 — Criteria in the RCC-M and RSE-M codes.a

RCC-M RSE-M

Level C Level D Level C Level D

T < RTndt - h60°C Kcp < Kic/1.6 Kcp < Kic/1.2 Kcp(1.3Cc) < min(Kic/1.35,Kjc/1.25) Kcp(1.3Cd) < min(Kic/1.35,Kjc/1.25)

T > RTndt - h40oC Option 1 Kcp < Kjc/1.3 Kcp < Kjc/1.0 J(1.3Cc) <Jo.2 J(1 .1Cd) <Jo. 2

Option 2 KCP < KJC/1.1 with a a margin of 1.2 is J(1 . 3Cc) < Jdo/1 .6 and J(1 . 3Cc) <Jo.2 J(1 .3Cd) <Jd0/1 .1

margin of 1.6 on verified against

ductile tearing ductile tearing

SIF, stress intensity factor.

a KCP is the total SIF including plastic correction, T is the material temperature at the point in time and at the point on the crack front under analysis, CC and CD mean the loads of Level C and Level D events, and KjC is the material toughness indicated by static measurements of JK.

crack is expected to be of an infinite length after initiation in the RSE-M code.

The margin is only applied on the material toughness in the RCC-M code. By contrast, margins are applied both on the toughness and the crack driving forces in the RSE-M code. The question is how to apply the margin on the crack driving forces, such as the thermal stress and residual stress in the three-dimensional finite element analysis (FEA). However, there is no clear description of the criteria in the codes. Thus, it may be difficult to carry out the assessment according to the RSE-M code.

The criterion in the ASME Code Sec. XI App. E is as follow.

1.4(K,m + k) + kir < Kic

where Kim is the SIF due to membrane stress, KIt is the SIF due to thermal stress, and KIr is the SIF due to residual stress.

According to Eq. (5), it implicitly endorses that the margin is applied on the SIF due to membrane stress and thermal stress in the ASME code, and only crack initiation assessment is required while crack arrest assessment is an option in the RCC-M and RSE-M codes. The residual stress is considered in the ASME code but not considered in the RCC-M and RSE-M codes.

It should be pointed out that both the RCC-M and RSE-M codes are based on DFM, while the screening criterion of the USA is based on PFM. The main differences among these codes are listed in Table 2.

i !* ■ ■ * ■ >—•

\ \ • pressure -■—Fluid temperature

ft __■

: ■ .........■..... :

-100 3

6,000 8,000 Time (s)

10,000 12,000 14,000

Fig. 4 - Pressure-temperature versus time in the IAEA report. IEA, International Atomic Energy Agency.

3. Case study

The example documented in the International Atomic Energy Agency (IAEA) report [15] is used to illustrate the detailed methodology and results according to the French codes. The time variations of pressure and fluid temperature around the beltline are shown in Fig. 4, and the HTCs are shown in Table 3.

-200 a.

- 150 m

Table 2 - Compare the guidelines in different codes.

RCC-M RSE-M USA criteria

Crack Size Min (1/4 thickness, 20 mm) Measured + uncertainties Probabilistic

Type Surface Real and subsurface Subsurface for the base metal crack

Location Beltline and nozzle Real, beltline, and nozzle Beltline

Orientation Longitudinal Circumferential or longitudinal Circumferential or longitudinal

Cladding Not considered in Considered Considered

fracture assessment

Ductile tearing Yes Yes Only after arrest

Thermal analysis Simplified analysis Exact analysis Exact analysis by RELAP 5 software

Failure criteria Model Initiation and ductile tearing Initiation and ductile tearing Initiation and ductile

tearing after arrest

Margin On toughness On force and toughness No

Residual stress Not considered Not considered Considered

DFM or PFM DFM DFM PFM

DFM, deterministic fracture mechanics; PFM, probabilistic fracture mechanics.

Nuclear Engineering and Technology xxx (2016) 1—10

Table 3 — HTCs around the beltline.

Temperature/0 C 37 48 49 59 69 96 106 115 152

HTCs/(W/(m2-°C)) 992 877 790 1,147 602 710 1,229 1,057 1,838

Temperature/0C 206 251 261 268 276 279 287 295 /

HTCs/W/(m2$0C) 1,581 4,834 1,757 6,232 3,453 1,054 24,696 24,125 /

HTC, heat transfer coefficients.

Fig. 5 - The postulated crack model in the core region of the RPV. RPV, reactor pressure vessel.

As shown in Fig. 5, the inner radius of the RPV Ri is 1994 mm, the thickness of the base metal t is 200 mm and the thickness of cladding tcladding is 7.5 mm, respectively [15]. The inner side of the RPV is assumed to be subjected to thermal shocks, and the thermal load is assumed to be rotationally symmetric and homogeneous along the Z-axis in the analysis. The beltline region of the RPV is sufficiently far away from the nozzle area to be treated as axisymmetric cylindrical shell.

The RPV was modeled with SA508 Class 3 steel and the cladding was made of austenitic stainless steel, respectively. Temperature dependent material properties used in the analyses are summarized in Table 4 [15].

1,800 s 3,600 s 4,400 s 7,200 s 14,985 s

60 90 120 150 180

Distance from the inner surface (mm)

Fig. 6 - The temperature field at different stages of the transient.

of the coolant is no longer fluctuant, isothermal conditions are achieved in the vessel wall at the end stage of the transient.

The elastic hoop stress in the PTS transient is shown in Fig. 7. The discontinuity of the stress in the clad-base metal interface is due to the different properties of the cladding and base materials. The higher thermal expansion coefficient and the lower thermal conductivity of the cladding are responsible for the increased stress in the cladding zone (reaching the yield stress). Due to the reduced temperature gradient, the thermal stress starts unloading in the end stage.

4. Results

4.1. Temperature and stress distributions

The temperature distribution through the vessel wall at different times of the transient is shown in Fig. 6. Due to rapid cooling, the temperature difference along the vessel wall increases in the beginning of the transients. As the temperature

4.2. Crack driving force KCP

The SIF is determined from the defect size under consideration, its position, and the associated stresses under analysis. This determination may be performed in accordance with the following procedure in the RCC-M code: (1) determination the distribution of stresses caused by all applied loads at the point in the time under consideration. The stress fit is carried out

Table 4 - Material properties of the base metal and cladding.

Material Temperature Young Poisson's Thermal Thermal Density Coefficient of Yield

(0C) modulus/E rationn conductivity diffusivitym = l/pC (103kg/m3) thermal expansion3 stress

(GPa) [W/(m0C)] (10~6 m2/s) (10-6/°C) (MPa)

Base metal 20 204 0.3 54.6 14.7 7.6 10.9 588

300 185 45.8 10.6 12.9 517

Cladding 20 197 0.3 14.7 4.1 7.6 16.4 380

300 176.5 18.6 4.3 17.7 270

a Mean value between 20° C and the temperature.

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1,800 s 3,600 s 5,400 s 7,200 s 14,985 s

Distance from the inner surface (mm)

Fig. 7 - The elastic hoop stress in the PTS transient. PTS, pressurized thermal shocks.

over a distance part L of the wall thickness of the studied zone, and only by taking into account the stresses normal to the postulated defect plane. The distribution of normal stress s(x) is fitted by a polynomial with variable x:

o(x) = oo + S1 (x/L) + ff2(x/L)2 + ff3(x/L)3 + ff4(x/L)4

where x is the distance to the wall 0 < x < t if t is the thickness of the studied zone. L is the distance over which the stress is expressed by the polynomial: 0 < L < t; (2) determination the SIF K, by associating an influence function to each term in the polynomial expression. Influence functions are represented by i0, i1, i2, and i3, and are the function of crack geometry, the zone in which the postulated crack is located, and the a/L ratio. The K, is expressed as follows, and the influence functions are given in RCC-M Z G 5120:

K, = (pa)1/2 (S0i0 + s1(a/L)i1 + a2(a/L)\ + ^(a/L)^) (7)

and (3) correction of the plastic zone must be applied according to the following procedure. Determine the radius ry of the plastic zone at the defect tip, as follows:

ry= 6P'-

where sy is the yield strength value for the material at the crack tip at the temperature of the point in time considered. Determine the corrected value of the intensity factor KCP as follows:

Kcp = aK^( a + ry)/a in which,

a = 1, if ry < 0.05(t - a)

a = 1 + 0.15

ry - 0.05(t - a)

0.035(t- a)

(9) (10a)

, if 0.05(t - a) <ry < 0.12(t - a) (10b)

: = 1.6, if ry > 0.12(t - a)

in which, a is the additional plasticity correction in order to take into account cladding yielding.

In reality, the method used to calculate KCP is based on the plane strain conditions in the RCC-M code which is implicitly endorsed in the Z G 5220 "Determination of crack-extension force J". In the Z G 5220, J may be computed from KCP using the following equations:

J = (1 - n2) KC^E, at DP J = kCp/E, at IP

(11a) (11b)

The plan strain assumption in the calculation of SIF for the IP is conservative according to the RCC-M code. The assessment of SIF for the point of intersection of the crack front with the free surface could also be performed by other more sophisticated methods, which take into account the plane stress conditions in this point.

In the RCC-M code Version 2007, the maximum flaw depth a is min (0.25t, 20 mm), and 2b/a = 6 (defects smaller than the maximum defect which must also be analyzed are not assessed in this case study). The temporal variation of the stress fields caused by the thermal and pressure loads are used to calculate the SIF. The results according to the RCC-M code are shown in Table 5, and they are also compared to the results of the 3-D FEA. The detailed methods of the 3-D FEA are described in reference [2,8,13]. The FEA was carried out using the general-purpose FEA program ABAQUS, Version 6.12, and only one quarter of the beltline was modeled considering symmetric conditions. The hexahedron element is used, and the pressure load on the crack surface was considered for the through-clad defect.

As shown in Table 5, the method to account for the influence of cladding on the SIF is nonconservative in the RCC-M code. As in the previous analysis, the stress in the cladding region is higher than the yield stress, so the influence of the cladding on the SIF is obvious. In this case study, the radius ry at the crack tip is always smaller than 0.05(t-a), this means that the influence of the cladding is actually ignored. Nevertheless, according to the FEA study, the influence of the cladding on SIF is obvious.

In the elastic-plastic analyses, the stress within the cladding will be limited, if the plasticity is incorporated, so the KCP values may be smaller than K for the DP [13]. While in the RCC-M code, the plasticity correction always increases the SIF.

Table 5 - SIF results at time 7,200 s of the transient.

Location

K^MPa-Vm )

KCP (MPa$ Vm )

RCC-M code 3-D FEA RCC-M codea 3-D FEA

47.11 30.67

67.68 68.78

47.56 30.78

SIF, stress intensity factor.

a Yield stress at crack tip temperatures is determined by the linear interpolation.

Nuclear Engineering and Technology xxx (2016) 1—10

100 90 80S 70-rà

gL 6040

-■— SIF for deepest point -•— SIF for interface point -o— Critical KC for interface point -□— Critical KC for deepest point-

Crack tip temperature ( C)

Fig. 8 - Elastic-plastic SIF and the safety assessment. SIF, stress intensity factor.

4.3. Safety assessment

The critical crack tip temperature is much lower than RTndt + 60oC in the IAEA report. Therefore, according to the RCC-M code, the failure criterion is as follow:

kcp < kic/1 . 6

The relationship between elastic-plastic SIF and crack tip temperature, calculated by the FEA method, is shown in Fig. 8. The maximum allowable RTndT is also calculated based on the tangent method. Due to the influence of the cladding, the IP is more dangerous than the DP in the case study (the plane strain conditions are defined for all points).

As shown in Fig. 8, the critical moment of fracture may not coincide with the time to get the maximum SIF, as the crack tip temperature may be higher at that time. Consequently, there may be a set of moments in which the safety assessment needs to be performed, according to the RCC-M code.

The results of the safety assessment at time of 7,200 s, based on the RCC-M code, are shown in Table 6. The allowed critical value of RTndT is only about 52° C for the DP which is much lower than the "screening criterion" of the USA. The main difference is due to the fact that the "screening criterion" is determined by a probabilistic approach, different flaws, different methods for considering cladding, safety margins, and failure criteria.

Discussion

4.4.1. Effect of weld residua! stress

Residual stress is not considered in the RCC-M and RSE-M codes, and the influence of the residual stress on the SIF of the circumferential surface-break cracks in the circumferential weld of the RPV beltline is shown in Table 7. The stress free temperature (SFT) is chosen to be 295° C and the default residual stress in the FAVOR is used in the study.

As shown in Table 7, the SIF increases about 18% after the residual stress through-wall distribution is considered, indicating that the influence of the residual stress cannot be ignored.

4.4.2. Effect of cladding

As the SIF of the subclad crack may be 50% lower than that of the surface breaking crack [12-14], the influence of the cladding is particularly significant on the safety margin, since the existence of cladding decreases the SIF significantly and consequently increases the maximum allowable RTndT.

SFT is used to consider the influence of the residual stress caused by the claddingin the FAVOR code. The SIF results of the DPs, with and without the influence of the weld residual stress caused by the cladding, are shown in Table 8. As shown in Table 8, the SIF increases significantly if the cladding residual stress is considered, and the SIF almost doubles when the crack size is small. This indicates that the influence of the cladding residual stress cannot be ignored. However, there is little material data on the cladding and there is also no description of it in the RCC-M and RSE-M codes. Therefore, the material data of the

Table 6 - Safety assessment results.

Location KCP(MPa-pm ) Crack tip temperature (°C) Allowed critical value of RTndT (°C)

Based on RCC-M method Based on 3-D FEA In the IAEA reporta

DP IP 47.56 30.78 66.58 76.86 52.02 69.9 93.26 52.8 57.5 77.9

DP, deepest point; IAEA, International Atomic Energy Agency; IP, interface point.

a The results of AREVA in the IAEA report are used. The distance of IP from the interface is 2 mm in the IAEA report. Also, the smaller crack (crack depth a = 12 mm) is postulated in the IAEA report.

Table 7 - SIF results with and without the residual stress.

Residual stress a = 6 mm, a/2b = 1/6 a = 6 mm, a/2b = 0 a = 12 mm, a/2b = 1/6 a = 12 mm, a/2b = 0 a = 24 mm, a/2b = 1/6 a = 24 mm, a/2b = 0

Not considered 42.45 49.90 45.93 53.61 48.72 57.85

Considered 50.28 58.57 54.57 63.72 57.67 69.13

Increment (%) 18.45 17.37 18.81 18.86 18.37 19.50

SIF, stress intensity factor.

Nuclear Engineering and Technology xxx (2016) 1—10 9

Table 8 - SIF results of DPs with and without the cladding residual stress.

SFT (°C) a = 6 mm, a/2 b = 1/6 a = 6 mm, a/2b = 0 a = 12 mm, a/2b = 1/6 a = 12 mm, a/2b = 0 a = 24 mm, a/2b = 1/6 a = 24 mm, a/2b = 0

20 295 Increment (%) 26.70 42.45 58.99 26.11 49.90 91.11 32.30 45.93 42.20 33.67 53.61 59.22 41.28 48.72 18.02 45.46 57.85 27.25

DP, deepest point, SIF, stress intensity factor.

cladding, such as the fracture toughness and weld residual stress, need to be defined in any future PTS assessment.

In the above analyses, the cladding is considered in the models. It was assumed that the cladding always bears the loads along with the base material during the PTS transients. In reality, there may be many small cracks in the cladding and the near surface crack is hard for the NDT to detect during the service period. According to the RSE-M and ASME codes, there is no need to assess the cracks which are located in the cladding region. Neglecting of the cracks embedded in the cladding is a conservative assumption.

When the cladding loses the strength to bear the loads (map cracking, MC) before PTS transient occurs, the MC effect on fracture analysis should be considered. In this case, the cladding may conduct heat flux but lose the strength to bear the loads during PTS transients. Fig. 9 shows the maximum thermal stress SIF with or without considering the MC effect under different cool-down rates [2]. When the MC effect is considered, the thermal stress SIF reduces obviously. The decrement of IPs is much larger than that of DPs. The MC effect means to release the constraints on the flaw, especially for the IPs.

rá CL

0.05 0.10 0.15 0.20 0.25

Crack depth, a/t

Fig. 9 - Influence of the MC on the peak thermal stress SIF. IP, interface point; MC, map cracking; SIF, stress intensity factor.

Table 9 — SIF of different crack shape parameters.

a = 10 mm a = 20 mm a = 40 mm

a/2b = 1/6 DP 63.67 67.68 81.58

IP 52.79 68.78 90.18

a/2b = 0 88.89 101.84 138.20

DP, deepest point; IP, interface point; SIF, stress intensity factor.

4.4.3. Crack arrest and ductile tearing assessments As shown in Table 1, only crack initiation assessment is considered during the transient period, according to RCC-M and RSE-M codes. By contrast, crack arrest assessment has been considered in the FAVOR code [6]. Concerning crack arrest, RCC-M and RSE-M codes are more conservative.

In the ductile tearing analysis in the high temperature region, the crack shape parameter a/2b is kept at 1/6 in the RCC-M code, while the crack shape parameter is expected to be zero (infinite) after crack initiation in the RSE-M code. In addition, the safety margin of IP may be smaller than that of DP [3,8]. However, there are few published papers that showed the differences among different codes, which may puzzle the user [25]. The SIFs at time of 7,200 s of the transient for the inner surface break cracks with different shape parameters are shown in Table 9. The comparison of SIFs shows that the criteria in the RSE-M code is more conservative than that in the RCC-M code.

5. Conclusion

Based on this study, the following conclusions can be drawn: (1) in the PTS assessment of RP, the approaches in RCC-M, RSE-M and ASME codes differs in many aspects, including flaw size, the role of cladding, safety margins, and failure criteria. The difference will result in different assessment results. Thus, the codes need to be homogenized concerning weld residual stress, cladding influence and the exact safety assessment criteria in the LTO of NPPs; (2) the method in the RCC-M code to account for the influence of cladding on the SIF is nonconser-vative. Neglecting the weld residual stress in the French codes leads to nonconservative results in the structural integrity assessment, but there are many factors influencing the assessment results which need to be studied in future work; and (3) the influence of the cladding on RPV integrity is significant. The material data of the cladding, such as the fracture toughness and weld residual stress, should be provided in the assessment. In order to perform a more realistic integrity assessment for the LTO of NPPs, accurate thermal analysis and exact crack arrest assessment criteria are needed.

Conflicts of interest

All authors have no conflicts of interest to declare. Acknowledgments

The project is supported by the National Natural Science Foundation of China (No. 51275338 and No. 51435012). The

Nuclear Engineering and Technology xxx (2016) 1—10

financial supports of both programs are greatly appreciated. We are also indebted to Mr. Terry Dickson of the Oak Ridge National Laboratory for providing the code FAVOR.

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