Improvement of plant reliability based on combining of prediction and inspection of crack growth due to intergranular stress corrosion cracking

Nuclear Engineering and Design 341 (2019) 112–123

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Improvement of plant reliability based on combining of prediction and inspection of crack growth due to intergranular stress corrosion cracking

T

⁎

Shunsuke Uchidaa, , Yasuhiro Chimia, Shigeki Kasaharaa, Satoshi Hanawaa, Hidetoshi Okadab, Masanori Naitohb, Masayoshi Kojimac, Hiroshige Kikurac, Derek H. Listerd a

Japan Atomic Energy Agency, Tokai-mura, Japan Institute of Applied Energy, Tokyo, Japan c Tokyo Institute of Technology, Tokyo, Japan d University of New Brunswick, Fredericton, Canada b

A R T I C LE I N FO

A B S T R A C T

Keywords: Plant reliability Risk evaluation IGSCC Prediction Inspection Uncertainty analysis

Improvement of plant reliability based on reliability-centred maintenance (RCM) is going to be implemented in nuclear power plants. RCM is supported by three types of maintenances: risk-based maintenance (RBM); timebased maintenance; and condition-based maintenance. RBM is supported by suitable combinations of prediction, inspection and maintenance (repair of elemental defects in their propagation stage). The combination of prediction and inspection is one of the key issues to promote RBM. Early prediction of IGSCC occurrence and its propagation should be confirmed throughout entire plant systems which should be accomplished by inspections at the target locations followed by timely applications of suitable countermeasures such as water chemistry improvements. At the same time, transparency and traceability as well as accuracy are strongly required for the prediction. A set of empirical formulas for evaluation of electrochemical corrosion potential (ECP) and crack growth rate due to IGSCC was applied for evaluation of IGSCC risk as well as IGSCC occurrence and propagation. The details of IGSCC formulas have been reported by various researchers along with the expected accuracy of prediction to prepare for ensuring their transparency and traceability. Based on prediction results, primary points for inspections will be determined. Unfortunately, it is still difficult to evaluate some key parameters in the plants, e.g., residual stress. From the inspections, accumulated data will be applied to confirm the accuracy of the IGSCC formulas and their computer codes, to tune some uncertainties of the key data for prediction, and then, to increase their accuracy. The synergetic effects of prediction and inspection on application of effective and suitable countermeasures are expected. In this paper, the procedures for the combination of prediction and inspection have been introduced.

1. Introduction

the inspection to maintain the plant reliability are divided into three categories: (1) dynamic equipment; (2) control equipment; and (3) static equipment. The reliability of the plants can be established by maintaining reliability of each piece of elemental equipment. The reliability of dynamic and control equipment can be maintained by

In order to maintain sufficient reliability of nuclear power plants (NPPs), especially aged NPPs, periodic, systematic and precise inspections are required throughout the entire plant systems. Major targets for

Abbreviations: ACD, allowable crack depth; AESJ, Atomic Energy Society of Japan; ASME, American Society of Mechanical Engineers; AT, acoustic emission testing; CBI, condition-based inspection; CBM, condition-based maintenance; CF, corrosion fatigue; CGR, crack growth rate; CS, carbon steel; CT, compact tension test; ECP, electrochemical corrosion potential; EPR, electrochemical potentiokinetic reactivation; FAC, flow-accelerated corrosion; HWC, hydrogen water chemistry; IASCC, irradiation assisted stress corrosion cracking; IGSCC, intergranular stress corrosion cracking; JSME, Japan Society of Mechanical Engineers; NPP, nuclear power plant; NWC, normal water chemistry; PDCA, plan-do-check-act cycle; PLEDGE, Plant Life Extension Diagnostics by GE (The name of computer package for lifetime evaluation); PT, penetration testing; RBI, risk-based inspection; RBM, risk-based maintenance; RCM, reliability-centered maintenance; SIF, stress intensity factor; SS, stainless steel; TBI, time-based inspection; TBM, time-based maintenance; UT, ultrasonic testing ⁎ Corresponding author. E-mail addresses: [email protected] (S. Uchida), [email protected] (Y. Chimi), [email protected] (S. Kasahara), [email protected] (S. Hanawa), [email protected] (H. Okada), [email protected] (M. Naitoh), [email protected] (M. Kojima), [email protected] (H. Kikura), [email protected] (D.H. Lister). https://doi.org/10.1016/j.nucengdes.2018.10.021 Received 12 January 2018; Received in revised form 19 October 2018; Accepted 24 October 2018 0029-5493/ © 2018 Elsevier B.V. All rights reserved.

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Nomenclatures a a* F FE

G K n npred sij

T TL

thickness of the pipe (m) [subscripts: o, initial crack depth; allow, allowable crack depth] thickness of pipe wall (m) F-value (–) components of F-value [subscripts: 1, carbon content in SS; 2, stabilization parameter; 3, low temperature aging; 4, post welding heat treatment; 5, stress ratio; 6, dissolved oxygen; 7, crevice; 8, conductivity] constants for SIF [subscripts: 0, 0 order; 1, first order; 2, second order; 3, third order] stress intensity factor (MPa m1/2) [subscripts: o, mean value] n-values [subscript: o, mean value] intermediate value of n (-) parameter to determine SIF as a function of crack depth

t x α Β1-β4 χ1-χ4 ε ϕ κ θ1,θ4 σst σ

temperature (K) lifetime (s) [subscripts: CG: lifetime due to crack growth; incubation, incubation time; lifetime: total lifetime] time (s) crack depth (m) geometry factor (α =1 for slab) constants to determine crack growth rate (–) constants SCC susceptibility, EPR (C/cm2) [subscript: o, mean value] ECP (mV-SHE) [subscript: o, mean value] conductivity (μS/cm) [subscript: o, mean value] constants to determine F-value (–) stress (MPa) [subscripts: o, mean value; 0, 0 order; 1, first order; 2, second order; 3, third order] deviation (–) [subscripts: ε, EPR; ϕ, ECP; κ, conductivity; K, stress intensity factor; σ, residual stress; T, temperature]

degradation models and inspection can contribute to synergetic effects for inspection rationalism and degradation prediction improvement (Kojima and Uchida, 2012). The combination of prediction and inspection should be supported by a well-arranged computer simulation model for prediction and a data acquisition system for comparison of the predicted and measured results. The computer model should be expressed by a formula with sufficient information on input data, which can prepare for transparency and traceability of prediction for back-checking by third parties, if necessary. The prediction results may at any time involve certain uncertainties caused by the model itself and major input data. Major mechanisms related to structural material degradation are divided into three categories: (1) FAC (Kojima and Uchida, 2012); (2) GSCC (Feron, 2012); and (3) corrosion fatigue (CF) (Hornbach and Prevéy, 2007), (Eason et al., 1998), which are from the interactions of materials, cooling water and other environmental parameters, e.g. residual stress, repeated stress and local turbulence in flow. In the authors’ previous paper, the effects of uncertainty of predicted wall thinning rate due to flow-accelerated corrosion (FAC) on pipe lifetime were evaluated (Uchida et al., 2018). The uncertainty of wall thinning rate was one of the consequences of propagation of uncertainties of elemental parameters. In order to improve wall thinning prediction based on the results of combination of prediction and inspection, uncertainty of each parameter and its propagation to that of wall thinning rate should be evaluated and the major parameters should be tuned based on the comparison. Suitable countermeasures can be applied to keep plant reliability by following these procedures. In this paper,

monitoring their performance during plant operation, testing them in operational and leakage tests, etc., overhauling them during plant shutdown periods and exchanging their component parts periodically. However, it is rather difficult to confirm the reliability of static equipment which often includes a pressure boundary and consists of structural materials that may often degrade with operation time without any change in their apparent performance. In order to maintain the reliability of the static equipment, its systematic and periodic nondestructive testing is required based on its degradation mechanismoriented scenario. Periodical inspections of structural materials are essential for maintaining reliability of the static equipment and, subsequently the plant reliability. The time-based inspection (TBI) and condition-based inspection (CBI) result in increased numbers of inspection points, and therefore also inspection times, inspection worker-hour and inspection costs with a reduction in plant operation duty factor. The optimal combination of plant reliability and plant duty factor can contribute to reliable, economical and safe plant operation. For this, primary static components with potentially higher risks are inspected based on precise understanding of the degradation mechanism and precise prediction of degradation risks (risk-based inspection (RBI)), which contributes to the concentration of inspection resources and rationalism of inspection while at the same time improving inspection quality. The secondary effects of RBI are acquisition of qualified data on important equipment and important materials, which can contribute to improving the degradation models and the major parameters applied for the models. The combination of prediction based on

Fig. 1. Conceptual diagram of system safety assessment. 113

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control equipment including DC power systems; and (3) static equipment. For dynamic equipment and control equipment, on-line inspections can be applied, while for static equipment, off-line inspections can be applied (Uchida et al., 2018). A material atlas, mainly for the static equipment, is shown in Fig. 2 (Uchida and Katsumura, 2013). In the cooling system, uniformly controlled cooling water is in contact with different materials, which complicates corrosion problems. Corrosion behaviors are much affected by water qualities and differ according to the water quality values and the materials themselves. Many problems have originated from materials and some have resulted in significant issues in plants.

procedures for the combination of prediction and inspection have been demonstrated for intergranular stress corrosion cracking (IGSCC) based on uncertainty propagation evaluation. 2. Combination of prediction and inspection Plant reliability can be established by a trio of procedures, i.e., prediction, detection (inspection) and maintenance when problems are indicated to be developing on structural materials. There are several approaches toward establishing plant reliabilities, e.g. time-based maintenance (TBM), condition-based maintenance (CBM) and riskbased maintenance (RBM). Reliability-centered maintenance (RCM) consists of TBM, CBM and RBM. Indications of the problems that might result in decreased plant reliabilities are predicted, they are detected and confirmed at their early stages and then they are removed by early maintenance to prevent future risks (Ling et al., 2007). Inspection targets are often selected based on inspection schedule charts (TBM), while the targets are selected based on experienced anomaly performance or experiences with other plants (CBM). The candidates for inspection targets which are selected based on risk prediction are confirmed as the maintenance targets where the maintenance is carried out (RBM). RBM is supported by risk-based inspection (RBI), where prediction of IGSCC crack initiation and its propagation and their inspection are tightly combined as a combination of prediction and inspection. Relationships among prediction, inspection and maintenance are shown in Fig. 1 (Uchida et al., 2018; Kojima et al, 2017). Based on analysis of occurrences of component failures due to IGSCC and other problems and their propagations to incidents and accidents, plant risks are predicted together with their prediction uncertainties. As a result of the prediction of the plant risks, the orders of priorities for inspections are determined to prepare for careful and precise inspections. The results of inspections are applied to decision making of maintenance, e.g., maintenance targets, maintenance timing and maintenance approaches. At the same time inspection results are fed back to predictions to confirm the accuracies of predictions and to improve the prediction models and their key constants. After the maintenance, the extent to which the risks are mitigated is evaluated by applying the prediction models. The trio of prediction, inspection and maintenance can increase plant reliability and may be applied to determine margins in plant system safety.

3.2. Material degradation Static equipment is important for maintaining pressure boundaries which contain cooling water and maintain reactor safety. Degradation of major materials of the static equipment can result in component problems and then serious loss of cooling accidents. However, even if such degradation is in progress, it is difficult to observe any anomaly in material performance during plant operation and their sudden defects often result in serious issues. It is difficult to monitor static components by operational tests. Monitoring of degradation of the static equipment should depend on non-destructive tests, e.g., ultrasonic testing (UT), penetration testing (PT) and acoustic emission testing (AT). In order to mitigate their costly inspections that require non-destructive tests, primary components should be selected based on their degradation predictions, which are prepared for major degradation mechanisms. Major mechanisms of structural material degradation and prediction models for evaluating lifetime are determined by the mechanisms summarized in Table 1 (Uchida et al., 2016; Chexal et al., 1997; Czajkowski, 1987; Gofuku et al., 1996; Kastner et al., 1990; Nuclear and Industrial Safety Agency, 2005; Suzuki et al., 2013; Trevin et al., 2009). The models for evaluating the lifetime of the materials of the equipment and its components should consist of well-described formulation to keep the transparency and the well-defined parameters applied in the models for keeping the traceability of the evaluation. Some of the major parameters can be determined by direct measurements but some should be determined by analytical procedures, which results in analytical errors derived from experimental errors. So, the lifetime of the materials has not been described by deterministic procedures but by probabilistic procedures, considering the analytical errors as well as original errors of the models themselves. The prediction models for FAC have been developed to evaluate the damage probability for each piece of equipment and risk evaluation due to FAC has been reported (Uchida et al., 2016). Models for IGSCC have been shown (Ford, 1990), but those for CF have not been developed yet. Suitable prediction of material degradation can contribute to RBI and at

3. Prediction models for material degradation 3.1. Inspection targets Major components for inspection targets are divided into three categories: (1) dynamic equipment including power supply systems; (2)

Fig. 2. A material Atlas and major subjects related to materials in cooling systems of BWR plants. (Uchida and Katsumura, 2013). 114

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Table 1 Mechanisms and evaluation procedures for major material degradation processes.

(CGR) was evaluated by applying the empirical formula

the same time it can contribute to effective improvement of the prediction models themselves.

3.3.1. An empirical formula for IGSCC crack growth rate Several empirical formulas to express CGR due to IGSCC have been reported (Ford, 1990), (Shoji, 2003). In the paper, Ford-Andresen model, the so-called PLEDGE model (Ford et al., 1987; Andresen et al., 2001), was applied for IGSCC CGR evaluation and for the demonstration of IGSCC risk analysis, because its major calculation constants were easily obtained for calculation. The CGR was defined as a function of n-value and stress intensity factor [PLEDGE model].

3.3. IGSCC crack growth rate prediction models IGSCC of stainless steel is one of the most frequently reported material problems for BWR plants but no serious accident related to it has been reported reflecting the good result of careful inspections and maintenances, which are supported by continuous and enthusiastic efforts of plant utilities and benders (Feron, 2012). IGSCC is known to occur as a result of overlapping effects of material, stress and environmental factors (Table 2). Under severe neutron and gamma ray irradiation in the reactor core region, corrosive conditions in the BWR primary cooling system are known to be determined by corrosive radiolytic species (Hanawa et al., 2013). At the same time, structural materials themselves are irradiated by neutrons and their physical and chemical properties are changed during plant operation. The phenomena are designated as irradiation accelerated stress corrosion cracking, where the parameters ② and ③ are strongly affected by neutron irradiation. This paper limited the discussion to only IGSCC without direct neutron irradiation. For sensitivity analysis of IGSCC crack growth rate estimation, ① electrochemical potentiokinetic reactivation (EPR) was selected as a parameter for the material factor, ③ electrochemical corrosion potential (ECP), ④ conductivity and ⑤ temperature were selected for the environmental factor and ⑥ residual stress was selected for the stress factor. The circle numbers are corresponding to those in Table 2. But ② hardness caused by neutron irradiation was not discussed in the paper, which was related to only IGSCC but not to irradiation assisted stress corrosion cracking (IASCC). The evaluation of IASCC would be discussed on the next stage. Corrosive conditions in the BWR primary cooling system are usually expressed by the corrosion index, ECP. In order to determine ECP at any location in the primary cooling system, ECP should be evaluated by computer simulation codes consisting of water radiolysis models to determine the concentrations of corrosive radiolytic species and mixed potential models to determine ECP based on corrosive species. The most recent target accuracy for evaluation of ECP was reported as ± 50 mV (Uchida et al., 2014). Based on the measured conductivity ④ and temperature ⑤ and the evaluated ECP ③, EPR ② and residual stress ⑥, IGSCC crack growth rate

da = A(κ, ϕ)(BK4) n dt

(1)

A(κ, ϕ) = 0.0078 n3.6

(2)

B = 6 × 10−14

(3)

χ f(κ) = χ1 + χ2log10 ⎛χ 3 κ + 4 ⎞ κ⎠ ⎝

(4)

f(ϕ) = 10 × (0.6 + 0.001ϕ)

(5)

Table 2 Major parameters to determine IGSCC CGR.

115

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e f(κ) ⎤ npred = ⎡ f(κ) f(ϕ) ⎥ ⎢ ⎣e + e ⎦ n=

(6)

npred 10 2.096

(7)

3.0

Major constants for the calculation of Eqs. (4)–(7) were shown elsewhere (Andresen, 2017).

σ

σ

1) A uniformly distributed residual stress

2σ

A uniform stress through the thickness direction was assumed to determine stress intensity factor as follows.

K= ασ0st (πa)1/2

for uniform stress in a slab

(8)

The CGR was determined as a function of the crack depth as shown in Eq. (9).

da 1 = A(κ, ϕ) π2 αB dt

(

)

4n

(

(σ st) 4na2n = A a (κ, ϕ,n)Bb (σ st. n)a2n 1

)

A a (κ, ϕ,n) = A(κ, ϕ) π2 αB

Fig. 4. Probability distribution.

(9)

da 1 = A(κ, ϕ) π2 αB dt

(

4n

(10)

Bb (σ st.n) = (σ st) 4n

(13)

a

i−1

⎝

⎣ i=1

⎠

4n

⎤ 2n ⎥ a ⎦ 4n

3

(

1

)

(14)

4n

(15) 4n

3 ⎡ 3 ⎧ a j − 1⎫ a i − 1⎤ ⎛ ⎞ ⎥ Bb (σ st.n)a2n = ⎢∑ σ ist ∑ sij ⎛ ∗ ⎞ ⎨ a ⎝ ⎠ ⎬ ⎝ a∗ ⎠ ⎥ ⎢ ⎩ j=1 ⎭ ⎣ i=1 ⎦

(16)

The details of the constants shown in Eqs. (12) and (13) are shown elsewhere (Miura et al., 2014). The distributions of residual stresses with a uniform distribution and a realistic distribution and SIF are shown in Fig. 3.

3

a a 2 a 3 K(a)=(σ st0 G0 + σ1st G1 ⎛ * ⎞ + σ st2 G2 ⎛ * ⎞ + σ 3st G3 ⎛ * ⎞ ⎝a ⎠ ⎝a ⎠ ⎝a ⎠

3

st ⎛ ⎞ ⎢∑ σ i Gi a∗

A a (κ, ϕ,n) = A(κ, ϕ) π2 αB

As a result of welding pipes, extension stress will remain both on inner and outer pipe surfaces and compression stress has been observed around the middle of pipe thickness, where the residual stress and stress intensity factor (SIF) were expressed as follows (Miura et al., 2014; Shiratori et al., 2011). (12)

4n ⎡

⎡ ⎧ a j − 1⎫ a i − 1⎤ 2n ⎛ ⎞ ⎥ a = A a (κ, ϕ,n) ⎢∑ σ ist ∑ sij ⎛ ∗ ⎞ ⎨ a ⎝ ⎠ ⎬ ⎝ a∗ ⎠ ⎥ ⎢ ⎩ j=1 ⎭ ⎣ i=1 ⎦ = A a (κ, ϕ,n)Bb (σ st.n)a2n

2) A realistic residual stress distribution

a a a σ st (a) = σ st0 + σ1st ⎛ * ⎞ + σ st2 ⎛ * ⎞ + σ 3st ⎛ * ⎞ ⎝a ⎠ ⎝a ⎠ ⎝a ⎠

)

3

(11)

2

2σ

3.3.2. Uncertainty analysis In the paper, normal distributions were assumed for uncertainties of major parameters (Fig. 4). The standard deviations of the probabilistic distributions of the major IGSCC factors (GCR, SIF), calculated by applying the uncertainties of major parameters (ECP, conductivity, EPR and residual stress), and CGR and lifetime obtained from the major IGSCC factors were defined as 16% and 84% on their cumulative probability distributions. Minimum lifetime was determined as 5% of the cumulative probability distribution (2σ) of the lifetime distribution.

2

a a G0 = s 00 + s 01 ⎛ ∗ ⎞ + s 02 ⎛ ∗ ⎞ ⎝a ⎠ ⎝a ⎠

a a 2 G1 = s10 + s11 ⎛ ∗ ⎞ + s12 ⎛ ∗ ⎞ ⎝a ⎠ ⎝a ⎠ a a 2 G2 = s20 + s21 ⎛ ∗ ⎞ + s22 ⎛ ∗ ⎞ ⎝a ⎠ ⎝a ⎠ a a 2 G3 = s30 + s31 ⎛ ∗ ⎞ + s32 ⎛ ∗ ⎞ ⎝a ⎠ ⎝a ⎠

1) Uncertainty of major parameters and factors

The CGR was determined as a function of the crack depth as shown in Eq. (14).

Each of the parameters has their own uncertainty as shown in

+σ −σ

Fig. 3. Examples of relationship of crack depth, residual stress and stress intensity. 116

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envelope curves, is shown (Japan Society of Mechanical Engineers, 2004). The CGR curves as a function of K are compared in Fig. 7 for various ECP and EPR with their guideline curves. The guideline curves were the envelope curves with the large safety factors. The standard deviation of the conductivity of the water was fixed at ± 0.05 μS/cm. The guideline curves were generally higher than the CGR curves calculated with the empirical formula. So in order to evaluate CGR with suitable safety margins, application of the guideline should be based on safety-side results.

Table 2. Uncertainties of water chemistry parameters were generally high and those of material parameters were rather low, while those of residual parameters were very low without direct measurement. The uncertainty of each parameter is shown as a function in Eqs. (17)–(22) (1) Elemental parameters (uncertainties: assumed) ⎡

⎢− 1 ECP F(ϕ) = e⎢⎣ (2πσϕ2)1/2

{ϕ − ϕo }2 ⎤ ⎥ 2σ 2ϕ ⎥ ⎦

(17) ⎡

Conductivity F(κ) =

⎢− 1 e⎣ (2πσk2)1/2 ⎡

EPR F(ε) =

⎢− 1 e⎣ (2πσe2)1/2

(18)

{ε − εo } ⎤ ⎥ 2σ 2ε ⎦

{σ − σo}2 ⎤ ⎥ 2σ 2σ ⎦

⎢− 1 e⎣ (2πσs2)1/2

(20) ⎡

⎡

One of the benefits of application of the empirical formula for evaluating CGR is that probability of crack growth as a function of exposure time can be estimated with the uncertainty in evaluation, then risks of IGSCC can be evaluated and the effects of countermeasures on mitigation of crack propagation are determined including the consideration of uncertainty in each of the parameters. In order to apply the empirical formula for risk analysis, uncertainty of formula should be evaluated first and then those uncertainties due to major parameters should be evaluated. From this, the total uncertainty caused by CGR estimation can be obtained. The CGR be divided into two periods, the crack incubation period and the crack growth period. At the specimen surface, the SIF, K in Eq. (1), is zero, which means the CGR is zero. The CGR was calculated by assuming existence of small-size initial crack on the surface (50 μm crack in depth was assumed.) (Fig. 8). The time when the crack grows to 50 μm in depth was designated as the incubation time. The incubation time can be determined by applying the F-value, which is shown as follows (Yamauchi et al., 1993). The F-value was determined based on the accelerated test for IGSCC occurrence, which was defined as a function of ECP, EPR, conductivity and SIF.

(19)

SIF as an elemental parameter F(κ) =

Temperature F(T) =

4.1. Plant risks due to IGSCC

2

⎡

Residual stress F(σ) =

4. Lifetime evaluations

{κ − κ o}2 ⎤ ⎥ 2σ 2κ ⎦

⎢− 1 e⎣ (2πσT2)1/2

⎢− 1 e⎣ 2 1/2 (2πσκ )

{κ − κ o}2 ⎤ ⎥ 2σκ2 ⎦

{T−To}2 ⎤ ⎥ 2σ 2T ⎦

(21)

(22)

The reference values of major parameters and their uncertainties to be applied for sensitivity analysis are shown in Table 3. (2) Combined factors (Major factors)

Water chemistry factor F(n) = fn (ϕ, κ, ε)F(ϕ)F(κ)F(ε)

SIF as an IGSCC factor F(K) =

fK (x,σ sti ,

s ij, Gi)

(23) (24)

calculated from residual stress distribution

TLincubation = βF

dx CGR F ⎛ ⎞ = f dx (n,K,T) dt ⎝ dt ⎠

(25)

Lifetime F(tL) = f tL (n,K,T)

(26)

(27)

6

∏ (FEi )

F= θ

(28)

i= 1 L TCG =

The uncertainties of n-value and CGR are shown in Fig. 5. The stress factor to determine CGR is not determined by only the residual stress but by SIF which can be determined by the residual stress, crack depth and geometrical parameters. Under the conditions of a compact tension (CT) test, the SIF is controlled at the target value. For the demonstration of the uncertainty analysis for SIF as an elementary parameter, SIF was fixed at 27 MPa m1/2.

TLtotal

=

t allow da dt L TCG

(29)

+

TLincubation

(30) (31)

t allow = 0.75t

The allowable flaw depth (allowable crack depth (ACD)) (was determined based on the ASME Boiler & Pressure Vessel Code, XI (ASME Boiler and Pressure Vessel Committee, 2015). In this paper, to demonstrate the evaluation procedure, it was assumed that the incubation period was zero for the lifetime evaluation and the residual stress was uniform along the pipe thickness direction (Eq. (5)). The lifetime to reach pipe rupture, TLtotal, was calculated as the summation of the incubation time TLincubation and TLCG. When applying the uniform residual stress through the pipe wall,

2) Uncertainty of the empirical model itself The CGR as a function of ECP was calculated based on Eqs. (1)–(7) by assuming that the standard deviation, σ, of conductivity was ± 0.05 μS/cm (Fig. 6). The calculated CGR agreed with the measured for conductivity 0.1 μS/cm but there were still some gaps between calculated and measured growth rates for conductivities of 0.25 and 0.5 μS/ cm. From Fig. 6a), it was concluded that the uncertainty of the empirical formula for low conductivity did not exceed a factor of 1.5 (+50, −25%). As conductivity increasing above 0.5 μS/cm, the uncertainty of the formula exceeded a factor of 2.0.

Table 3 Reference values of major parameters and their uncertainties to be applied for sensitivity analysis.

3) Comparison between the guideline values and the calculated ones with uncertainties In the IGSCC guideline of Japan Society of Mechanical Engineers, the relationship between the CGR and SIF, especially their largest

Major parameters (units)

Reference values

Ranges for analysis

Uncertainties*

ECP (mV-SHE) Conductivity (μS/cm) EPR (C/cm2) Residual stress (MPa)

0 0.3 15 100

− 600 to +400 0.1–1.0 1–30 30–300

± 100 ± 05 ±1 factor 1.2

* Uncertainty values were just assumed. 117

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Fig. 5. Uncertainties of elemental parameters and their propagation to major IGSCC factors, CGR and lifetime.

stopped. The uncertainties of IGSCC parameters propagated to major IGSCC factors and CGR, and finally evaluation as uncertainty of lifetime. Plant risks due to IGSCC were determined not only by probability but also by the hazard scale due to pipe rupture resulting from IGSCC. For the risk evaluation, the probability of occurrence of event (pipe

the SIF was a function of crack depth as shown in Fig. 9a). So the uncertainties at a certain crack depth could be calculated by combining uncertainty of each parameter. When applying the realistic stress distribution, crack growth rate increased with crack depth first and then decreased due to decreasing K, and that is shown in Fig. 9b). When crack depth exceeded the value where K became negative, crack growth

Fig. 6. Predicted CGR for EPR = 15C/m2, K = 30 MPam1/2. 118

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lifetime, TLincubation+TLCG allowable crack depth, TLallow crack growth incubation period, period TLincubation 0

0

uncertainty in lifetime

been discussed to show the basic methodology for synthesizing the uncertainty propagation. Some examples of the risk evaluation base on FAC pipe rupture were shown previously (Uchida et al., 2016). Simply put, the hazard scale is defined as the volume of effluent of steam and water from the ruptured mouth, which is the enthalpy of water originally flowing in the pipe multiplied by the square of the pipe inner diameter.

probability of lifetime (arbitrary unit)

crack depth (arbitrary unit)

Fig. 7. Relationship between the stress intensity factor and CGR for normal water chemistry (NWC) and hydrogen water chemistry (HWC) conditions. a) NWC for sensitized specimen, b) NWC for non-sensitized specimen, c) HWC for sensitized specimen and d) NWC for non-sensitized specimen.

4.2. Uncertainty propagation 4.2.1. Uncertainty of IGSCC CGR The IGSCC CGR is designated as a function of the crack depth, which has been calculated with the procedure shown in Fig. 6.

0 exposure time (arbitrary unit)

Fig. 8. Crack depth trend and lifetime to reach the allowable crack depth.

4.2.2. Lifetime evaluation Time to reach the ACD was determined by Eq. (32).

rupture), its hazard scale (the scale of the rupture) and its propagation to the reactor core damage should be evaluated based on the fault tree analysis but in the demonstration here only pipe rupture probability has

L TCG =

119

tallow

∫a=a

0

⎡a ⎤ ⎢ da ⎥ da ⎢ ⎣ dt ⎥ ⎦

(32)

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Fig. 9. Examples of relationship of crack depth, CGR and time to reach the crack depth. ECP = +150 mV-SHE; k = 0.1 μS/cm; EPR = 15 Cm2; σ: ± 100 MPa.

calculated crack depths, residual stress at the region of interest can be tuned. In Fig. 12c), uncertainty of residual stress was shown as a factor, where a factor of 2 meant +100% and −50% of uncertainty.

CGR, da/dt, was determined by Eqs. (9) or (14). By applying uncertainties in the CGR and the ACD, elapsed time for the ACD, which was designated as time margin for pipe rupture, could be calculated as shown in Fig. 10 for different ECP values. Even if the uncertainty in ECP was fixed at ± 50 mV, uncertainty of ECP dependent lifetime was so large in the region of −100 ≥ +150 mV-SHE that the lifetime was determined as 5% of cumulative lifetime distribution. As the elapsed time for pipe rupture, the minimum lifetime (the discussion point in this paper) was designated as lifetime to reach 5% of the cumulative probability shown in Fig. 10. The lifetimes (time to rupture) for changing ECP and residual stress are shown in Fig. 11. There was much more dependence on ECP and residual stress than on conductivity and EPR.

The uncertainty-dependent lifetimes for the realistic residual stress distribution shown in Figs. 3b) and 9b) were redrawn in Fig. 13, where uncertainty of only the constant part of residual stress (σst o in Eq. (12)) was considered in the present evaluation. The uncertainties of disst tribution pattern of residual stress, i.e., σst 1 –σ3 , along with G factors for SIF should be also discussed as a check for sensitivity analysis, which is a future subject.

4.2.3. Uncertainty-dependent lifetime

5. Discussions

1) Uniform stress

5.1. Uncertainties of CGR and SIF models

The calculated lifetime depended on the uncertainty of each parameter (Fig. 12). The results showed that uncertainties in both ECP and residual stress resulted in much larger effects on lifetime evaluation, which meant that the uncertainty in ECP should be lowered by precise measurement and prediction. The uncertainty in ECP was now around ± 100 mV and it was expected to reduce to ± 50 mV by applying suitable verification and validation procedures for ECP evaluation based on coupled analyses of water radiolysis and ECP calculations (Uchida et al., 2014). However it is very difficult to determine residual stress of piping at constructed power plants and the residual stress value is tuned by the measured crack depth on piping. By comparing the measured and

In the paper, the effects of uncertainties of major parameters, i.e., ECP, conductivity, EPR and residual stress, on lifetime were discussed. For real application of the method for plant reliability analysis, more parameters should be evaluated. And also, the effects of uncertainties of CGR and SIF models themselves, even if they have been validated, on lifetime and crack depth should be evaluated in the same way as uncertainty analysis of the FAC model (Uchida et al., 2018). The evaluations of the uncertainties of the models should be added to CGR and SIF evaluations in Fig. 5. In the analysis, incubation time for crack initiation occurrence was neglected. The initial crack depth was fixed at 50 μm. The effects of uncertainty of the ACD determined based on the ASME Code should be

2) A realistic residual stress distribution

Fig. 10. Uncertainty of lifetime for different ECPs. a) ECP = −100 mV-SHE, b) ECP = 0 mV-SHE and c) ECP = +150 mV-SHE. 120

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Fig. 11. Effects of major parameters on lifetime (time to rupture) a) ECP and b) Residual stress.

Fig. 12. Effects of uncertainty of each parameter on lifetime a) ECP, b) EPR, c) Conductivity and d) Residual stress,

5.2. Uncertainty of residual stress In order to evaluate IGSCC occurrence and propagation, it is important to determine the residual stress distribution along the pipe thickness direction around the welded zone. At the same time, it is very difficult to determine them. Direct measurement of the residual stress distribution at operating plants is almost impossible. Their determinations were mainly from semi-empirical calculation based on precise analysis of welding processes. If sufficient data on welding processes (welding procedures, heating histories and so on) are available, residual stress distribution can be evaluated with large uncertainty, and then, the effects of uncertainty of residual stress on lifetime estimation are also evaluated with large uncertainty. Precise evaluation of the effects of the uncertainty in residual stress distribution at welded zone, which are shown in the operating plants, is the future subjects.

Fig. 13. Effects of uncertainty of residual stress on lifetime for realistic stress distribution.

also evaluated. Crack tip sharps also result in uncertainties in the lifetime. Evaluation of the effects of those parameters on the lifetime and crack depth is the future subjects. 121

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Fig. 14. Inspection based on prediction and parameter tuning based on inspection (combination of prediction and inspection).

One of the merits with applying the combination of prediction and inspection is mitigation of the effects of uncertainties of major parameters by tuning the original values of major parameters and their uncertainties based on repeated evaluations. Especially, evaluated residual stress distributions contain large uncertainties, which result in large uncertainties in CGR and lifetime evaluations. Only way to bridge the gap between the estimated residual stresses and the real ones is application of the combination of prediction and inspection. Even if first estimation of the residual stress distribution results in fairly large uncertainty, which decreases and decreases by applying repeated evaluations based on the combination of prediction and inspection.

2) A methodology for evaluating plant reliability based on the combination of the prediction and inspection procedures was proposed. The procedures for applying the IGSCC crack growth model were demonstrated. 3) One of the key points in combining the prediction and inspection was uncertainty analysis for the prediction model. Uncertainty of prediction results was acceptable and the allowed lifetime of the piping was evaluated with this uncertainty. Then the inspection plan was determined taking into consideration of uncertainty. Subsequently, uncertainty was minimized based on inspection results. 4) Experience gained through plant risk analysis will allow engineers to extend the methodology for quantitative evaluation of the effects of FAC and CF of structural materials on plant reliability.

6. Proposed inspection procedures

Acknowledgements

The proposed combination of prediction and inspection is shown in Fig. 14. Effective inspections can be prepared based on evaluation of pipe rupture occurrence and a hazard scale for pipe rupture and on confirmation of the pipe status, e.g., crack initiation and crack size. Plant inspections may provide many important piping data, which can be applied to minimize the uncertainties of residual stress and other important parameters. Risk evaluation based on pipe rupture occurrence due to IGSCC and the hazard scale from pipe rupture can ensure suitable and effective inspections with minimum labor cost, and they may provide important data on IGSCC occurrence and CGR when cracks are detected. The data can be applied to lessen the uncertainties in elemental parameters, e.g., residual stress, which will lead to improved lifetime evaluation. The cycle of prediction, inspection, data acquisition and model improvement hold the promise of higher plant reliability.

The uncertainty analysis of the IGSCC crack growth model has been carried out based on the IGSCC crack growth model (PLEDGE Model). Some constants for the PLEDGE model were not obtained from the literature but from Dr. P. L. Andresen of Andresen Consulting. The authors express their sincere thanks to Dr. Andresen for his support of this work.

5.3. Reduction procedures of uncertainty

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