Formulation of the Stress Corrosion Crack Growth Rates Based on the Theoretical Strain Rate Model for Light Water Reactors

Koshiishi, Masato; Akazawa, Dan; Miura, Yasufumi; Kako, Kenji

doi:10.1115/1.4068490

Abstract

The stress corrosion cracking (SCC) growth rate in a light water reactor environment is usually expressed in the form of a power law of the stress intensity factor, K. However, the power law of K was originally introduced with reference to the Paris law in fatigue crack growth and it is not based on SCC growth theory. Based on the theoretical equation for the strain rate ahead of the crack tip of a growing crack, it is appropriate to express the SCC growth rate in the form of a power law of log(K/K₀). On the other hand, the conventional equation in the form of a power law of K is based on the strain distribution ahead of the stationary crack and it is not theoretically appropriate for growing cracks. This study developed a formulation method for SCC growth rate based on SCC growth theory and the theoretical equation of strain distribution ahead of the crack tip. And it confirmed the applicability of the proposed formulation method for several types of materials.

1 Introduction

Stress corrosion cracking (SCC) in high-temperature water is a critical issue for LWR components [1,2] to assure their integrity. SCC crack growth rate (CGR) is necessary for the integrity assessment of the components. CGR disposition curves have been proposed as a function of the stress intensity factor (K) and the type of equation is a power law of K. However, the power law of K was introduced with reference to the Paris law in fatigue crack growth and it is not based on SCC growth theory.

In this study, a formulation method of SCC growth rate was investigated based on SCC growth theory and the theoretical equation of strain distribution ahead of the crack tip.

The SCC growth rate equation was developed based on the conventional relationship between SCC CGR and the crack tip strain rate proposed by Ford with global consensus among experts knowledgeable in SCC [3,4]. In this paper, the theoretical equation for the strain rate ahead of the crack tip of a growing crack, such as the Gao–Hwang equation [5] and Rice–Drugan–Sham (RDS) equation [6], were combined with Ford's relationship [3,4].

The applicability of the developed SCC CGR model equations was verified by comparing their results with actual experimental SCC CGR data. The model input coefficients were obtained so that the calculated results fitted the SCC CGR data for Alloy 82, Alloy X-750, cold worked stainless steels (SSs), and irradiated SSs. Comparisons were also made with results obtained using the power law of K equation.

2 Stress Corrosion Cracking Crack Growth Rate Model Equations

The concept of the slip oxidation mechanism is illustrated in Fig. 1. Illustrations were drawn based on information in the literature [3,4].

Fig. 1

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Illustration of the slip oxidation mechanism

At the crack tip, the oxidation current flows on the bare surface without a protective film. Repassivation then occurs at the crack tip where the protective film grows and the oxidation current decreases. When the protective oxide film ruptures under strain, the oxidation current flows again on the bare surface without the protective film. This process is repeated as the slip oxidation mechanism.

The following relationship between SCC growth rate and strain rate at the crack tip is known to hold based on the slip oxidation mechanism [3,4]

\frac{d a}{d t} = A \cdot {(\frac{d ε}{d t})}^{m}

(1)

Here, a is crack length, t is time, ε is strain at crack tip, A is a variable related to charge per cycle of slip oxidation, and m is the exponent of the oxidation current decay curve constant. This equation is valid if m < 1 and loses its validity if m = 1 [7]. (In this equation and those of Secs. 2.1 and 2.2, three Greek letter symbols, β, λ, and α of the original literature are used to represent the dimensionless constant for crack tip plastic strain rate.)

To determine the crack tip strain rate in Eq. (1), it is necessary to know the strain distribution near the crack tip. Various theoretical equations have been obtained for the strain distribution equation near the crack tip. Gerberich et al. [8] summarized the theoretical equations for strain distribution as shown in Tables 1 and 2 of their paper. Three typical equations are described in Secs. 2.1–2.3 by using the summarized information [8].

2.1 Gao–Hwang Equation.

The Gao–Hwang strain equation [5] was derived for a growing crack in strain hardening materials

ε (r) = β \cdot \frac{σ_{y}}{E} {[\ln (\frac{λ}{r} {(\frac{K}{σ_{y}})}^{2})]}^{\frac{n}{n - 1}}

(2)

Here, $β$ and $λ$ are dimensionless constants related to crack tip plastic strain, $σ_{y}$ is the yield stress, $E$ is Young's modulus of the metal, $n$ is the strain hardening exponent as defined by Gao and Hwang, and $K$ is the stress intensity factor. r is the distance from the crack tip.

The strain rate at the crack tip is expressed as the following equation when

d K / d t

is zero or negligible. In the case of the CGR test using the compact tension specimen,

d K / d t

is zero or negligible under the constant K and/or constant load conditions

\frac{d ε}{d t} = β \cdot \frac{σ_{y}}{E r_{0}} \frac{n}{n - 1} {\ln (\frac{λ}{r_{0}} {(\frac{K}{σ_{y}})}^{2})}^{\frac{1}{n - 1}} \cdot \frac{d a}{d t}

(3)

Here, $r_{0}$ is a characteristic distance from the crack tip at which the strain rate is defined.

Substituting Eq. into Eq. , the following model Eq. is obtained

\begin{matrix} \frac{d a}{d t} = A^{\frac{m}{1 - m}} \cdot {[β \cdot \frac{σ_{y}}{E r_{0}} \cdot \frac{n}{n - 1} \cdot {[\ln {\frac{λ}{r_{0}} {(\frac{K}{σ_{y}})}^{2}}]}^{\frac{1}{n - 1}}]}^{\frac{m}{1 - m}} \\ = A^{\frac{m}{1 - m}} \cdot {[\frac{β}{E r_{0}} \cdot \frac{n}{n - 1} \cdot {(\frac{2}{\log (e)})}^{\frac{1}{n - 1}} \cdot σ_{y} \cdot {[\log K - \log (\sqrt{\frac{r_{0}}{λ}} \cdot σ_{y})]}^{\frac{1}{n - 1}}]}^{\frac{m}{1 - m}} \\ = B \cdot {[b \cdot N \cdot {(\frac{2}{\log (e)})}^{N - 1} \cdot σ_{y} \cdot {[\log K - \log (c \cdot σ_{y})]}^{N - 1}]}^{\frac{m}{1 - m}} \end{matrix}

(4)

where

B = A^{\frac{m}{1 - m}}

(5)

b = \frac{β}{E r_{0}}

(6)

N = \frac{n}{n - 1}

(7)

c = \sqrt{\frac{r_{0}}{λ}}

(8)

2.2 Rice–Drugan–Sham Equation.

The RDS equation [6] expresses the crack tip strain rate of a growing crack in elastic-ideally plastic materials as follows:

\frac{d ε}{d t} = 2 K \cdot \frac{d K}{d t} \cdot \frac{α}{r_{0} E σ_{y}} + β \cdot \frac{σ_{y}}{E r_{0}} {\ln (\frac{λ}{r_{0}} {(\frac{K}{σ_{y}})}^{2})} \cdot \frac{d a}{d t}

(9)

Here, α represents a dimensionless constant related to crack tip plastic strain.

In the case of the CGR test using the compact tension specimen,

d K / d t

is zero or negligible under the constant K and/or constant load conditions. Then, Eq. can be rewritten as follows:

\frac{d ε}{d t} = β \cdot \frac{σ_{y}}{E r_{0}} {\ln (\frac{λ}{r_{0}} {(\frac{K}{σ_{y}})}^{2})} \cdot \frac{d a}{d t}

(10)

Substituting Eq. into Eq. , the following model Eq. is obtained:

\begin{matrix} \frac{d a}{d t} = A^{\frac{m}{1 - m}} \cdot {[β \cdot \frac{σ_{y}}{E r_{0}} \cdot [\ln {\frac{λ}{r_{0}} {(\frac{K}{σ_{y}})}^{2}}]]}^{\frac{m}{1 - m}} \\ = A^{\frac{m}{1 - m}} \cdot {[\frac{β}{E r_{0}} \cdot \frac{2}{\log (e)} \cdot σ_{y} \cdot [\log K - \log (\sqrt{\frac{r_{0}}{λ}} \cdot σ_{y})]]}^{\frac{m}{1 - m}} \\ = B \cdot {[d \cdot σ_{y} \cdot [\log K - \log (c \cdot σ_{y})]]}^{\frac{m}{1 - m}} \end{matrix}

(11)

where

d = \frac{β}{E r_{0}} \cdot \frac{2}{\log (e)}

(12)

2.3 Hutchinson–Rice–Rosengren Equation.

The Hutchinson, Rice, and Rosengren strain equation [9,10] was derived for a stationary crack of strain hardening materials

ε (r) = α \cdot \frac{σ_{y}}{E} {\frac{λ}{r} {(\frac{K}{σ_{y}})}^{2}}^{\frac{n^{'}}{n^{'} + 1}}

(13)

Here, α represents a dimensionless constant related to crack tip plastic strain and $n'$ is the strain hardening exponent in the Ramberg–Osgood equation.

The strain rate at the crack tip is expressed as the following equation when

d K / d t

is zero or negligible. In the case of the CGR test using the compact tension specimen,

d K / d t

is zero or negligible under the constant K and/or constant load conditions

\frac{d ε}{d t} = α \cdot \frac{σ_{y}}{E} \frac{n'}{n^{'} + 1} \cdot {(\frac{1}{r_{0}})}^{\frac{2 n' + 1}{n' + 1}} {λ {(\frac{K}{σ_{y}})}^{2}}^{\frac{n'}{n^{'} + 1}} \cdot \frac{d a}{d t}

(14)

Substituting Eq. into Eq. , Eq. is obtained

\frac{d a}{d t} = B \cdot {[α \cdot \frac{σ_{y}}{E} \cdot \frac{n^{'}}{n^{'} + 1} \cdot {(\frac{1}{r_{0}})}^{\frac{2 n^{'} + 1}{n^{'} + 1}} {λ {(\frac{K}{σ_{y}})}^{2}}^{\frac{n^{'}}{n^{'} + 1}}]}^{\frac{m}{1 - m}}

(15)

2.4 Appropriate Equation Method for the Growing Stress Corrosion Cracking.

Equation (15) can be rewritten as a power law of K (i.e., $\frac{d a}{d t} = p \cdot K^{q}$ ⁠). This means that the conventional power law of K equation uses the strain distribution for the stationary crack.

Gerberich et al. [8] measured the plastic strain at the crack tip of a single crystal of Fe-3 wt. %Si after crack propagation using the selected-area channeling patterns technique and reported that the calculated values obtained using Eq. agreed well with the measured results. In view of these findings, the following equation is considered appropriate as the growth rate equations for growing SCC cracks:

\frac{d a}{d t} = f \cdot {(\log (K) - \log (K_{0}))}^{g}

(16)

where

K_{0} = c \cdot σ_{y}

(17)

Here, f and g are constants, and $K_{0}$ represents the threshold of K at which SCC can progress.

Equation (16) is more accurately expressed as Eq. (4) for strain hardening materials, and Eq. (11) for the elastic-ideally plastic materials.

Equation (15) is derived from the strain distribution of a crack at rest and has the same form as the Paris law and it is not appropriate for the growing crack.

3 Setting Input Parameters by Comparing With Experimental Stress Corrosion Cracking Crack Growth Rate Data

3.1 Alloy 82 in the Boiling Water Reactor Normal Water Chemistry Environment.

The applicability of the proposed model Eq. (4) to SCC growth rate data for Alloy 82, a nickel-based weld metal, was studied. Alloy 82 is used in boiling water reactors (BWRs) in areas of the pressure boundary, such as the welding of the shroud support to the reactor pressure vessel.

The data covered were those used to obtain the SCC CGR disposition curve developed by the EPRI Expert Panel [11,12] and they were obtained under the simulated BWR normal water chemistry (NWC) condition at 288 °C. Specimens were taken from the weld and no heat treatment was applied, i.e., specimens were in the as-welded condition. Alloy 82 is a strain hardening material after yielding, so model Eq. (4) was fitted to the data to obtain the input coefficients. For the yield stress $σ_{y}$ ⁠, a value of 350 MPa at 288 °C was estimated from the literature [13].

Figure 2 compares the SCC CGR data for Alloy 82 [11,12] with the calculated results of model Eq. (4). The results of the calculations using the power law of K, $d a / d t = p \cdot K^{q}$ ⁠, and the SCC CGR disposition curve proposed by EPRI [11,12] are also shown. To fit the calculation results to the data, the input coefficients were obtained by the least squares method and the following values were obtained: B = 1.047 × 10⁻⁴, b = 1.072 × 10⁻⁵ (/(MPa $\cdot m))$ ⁠, N = 1.883, c = 2.634 × 10⁻² $(\sqrt m)$ ⁠, m = 0.775, and K₀ = 9.2 MPa √m. The unit of K is MPa √m, and the unit of $d a / d t$ obtained in the calculation is m/s. As shown in the figure, the calculated results of model Eq. (4) fitted the K dependency trend of the SCC CGR data well.

Fig. 2

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Comparison between the SCC CGR data of Alloy 82 in BWR NWC condition at 288 °C and the calculation results. Plotted experimental data were from the literature [11,12].

Figure 3 compares the results of the calculations using model Eq. (4) with those using the power law of K and the SCC CGR disposition curve proposed by EPRI [11,12]. As seen in the figure, the results of the calculations using the power law of K type equation provided CGRs that were more than one order of magnitude faster in the region K < 12 MPa√m than the results of the SCC CGR disposition curve proposed by EPRI [11,12]. On the other hand, the results obtained using model Eq. (4) were in good agreement with the SCC CGR disposition curve proposed by EPRI [11,12].

Fig. 3

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Comparison between the results of the calculations using model Eq. (4) and those using the power law of K and the SCC CGR disposition curve proposed by EPRI [11,12] for SCC CGR of Alloy 82 in BWR NWC condition at 288 °C.

Figure 4 compares the SCC CGR data for Alloy X-750 [14] with the results of the calculation using model Eq. (4). The results of the calculations using the power law of K, $d a / d t = p \cdot K^{q}$ are also shown. The experimental data were obtained under the simulated BWR NWC condition at 288 °C, and 0–10 ppb SO₄ was added. Specimens were taken from the plate with T-L and S-L orientations. Alloy X-750 is a strain hardening material after yielding [15], so model Eq. (4) was fitted to the data to obtain the input coefficients. For the yield stress $σ_{y}$ ⁠, a value of 713.5 MPa at 288 °C was estimated from the literature [15]. To fit the calculation results to the data, the input coefficients were obtained by the least squares method and the following values were obtained: B = 5.762 × 10⁻⁶, b = 2.863 × 10⁻⁶ (/(MPa $\cdot m))$ ⁠, N = 1.705, c = 1.211 × 10⁻² $(\sqrt m)$ ⁠, m = 0.636, and K₀ = 8.6 MPa √m. The unit of K is MPa √m, and the unit of $d a / d t$ obtained in the calculation is m/s. As shown in the figure, the calculated results of model Eq. (4) fitted the K dependency trend of the SCC CGR data well. As seen in the figure, the results of the calculations using the power law of K type equation provided CGRs that were 4 to 5 orders of magnitude faster in the region of K around 10 MPa√m than the experimental SCC CGR [14].

Fig. 4

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Comparison between the SCC CGR data of Alloy X-750 in BWR NWC condition at 288 °C and the calculation results. Plotted experimental data were from the literature [14].

3.2 Cold Worked Type 316 L Stainless Steels in Boiling Water Reactor Normal Water Chemistry Environment.

The applicability of the proposed model Eq. (11) to SCC CGR of cold worked SSs was then investigated. First, SCC CGR data in the BWR NWC environment at 288 °C were compared with the calculation results obtained using the proposed model Eq. (11). SCC CGR data for 15% cold worked 316 L SSs reported by the present authors and other researchers [16], as data obtained from the same test institute, were selected for this task. Since it has been reported that the SCC CGR calculation for 15% cold worked SS for the constant K condition was appropriate to use with the RDS equation for the crack tip strain rate [17], the input coefficients for model Eq. (11) were fitted using the least squares method. The following values were obtained: B = 5.339 × 10⁻⁴, d = 1.254 × 10⁻⁵ $(/ (MPa \cdot m))$ ⁠, c = 2.211 × 10⁻³ $(\sqrt m)$ ⁠, and m = 0.762. The unit of K is MPa √m, and the unit of $d a / d t$ obtained in the calculation is m/s. For the cold work materials for which SCC CGR data were obtained, the yield stress $σ_{y}$ values were 455 MPa and 478 MPa. K₀ = 1.0 MPa√m for $σ_{y}$ = 455 MPa and K₀ = 1.1 MPa√m for $σ_{y}$ = 478 MPa.

Figure 5 compares the calculation results obtained using model Eq. (11) with the experimental data. The calculation results are shown for two different yield stresses $σ_{y}$ ⁠, and both were in good agreement with the experimental data. The difference in yield stress was small, but the material with the higher yield stress had a faster growth rate.

Fig. 5

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Comparison between the results of the calculations using model Eq. (11) and the experimental data for 15% cold worked Type 316 L SSs in simulated BWR condition at 288 °C. Plotted experimental data were from the literature [16].

Figure 6 compares the calculation results obtained using model Eq. (11) and those obtained using the power law of K from the data with a yield stress $σ_{y}$ of 478 MPa. In the range of K for which data were available, the two were in close agreement. However, in the range K < 15 MPa√m, the results calculated by the power law of K gave a faster SCC growth rate than those calculated by model Eq. (11) and the difference increased as K became smaller.

Fig. 6

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Comparison of the calculation results obtained using model Eq. (11) and those obtained using the power law of K from the data with a yield stress $σ_{y}$ of 478 MPa for 15% cold worked Type 316 L SSs in simulated BWR condition.

3.3 Neutron Irradiated L-Grade Stainless Steels in Boiling Water Reactor Normal Water Chemistry Environment.

The SCC CGR data of neutron irradiated L-grade SSs (e.g., Type 304 L and Type 316 L SSs) in the BWR NWC environment at 288 °C were compared with the calculation results obtained using the proposed model Eq. (11). SCC CGR data for irradiated L-grade SSs with $σ_{y}$ of 600–700 MPa were reported by the Japan Nuclear Energy Safety Organization (JNES) [18,19], and as data obtained from the same test institute, were selected for the comparison task. Since it has been reported that the highly irradiated SSs did not show strain hardening after the yield point and their SCC CGR under the constant K condition was appropriate to use with the RDS equation for the crack tip strain rate [20], the input coefficients for model Eq. (11) were fitted using the least squares method. The following values were obtained: B = 3.639 × 10⁻⁴, d = 9.595 × 10⁻⁶ $(/ (MPa \cdot m))$ ⁠, c = 3.016 × 10⁻³ $(\sqrt m)$ ⁠, and m = 0.702. The unit of K is MPa √m, and the unit of $d a / d t$ obtained in the calculation is m/s. K₀ = 1.8 MPa√m for $σ_{y}$ = 600 MPa and K₀ = 2.1 MPa√m for $σ_{y}$ = 700 MPa. Figure 7 compares the calculation results obtained using model Eq. (11) with the experimental data. $σ_{y} =$ 650 MPa was used for the calculation as the median value for $σ_{y}$ of specimens.The calculation results obtained using the power law of K from the JNES data with a yield stress $σ_{y}$ of 600–700 MPa are also plotted in the figure. In the range of K for which JNES data were available, the two were in close agreement. However, in the range K < 10 MPa√m, the results calculated by the power law of K gave a faster SCC growth rate than those calculated by model Eq. (11) and the difference increased as K became smaller.

Fig. 7

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Comparison between the calculation results obtained using model Eq. (11) with the experimental data [18,19]. $σ_{y} =$ 650 MPa was used for the calculation.

No CGR data for irradiated L-grade SSs at K < 10 MPa√m were found in a literature search by the authors. However, although the steel type and other detailed experimental conditions are unknown, data normalized to CGR at $σ_{y}$ = 700 MPa for a SS specimen in a BWR NWC environment were reported by Eason et al. [21]. Figure 8 compares the calculation results obtained using model Eq. (11) for $σ_{y} =$ 700 MPa with the normalized NWC data. The calculation results obtained using the power law of K from the JNES data with a yield stress $σ_{y}$ of 600–700 MPa are also plotted in the figure. As there are not many data points, a final conclusion awaits further data expansion, but at present, the calculation results of the power law of log(K/K₀) are more consistent with the data than the calculation results of the power law of K.

Fig. 8

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Comparison between the calculation results obtained using model Eq. (11) for $σ_{y}$ = 700 MPa with the normalized NWC data [21]. $σ_{y} =$ 700 MPa was used for the calculation.

3.4 Comparison Between Stress Corrosion Cracking Crack Growth Rate Calculation by Power Law of K and Power Law of Log(K/K₀).

The SCC CGR calculations using the power law of K and the power law of log(K/K₀) were compared for Alloy 82, Alloy X-750, cold-worked Type 316 L SS, and irradiated L-grade SS under BWR NWC condition. In all cases, as K decreased, the calculation results for the SCC CGR using the power law of K were faster than the calculation results using the power law of log(K/K₀). In addition, for the Alloy 82 and Alloy X-750 cases, the results of the calculations using the power law of log(K/K₀) were more consistent with the experimental data trends than the results of the calculations using the power law of K for the SCC CGR. In the case of irradiated L-grade SS, although it is necessary to expand the data and recheck the calculations, when comparing the existing data for K < 10 MPa√m and the calculation results, the latter obtained using the power law of log(K/K₀) were more consistent with the experimental data than those obtained using the power law of K for the SCC CGR.

From the above it was concluded that the results obtained using the power law of log(K/K₀) fitted the experimental data of various types of material more accurately than those obtained using the conventional power law of K. In the case of the power law of K equation, the CGR was faster than that predicted by the power law of log(K/K₀) equation in the low K region.

4 Conclusions

Based on the SCC growth theory and the theoretical equation of strain rate, the following findings were obtained during the development of a formulation method for SCC growth rate.

It was determined as appropriate to express the SCC CGR for the growing crack in the form of a power law of log(K/K₀). The conventional CGR equation, based on the power law of K, was judged to correspond to the evaluation of the strain rate at the crack tip by the strain distribution in a crack at rest.
Based on the findings, model equations for SCC CGR were proposed for both strain hardened and nonstrain hardened materials.
The applicability of each proposed model equation was investigated for Alloy 82, Alloy X-750, cold worked Type 316 L, and irradiated L-grade SSs. The results confirmed that each proposed equation could well predict the trends seen in the experimental data. In all cases, as K decreased, the calculation results for the SCC CGR using the power law of K became faster than the calculation results using the power law of log(K/K₀).

Nomenclature

a =: crack length
A =: variable related to charge per cycle of slip oxidation
da/dt =: crack growth rate
e =: natural logarithm base
E =: Young's modulus of the metal
K =: stress intensity factor
m =: exponent of the oxidation current decay curve
n =: strain hardening exponent defined by Gao and Hwang
n' =: strain hardening exponent defined by Ramberg and Osgood
r =: distance from the crack tip
r₀ =: characteristic distance from the crack tip at which the strain rate is defined

dε/dt =: strain rate ahead of the crack tip
α =: dimensionless constant for crack tip plastic strain
β =: dimensionless constant for crack tip plastic strain
ε =: true strain
λ =: dimensionless constant for crack tip plastic strain
$σ_{y}$ =: yield stress

BWR =: boiling water reactor
CGR =: crack growth rate
JNES =: Japan Nuclear Energy Safety Organization
LWR =: light water reactor
NWC =: normal water chemistry
RDS =: Rice, Drugan, and Sham
SCC =: stress corrosion cracking
SS =: stainless steel

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

References

1.

Andresen

,

P. L.

,

2019

, “

A Brief History of Environmental Cracking in Hot Water

,”

Corrosion

,

75

(

3

), pp.

240

–

253

.10.5006/2881

Google Scholar

Crossref

2.

Okamura

,

Y.

,

Sakashita

,

A.

,

Fukuda

,

T.

,

Yamashita

,

H.

, and

Futami

,

T.

,

2003

, “

Latest SCC Issues of Core Shroud and Recirculation Piping in Japanese BWRs

,”

Transactions of the 17th International Conference on Structural Mechanics in Reactor Technology (SMiRT 17S)

, Prague, Czech Republic, Aug. 17–22, pp.

1421

–

1430

.http://www.lib.ncsu.edu/resolver/1840.20/27435

3.

Ford

,

F. P.

,

1990

, “

The Crack-Tip System and Its Relevance to the Prediction of Cracking in Aqueous Environments

,”

Proceedings of the First International Conference on Environment-Induced Cracking of Metals, NACE-10

, Houston, TX, Oct. 2–7, p.

139

.https://apps.dtic.mil/sti/tr/pdf/ADA228834.pdf

4.

Ford

,

F. P.

,

1996

, “

Quantitative Prediction of Environmentally Assisted Cracking

,”

Corrosion

,

52

(

5

), pp.

375

–

395

.10.5006/1.3292125

Google Scholar

Crossref

5.

Gao

,

Y.

, and

Hwang

,

K.

,

1981

, “

Elastic-Plastic Fields in Steady Crack Growth in a Strain-Hardening Material

,”

Advances in Fracture Research: Proceedings of the 5th International Conference on Fracture

, Cannes, France, Mar. 29–Apr. 3, p.

669

.https://catalog.princeton.edu/catalog/SCSB-2212135

6.

Rice

,

J. R.

,

Drugan

,

W. J.

, and

Sham

,

T. L.

,

1980

, “

Elastic-Plastic Analysis of Growing Cracks

,” Fracture Mechanics (

Proceedings of the Twelfth National Symposium on Fracture Mechanics

),

ASTM

, St. Louis, MO, p.

189

.https://inl.elsevierpure.com/en/publications/elastic-plastic-analysis-of-growing-cracks-4

7.

Hashimoto

,

T.

, and

Koshiishi

,

M.

,

2009

, “

Modification of the FRI Crack Growth Model Equation From a Mathematical Viewpoint

,”

J. Nucl. Sci. Technol.

,

46

(

3

), pp.

295

–

302

.10.1080/18811248.2007.9711533

Google Scholar

Crossref

8.

Gerberich

,

W. W.

,

Davidson

,

D. L.

, and

Kaczorowski

,

M.

,

1990

, “

Experiment and Theoretical Strain Distributions for Stationary and Growing Cracks

,”

J. Mech. Phys. Solids

,

38

(

1

), pp.

87

–

113

.10.1016/0022-5096(90)90022-V

Google Scholar

Crossref

9.

Hutchinson

,

J. W.

,

1968

, “

Singular Behavior at the End of a Tensile Crack in a Hardening Material

,”

J. Mech. Phys. Solids

,

16

(

1

), pp.

13

–

31

.10.1016/0022-5096(68)90014-8

Google Scholar

Crossref

10.

Rice

,

J. R.

, and

Rosengren

,

G. F.

,

1968

, “

Plane Strain Deformation Near a Crack Tip in a Power-Law Hardening Material

,”

J. Mech. Phys. Solids

,

16

(

1

), pp.

1

–

12

.10.1016/0022-5096(68)90013-6

Google Scholar

Crossref

11.

Andresen

,

P. L.

,

Carter

,

R. G.

, and

Kumagai

,

K.

,

2022

, “

Proposed Crack Growth Rate Disposition Curves for Stress Corrosion Cracking of Alloy 82 in BWR Environments

,”

Proceedings of the 20th International Conference on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors

, Snowmass Village, CO, July 17--21.https://research.com/conference/the-20th-international-conference-on-environmentaldegradation-of-materials-in-nuclear-power-systems-water-reactor

12.

Carter

,

R.

,

2023

, “

BWRVIP-358: BWR Vessel and Internals Project Stress Corrosion Crack Growth Rate Behavior of Alloy 82 Weld Metal in Boiling Water Reactor Environments

,”

EPRI

, Palo Alto, CA, Report No. 3002023758.

13.

Kumagai

,

K.

,

Sakai

,

Y.

, and

Kaminaga

,

T.

,

2017

, “

Technical Basis and SCC Growth Rate Data to Develop an SCC Disposition Curve for Alloy 82 BWR Environments

,”

Proceedings of the 19th International Conference on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors

, Boston, MA, p.

373

.https://link.springer.com/chapter/10.1007/978-3-030-04639-2_106

Google Scholar

Crossref

14.

Andresen

,

P.

, and

Carter

,

R. G.

,

2015

, “

Development and Analysis of an Alloy X-750 SCC Growth Rate Database

,”

Proceedings of the 17th International Conference on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors

,

CNS

,

Ottawa, ON, Canada

, Aug. 9–13, pp.

1071

–

1095

.https://www.proceedings.com/28159.html

15.

Jackson

,

J. H.

,

Heighes

,

M.

, and

Andresen

,

P. L.

,

2020

, “

Irradiation and PIE of Alloys X-750 and XM-19 (EPRI Phase III)

,”

Idaho National Laboratory

, Idaho Falls, ID, Report No. INL/EXT-20-58432, Revision 1.

16.

Akazawa

,

D.

,

Koshiishi

,

M.

,

Miura

,

Y.

, and

Kako

,

K.

,

2024

, “

Evaluation of Probabilistic Distribution of SCC Growth Rates Obtained Under the Same Test Conditions in Cold Worked Stainless Steel

,”

Nucl. Eng. Des.

,

430

, p.

113669

.10.1016/j.nucengdes.2024.113669

Google Scholar

Crossref

17.

Koshiishi

,

M.

,

Akazawa

,

D.

,

Miura

,

Y.

, and

Kako

,

K.

,

2024

, “

Prediction of Stress Corrosion Crack Growth Rate of Cold Worked Stainless Steels in BWR Conditions by the Slip Oxidation Model

,”

Nucl. Eng. Des.

,

421

, p.

113060

.10.1016/j.nucengdes.2024.113060

Google Scholar

Crossref

18.

Takakura

,

K.

,

Nakata

,

K.

,

Tanaka

,

S.

,

Nakamura

,

T.

,

Chatani

,

K.

, and

Kaji

,

Y.

,

2009

, “

Crack Growth Behavior of Neutron Irradiated L-Grade Austenitic Stainless Steel in Simulated BWR Conditions

,”

Proceedings of the 14th International Symposium on Environmental Degradation of Materials in Nuclear Power System—Water Reactors

, ANS, Virginia Beach, VA, Aug. 23--27, pp.

1193

–

1203

.https://www.ans.org/meetings/file/view-117/

19.

Japan Nuclear Energy Safety Organization

,

2009

, “

Annual Report of IASCC Assessment Technology of JFY 2008

,”

Japan Nuclear Energy Safety Organization

,

Tokyo, Japan

(in Japanese).

20.

Eason

,

E. D.

,

Ilevbare

,

G.

, and

Pathania

,

R.

,

2011

, “

Preliminary Hybrid Model of Irradiation-Assisted Stress Corrosion Cracking of 300 Series Stainless Steels in PWR Primary Environment

,”

Proceedings of the 15th International Conference on Environmental Degradation of Materials in Nuclear Power Systems—Water Reactors

, TMS,

Springer

,

Cham, Switzerland

, pp.

1309

–

1324

.10.1007/978-3-319-48760-1_80

21.

Eason

,

E. D.

,

Pathania

,

R.

,

Jenssen

,

A.

, and

Weakland

,

D. P.

,

2021

, “

Technical Basis Part 2 for Code Case N-889: Reference Stress Corrosion Crack Growth Rate Curves for Irradiated Austenitic Stainless Steels in Light Water Reactor Environments

,”

ASME J. Pressure Vessel Technol.

,

143

(

2

), p.

021202

.10.1115/1.4047878

Google Scholar

Crossref

Formulation of the Stress Corrosion Crack Growth Rates Based on the Theoretical Strain Rate Model for Light Water Reactors

Abstract

1 Introduction

2 Stress Corrosion Cracking Crack Growth Rate Model Equations

2.1 Gao–Hwang Equation.

2.2 Rice–Drugan–Sham Equation.

2.3 Hutchinson–Rice–Rosengren Equation.

2.4 Appropriate Equation Method for the Growing Stress Corrosion Cracking.

3 Setting Input Parameters by Comparing With Experimental Stress Corrosion Cracking Crack Growth Rate Data

3.1 Alloy 82 in the Boiling Water Reactor Normal Water Chemistry Environment.

3.2 Cold Worked Type 316 L Stainless Steels in Boiling Water Reactor Normal Water Chemistry Environment.

3.3 Neutron Irradiated L-Grade Stainless Steels in Boiling Water Reactor Normal Water Chemistry Environment.

3.4 Comparison Between Stress Corrosion Cracking Crack Growth Rate Calculation by Power Law of K and Power Law of Log(K/K₀).

4 Conclusions

Nomenclature

Data Availability Statement

References

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Formulation of the Stress Corrosion Crack Growth Rates Based on the Theoretical Strain Rate Model for Light Water Reactors Open Access

Abstract

1 Introduction

2 Stress Corrosion Cracking Crack Growth Rate Model Equations

2.1 Gao–Hwang Equation.

2.2 Rice–Drugan–Sham Equation.

2.3 Hutchinson–Rice–Rosengren Equation.

2.4 Appropriate Equation Method for the Growing Stress Corrosion Cracking.

3 Setting Input Parameters by Comparing With Experimental Stress Corrosion Cracking Crack Growth Rate Data

3.1 Alloy 82 in the Boiling Water Reactor Normal Water Chemistry Environment.

3.2 Cold Worked Type 316 L Stainless Steels in Boiling Water Reactor Normal Water Chemistry Environment.

3.3 Neutron Irradiated L-Grade Stainless Steels in Boiling Water Reactor Normal Water Chemistry Environment.

3.4 Comparison Between Stress Corrosion Cracking Crack Growth Rate Calculation by Power Law of K and Power Law of Log(K/K0).

4 Conclusions

Nomenclature

Data Availability Statement

References

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Formulation of the Stress Corrosion Crack Growth Rates Based on the Theoretical Strain Rate Model for Light Water Reactors

3.4 Comparison Between Stress Corrosion Cracking Crack Growth Rate Calculation by Power Law of K and Power Law of Log(K/K₀).