# Characterization of Austenitic Stainless Steels with Regard to Environmentally Assisted Fatigue in Simulated Light Water Reactor Conditions

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## Abstract

**:**

## 1. Introduction

## 2. Materials

## 3. Test Programme

#### 3.1. Main Programme

#### 3.1.1. Test Conditions

#### 3.1.2. Data Overview

#### 3.1.3. Data Analysis

#### 3.1.4. Discussion

#### 3.2. Sub-Programme on Low ${F}_{\mathrm{en}}$ Conditions

#### 3.2.1. Test Conditions

#### 3.2.2. Data Overview

#### 3.2.3. Data Analysis

#### 3.2.4. Discussion

#### 3.3. Sub-Programme on Hold Times

#### 3.3.1. Data from Hold Time Testing

#### 3.3.2. Discussion of Hold Time Data

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AdFaM | Advanced Fatigue Methodologies (name of a project) |

DOE | design of experiments |

EAF | environmentally assisted fatigue |

LTO | long-term operation |

NPP | nuclear power plant |

PWR | pressurized water reactor |

VVER | voda-vodyanoi energetichesky reaktor (Russian: pressurized water reactor) |

${\alpha}_{i}$ | model parameter |

BIC | Bayesian information criterion |

DH2 | dissolved hydrogen content |

DO | dissolved oxygen content |

E | categorical variable for environment; either “air” or “LWR” |

${E}^{\mathrm{n}}$ | normalized categorical variable for environment; either “−1” or “+1” |

${\epsilon}_{\mathrm{r}}$ | strain range: difference between the maximum and minimum strain during a test |

${\epsilon}_{\mathrm{r}}^{\mathrm{n}}$ | normalized strain range |

$\dot{\epsilon}$ | strain rate |

${\dot{\epsilon}}^{\mathrm{n}}$ | normalized strain rate |

${\dot{\epsilon}}^{*}$ | strain rate parameter defined in CR-6909 [4] |

${\epsilon}_{\mathrm{m}}$ | mean strain: strain level in the middle between the maximum and minimum strain in a strain controlled test |

${\epsilon}_{\mathrm{m}}^{\mathrm{n}}$ | normalized mean strain |

${F}_{\mathrm{en}}$ | environmental factor |

I | intercept in model |

$\mathrm{LogLikelihood}$ | natural log of the likelihood function |

${N}_{25}$ | fatigue life, 25% force drop compared to stabilized linear behaviour |

${N}_{\mathrm{f}}$ | fatigue life |

${N}_{\mathrm{f},\mathrm{air},\mathrm{RT}}$ | fatigue life in air at room temperature |

${N}_{\mathrm{f},\mathrm{LWR}}$ | fatigue life in LWR environment |

${N}_{X}$ | fatigue life, X% force drop |

${O}^{*}$ | dissolved oxygen parameter defined in CR-6909 [4] |

${r}_{i,j}$ | correlation between two variables ${x}_{i}$ and ${x}_{j}$ |

${R}_{\mathrm{a}}$ | average surface roughness as defined in ISO 4287 [30] |

${R}_{\mathrm{t}}$ | maximum roughness height as defined in ISO 4287 [30] |

${R}_{\mathrm{t}}^{\mathrm{n}}$ | normalized surface roughness Rt |

${\sigma}_{\mathrm{e}}$ | electric conductivity |

${t}_{\mathrm{h}}$ | categorical variable for hold time |

${t}_{\mathrm{h}}^{\mathrm{n}}$ | normalized hold time |

T | temperature |

${T}^{\mathrm{n}}$ | normalized temperature |

${T}^{*}$ | temperature parameter defined in CR-6909 [4] |

## Appendix A

Algorithms A1 Matlab Function for Model (a) |

function N25 = model_a(epsn,Rtn,En) |

% MODEL_A |

% This function calculates the fatigue life according to the model (a) in Table 6 |

% The entries are the normalized values of strain range, surface |

% roughness and environment as in Table 5. |

% The coefficients according to Table 6 (a) |

% main effects and sigma |

I = 9.1695785; |

epsn_coeff = −0.90106; |

switch En |

case −1 |

En_coeff = 0; |

case 1 |

En_coeff = −1.637142; |

end |

Rtn_coeff = −0.199527; |

sigma = 0.2849506; |

% coefficients and offsets for the interaction terms |

% interaction between epsn and En |

switch En |

case −1 |

epsn_x_En_coeff = 0; |

case 1 |

epsn_x_En_coeff = 0.144387; |

end |

epsn_offset1 = −0.06958; |

% interaction between epsn and Rtn |

epsn_x_Rtn_coeff = 0.0953654; |

epsn_offset2 = −0.06958; |

Rtn_offset = 0.51401; |

N25 = exp(I + epsn_coeff*epsn + En_coeff*En + Rtn_coeff*Rtn +... |

epsn_x_En_coeff*(epsn + epsn_offset1)*En +... |

epsn_x_Rtn_coeff*(epsn + epsn_offset2)*(Rtn + Rtn_offset) +... |

sigma2/2); |

end |

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**Figure 1.**Correlation between ${R}_{\mathrm{t}}$ and ${R}_{\mathrm{a}}$ for the specimens in the database (throughout this work, the symbol ▹ indicates runout specimens). The ratio between ${R}_{\mathrm{t}}$ and ${R}_{\mathrm{a}}$ is 8.7.

**Figure 2.**Data from the main programme (${F}_{\mathrm{en}}$ = 4.57). The colours refer to the test environment. The ▹ indicate runouts, i.e., tests that were stopped before specimen failure (e.g., because of a technical problem with the test rig).

**Figure 4.**Comparison of the model performances as a function of the step in the algorithm, i.e., the number of factors that were removed from the model. Note that progression on the abscissa is from right to left. The vertical red line indicates the optimal model according to the algorithm. (

**a**) -LogLikelihood for the training and validation sets. (

**b**) BIC for the full data set; the green area indicates “very good” model performance (strong evidence that a model is comparable to the best model); the yellow area indicates “good” model performance (weak evidence that a model is comparable to the best model) [39].

**Figure 5.**Model predictions for ${N}_{25}$ vs. experimental values: (

**a**) comparison between the models (

**a**–

**c**). For the predictions with Model (

**a**), colour coding highlights the different environments (

**b**), strain ranges (

**c**) and the surface roughnesses (

**d**).

**Figure 6.**Data in the low ${F}_{\mathrm{en}}$ programme; the reference curves are calculated from the NUREG/CR-6909 mean air curve and the two ${F}_{\mathrm{en}}$ values considered here.

**Figure 8.**Variation of BIC during the iteration steps of the backward elimination algorithm for the low ${F}_{\mathrm{en}}$ model.

**Figure 9.**Maximum stress as a function of cycle; all tests were carried out at a strain range of 0.4%. The tests “EDF AIR 2” and “LEI-21” are the only tests that did not have holds.

**Table 1.**Chemical composition of the different steels (wt.%). The common material (see column “Comment”) was used in the majority of the tests; the other materials were only used by the indicated organizations.

Material | Al | B | C | Co | Cr | Cu | Fe | Mn | Mo | N |
---|---|---|---|---|---|---|---|---|---|---|

304L | 0.029 | 18.00 | 0.02 | bal. | 1.86 | 0.04 | 0.056 | |||

304L | 0.029 | 0.0005 | 0.026 | 0.016 | 18.626 | 0.046 | bal. | 1.558 | 0.227 | 0.074 |

316L | 0.022 | 0.001 | 0.028 | 0.007 | 17.562 | 0.049 | bal. | 1.779 | 2.393 | 0.062 |

304 | 0.035 | 0.05 | 18.39 | 0.17 | bal. | 1.83 | 0.2 | 0.079 | ||

321 | 0.109 | 0.102 | 18.08 | 0.048 | bal. | 1.446 | 0.023 | |||

Material | Nb | Ni | P | S | Si | Ta | Ti | V | W | Comment |

304L | 10.00 | 0.029 | 0.004 | 0.37 | Common | |||||

304L | 0.003 | 9.737 | 0.0133 | 0.0005 | 0.527 | 0.01 | IRSN | |||

316L | 0.002 | 11.947 | 0.0121 | 0.0084 | 0.642 | 0.01 | IRSN | |||

304 | 8.07 | 0.031 | 0.001 | 0.32 | 0.05 | Jacobs | ||||

321 | 9.79 | 0.023 | 0.52 | 0.61 | 0.013 | UJV |

**Table 2.**Test conditions in the main programme and the sub-programme on low ${F}_{\mathrm{en}}$ testing.

Parameter | Low Level | Middle Level | High Level | Comment |
---|---|---|---|---|

${\epsilon}_{\mathrm{r}}$ (%) | 0.6 | 1.2 | ||

${\epsilon}_{\mathrm{m}}$ (%) | 0 | 0.5 | only for Phase I | |

${R}_{\mathrm{t}}$ ($\mathsf{\mu}\mathrm{m}$) | 0.76 | ≈20 | >40 | ${R}_{\mathrm{t}}40$ for Phase II only |

${t}_{\mathrm{h}}$ (h) | 0 | 72 | 0 or 3 holds of 72 h at mean strain; | |

cycles with holds depend on test conditions | ||||

$\dot{\epsilon}$ (%/s) | 0.01 | 0.1 | rising $\dot{\epsilon}$ in PWR env., falling $\dot{\epsilon}$ and air tests may vary; | |

$\dot{\epsilon}$ = 0.1 %/s in low ${F}_{\mathrm{en}}$ tests only | ||||

T (${}^{\xb0}\mathrm{C}$) | 230 | 300 | $T=230{}^{\xb0}\mathrm{C}$ in low ${F}_{\mathrm{en}}$ tests only |

**Table 3.**Definition of the water chemistry; ${\sigma}_{\mathrm{e}}$ is the electric conductivity; DH2 and DO are the dissolved hydrogen and oxygen contents.

Reactor | T${}^{\xb0}\mathbf{C}$ | p MPa | pH @ 300 ${}^{\xb0}\mathbf{C}$ | Li ppm | B ppm | K ppm | ${\mathbf{NH}}_{3}$ ppm | DH2 cc(STP)${\mathbf{H}}_{2}$/kg | DO ppb | ${\mathit{\sigma}}_{\mathbf{e}}$ @ 25 ${}^{\xb0}\mathbf{C}$ $\mathsf{\mu}\mathbf{S}/\mathbf{cm}$ |
---|---|---|---|---|---|---|---|---|---|---|

PWR | 300 | 15 | 6.95 | 2 | 1000 | 25 | <5 | 30 | ||

VVER | 300 | 12.5 | 7 | 1189 | 16.4 | 9.7 | 2 | 22 | 80–110 |

${\mathit{\epsilon}}_{\mathbf{r}}$ | ${\mathit{\epsilon}}_{\mathbf{m}}$ | ${\mathit{R}}_{\mathbf{t}}$ | ${\mathit{t}}_{\mathbf{h}}$ | E | |
---|---|---|---|---|---|

${\epsilon}_{\mathrm{r}}$ | $1.0000$ | $-0.0183$ | $0.1443$ | $0.0252$ | $0.0492$ |

${\epsilon}_{\mathrm{m}}$ | $-0.0183$ | $1.0000$ | $-0.1402$ | $-0.0168$ | $-0.0089$ |

${R}_{\mathrm{t}}$ | $0.1443$ | $-0.1402$ | $1.0000$ | $0.0952$ | $-0.0094$ |

${t}_{\mathrm{h}}$ | $0.0252$ | $-0.0168$ | $0.0952$ | $1.0000$ | $0.0409$ |

E | $0.0492$ | $-0.0089$ | $-0.0094$ | $0.0409$ | $1.0000$ |

Factor | Low Value (−1) | High Value (1) | Comment |
---|---|---|---|

${\epsilon}_{\mathrm{r}}$ (%) | 0.6 | 1.2 | min. and max. values according to the test matrix |

${\epsilon}_{\mathrm{m}}$ (%) | 0 | 0.5 | min. and max. values according to the test matrix |

${R}_{\mathrm{t}}$ ($\mathsf{\mu}\mathrm{m}$) | 0.194 | 65.5 | min. and max. values in the dataset |

${t}_{\mathrm{h}}$ | no hold | incl.holds | categorical variable indicating if the test had holds (Table 2) |

E | air | PWR, VVER | categorical variable indicating the environment |

**Table 6.**Coefficients for the best models in Figure 4. Note that the normalized versions of the factors need to be used (Table 5); in the case of the categorical variable ${E}^{\mathrm{n}}$ the coefficient is zero for ${E}^{\mathrm{n}}$= −1 and the value in the table for ${E}^{\mathrm{n}}$= +1. The p-value in the last column is an indication of the statistical significance of an effect; a threshold of 0.05 is often used as criterion for statistical significance with lower values indicating higher significance. $\sigma $ is a parameter in the lognormal distribution (Equation (10)).

Model | Factor | Estimate | Std Error | p-Value |
---|---|---|---|---|

Model (a) | I | 9.170 | 0.04524 | <0.0001 |

${\epsilon}_{\mathrm{r}}^{\mathrm{n}}$ | −0.9011 | 0.04644 | <0.0001 | |

${E}^{\mathrm{n}}$ [+1] | −1.637 | 0.05123 | <0.0001 | |

${R}_{\mathrm{t}}^{\mathrm{n}}$ | −0.1995 | 0.04137 | <0.0001 | |

(${\epsilon}_{\mathrm{r}}^{\mathrm{n}}$−0.06958) * ${E}^{\mathrm{n}}$ [+1] | 0.1444 | 0.05558 | 0.0094 | |

(${\epsilon}_{\mathrm{r}}^{\mathrm{n}}$−0.06958) * (${R}_{\mathrm{t}}^{\mathrm{n}}$+0.51401) | 0.09537 | 0.04329 | 0.0276 | |

$\sigma $ | 0.2850 | 0.02844 | <0.0001 | |

Model (b) | I | 9.157 | 0.04059 | <0.0001 |

${\epsilon}_{\mathrm{r}}^{\mathrm{n}}$ | −0.9355 | 0.04578 | <0.0001 | |

${E}^{\mathrm{n}}$ [+1] | −1.637 | 0.04594 | <0.0001 | |

${R}_{\mathrm{t}}^{\mathrm{n}}$ | −0.2169 | 0.03702 | <0.0001 | |

(${\epsilon}_{\mathrm{r}}^{\mathrm{n}}$−0.06958) * ${E}^{\mathrm{n}}$ [+1] | 0.1766 | 0.05218 | 0.0007 | |

(${\epsilon}_{\mathrm{r}}^{\mathrm{n}}$−0.06958) * (${R}_{\mathrm{t}}^{\mathrm{n}}$+0.51401) | 0.1097 | 0.04005 | 0.0062 | |

$\sigma $ | 0.2913 | 0.02543 | <0.0001 |

**Table 7.**Coefficients for a reduced model including only the main effects. Note that the normalized versions of the factors need to be used (Table 5); in the case of the categorical variable ${E}^{\mathrm{n}}$ the coefficient is 0 for ${E}^{\mathrm{n}}$= −1, and the value in the table for ${E}^{\mathrm{n}}$= +1.

Model | Factor | Estimate | Std Error | p-Value |
---|---|---|---|---|

Model (c) | I | 9.173 | 0.04283 | <0.0001 |

${\epsilon}_{\mathrm{r}}^{\mathrm{n}}$ | −0.8354 | 0.02690 | <0.0001 | |

${E}^{\mathrm{n}}$ [+1] | −1.650 | 0.05097 | <0.0001 | |

${R}_{\mathrm{t}}^{\mathrm{n}}$ | −0.2160 | 0.03696 | <0.0001 | |

$\sigma $ | 0.3124 | 0.03103 | <0.0001 |

${\mathit{R}}_{\mathbf{t}}$ | $\dot{\mathit{\epsilon}}$ | T | |
---|---|---|---|

${R}_{\mathrm{t}}$ | $1.0000$ | $-0.0589$ | $0.0823$ |

$\dot{\epsilon}$ | $-0.0589$ | $1.0000$ | $0.1846$ |

T | $0.0823$ | $0.1846$ | $1.0000$ |

**Table 9.**Normalization of the factors T and $\dot{\epsilon}$ for the tests at reduced ${F}_{\mathrm{en}}$.

Factor | Low Value (−1) | High Value (1) | Comment |
---|---|---|---|

T (${}^{\xb0}\mathrm{C}$) | 230 | 302.3 | min. and max. values in the dataset |

$\dot{\epsilon}$ (%/s) | 0.01 | 0.1 | min. and max. values according to test matrix |

${R}_{\mathrm{t}}$ ($\mathsf{\mu}\mathrm{m}$) | 0.335 | 49.75 | min. and max. values in the dataset |

**Table 10.**Coefficients of the optimal model for the low ${F}_{\mathrm{en}}$ data. Note that the normalized versions of the factors need to be used (Table 9).

Factor | Estimate | Std Error | p-Value |
---|---|---|---|

I | 8.643 | 0.05659 | <0.0001 |

${R}_{\mathrm{t}}^{\mathrm{n}}$ | −0.2879 | 0.05369 | <0.0001 |

${\dot{\epsilon}}^{\mathrm{n}}$ | 0.2048 | 0.05023 | <0.0001 |

${T}^{\mathrm{n}}$ | −0.2091 | 0.03572 | <0.0001 |

$\sigma $ | 0.2303 | 0.02785 | <0.0001 |

**Table 11.**Fatigue lives calculated with the model in Table 10.

${\mathit{R}}_{\mathbf{t}}^{\mathbf{n}}$ | ${\dot{\mathit{\epsilon}}}^{\mathbf{n}}$ | ${\mathit{T}}^{\mathbf{n}}$ | ${\mathit{N}}_{25}$ |
---|---|---|---|

−1 | −1 | 1 | 5131 |

−1 | −1 | −1 | 7794 |

−1 | 1 | 1 | 7728 |

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**MDPI and ACS Style**

Bruchhausen, M.; Dundulis, G.; McLennan, A.; Arrieta, S.; Austin, T.; Cicero, R.; Chitty, W.-J.; Doremus, L.; Ernestova, M.; Grybenas, A.;
et al. Characterization of Austenitic Stainless Steels with Regard to Environmentally Assisted Fatigue in Simulated Light Water Reactor Conditions. *Metals* **2021**, *11*, 307.
https://doi.org/10.3390/met11020307

**AMA Style**

Bruchhausen M, Dundulis G, McLennan A, Arrieta S, Austin T, Cicero R, Chitty W-J, Doremus L, Ernestova M, Grybenas A,
et al. Characterization of Austenitic Stainless Steels with Regard to Environmentally Assisted Fatigue in Simulated Light Water Reactor Conditions. *Metals*. 2021; 11(2):307.
https://doi.org/10.3390/met11020307

**Chicago/Turabian Style**

Bruchhausen, Matthias, Gintautas Dundulis, Alec McLennan, Sergio Arrieta, Tim Austin, Román Cicero, Walter-John Chitty, Luc Doremus, Miroslava Ernestova, Albertas Grybenas,
and et al. 2021. "Characterization of Austenitic Stainless Steels with Regard to Environmentally Assisted Fatigue in Simulated Light Water Reactor Conditions" *Metals* 11, no. 2: 307.
https://doi.org/10.3390/met11020307