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A bayesian analysis of the influence of neutron irradiation on embrittlement in ferritic submerged arc weld metal

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Abstract

The effect of neutron irradiation and temperature on Charpy-impact-energy properties has been studied to assess the irradiation embrittlement of submerged-arc-weld metal. Measurements of Charpy-impact-energy data are available from irradiation exposures carried out under surveillance conditions at 190 °C and 198 °C and from irradiation at accelerated dose rates carried out over a temperature range from 186 °C to 292 °C. Neutron irradiation at accelerated dose rates was carried out on specimens which were previously subjected to surveillance irradiation. The test-temperature dependence of Charpy impact energy was represented by a relationship based on the Burr distribution function in which some of the parameters were dependent on the neutron dose, irradiation dose rate, and temperature. The analysis of the data was carried out in the Bayesian framework. The posterior probability distributions of the model parameters were computed using Markov chain Monte Carlo based techniques. It has been found that the upper-shelf Charpy impact energy changes by a constant amount, neutron dose independent, between the unirradiated, surveillance-irradiated, and double-irradiated conditions. The temperature shift in the Charpy-impact-energy curves is independent of dose rate but decreases with increasing irradiation temperature. The remaining model parameters were found to be unaffected by neutron irradiation. It has been found that accelerated reirradiation experiments can be used to extend the range of applicability of the surveillance-monitoring scheme.

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Abbreviations

A :

constant for rate of embrittlement in trend curve

A 1 :

constant for rate of embrittlement in trend curve for surveillance dose rate

A 2 :

constant for rate of embrittlement in trend curve for accelerated dose rate during reirradiation

B :

constant for intercept of trend curve

C :

sample of observed Charpy impact energy data

C i :

observed (measured) Charpy impact energy values

C L :

lower shelf Charpy impact energy

C U :

upper shelf Charpy impact energy

D 1 :

neutron dose (dpa × 105)

D 11 :

neutron dose (dpa × 105) during surveillance irradiation

D 21 :

neutron dose (dpa × 105) during accelerated irradiation

E :

constant for the change of rate of embrittlement in trend curve with temperature

E 1 :

constant for the change of rate of embrittlement in trend curve with temperature under surveillance dose rate

E 2 :

constant for the change of rate of embrittlement in trend curve with temperature under accelerated dose rate

F(T i ):

Burr distribution function

F T , F T 1, F T 2:

irradiation temperature dependence parameter relative to the rate of embrittlement at 190 °C

L :

likelihood

L(Θ|C):

likelihood of a set of parameters, Θ, conditional on a set of Charpy values, C

L(Θ t|C):

likelihood of a set of parameters, Θ, at time t conditional on a set of Charpy values, C

L(Θ*|C):

likelihood of a set of proposed parameters, Θ*, conditional on a set of Charpy values, C

L(θ* i |C):

likelihood of parameter θ* i , conditional on a set of Charpy values, C

L(θ t i |C):

likelihood of parameter θ t i , conditional on a set of Charpy values, C

P(Θ):

prior probability of Θ

P(Θ|C):

posterior probability of Θ given data C

T i :

test temperature

T ir :

irradiation temperature

T ir 1:

irradiation temperature during surveillance irradiation

T ir 2:

irradiation temperature during accelerated irradiation

T 0 :

location parameter

T 40J :

temperature at which 40 J Charpy impact energy is achieved

ΔT 40J :

temperature shift at the 40 J Charpy impact energy level

U :

random value from a uniform distribution

U(0, 1):

uniform distribution bounded by 0 and 1

a :

constant in the relationship for F T

b :

constant in the relationship for F T

i :

index for Charpy data

j :

index for model parameters

l :

index for neutron dose

t :

time

p(θ* i ):

prior probability of θ* i

p(θ t i ):

prior probability of θ t i

q(Θ t|Θ*):

transition probability for drawing Θ t from a distribution centered on Θ*

q(Θ*|Θ t):

transition probability for drawing Θ* from a distribution centered on Θ t

q(Θ t):

probability of sampling Θ t

q(θ* l ):

transitional probability of θ* i

q(θ*|θ t):

transition probability for drawing θ* from a distribution centered on θ t

q(θ t i ):

transitional probability of θ ti

w(θ* i ):

weight of θ* i

w(θ ti ):

weight of θ ti

α(Θ t, Θ*):

acceptance probability for a set of proposed model parameters Θ*

α(θ ti , θ* i ):

acceptance probability for a proposed model parameter θ* i

γ 01 :

parameters for T 0 used to model unirradiated data

γ 02, γ 12 :

parameters for T 0 used to model surveillance data

γ 03, γ 13, γ 23 :

parameters for T 0 used to model reirradiated data

ε i :

random error in Charpy impact energy

θ i :

general notation for model parameters

θ 0 :

lower shelf Charpy impact energy

θ 1, θ 2, θ 3 :

upper shelf Charpy impact energy specific to unirradiated, surveillance irradiated, and reirradiated data

Θ :

general notation for a set of model parameters

Θ t, Θ t+1 :

vectors of the model parameters at times t and t + 1

Θ*:

proposed vector of the model parameters

v :

shape parameter

ξ :

scale parameter

ξ 1, ξ 2 ξ 3 :

scale parameters specific to unirradiated, surveillance, and reirradiated

Σ:

covariance matrix

σ 2T :

variance of Charpy impact energy values

σ 1, σ 2, σ 3 :

parameters for σ T

References

  1. R. Moskovic, P.L. Windle, and A.F.M. Smith: Metall. Mater. Trans. A, 1997, vol. 28A, pp. 1181–93.

    CAS  Google Scholar 

  2. P.I. Windle, R. Moskovic, and M.J. Crowder: Nucl. Eng. Design, 1966, vol. 165, pp. 43–56.

    Article  Google Scholar 

  3. P.J.E. Bischler and R.K. Wild: 17th Int. Symp., ASTM STP 1270, ASTM, Philadelphia, PA, 1966, pp. 260–73.

    Google Scholar 

  4. J.T. Buswell, P.J.E. Bischler, S.T. Fenton, A.E. Ward, and W.J. Phythian: J. Nucl. Mater., 1993, vol. 205, pp. 198–205.

    Article  CAS  Google Scholar 

  5. R.B. Jones and T.J. Williams: Effects of Radiation on Materials: 17th Int. Symp., ASTM STP 1270, ASTM, Philadelphia, PA, 1966, pp. 569–90.

    Google Scholar 

  6. C.J. Bolton: BNFL Magnox Generation, Gloucestershire, unpublished work, 1991.

  7. W.K. Hastings: Biometrika, 1970, vol. 57, pp. 97–109.

    Article  Google Scholar 

  8. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, and E.J. Teller: J. Chem. Phys., 1953, vol. 21, pp. 1087–91.

    Article  CAS  Google Scholar 

  9. D.A. Stephens, R. Moskovic, and A.F. Smith: Appl. Stat., 1997, vol. 46, pp. 477–92.

    Google Scholar 

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Authors and Affiliations

  1. BNFL Magnox Generation, GL13 9PB, Gloucestershire, United Kingdom

    R. Moskovic (Senior Researcher)

  2. the Institute of Astronomy, Cambridge University, CB3 0HA, Cambridge, United Kingdom

    C. Jordinson (Research Student)

  3. the Department of Mathematics, Imperial College, SW7 2BZ, London, United Kingdom

    D. A. Stephens (Lecturer)

  4. Queen Mary and Westfield College, E14NS, London, United Kingdom

    A. F. M. Smith (Principal)

Authors
  1. R. Moskovic
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  2. C. Jordinson
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  3. D. A. Stephens
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  4. A. F. M. Smith
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Moskovic, R., Jordinson, C., Stephens, D.A. et al. A bayesian analysis of the influence of neutron irradiation on embrittlement in ferritic submerged arc weld metal. Metall Mater Trans A 31, 445–459 (2000). https://doi.org/10.1007/s11661-000-0281-1

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