Ever since the 1980s there is a sustained interest in the size effect, as one of the most pronounced consequences of fracture mechanics. In the present study, the investigation of the size effect is focused on estimation of the Weibull cumulative distribution function (CDF) of the critical value of the J-integral (J(c)) in the transition temperature region under constraint of a small statistical sample size. Specifically, the J(c) experimental data correspond to the C(T) specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two geometrically-similar sizes. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the C(T) specimen size on the J(c) CDF under these circumstances. Due to the specific form of the two-parameter Weibull CDF, F(J(c) vertical bar beta, eta), the scaling procedure is applied according to a two-step scheme. First, the J(c)-scaling is performed to ensure the approximate overlap of the points that correspond to the ...CDF value F(J(c) = eta) = 1 - 1/e approximate to 0.632 for different C(T) specimen widths (W), which assumes eta.W-kappa= const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F.W(xi)vs. J(c).W-kappa) space. The objective of the sketched approach is to obtain a size-dependent J(c) CDF that encapsulates a reasonably conservative data extrapolation.
Keywords:
Weibull distribution / Size effect / Scaling / Lower bound / Cumulative distribution function
Source:
Engineering Failure Analysis, 2022, 131
Publisher:
Elsevier
Funding / projects:
Ministry of Education, Science and Technological Development of the Republic of Serbia
Note:
The authors regret that a typographical error was made in Eqs. (15), (16), (20). In these three forms of the Jc cumulative distribution function (CDF), we omitted the minus sign in front of the argument of the exponential function.
Corrigendum at:https://rimsi.imsi.bg.ac.rs/handle/123456789/1577
TY - JOUR
AU - Mastilović, Sreten
AU - Đorđević, Branislav
AU - Sedmak, Aleksandar
PY - 2022
UR - http://rimsi.imsi.bg.ac.rs/handle/123456789/1536
AB - Ever since the 1980s there is a sustained interest in the size effect, as one of the most pronounced consequences of fracture mechanics. In the present study, the investigation of the size effect is focused on estimation of the Weibull cumulative distribution function (CDF) of the critical value of the J-integral (J(c)) in the transition temperature region under constraint of a small statistical sample size. Specifically, the J(c) experimental data correspond to the C(T) specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two geometrically-similar sizes. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the C(T) specimen size on the J(c) CDF under these circumstances. Due to the specific form of the two-parameter Weibull CDF, F(J(c) vertical bar beta, eta), the scaling procedure is applied according to a two-step scheme. First, the J(c)-scaling is performed to ensure the approximate overlap of the points that correspond to the CDF value F(J(c) = eta) = 1 - 1/e approximate to 0.632 for different C(T) specimen widths (W), which assumes eta.W-kappa= const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F.W(xi)vs. J(c).W-kappa) space. The objective of the sketched approach is to obtain a size-dependent J(c) CDF that encapsulates a reasonably conservative data extrapolation.
PB - Elsevier
T2 - Engineering Failure Analysis
T1 - A scaling approach to size effect modeling of J(c) CDF for 20MnMoNi55 reactor steel in transition temperature region
VL - 131
DO - 10.1016/j.engfailanal.2021.105838
ER -
@article{
author = "Mastilović, Sreten and Đorđević, Branislav and Sedmak, Aleksandar",
year = "2022",
abstract = "Ever since the 1980s there is a sustained interest in the size effect, as one of the most pronounced consequences of fracture mechanics. In the present study, the investigation of the size effect is focused on estimation of the Weibull cumulative distribution function (CDF) of the critical value of the J-integral (J(c)) in the transition temperature region under constraint of a small statistical sample size. Specifically, the J(c) experimental data correspond to the C(T) specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two geometrically-similar sizes. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the C(T) specimen size on the J(c) CDF under these circumstances. Due to the specific form of the two-parameter Weibull CDF, F(J(c) vertical bar beta, eta), the scaling procedure is applied according to a two-step scheme. First, the J(c)-scaling is performed to ensure the approximate overlap of the points that correspond to the CDF value F(J(c) = eta) = 1 - 1/e approximate to 0.632 for different C(T) specimen widths (W), which assumes eta.W-kappa= const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F.W(xi)vs. J(c).W-kappa) space. The objective of the sketched approach is to obtain a size-dependent J(c) CDF that encapsulates a reasonably conservative data extrapolation.",
publisher = "Elsevier",
journal = "Engineering Failure Analysis",
title = "A scaling approach to size effect modeling of J(c) CDF for 20MnMoNi55 reactor steel in transition temperature region",
volume = "131",
doi = "10.1016/j.engfailanal.2021.105838"
}
Mastilović, S., Đorđević, B.,& Sedmak, A.. (2022). A scaling approach to size effect modeling of J(c) CDF for 20MnMoNi55 reactor steel in transition temperature region. in Engineering Failure Analysis
Elsevier., 131.
https://doi.org/10.1016/j.engfailanal.2021.105838
Mastilović S, Đorđević B, Sedmak A. A scaling approach to size effect modeling of J(c) CDF for 20MnMoNi55 reactor steel in transition temperature region. in Engineering Failure Analysis. 2022;131.
doi:10.1016/j.engfailanal.2021.105838 .
Mastilović, Sreten, Đorđević, Branislav, Sedmak, Aleksandar, "A scaling approach to size effect modeling of J(c) CDF for 20MnMoNi55 reactor steel in transition temperature region" in Engineering Failure Analysis, 131 (2022),
https://doi.org/10.1016/j.engfailanal.2021.105838 . .
