Size/Effect Modeling of Weibull Jc Cumulative Distribution Function Based on a Scalling Approach
Abstract
Ever since the 1980s there have been a surge of 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 CDF of the critical value of the J-integral (Jc) under
constraint of a small sample size in the transition temperatrure range. Specifically, the Jc
experimental data correspond to the CT specimen testing of the reactor pressure-vessel steel
20MnMoNi55 at only two sizes and temperature of 60°C. Thus, a simple approximate scaling
algorithm has been developed to tackle the effect of the CT specimen size on the J c CDF for such
small sample size. Due to the specific form of the two-parameter Weibull CDF, F(Jc | β, η), 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 values F(Jc = η) =
1 – 1/e ≈ 0.632 for different ...CT specimen widths (W), which assumes η·W κ = const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F·W ξ vs. J c ·W κ ) space. The objective of the sketched approach is to obtain a conservative estimate of J c CDF that encapsulates the CT specimen size.
Keywords:
size effect / J integral / Weibull distribution / cumulative distribution function / lower boundSource:
8th International Congress of the Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021, 2021Collections
Institution/Community
Inovacioni centarTY - CONF AU - Mastilović, Sreten AU - Đorđević, Branislav AU - Sedmak, Aleksandar PY - 2021 UR - https://machinery.mas.bg.ac.rs/handle/123456789/6361 AB - Ever since the 1980s there have been a surge of 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 CDF of the critical value of the J-integral (Jc) under constraint of a small sample size in the transition temperatrure range. Specifically, the Jc experimental data correspond to the CT specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two sizes and temperature of 60°C. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the CT specimen size on the J c CDF for such small sample size. Due to the specific form of the two-parameter Weibull CDF, F(Jc | β, η), 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 values F(Jc = η) = 1 – 1/e ≈ 0.632 for different CT specimen widths (W), which assumes η·W κ = const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F·W ξ vs. J c ·W κ ) space. The objective of the sketched approach is to obtain a conservative estimate of J c CDF that encapsulates the CT specimen size. C3 - 8th International Congress of the Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021 T1 - Size/Effect Modeling of Weibull Jc Cumulative Distribution Function Based on a Scalling Approach UR - https://hdl.handle.net/21.15107/rcub_machinery_6361 ER -
@conference{ author = "Mastilović, Sreten and Đorđević, Branislav and Sedmak, Aleksandar", year = "2021", abstract = "Ever since the 1980s there have been a surge of 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 CDF of the critical value of the J-integral (Jc) under constraint of a small sample size in the transition temperatrure range. Specifically, the Jc experimental data correspond to the CT specimen testing of the reactor pressure-vessel steel 20MnMoNi55 at only two sizes and temperature of 60°C. Thus, a simple approximate scaling algorithm has been developed to tackle the effect of the CT specimen size on the J c CDF for such small sample size. Due to the specific form of the two-parameter Weibull CDF, F(Jc | β, η), 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 values F(Jc = η) = 1 – 1/e ≈ 0.632 for different CT specimen widths (W), which assumes η·W κ = const. Second, the F-scaling is performed to ensure the equality of the slopes of the CDF in the scaled (F·W ξ vs. J c ·W κ ) space. The objective of the sketched approach is to obtain a conservative estimate of J c CDF that encapsulates the CT specimen size.", journal = "8th International Congress of the Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021", title = "Size/Effect Modeling of Weibull Jc Cumulative Distribution Function Based on a Scalling Approach", url = "https://hdl.handle.net/21.15107/rcub_machinery_6361" }
Mastilović, S., Đorđević, B.,& Sedmak, A.. (2021). Size/Effect Modeling of Weibull Jc Cumulative Distribution Function Based on a Scalling Approach. in 8th International Congress of the Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021. https://hdl.handle.net/21.15107/rcub_machinery_6361
Mastilović S, Đorđević B, Sedmak A. Size/Effect Modeling of Weibull Jc Cumulative Distribution Function Based on a Scalling Approach. in 8th International Congress of the Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021. 2021;. https://hdl.handle.net/21.15107/rcub_machinery_6361 .
Mastilović, Sreten, Đorđević, Branislav, Sedmak, Aleksandar, "Size/Effect Modeling of Weibull Jc Cumulative Distribution Function Based on a Scalling Approach" in 8th International Congress of the Serbian Society of Mechanics, Kragujevac, Serbia, June 28-30, 2021 (2021), https://hdl.handle.net/21.15107/rcub_machinery_6361 .