Proposal of a Probabilistic Model on Rotating Bending Fatigue Property of a Bearing Steel in a Very High Cycle Regime

Sakai, Tatsuo; Nakagawa, Akiyoshi; Nakamura, Yuki; Oguma, Noriyasu

doi:10.3390/app11072889

Cited by 4 publications

(13 citation statements)

References 25 publications

(45 reference statements)

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“…In the case of rotating bending, the inclusion site is also important factor to determine the fatigue strength due to the stress distribution across the specimen section. In such a situation, when the fatigue strength is evaluated by nominal bending stress, the fatigue strength at

N = 10^{9}

σ_{w 9}^{*}

, is given by the following 100 :

σ_{w 9}^{*} goodbreak= \frac{1910}{1.5 - ξ} ρ^{- 1 / 6} .

If n inclusions are included in a specimen, the largest inclusion size

ρ_{n}

governs the fatigue strength. Based on this aspect, Sakai et al had derived the probability density function

f ((), ρ_{n})

as follows 100 :

f ((), ρ_{n}) goodbreak= n {\{F_{0} (ρ_{n})\}}^{n - 1} \frac{a}{b} {(\frac{ρ_{n}}{b})}^{a - 1} italicexp ({}, goodbreak- {(\frac{ρ_{n}}{b})}^{a}),

a , b and c are Weibull parameters.…”

Section: Brief Review For Researches On Vhcfmentioning

confidence: 99%

“…In such a situation, when the fatigue strength is evaluated by nominal bending stress, the fatigue strength at

N = 10^{9}

σ_{w 9}^{*}

, is given by the following 100 :

σ_{w 9}^{*} goodbreak= \frac{1910}{1.5 - ξ} ρ^{- 1 / 6} .

If n inclusions are included in a specimen, the largest inclusion size

ρ_{n}

governs the fatigue strength. Based on this aspect, Sakai et al had derived the probability density function

f ((), ρ_{n})

as follows 100 :

f ((), ρ_{n}) goodbreak= n {\{F_{0} (ρ_{n})\}}^{n - 1} \frac{a}{b} {(\frac{ρ_{n}}{b})}^{a - 1} italicexp ({}, goodbreak- {(\frac{ρ_{n}}{b})}^{a}),

a , b and c are Weibull parameters. In addition, the probability density function of the inclusion depth

ξ

is derived as follows 100 :

f_{0} ((), ξ) goodbreak= \frac{2}{r F_{c}} ((), 1 goodbreak- \frac{ξ}{r}), true[0 < ξ < 250 μm

In Equation (16), r means the radius of the specimen and

F_{c}

indicates the probability giving the condition of 0 <

ξ

< 250 μm.…”

Section: Brief Review For Researches On Vhcfmentioning

confidence: 99%

“…Based on this aspect, Sakai et al had derived the probability density function

f ((), ρ_{n})

as follows 100 :

f ((), ρ_{n}) goodbreak= n {\{F_{0} (ρ_{n})\}}^{n - 1} \frac{a}{b} {(\frac{ρ_{n}}{b})}^{a - 1} italicexp ({}, goodbreak- {(\frac{ρ_{n}}{b})}^{a}),

a , b and c are Weibull parameters. In addition, the probability density function of the inclusion depth

ξ

is derived as follows 100 :

f_{0} ((), ξ) goodbreak= \frac{2}{r F_{c}} ((), 1 goodbreak- \frac{ξ}{r}), true[0 < ξ < 250 μm

In Equation (16), r means the radius of the specimen and

F_{c}

indicates the probability giving the condition of 0 <

ξ

< 250 μm. In the present case, the value of

F_{c}

is given as 0.3055 100 …”

Section: Brief Review For Researches On Vhcfmentioning

confidence: 99%

“…In addition, the probability density function of the inclusion depth

ξ

is derived as follows 100 :

f_{0} ((), ξ) goodbreak= \frac{2}{r F_{c}} ((), 1 goodbreak- \frac{ξ}{r}), true[0 < ξ < 250 μm

In Equation (16), r means the radius of the specimen and

F_{c}

indicates the probability giving the condition of 0 <

ξ

< 250 μm. In the present case, the value of

F_{c}

is given as 0.3055 100 …”

Section: Brief Review For Researches On Vhcfmentioning

confidence: 99%

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Historical review and future prospect for researches on very high cycle fatigue of metallic materials

Sakai

2023

Fatigue Fract Eng Mat Struct

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Since the first paper on the fatigue of metallic materials by J. Albert in 1837, tremendous numbers of papers have been published in various journals by many researchers all over the world. Based on such a long history, several papers on the very high cycle fatigue (VHCF) in the life-time longer than 10 7 cycles had appeared in some journals during the period of 1980's. One characteristic finding in these works is the fact that the metallic material can fail even at the stress level lower than the conventional fatigue limit. This fact means that the conventional fatigue design of mechanical structures cannot give the safety of the practical products in the very high cycle regime. Due to this fact, fatigue properties of structural materials in very long life regime has become an important subject; and a lot of studies have been carried out, and many important results have been accumulated until now. Typical aspects on VHCF property are summarized as follows: (1) the fatigue crack tends to occur around the interior inclusion, (2) fine granular area (FGA) is formed around such an inclusion, and (3) duplex S-N characteristics appear in the VHCF regime. In this paper, a brief historical review together with the future prospect on the very high cycle fatigue of metallic materials is attempted for the sake of reference to facilitate the research in this area.

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N = 10^{9}

σ_{w 9}^{*}

, is given by the following 100 :

σ_{w 9}^{*} goodbreak= \frac{1910}{1.5 - ξ} ρ^{- 1 / 6} .

If n inclusions are included in a specimen, the largest inclusion size

ρ_{n}

governs the fatigue strength. Based on this aspect, Sakai et al had derived the probability density function

f ((), ρ_{n})

as follows 100 :

f ((), ρ_{n}) goodbreak= n {\{F_{0} (ρ_{n})\}}^{n - 1} \frac{a}{b} {(\frac{ρ_{n}}{b})}^{a - 1} italicexp ({}, goodbreak- {(\frac{ρ_{n}}{b})}^{a}),

a , b and c are Weibull parameters.…”

Section: Brief Review For Researches On Vhcfmentioning

confidence: 99%

“…In such a situation, when the fatigue strength is evaluated by nominal bending stress, the fatigue strength at

N = 10^{9}

σ_{w 9}^{*}

, is given by the following 100 :

σ_{w 9}^{*} goodbreak= \frac{1910}{1.5 - ξ} ρ^{- 1 / 6} .

If n inclusions are included in a specimen, the largest inclusion size

ρ_{n}

governs the fatigue strength. Based on this aspect, Sakai et al had derived the probability density function

f ((), ρ_{n})

as follows 100 :

f ((), ρ_{n}) goodbreak= n {\{F_{0} (ρ_{n})\}}^{n - 1} \frac{a}{b} {(\frac{ρ_{n}}{b})}^{a - 1} italicexp ({}, goodbreak- {(\frac{ρ_{n}}{b})}^{a}),

a , b and c are Weibull parameters. In addition, the probability density function of the inclusion depth

ξ

is derived as follows 100 :

f_{0} ((), ξ) goodbreak= \frac{2}{r F_{c}} ((), 1 goodbreak- \frac{ξ}{r}), true[0 < ξ < 250 μm

In Equation (16), r means the radius of the specimen and

F_{c}

indicates the probability giving the condition of 0 <

ξ

< 250 μm.…”

Section: Brief Review For Researches On Vhcfmentioning

confidence: 99%

“…Based on this aspect, Sakai et al had derived the probability density function

f ((), ρ_{n})

as follows 100 :

f ((), ρ_{n}) goodbreak= n {\{F_{0} (ρ_{n})\}}^{n - 1} \frac{a}{b} {(\frac{ρ_{n}}{b})}^{a - 1} italicexp ({}, goodbreak- {(\frac{ρ_{n}}{b})}^{a}),

a , b and c are Weibull parameters. In addition, the probability density function of the inclusion depth

ξ

is derived as follows 100 :

f_{0} ((), ξ) goodbreak= \frac{2}{r F_{c}} ((), 1 goodbreak- \frac{ξ}{r}), true[0 < ξ < 250 μm

In Equation (16), r means the radius of the specimen and

F_{c}

indicates the probability giving the condition of 0 <

ξ

< 250 μm. In the present case, the value of

F_{c}

is given as 0.3055 100 …”

Section: Brief Review For Researches On Vhcfmentioning

confidence: 99%

“…In addition, the probability density function of the inclusion depth

ξ

is derived as follows 100 :

f_{0} ((), ξ) goodbreak= \frac{2}{r F_{c}} ((), 1 goodbreak- \frac{ξ}{r}), true[0 < ξ < 250 μm

In Equation (16), r means the radius of the specimen and

F_{c}

indicates the probability giving the condition of 0 <

ξ

< 250 μm. In the present case, the value of

F_{c}

is given as 0.3055 100 …”

Section: Brief Review For Researches On Vhcfmentioning

confidence: 99%

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Historical review and future prospect for researches on very high cycle fatigue of metallic materials

Sakai

2023

Fatigue Fract Eng Mat Struct

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“…The most known ways of degradation of a steel member are corrosion of steel and fatigue processes [4][5][6][7][8][9][10]. Verifying structure in terms of fatigue is an inseparable part of the new structural design or part of verifying the existing bridge structures [11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Influence of Fatigue Crack Formation and Propagation on Reliability of Steel Members

Koteš

Vičan

2021

Applied Sciences

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During the years of bridge exploitation, many degradation processes and external influences attack its structure. Therefore, bridge reliability and durability is decreasing in time. On the other hand, the traffic load remains almost the same or even higher than in the past. However, bridges should not to become the limiting component of communication capacity and traffic reliability. Regarding to reliability, bridges should be assessed from the viewpoint of the Ultimate Limit States (ULS) and Serviceability Limit States (SLS). Within the ULS, cross-sections and members are verified for various types of stressing and their combinations, and also for fatigue at the same time. The cross-sectional verification, e.g., for bending stresses and fatigue, is done independently according to corresponding criteria of the ULS determined for strength verification a fatigue assessment separately. The presented article deals with the steel railway plate girder bridge with bottom member deck, in which there is an effort to prove the effect of the crack in tension bottom flange due to fatigue stressing on the change of bending resistance over time. The analytical calculation was derived and at the same time, the probabilistic approach of the influence of the fatigue crack size on the change of the cross-sectional resistance and reliability over time was used.

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Probabilistic Prediction Synthesizing Data and Science-Based Modeling for Very High Cycle Fatigue

Harlow

2023

Materials Performance and Characterization

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Epistemic and aleatoric uncertainty are inherent in engineering modeling and experimentation. Uncertainty, which must be considered for accurate life estimation and prediction, is an undeniable aspect of very high cycle fatigue (VHCF). Frequently, limited data are available for VHCF. The magnitude and extent of uncertainty are increased for high reliability applications or gigacycle predictions. The purpose herein is to present a methodology for managing uncertainty satisfactorily. The procedure integrates data with science-based modeling (SBM) for VHCF. An extensive set of data for SUJ2 steel, which exhibits bimodal damage growth for some loading conditions, will be used. One mode is associated with damage nucleating from internal particles, and the other is surface-induced damage, both of which can have fatigue lives in excess of 108cycles. One important conclusion is that synthesis of SBM with data greatly improves reliability estimation and prediction. As the accuracy of the SBM increases, the effect of uncertainty is reduced; however, even basic approximations are more beneficial than empirical analysis alone. Consequently, an SBM that reasonably predicts VHCF behavior resulting from multiple modes of damage growth, which is tuned subsequently by infusing VHCF data, is warranted. The approach focuses on the estimation and prediction of the cumulative distribution functions for life given the loading condition and their statistical goodness of fit.

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Proposal of a Probabilistic Model on Rotating Bending Fatigue Property of a Bearing Steel in a Very High Cycle Regime

Cited by 4 publications

References 25 publications

Historical review and future prospect for researches on very high cycle fatigue of metallic materials

Historical review and future prospect for researches on very high cycle fatigue of metallic materials

Influence of Fatigue Crack Formation and Propagation on Reliability of Steel Members

Probabilistic Prediction Synthesizing Data and Science-Based Modeling for Very High Cycle Fatigue

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