Probabilistic fatigue life prediction model of natural rubber components based on the expanded sample data

Liu, Xiangnan; Zhao, Xuezhi; Shangguan, Wen-Bin

doi:10.1016/j.ijfatigue.2022.107034

Cited by 13 publications

(12 citation statements)

References 31 publications

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“…Figure 5 shows a schematic diagram of the P-S-N curve for NR material, where S 1 , S 2 , S 3 , and S 4 are constant amplitude loads with different logarithmic strain amplitudes. Liu et al 19 showed that the fatigue life of NR components under the same constant amplitude load obeys a log-normal distribution. Accordingly, the probability density function (PDF) of NR components can be expressed in the form below:…”

Section: P-s -N Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

“…When establishing the rubber P-S-N curve, the calculated value from Equation ( 7) can be used as the measured fatigue life of the NR under given reliability. 19 This can be mathematically expressed as follows:…”

Section: P-s -N Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

“…Then the fatigue life distribution curve can be established. The P – S – N curve with a given reliability is obtained by connecting the points with equal reliability on the fatigue life distribution curve under various strain levels. Figure 5 shows a schematic diagram of the P – S – N curve for NR material, where S 1 , S 2 , S 3 , and S 4 are constant amplitude loads with different logarithmic strain amplitudes. Liu et al 19 showed that the fatigue life of NR components under the same constant amplitude load obeys a log‐normal distribution. Accordingly, the probability density function (PDF) of NR components can be expressed in the form below:

f ((), N (|, S)) goodbreak= \frac{1}{italicNσ \sqrt{2 π}} \exp ([], goodbreak- \frac{{((), \ln N goodbreak- u)}^{2}}{2 σ^{2}}),

where

u

and

σ^{2}

are the log mean and log variance of the measured fatigue life of NR, respectively.…”

Section: P–s–n Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

“…Meanwhile, it is found that the fatigue life of NR under the same working conditions is inversely proportional to the reliability. When establishing the rubber P – S – N curve, the calculated value from Equation (7) can be used as the measured fatigue life of the NR under given reliability 19 . This can be mathematically expressed as follows:

N_{P} goodbreak= \exp ([], {σϕ}_{P}^{- 1} goodbreak+ u),

where

ϕ_{P}^{- 1}

is the inverse of the standard normal distribution function.…”

Section: P–s–n Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

“…Moreover, some researchers studied the distribution of fatigue life for NR components. For example, Liu et al 19 carried out uniaxial tensile fatigue tests and analyzed vulcanized dumbbell‐shaped rubber specimen (DSRS) from different aspects. Based on the SVM model, the NR fatigue life data were expanded and statistically analyzed.…”

Section: Introductionmentioning

confidence: 99%

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A unified probabilistic fatigue life prediction model for natural rubber components considering strain ratio effect

Liu

Zhao

Liu

2022

Fatigue Fract Eng Mat Struct

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The fatigue life of natural rubber (NR) components under a constant‐amplitude load is dispersed. The dispersion can be reflected by establishing a probabilistic fatigue life prediction model (also called the P–S–N curve). However, the effect of strain ratio on fatigue life is typically ignored in conventional P–S–N curves. Aiming at improving the prediction accuracy of conventional models, a unified P–S–N curve for NR components is proposed in the present study, in which the strain ratio effect is considered in the calculations. Using the dumbbell‐shaped rubber specimen fatigue test data, a polynomial function is proposed to describe the correlation between the equivalent strain amplitude, strain amplitude, and strain ratio. Then a calculation model of equivalent strain amplitude is established. Furthermore, a unified P–S–N curve for NR is established with equivalent strain amplitude as the damage parameter. By comparing the measured and predicted fatigue life of NR under different reliabilities, the accuracy of the established unified P–S–N curve is verified.

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Section: P-s -N Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

Section: P-s -N Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

f ((), N (|, S)) goodbreak= \frac{1}{italicNσ \sqrt{2 π}} \exp ([], goodbreak- \frac{{((), \ln N goodbreak- u)}^{2}}{2 σ^{2}}),

where

u

and

σ^{2}

are the log mean and log variance of the measured fatigue life of NR, respectively.…”

Section: P–s–n Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

N_{P} goodbreak= \exp ([], {σϕ}_{P}^{- 1} goodbreak+ u),

where

ϕ_{P}^{- 1}

is the inverse of the standard normal distribution function.…”

Section: P–s–n Curve Based On the Logarithmic Strain Amplitudementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A unified probabilistic fatigue life prediction model for natural rubber components considering strain ratio effect

Liu

Zhao

Liu

2022

Fatigue Fract Eng Mat Struct

Self Cite

View full text Add to dashboard Cite

show abstract

Fatigue assessment of cord rubber composite air spring bellows based on specimen testing and numerical analysis

Torggler,

Faethe,

Müller

et al. 2024

J of Applied Polymer Sci

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Rail vehicle air spring bellows consisting of cord rubber composites are subject to a wide variety of stresses. It is therefore crucial to understand the fatigue behavior of such components, as the development process involves the use of empirical methods, which are both time‐consuming and costly. This paper outlines a methodology for assessing the fatigue strength of air spring bellows through representative specimen testing. Ten component tests and a validated numerical model of the air spring bellows are presented. The primary loading scenario investigated in this study is pure pulsating tensile stress with a strain ratio R in the range of 0–0.25. This scenario is considered to be highly damaging, leading to delamination. Comprehensive damage analysis of the specimen is performed using microcomputed tomography. To ensure the transferability of the results, a failure criterion is defined as 20% elongation of the specimen, based on the defined 10% internal pressure drop for the bellow. After statistical evaluation, the transferability of the specimen tests to the component is validated using a local fatigue approach. The correlation coefficient R2 is 0.84, indicating a sound agreement between model and tests with 7 points out of 10 within a scatter factor of 2.

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Revealing the Structure-Property Difference of Natural Rubber Prepared by Different Methods: Protein and Gel Content are Key Factors

Huang,

Zhang,

Zhu

et al. 2023

Chin J Polym Sci

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Probabilistic fatigue life prediction model of natural rubber components based on the expanded sample data

Cited by 13 publications

References 31 publications

A unified probabilistic fatigue life prediction model for natural rubber components considering strain ratio effect

A unified probabilistic fatigue life prediction model for natural rubber components considering strain ratio effect

Fatigue assessment of cord rubber composite air spring bellows based on specimen testing and numerical analysis

Revealing the Structure-Property Difference of Natural Rubber Prepared by Different Methods: Protein and Gel Content are Key Factors

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