Abstract
Multiaxial fatigue life analysis of notched specimens is a critical issue for structural integrity design. However, there is still a lack of multiaxial fatigue life prediction models with coupled notch effect and probability distributions, which are vital for the fatigue design of key components. Therefore, in this study, a new probabilistic fatigue life prediction model is proposed for notched specimens in structural integrity design, which combines the three-parameter Weibull distribution (TPWD) with the effective strain energy density (ESED) to estimate the fatigue life of notched specimens with different survival probabilities. Meanwhile, the study involves the numerical calculation of the critical plane, extraction of the stress–strain distribution, calculation of strain energy density (SED), determination of critical damage region (CDR), and introduction of a weight function to quantify the damage weights of stress–strain at different locations around the notch on the effective damage parameters of the notch. The proposed model and three other energy-based models are validated using experimental data from notched specimens of Al7050, GH4196 alloys and medium steel En8, and the comparison results exhibit that the proposed model yields higher accuracy than three other models within the ± 3 life factor. Meanwhile, P-Weff-Nf curves of notched specimens with different survival probabilities are presented and analyzed under multiaxial loading. Overall, the proposed approach provides a new way to estimate the fatigue life of notched specimens, which can be useful for the fatigue design of key components.
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Abbreviations
- TPWD:
-
Three-parameter Weibull distribution
- ESED:
-
Effective strain energy density
- SED:
-
Strain energy density
- CDR:
-
Critical damage region
- HSV:
-
High stress volume
- TCD:
-
Theory of critical distances
- HCF:
-
High cycle fatigue
- LCF:
-
Low cycle fatigue
- \(\varepsilon^{\prime}_{xy}, \varepsilon^{\prime}_{xz}\) :
-
Shear strains after coordinate transformation
- \(\varepsilon^{\prime}_{xx}\) :
-
Normal strain after conversion
- n%:
-
Experience parameter to determine the HSV range
- \(\sigma_{n}\) :
-
Lower stress limit of HSV
- \(A^{\prime } ,r^{\prime }\) :
-
Material constants
- W c :
-
Plastic work per cycle per unit volume
- \(\varepsilon_{p}\) :
-
Plastic normal strain
- \(\gamma_{p}\) :
-
Plastic shear strain
- \(\sigma\) :
-
Normal stress
- \(\tau\) :
-
Shear stress
- \(\Delta W_{t}\) :
-
Total cyclic SED
- \(k_{0}, \alpha, C\) :
-
Material constants
- \(W^{*}\) :
-
SED at any point
- W max :
-
Maximum local SED
- W n :
-
Lower limit of SED in the effective region
- L LM :
-
Critical distance
- W(r):
-
Energy density function
- \(\gamma\) :
-
Relative stress gradient
- r :
-
Radius from the notch root
- \(\sigma (r)\) :
-
Stress function
- Y w :
-
Strain energy gradient of the notched component
- \(S_{\sigma ,0.5} ,S_{\tau ,0.5}\) :
-
Area surrounded by normal stress and shear stress normalization curves
- \(\omega (r)\) :
-
Normalized curve expression
- p, q, z :
-
Material constants
- \(\varphi (r)\) :
-
Weight function
- \(\varphi^{\prime}(r)\) :
-
Modified weight function
- S :
-
Maximum stress
- N :
-
Number of fatigue cycles
- S 0 :
-
Maximum stress correction parameter
- N 0 :
-
Life correction parameter
- D:
-
Constant
- x :
-
Independent variable
- \(\alpha\) :
-
Position parameter
- \(\beta\) :
-
Scale parameter
- \(\gamma\) :
-
Shape parameter
- A, B :
-
Calibration parameters
- \(\mu^{\prime}\) :
-
Number of fatigue cycles
- W eff,i :
-
Effective strain energy density
- \(n^{\prime}\) :
-
Sample size
- N f,i :
-
Number of fatigue failure cycles corresponding to each effective strain energy density Weff,i
- N e :
-
Experimental life
- N p :
-
Predicted life
- E N :
-
Prediction error
- μ :
-
Mean value
- δ :
-
Standard deviation of EN
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Acknowledgements
This research was supported by the National Natural Science Foundation of China, Grant/Award Number: 51605212; Natural Science Foundation of Gansu Province, Grant/Award Number: 20JR10RA161; Project of Hongliu Excellent Youth Program of Lanzhou University of Technology Grant/Award Number: 2020062001. Innovation Star Project for Outstanding Graduate Students of Gansu Province, Grant/Award Number: 2022CXZX-413; Innovation Star Project for Outstanding Graduate Students of Gansu Province, Grant/Award Number: 2022CXZX-417.
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Liu, J., Wang, J., Wu, K. et al. Multiaxial notch fatigue probability modeling based on three-parameter Weibull distribution and effective strain energy density. J Braz. Soc. Mech. Sci. Eng. 45, 404 (2023). https://doi.org/10.1007/s40430-023-04312-9
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DOI: https://doi.org/10.1007/s40430-023-04312-9