Abstract
Modeling fatigue life is complex whether it is applied to structures or experimental programs. Through the years several empirical approaches have been utilized. Each approach has positive aspects; however, none have been acceptable for every circumstance. On many occasions the primary shortcoming for an empirical method is the lack of a sufficiently robust database for statistical modeling. The modeling is exacerbated for loading near typical operating conditions because the scatter in the fatigue lives is quite large. The scatter may be attributed to microstructure, manufacturing, or experimental inconsistencies, or a combination thereof. Empirical modeling is more challenging for extreme life estimation because those events are rare. The primary purpose herein is to propose an empirically based methodology for estimating the cumulative distribution functions for fatigue life, given the applied load. The methodology incorporates available fatigue life data for various stresses or strains using a statistical transformation to merge all the life data so that distribution estimation is more accurate than traditional approaches. Subsequently, the distribution for the transformed and merged data is converted using change-of-variables to estimate the distribution for each applied load. To assess the validity of the proposed methodology percentile bounds are estimated for the life data. The development of the methodology and its subsequent validation is illustrated using three sets of fatigue life data which are readily available in the open literature.
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Abbreviations
- α, β, γ:
-
Weibull cdf parameters
- αs:
-
significance
- AD:
-
Anderson–Darling goodness of fit test
- cdf:
-
cumulative distribution function
- cv :
-
coefficient of variation
- Δε:
-
strain range
- Δσ:
-
stress range
- FLT:
-
Fatigue Life Transformation
- F(•):
-
cdf
- KS:
-
Kolmogorov–Smirnov goodness of fit test
- MLE:
-
maximum likelihood estimation
- N A :
-
arbitrary normalization constant
- N f :
-
cycles to failure
- n :
-
sample size
- m :
-
number of different values of applied stress
- p :
-
percentile
- s :
-
sample standard deviation
- s A :
-
arbitrary normalization constant
- S–N:
-
stress–number of cycles
- t :
-
time, cycles
- W(α, β, γ):
-
three parameter Weibull cdf
- y 1/2 :
-
median
- \(\bar{y}\) :
-
sample average
References
Harlow DG, Wei RP, Sakai T, Oguma N (2006) Crack growth based probability modeling of S-N response for high strength steel. Int J Fatigue 28:1479–1485
Castillo E, Fernández-Canteli A (2009) A unified statistical methodology for modeling fatigue damage. Springer Science and Business Media B.V., Berlin
Schneider CRA, Maddox SJ (2003) Best practice guide on statistical analysis of fatigue data. International Institute of Welding, IIW-XIII-WG1-114-03, United Kingdom
Collins JA (1993) Failure of materials in mechanical design: analysis, prediction, prevention, 2nd edn. Wiley-Interscience Publications, New York
Little RE, Ekvall JC (eds) (1981) Statistical analysis of fatigue data. ASTM STP744, American Society for Testing and Materials, Philadelphia
Zheng X-L, Jiang B, Lü H (1995) Determination of probability distribution of fatigue strength and expressions of P–S–N curves. Eng Fracture Mech 50:483–491
Shimizu S (2005) P–S–N/P–F–L curve approach using three-parameter Weibull distribution for life and fatigue analysis of structural and rolling contact components. Tribol Trans 48:576–582
Fernández–Canteli A, Blasón S, Correia JAFO, de Jesus AMP (2014) A probabilistic interpretation of the miner number for fatigue life prediction. FratturaedIntegrità Strutturale 30:327–339
Shimokawa T, Hamaguchi Y (1985) Relationship between fatigue life distribution, notch configuration, and S-N curve of a 2024–T4 Aluminum Alloy. Trans ASME J Eng Mater Technol 107:214–220
Harlow DG (2005) Probability versus statistical modeling: examples from fatigue life prediction. Int J Reliab Qual Saf Eng 12:1–16
Harlow DG (2011) Generalized probability distributions for accelerated life modeling. SAE Int J Mater Manuf 4:980–991
Sakai T, Nakajima M, Tokaji K, Hasegawa N (1997) Statistical distribution patterns in mechanical and fatigue properties of metallic materials. Mater Sci Res Int 3:63–74
IF_DDQ_HDG70G_Strain_Life_Fatigue.xls www.autosteel.org (2004). Automotive Applications Council, Steel Market Development Institute, Auto/Steel–Partnership Fatigue Data
Harlow DG (2014) Low cycle fatigue: probability and statistical modeling of fatigue life. In: Proceedings of the ASME 2014 pressure vessels and piping conference, PVP2014–28114, Anaheim, CA, 20–24 July 2014, V06BT06A045. ISBN 978–0–7918–4604–9
Harlow DG (2017) Confidence bounds for fatigue distribution functions. In: Proceedings of the ASME 2017 pressure vessels and piping conference, PVP2017–65416, Waikoloa, HI, 16–20 July 2017. V01AT01A011. ISBN 978–0–7918–5790–8
Thomas GB, Varma RK (1993) Evaluation of low cycle fatigue test data in the BCR/VAMAS intercomparison programme. Commission of the European Communities, BCR Information Applied Metrology, Brussels, Luxembourg
Harlow DG (2007) Probabilistic property prediction. Eng Fract Mech 74:2943–2951
Weibull EHW (1951) A statistical distribution function of wide applicability. ASME J Appl Mech 18:293–297
Abernethy RB (2006) In: Abernethy RB (ed) The new Weibull handbook, 5th edn. 536 Oyster Road, North Palm Beach, Florida, pp 33408–34328
Rinne H (2009) The Weibull distribution. CRC Press, Chapman-Hall, Taylor and Francis Group, Boca Raton
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Gary Harlow, D. (2020). Fatigue Life Distribution Estimation. In: Pham, H. (eds) Reliability and Statistical Computing. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-43412-0_1
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