Accurate prediction of the fatigue life of API X65 steel is crucial in various applications. However, the traditional bootstrap method has inherent limitations, such as a tendency to deviate from the true distribution with insufficient sample sizes, difficulty in identifying extreme statistics, and an inability to generate distributions closer to the original sample. These deficiencies lead to overly conservative S-N curve designs and pose challenges in data collection, particularly for small samples. To address these issues, we propose an improved bootstrap method using a composite probability distribution. This method enhances the sampling range and improves prediction accuracy for parameter uncertainty ranges by considering both small samples and extended virtual samples’ probability distribution. Comparative analysis through Monte Carlo simulation demonstrates the superior parameter estimation of our method for small samples. Our case analysis further explores the relationships between Vickers hardness, tensile strength, surface roughness factor, and intercept constant. The findings led to a novel method for estimating the S-N curve confidence interval of API X65 steel from Vickers hardness. Analysis of fatigue life test data for API X65 steel yielded favorable results, confirming the effectiveness and feasibility of our improved method.
BrünigMKoiralaSGerkeS (2023) A stress-state-dependent damage criterion for metals with plastic anisotropy. International Journal of Damage Mechanics32(6): 811–832.
2.
BS 7608 (2014) Guide to Fatigue Design and Assessment of Steel Products. London, UK: British Standards Institution (BSI).
3.
ChenHDöringMJensenU (2018) Test for model selection using Cramér-von Mises distance in a fixed design regression setting. AStA—Advances in Statistical Analysis102: 505–535.
DuZWangWChaiH, et al. (2022) Configuration analysis method and geometric interpretation of UUVs cooperative localization based on error ellipse. Ocean Engineering244: 110299.
7.
EfronB (1979) Bootstrap methods: Another look at the jackknife. Springer New York7: 1–26.
8.
FKM-Guideline (2003) Analytical Strength Assessment of Components in Mechanical Engineering. Germany: Forschungskuratorium Maschinenbau (FKM).
9.
GeHYLiuXTWangX, et al. (2021) Effect of fisheye failure on material performance inducing error circle under high cycles. International Journal of Damage Mechanics30(10): 1524–1541.
10.
GengSLLiuXTLiangZQ, et al. (2020) Tolerance analysis and evaluation of uncertain automatic battery replacement system. Structural and Multidisciplinary Optimization61(1): 239–252.
11.
HamidGSaeidHPedramG, et al. (2018) Radiometric normalization of multitemporal and multisensor remote sensing images based on a Gaussian mixture model and error ellipse. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing11(11): 4526–4533.
12.
HanKJuJWWZhangC, et al. (2024) A resilience assessment framework for microencapsulated self-healing cementitious composites based on a micromechanical damage-healing model. International Journal of Damage Mechanics33(1): 39–56.
13.
HashemiSH (2011) Strength-hardness statistical correlation in API X65 steel. Materials Science and Engineering A528(3): 1648–1655.
14.
HeJCZhuSPLiaoD, et al. (2020) Probabilistic fatigue assessment of notched components under size effect using critical distance theory. Engineering Fracture Mechanics235: 107150.
15.
HesterbergT (2014) What teachers should know about the bootstrap: Resampling in the undergraduate statistics curriculum. The American Statistician69: 371–386.
16.
HuangHBHuangZMWanYP (2024) Elastic moduli prediction of a short fiber composite with interface debonding at fiber ends. International Journal of Damage Mechanics33(5): 378–412.
17.
HusnainMNMAkraminMRMChuanZL, et al. (2020) Fatigue crack growth analysis using bootstrap S-version finite element model. Journal of the Brazilian Society of Mechanical Sciences and Engineering42: 184.
18.
ISO 18265 (2014) Metallic Materials-conversion of Hardness Values. Geneva, Switzerland: International Organization for Standardization.
LiHQianLYangJ, et al. (2023) Parameter estimation for univariate hydrological distribution using improved bootstrap with small samples. Water Resources Management37(5): 1055–1082.
21.
LiMYWangZQ (2019) Active resource allocation for reliability analysis with model bias correction. Journal of Mechanical Design141: 1–13.
22.
LiaoDZhuSPKeshtegaraB, et al. (2020) Probabilistic framework for fatigue life assessment of notched components under size effects. International Journal of Mechanical Sciences181: 105685.
23.
LiuFXuGHLiangL, et al. (2016) Least squares evaluations for form and profile errors of ellipse using coordinate data. Chinese Journal of Mechanical Engineering29(5): 1020–1028.
24.
LiuXTKanFHWangHJ, et al. (2020a) Fatigue life prediction of clutch sleeve based on abrasion mathematical model in service period. Fatigue and Fracture of Engineering Materials and Structures43(3): 488–501.
25.
LiuXTMaoKWangXL, et al. (2020b) A modified quality loss model of service life prediction for products via wear regularity. Reliability Engineering & System Safety204: 107187.
26.
LovisonG (2005) On Rao score and Pearson X2 statistics in generalized linear models. Statistical Papers46: 555–574.
27.
MassinissaSSofianeOKarimA (2018) Taylor series expansion approach for epistemic uncertainty propagation in queueing-inventory models. Mathematical Methods in the Applied Sciences41(18): 9164–9175.
28.
MeggiolaroMACastroJTP (2004) Statistical evaluation of strain-life fatigue crack initiation predictions. International Journal of Fatigue26: 463–476.
29.
MenéndezMSierraHMGentM, et al. (2018) The comminution energy-size reduction of the bond mill and its relation to Vickers hardness. Minerals Engineering119: 228–235.
30.
NaibSWaeleWDStefaneP, et al. (2018) Crack driving force prediction in heterogeneous welds using Vickers hardness maps and hardness transfer functions. Engineering Fracture Mechanics201: 322–335.
31.
PengWWZhuSPShenLJ (2019) The transformed inverse Gaussian process as an age- and state-dependent degradation model. Applied Mathematical Modelling75: 837–852.
32.
PhillipsDT (1972) Applied Goodness of Fit Testing. Atlanta, GA: American Institute of Industrial Engineers.
33.
PortalésRMdel Mar Bochons SaniaMKlemencJ (2018) Theoretical framework for estimating a product’s reliability using a variable-amplitude loading spectrum and a stress-based approach. Fatigue and Fracture of Engineering Materials and Structures41(6): 1662–1673.
34.
QinDWJuJWWZhangKS, et al. (2020) Inhomogeneous deformation growth of a metal under cyclic loading and its influence on fatigue. Acta Mechanica231: 701–713.
35.
RickHH (1999) Statistical Strategies for Small Sample Research. Thousand Oaks, CA, USA: Sage Publications.
36.
RoessleMLFatemiA (2000) Strain-controlled fatigue properties of steels and some simple approximations. International Journal of Fatigue22(6): 495–511.
37.
Soleimani Vosta KolaeiFAkhoondzadehMGhanbariH (2017) Improved ISAC algorithm to retrieve atmospheric parameters from HyTES hyperspectral images using Gaussian mixture model and error ellipse. IEEE Geoscience and Remote Sensing Letters14(11): 2087–2091.
38.
SuHZWenZPSunXR, et al. (2017) Rough set-support vector machine-based real-time monitoring model of safety status during dangerous dam reinforcement. International Journal of Damage Mechanics26(4): 501–522.
39.
SuWLiuXXuS, et al. (2023) Uncertainty for fatigue life of low carbon alloy steel based on improved bootstrap method. Fatigue and Fracture of Engineering Materials and Structures46(10): 3858–3871.
40.
TolikasKHeraviS (2008) The anderson-darling goodness-of-fit test statistic for the three-parameter lognormal distribution. Communications in Statistics—Theory and Methods37(19): 3135–3143.
41.
TuWWangSChenQ (2023) Continuum damage mechanics-based finite-volume homogenization of unidirectional elastoplastic fiber-reinforced composites. International Journal of Damage Mechanics32(4): 549–578.
42.
VranaI (1982) On a direct method of analysis and synthesis of the SPRT. IEEE Transactions on Information Theory28(6): 905–911.
43.
WangMLLiuXTWangXL, et al. (2018a) Probabilistic modeling of unified S-N curves for mechanical parts. International Journal of Damage Mechanics27(7): 979–999.
44.
WangMLLiuXTWangXL, et al. (2018b) Research on load-spectrum construction of automobile key parts based on Monte Carlo sampling. Journal of Testing and Evaluation46(3): 1099–1110.
45.
WangSCLiuXTJiangC, et al. (2020) Prediction and evaluation of fatigue life for mechanical components considering anelasticity-based load spectrum. Fatigue and Fracture of Engineering Materials and Structures44(1): 129–140.
46.
WangXJMaYJWangL, et al. (2017) Composite laminate oriented reliability analysis for fatigue life under non-probabilistic time-dependent method. Computer Methods in Applied Mechanics and Engineering326: 1–19.
47.
WilcoxRR (2005) Introduction to Robust Estimation and Hypothesis Testing. San Diego, CA, USA: Academic Press.
48.
WormsenAAviceWFjeldstadA, et al. (2015) Base material fatigue data for low alloy forged steels used in the subsea industry. Part 1: In air S-N data. International Journal of Fatigue80: 447–495.
49.
WuJNYanSZLiJL, et al. (2018) Mechanism reliability of bistable compliant mechanisms considering degradation and uncertainties: Modeling and evaluation method. Applied Mathematical Modelling40(23–24): 10377–10388.
50.
WuJNYanSZZuoMJ (2016) Evaluating the reliability of multi-body mechanisms: A method considering the uncertainties of dynamic performance. Reliability Engineering & System Safety149: 96–106.
51.
XieW (2019) Design of switched linear control systems based on Youla parameterization with average dwell time. International Journal of Systems Science50(1): 203–215.
52.
XieWMorganD (2017) CALPHAD Modeling and ab initio calculations of the Np-U-Zr system. Journal of Condensed Matter143: 505–514.
53.
YiCZhangYBWangZH, et al. (2018) Interval statistic-based reliability analysis method on small sample hot test of satellite thruster. Applied Mathematical Modelling60: 581–591.
54.
ZengXHLiGHYinGD, et al. (2018) Model predictive control-based dynamic coordinate strategy for hydraulic hub-motor auxiliary system of a heavy commercial vehicle. Mechanical Systems and Signal Processing101: 97–120.
55.
ZhangKSJuJWWLiZ, et al. (2015) Micromechanics-based fatigue life prediction of a polycrystalline metal applying crystal plasticity. Mechanics of Materials85: 16–37.
56.
ZhangMHLiuXTWangYS (2019) Parameter distribution characteristics of material fatigue life using improved bootstrap method. International Journal of Damage Mechanics28(5): 772–793.
57.
ZhangZWangYYuC, et al. (2022) Simulation and verification of master S-N curves of titanium alloy welded structures based on bootstrap method. Advances in Mechanical Engineering14(7): 168781322211074.
58.
ZhuMZhaoJYWangQM (2018b) Reliability evaluation of key hydraulic components for actuators of FAST based on small sample test. International Journal of Precision Engineering and Manufacturing18(11): 1561–1566.
59.
ZhuSPHuangHZLiaoQ (2012) Probabilistic modeling of damage accumulation for fatigue reliability analysis. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit229(1): 23–33.
60.
ZhuSPKeshtegarBChakrabortyS, et al. (2020a) Novel probabilistic model for searching most probable point in structural reliability analysis. Computer Methods in Applied Mechanics and Engineering366: 113027.
61.
ZhuSPLiuQZhouJ, et al. (2018a) Fatigue reliability assessment of turbine discs under multi-source uncertainties. Fatigue and Fracture of Engineering Materials and Structures41(6): 1291–1305.
62.
ZhuSPYuZYLiuQ, et al. (2020b) Strain energy-based multiaxial fatigue life prediction under normal-shear stress interaction. International Journal of Damage Mechanics28(5): 708–739.
