Probabilistic modeling of fatigue life distribution and size effect of components with random defects

Abstract Engineering components made of ductile cast irons and aluminum alloys, show fatigue lives which are normally dominated by crack initiation from defects raised by manufacturing processes. This study presents a probabilistic model to account for the influence of manufacturing defects on fatigue life, based on size and position of those defects. Specifically, a correction factor considering the influence of defect surface position is developed by modeling the damage mechanism of surface initial cracks with Weibull distribution. Experimental data of three cast irons and aluminum alloys are used for model validation and comparison. Moreover, the statistical size effect influence on fatigue life distribution under constant amplitude loading is explored. Fatigue lives of three materials with different sizes are evaluated respectively, and P–S–N diagrams show that proposed model predictions agree well with the probabilistic scatter bands.

[1]  G. T. Cashman,et al.  A Statistical Methodolgy for the Preparation of a Competing Modes Fatigue Design Curve , 2007 .

[2]  M. Muñiz‐Calvente,et al.  Probabilistic assessment of fatigue data from shape homologous but different scale specimens. Application to an experimental program , 2017 .

[3]  Guang-Chen Bai,et al.  Probabilistic LCF life assessment for turbine discs with DC strategy-based wavelet neural network regression , 2019, International Journal of Fatigue.

[4]  José A.F.O. Correia,et al.  A methodology for probabilistic prediction of fatigue crack initiation taking into account the scale effect , 2017 .

[5]  Michael Vormwald,et al.  Statistical and geometrical size effects in notched members based on weakest-link and short-crack modelling , 2012 .

[6]  Shan-Tung Tu,et al.  High temperature fatigue and creep-fatigue behaviors in a Ni-based superalloy: Damage mechanisms and life assessment , 2019, International Journal of Fatigue.

[7]  F. Wang,et al.  Modified Weibull Distribution for Analyzing the Tensile Strength of Bamboo Fibers , 2014 .

[8]  Dianyin Hu,et al.  A non-local approach for probabilistic assessment of LCF life based on optimized effective-damage-parameter , 2018, Engineering Fracture Mechanics.

[9]  Z. P. BazÏant,et al.  Size effect on structural strength : a review , 1999 .

[10]  G. Qian,et al.  Non-proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions , 2018 .

[11]  M. Tiryakioğlu.  Relationship between Defect Size and Fatigue Life Distributions in Al-7 Pct Si-Mg Alloy Castings , 2009 .

[12]  Alfonso Fernández-Canteli,et al.  Deriving the primary cumulative distribution function of fracture stress for brittle materials from 3- and 4-point bending tests , 2011 .

[13]  Guian Qian,et al.  Statistical assessment of notch toughness against cleavage fracture of ferritic steels , 2018 .

[14]  Cheng-Wei Fei,et al.  Novel method and model for dynamic reliability optimal design of turbine blade deformation , 2014 .

[15]  Alfonso Fernández-Canteli,et al.  An iterative method to obtain the specimen-independent three-parameter Weibull distribution of strength from bending tests , 2011 .

[16]  Gunnar Härkegård,et al.  Fatigue life distribution and size effect in ductile cast iron for wind turbine components , 2011 .

[17]  N. Dowling.  Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue , 1993 .

[18]  Weiwen Peng,et al.  Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks , 2018, International Journal of Mechanical Sciences.

[19]  G. Härkegård,et al.  Casting defects and fatigue behaviour of ductile cast iron for wind turbine components: A comprehensive study , 2011 .

[20]  Michael Gschweitl,et al.  Qualification of AM parts: Extreme value statistics applied to tomographic measurements , 2017 .

[21]  A. Fernández‐Canteli,et al.  Probabilistic Characterization of Glass under Different Type of Testing , 2014 .

[22]  Gunnar Härkegård,et al.  Large scale axial fatigue testing of ductile cast iron for heavy section wind turbine components , 2011 .

[23]  M. Tiryakioğlu,et al.  Weibull Analysis of Mechanical Data for Castings: A Guide to the Interpretation of Probability Plots , 2010 .

[24]  Qiang Liu,et al.  Probabilistic fatigue life prediction and reliability assessment of a high pressure turbine disc considering load variations , 2017 .

[25]  E. C. Ron,et al.  A model allowing for the influence of geometry and stress in the assessment of fatigue data , 2013 .

[26]  Hong-Zhong Huang,et al.  Bayesian framework for probabilistic low cycle fatigue life prediction and uncertainty modeling of aircraft turbine disk alloys , 2013 .

[27]  Shun-Peng Zhu,et al.  Probabilistic framework for multiaxial LCF assessment under material variability , 2017 .

[28]  José A.F.O. Correia,et al.  Statistical evaluation of fatigue strength of double shear riveted connections and crack growth rates of materials from old bridges , 2017 .

[29]  Y. C. Lin,et al.  Effects of initial microstructures on hot tensile deformation behaviors and fracture characteristics of Ti-6Al-4V alloy , 2018 .

[30]  Gunnar Härkegård,et al.  Fatigue life prediction of components made of spheroidal graphite cast iron , 2010 .

[31]  Dianyin Hu,et al.  A combined critical distance and highly-stressed-volume model to evaluate the statistical size effect of the stress concentrator on low cycle fatigue of TA19 plate , 2017 .

[32]  H. Ko,et al.  Effects of humidity on crack initiation mechanism and associated S-N characteristics in very high strength steels , 2003 .

[33]  C. Zou,et al.  Effect of Micro-porosities on Fatigue Behavior in Aluminum Die Castings by 3D X-ray Tomography Inspection , 2014 .

[34]  Michael Vormwald,et al.  Statistical size effect on multiaxial fatigue strength of notched steel components , 2017 .

[35]  Henrik Stensgaard Toft,et al.  Defect Distribution and Reliability Assessment of Wind Turbine Blades , 2011 .

[36]  Rongqiao Wang,et al.  Effect of inclusions on low cycle fatigue lifetime in a powder metallurgy nickel-based superalloy FGH96 , 2019, International Journal of Fatigue.

[37]  Rongqiao Wang,et al.  Probabilistic evaluation on fatigue crack growth behavior in nickel based GH4169 superalloy through experimental data , 2018, Engineering Fracture Mechanics.

[38]  John Dalsgaard Sørensen,et al.  Stochastic Models of Defects in Wind Turbine Drivetrain Components , 2014 .

[39]  K. Chandran,et al.  Duality of the S-N fatigue curve caused by competing failure modes in a titanium alloy and the role of Poisson defect statistics , 2005 .

[40]  Peter D. Lee,et al.  Scatter in fatigue life due to effects of porosity in cast A356-T6 aluminum-silicon alloys , 2003 .

[41]  Gunnar Härkegård,et al.  Damage tolerant design of cast components based on defects detected by 3D X-ray computed tomography , 2012 .

[42]  Pedro M.G.P. Moreira,et al.  A generalization of the fatigue Kohout-Věchet model for several fatigue damage parameters , 2017 .

[43]  José A.F.O. Correia,et al.  A probabilistic analysis of Miner's law for different loading conditions , 2016 .

[44]  Hong-Zhong Huang,et al.  Probabilistic Low Cycle Fatigue Life Prediction Using an Energy-Based Damage Parameter and Accounting for Model Uncertainty , 2012 .

[45]  Weiwen Peng,et al.  Probabilistic Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty , 2016, Reliab. Eng. Syst. Saf..

[46]  Guozheng Kang,et al.  On the fatigue performance and residual life of intercity railway axles with inside axle boxes , 2018, Engineering Fracture Mechanics.

[47]  Arne Fjeldstad,et al.  Non‐local stress approach for fatigue assessment based on weakest‐link theory and statistics of extremes , 2007 .

[48]  Jie Wen,et al.  Multi-objective reliability-based design optimization approach of complex structure with multi-failure modes , 2017 .

[49]  Alfonso Fernández-Canteli,et al.  Maximum likelihood estimation for the three-parameter Weibull cdf of strength in presence of concurrent flaw populations , 2013 .

[50]  A. A. Mar'yakhin,et al.  Size Effect on , 1966 .

[51]  N. Saintier,et al.  The effect of microstructural heterogeneities on the High Cycle Fatigue scatter of cast aluminium alloys: from an elementary volume to the structure , 2018 .

[52]  Jiao Deng,et al.  Effects of initial δ phase on hot tensile deformation behaviors and fracture characteristics of a typical Ni-based superalloy , 2014 .

[53]  V. F. González-Albuixech,et al.  On the temperature independence of statistical model parameters for cleavage fracture in ferritic steels , 2018 .

[54]  Y. C. Lin,et al.  A unified physically based constitutive model for describing strain hardening effect and dynamic recovery behavior of a Ni-based superalloy , 2015 .

[55]  Shun-Peng Zhu,et al.  Fatigue reliability assessment of turbine discs under multi‐source uncertainties , 2018 .

[56]  K. Walker.  The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T6 Aluminum , 1970 .

[57]  K. Chandran,et al.  An unusual fatigue phenomenon: duality of the S–N fatigue curve in the β-titanium alloy Ti–10V–2Fe–3Al , 2003 .

[58]  Rui Calçada,et al.  Computational framework for multiaxial fatigue life prediction of compressor discs considering notch effects , 2018, Engineering Fracture Mechanics.

[59]  Shun-Peng Zhu,et al.  Evaluation of size effect on strain-controlled fatigue behavior of a quench and tempered rotor steel: Experimental and numerical study , 2018, Materials Science and Engineering: A.

[60]  M. Menéndez,et al.  Contrast of a Probabilistic Design Model for Laminated Glass Plates , 2012 .

[61]  Arne Fjeldstad,et al.  Simulation of fatigue crack growth in components with random defects , 2008 .

[62]  Hong-Zhong Huang,et al.  Probabilistic modeling of damage accumulation for time-dependent fatigue reliability analysis of railway axle steels , 2015 .

[63]  Gunnar Härkegård,et al.  Assessment of methods for prediction of notch and size effects at the fatigue limit based on test data by Böhm and Magin , 2010 .