Härtelt, M.

Khader, I.

Kraft, O.

Riesch-Oppermann, H.

KITopen

KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz AssociationKarlsruhe Institute of Technology (KIT), Institute for Applied Materials (IAM)www.kit.edu10-1410-1310-1210-1110-1010-910-810-7-0.5 -0.4 -0.3 -0.2 -0.1 0lg(Δ K/K Ic )100 101 102 103 104 105 1060.99940.63210.12660.0181-4-3-2-101230 5 10 15zyklisch, Wasserzyklisch, LuftunterkritischStahlrolleSi3N4-RolleSTAUPROBABILISTIC ANALYSIS OF A ROLLING CONTACT FATIGUE TEST FOR SILICON NITRIDEM. Härtelt, H. Riesch-Oppermann, I. Khader, O. KraftHochbeanspruchteGleit- und Friktionssystemeauf Basis ingenieurkeramischer WerkstoffeKarlsruhe Institute of Technology (KIT), IAM2 27.06.2011 H. Riesch-OppermannMotivationFraunhofer Gesellschaft, IWM, FreiburgHigh strength ceramics (Si3N4) are used in rolling applicationsTime-dependent failure due to slow crack propagationDesign of such components requires probabilistic methodsRolling contact fatigue test as model system for rolling applicationsHot wire rollingwireceramic rollKarlsruhe Institute of Technology (KIT), IAM3 27.06.2011 H. Riesch-OppermannTheory: Crack propagation mechanismsSubcritical crack propagationStress corrosion/ chemical reactionQuasi-static effectSISIcddnKa At K⎛ ⎞= ⋅⎜ ⎟⎝ ⎠AS ,nS: material propertiesCyclic crack propagation (fatigue)Depends on load sequenceDegradation of strengthening effects(grain bridging)IIcdd (1 )nn pA KaN R K−⎛ ⎞Δ= ⋅⎜ ⎟− ⎝ ⎠A ,n ,p: material propertiesKKminKmaxΔK tΔK=Kmax-KminKminKmaxR=Crack loadingKarlsruhe Institute of Technology (KIT), IAM4 27.06.2011 H. Riesch-OppermannTheory: Failure probabilitySubcritical crack propagation2 220[0, ]0 0 00( ) ( ')1 11 exp max '  2S S Smn n nteq eqf t TAt tP dt d dAA Bασ σσ απ σ σ− −∈⎡ ⎤⎛ ⎞⎧ ⎫⎢ ⎥⎛ ⎞ ⎛ ⎞⎪ ⎪⎜ ⎟= − − +⎨ ⎬⎜ ⎟ ⎜ ⎟⎢ ⎥⎜ ⎟⎝ ⎠ ⎝ ⎠⎪ ⎪⎢ ⎥⎩ ⎭⎝ ⎠⎣ ⎦∫ ∫ ∫Cyclic crack propagation112 22,max ,max0[ , ]0 0 0( ) ( ')1 11 exp max (1 ( ')) '  2 Kmn n neq eq pf N NA NNP R N dN d dAA Bηηασ η σσ απ σ σ− −∈⎡ ⎤⎛ ⎞⎧ ⎫⎢ ⎥⎛ ⎞ ⎛ ⎞⎪ ⎪⎜ ⎟= − − + −⎨ ⎬⎜ ⎟ ⎜ ⎟⎢ ⎥⎜ ⎟⎝ ⎠ ⎝ ⎠⎪ ⎪⎢ ⎥⎩ ⎭⎝ ⎠⎣ ⎦∫ ∫ ∫Time/Cycle dependent load historyWeibull Theory? Integration over component surface/ volume and flaw orientation? Equivalent stress σeq: local failurecriterionKarlsruhe Institute of Technology (KIT), IAM5 27.06.2011 H. Riesch-OppermannSTAU1: Finite-Element Postprocessor for reliability assessment of ceramicsTheory: Numerical evaluation1 H. Riesch-Oppermann, M. Härtelt, O. Kraft, Int. J. Mat. Res. 99 (2008)STAUCeramic-specificmaterial propertiesFE-Stress analysis FailureProbability PfReliability analysis for rolls? Complex load history must be consideredElement 1Element 2Element 3StressTimeKarlsruhe Institute of Technology (KIT), IAM6 27.06.2011 H. Riesch-OppermannResults: Material parameters Si3N4-SL200Crack growth exponent n depends on loadratio R (n=20,31)Curves must be represented by commonexponent n:n=24, p=2.2, A=3·10-8 m/cycleCyclic fatigue parameters (air)Subcritical crack growthn=42, AS=10-6 m/sLube and Dusza, J.Eur.Ceram.Soc., 27(2-3),2007 Strengthσ4PB=1044 MPam=11.5Härtelt et al., J Am Ceram Soc, 2011, in press IIcdd (1 )nn pA KaN R K−⎛ ⎞Δ= ⋅⎜ ⎟− ⎝ ⎠10-1410-1310-1210-1110-1010-0910-0810-07-0.5 -0.4 -0.3 -0.2 -0.1 0log(ΔK/KIc)da/dN [m/cycle]R=0.5 R=0.1n=20n=31n=24n=20n=31Karlsruhe Institute of Technology (KIT), IAM7 27.06.2011 H. Riesch-OppermannResults: Material parameters Si3N410-1410-710-810-910-1010-1110-1210-13-0.6 -0.5 -0.4 -0.3log(ΔK/KIc)da/dN [m/cycle]R=0.5n=31n=30airwaterCyclic fatigue parameters (water)Water enhances fatigue effect!Measurements for R=0.5: n=29.9Parameters are evaluated assumingp=2.2 (air):n=29.9, p=2.2, A=5·10-5 m/cycleIIcdd (1 )nn pA KaN R K−⎛ ⎞Δ= ⋅⎜ ⎟− ⎝ ⎠Karlsruhe Institute of Technology (KIT), IAM8 27.06.2011 H. Riesch-OppermannResults: Rolling contact fatigue (RCF) testSchmierstoff-TauchbadStahlscheibeKeramikrolle Si3N4ω1ω2FF lubri antSi3N4-diskSteel-diskDamage after 105 rotationslubricant: friction coefficient μ=0.085F=1700Nrelative slip: ~22%max. principal stress: ~1100 MPaStress distributionRCF tests: Iyas Khader, Fraunhofer Institute IWM, FreiburgKarlsruhe Institute of Technology (KIT), IAM9 27.06.2011 H. Riesch-OppermannResults: Rolling contact fatigue (RCF) testStress distributionKarlsruhe Institute of Technology (KIT), IAM10 27.06.2011 H. Riesch-OppermannResults: Rolling contact fatigue (RCF) testSchmierstoff-TauchbadStahlscheibeKeramikrolle Si3N4ω1ω2FF lubri antSi3N4-diskSteel-diskDamage after 105 rotationslubricant: friction coefficient μ=0.085F=1700Nrelative slip: ~22%max. principal stress: ~1100 MPaStress distributionRCF tests: Iyas Khader, Fraunhofer Institute IWM, FreiburgKarlsruhe Institute of Technology (KIT), IAM11 27.06.2011 H. Riesch-OppermannResults: STAU analysisContact damage:  initiation of macroscopic flawsPredicting of a certain flaw density on the surfaceSi3N4rollsubarea of surfaceSTAU: probability of the initiation of one flawin the considered subareaSize of subarea ↔ crack densityResults refer to crack density of 1 crack per 250 μm along the circumferenceKarlsruhe Institute of Technology (KIT), IAM12 27.06.2011 H. Riesch-OppermannResults: Failure probability100 101 102 103 104 105 106 107 108 1090.99940.63210.12660.01810.00250.0003-10-8-6-4-20240 5 10 15 20 25ln(Z) Zln(ln(1/(1-Pf(Z))))Pf(Z)CCG waterCCG airSCG airf01 expmZPN⎡ ⎤⎛ ⎞⎢ ⎥= − −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦Weibull functionm – slope of the curveN0 - characteristic lifetime(63%-quantile)Z – no. of rotationsProbability to initiate one macroscopic crack every 250 μmHighest failure probability obtained for fatigue parameters in water. Karlsruhe Institute of Technology (KIT), IAM13 27.06.2011 H. Riesch-OppermannResults: Failure probability100 101 102 103 104 105 106 107 108 1090.99940.63210.12660.01810.00250.0003-10-8-6-4-20240 5 10 15 20 25ln(Z) Zln(ln(1/(1-Pf(Z))))Pf(Z)CCG waterCCG airSCG airRelation with experimental crack density after 10 hInitiation probability low for parameters in (air) Karlsruhe Institute of Technology (KIT), IAM14 27.06.2011 H. Riesch-OppermannResults: Parametric studyCrack growth exponent has a strong influence on the results:For n<25, crack initiation probability is >70%;                     Characteristic lifetimes are below 10 hInfluence of crack growth exponent n 0.1120 22 24 26 28 300.111010010001000020 22 24 26 28 30n nPf N0 (h)Characteristic lifetime N0 (h)Karlsruhe Institute of Technology (KIT), IAM16 27.06.2011 H. Riesch-OppermannDiscussionAgreement with experimental results for lower n-values if waterparameters are used-3500-3000-2500-2000-1500-1000-5000500100015000 1 2 3 4 5Maximum1 Maximum2Minimum1 Minimum2Δσ1=1085 MPa R=0Δσ2=113 MPa R=0.2max. principalstressσ[MPa]max. equivalentstresst [ms]Stress history: R=0 dominates? Using a lower n value (n≈20) in the case of water.Limitations of the analysis scheme:- Stress gradients in the range of natural flaws- Interaction of macroscopic cracks- WearKarlsruhe Institute of Technology (KIT), IAM17 27.06.2011 H. Riesch-OppermannSummarySTAU as general tool for reliability assessment under complex loadingprediction of evolving crack patterns on roll surface is possiblesensitivity to crack growth parameters is challengingKarlsruhe Institute of Technology (KIT), IAM18 27.06.2011 H. Riesch-OppermannAcknowledgementsFinancial support by the “Deutsche Forschungsgemeinschaft” (DFG) isgratefully acknowledged. The work was performed within the framework of the Collaborative Research Centre 483 “High performance sliding and friction systems based on advanced ceramics” at the University of Karlsruhe (now: Karlsruhe Institute of Technology KIT).HochbeanspruchteGleit- und Friktionssystemeauf Basis ingenieurkeramischer Werkstoffe

Probabilistic analysis of a rolling contact fatigue test for silicon nitride

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Probabilistic analysis of a rolling contact fatigue test for silicon nitride

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