1Over the Next Several Days What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾Uniaxial Fully Reversed¾Uniaxial Fluctuating¾MultiaxialSome History Rail car axles The all-important microcrack Role of stress concentrations¾Comet airplanesThree Stages of Fatigue Failure Crack Initiation Crack Propagation¾oscillating stress… crack grows, stops growing, grows, stops growing… with crack growth due to tensile stresses Fracture¾sudden, brittle-like failureIdentifying Fatigue FracturesbeachmarksThree Theoriesbest model of crack propagation, for low-cycle fatigueLEFM (Fracture Mechanics)useful when yielding begins (i.e., during crack initiation), for low-cycle fatigueStrain-Lifestress-based, for high-cycle fatigue, aims to prevent crack initiationStress-LifeLow vs. High Cycle>103cycles, high cycle fatigue<103cycles, low cycle fatiguecar crank shaft –manufacturing equipment @ 100 rpm –ships, planes, vehicle chassis~2.5 E8 Rev/105miles1.25 E8 Rev/year2Types of Fatigue Loadingminmaxσσσ−=∆2σσ∆=a2minmaxσσσ+=mmaAσσ=maxminσσ=Rstress rangealternating componentmean componentstress ratioamplitude ratioFully ReversedRepeated FluctuatingUpdate What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾Uniaxial Fully Reversed¾Uniaxial Fluctuating¾MultiaxialTesting Fatigue Properties Rotating Beam – most data is from this type Axial¾lower or higher? Why? Cantilever TorsionFully Reversed Empirical DataWrought SteelAn S-N Curve (Stress-Life)Fully Reversed Empirical DataAluminumEndurance LimitA stress level below which a material can be cycled infinitely without failureMany materials have an endurance limit:low-strength carbon and alloy steels, some stainless steels, irons, molybdenum alloys, titanium alloys, and some polymersMany other materials DO NOT have an endurance limit:aluminum, magnesium, copper, nickel alloys, some stainless steels, high-strength carbon and alloy steelseS′for these, we use a FATIGUE STRENGTH defined for a certain number of cycles (5E8 is typical)fS′3Update What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾Uniaxial Fully Reversed¾Uniaxial Fluctuating¾MultiaxialTypes of Fatigue Loadingminmaxσσσ−=∆2σσ∆=a2minmaxσσσ+=mmaAσσ=maxminσσ=Rstress rangealternating componentmean componentstress ratioamplitude ratioFully ReversedRepeated FluctuatingGetting Fatigue Data1) Test a prototype2) Test the exact material used3) Published fatigue data4) Use static data to estimateEstimating Se´From Static Datasee page 345 in your book…ksi 40for ksi 19ksi 40for 4.0ksi 60for ksi 24ksi 60for 4.0ksi 200for 100ksi 200for 5.085@85@≥≅≤≅≤≅≤≅≥≅≤≅′′′′′′utfututfuteututeuteututeSSSSSSSSSSSksiSSSSEEsteelsironsaluminumsBUT, these are all for highly polished, circular rotating beams of a certain sizeCorrection FactorsfreliabtempsurfsizeloadfereliabtempsurfsizeloadeSCCCCCSSCCCCCS′′==pages 348-353 in your bookResidual Stresses Temperature¾through hardening¾case hardening Surface Treating¾cold forming¾shot peening: Csurf=14Constructing Estimated S-N CurvesSm=0.9Sutfor bendingSm=0.75Sutfor axial loadingThe material strength at 103cycles, Sm:The line from Smto Seor Sf, Sn=aNbor logSn=loga + blogNConstructing S-N CurvesSn=aNb21loglog wherelog1NNzSSzbem−==bSNbSamm3loglogloglog1−=−=Fatigue Stress ConcentrationKf= 1+q(Kt-1)q = notch sensitivityfunction of material, Sut, Neuber constant, anotch radius, rraq+=11Update What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾Uniaxial Fully Reversed¾Uniaxial Fluctuating¾Multiaxial0=mσ0≠mσUniaxialMultiaxialTypes of Fatigue Loadingminmaxσσσ−=∆2σσ∆=a2minmaxσσσ+=mmaAσσ=maxminσσ=Rstress rangealternating componentmean componentstress ratioamplitude ratioFully ReversedRepeated FluctuatingUniaxial, Fully Reversed StrategyLoading & Stress HalfN (umber of cycles) Fluctuating Load (Fa)Tentative DesignTentative MaterialKtσa(nominal)σ1, σ2, σ3(principal)σ´ (von Mises)Kfσa5Uniaxial, Fully Reversed StrategyFatigue HalfSe´or Sf´Seor SfCloadCsurfCsizeCtempCreliabEstimated S-N CurveN (umber of cycles) Fluctuating Load (Fa)Tentative DesignTentative Material Tentative DesignTentative Materialσ1, σ2, σ3(principal)σ´ (von Mises)σ1, σ2, σ3(principal)σ´ (von Mises)KfKfσaσaKtσa(nominal)Ktσa(nominal)Ktσa(nominal)Uniaxial Fully Reversed StrategySe´or Sf´Seor SfSeor SfCloadCsurfCsizeCtempCreliabCloadCsurfCsizeCtempCreliabEstimated S-N CurveEstimated S-N Curveσ′=nfSNNf= fatigue safety factor; Sn= Fatigue strength at n cycles;σ ´= largest von Mises alternating stressUniaxial, Reversed Example3032 353875 100250 12510306.8 kN10ABCDABCDMBMcMmax(mm)3mm filletsSut=690 MPaSy=580 MpaUpdate What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾Uniaxial Fully Reversed¾Uniaxial Fluctuating¾Multiaxial0=mσ0≠mσUniaxialMultiaxialTypes of Fatigue Loadingminmaxσσσ−=∆2σσ∆=a2minmaxσσσ+=mmaAσσ=maxminσσ=Rstress rangealternating componentmean componentstress ratioamplitude ratioFully ReversedRepeated FluctuatingDoes Mean Stress Matter?6Fluctuating Stress Failure PlotσaσmSySeor SfSutSyFailureSafetyconstructed for a given number of cycles NGerberSoderbergYieldmodified-GoodmanThe Data“Augmented” Modified-Goodman Plotvon Mises calculated for σaand for σmseparatelyσaσmSeor SfSutSySySyc1=′+′yaymSSσσ1=′+′fautmSSσσ1=′+′−ycaycmSSσσfaS=′σStress Concentration Factorsσa– same as for fully reversedσmBrittleuse static KtDuctile0 so ,02 if if ifminmaxmaxmaxnomnomnom==>−−=>=<fmmyfmafyfmyfffmyfKSKKSKSKKKSKnomnomnomσσσσσσσFactors of Safety Four cases1) σaconstant, σmvaries2) σavaries, σmconstant3) σa and σmincrease at constant ratio4) σa and σmincrease independently If you know how the stress can vary, only use one of four cases If stress can vary in any manner, Case 4 should be used (the most conservative)Factors of Safety – Case 1σaconstant, σmvaries1=′+′yaymSSσσ1=′+′fautmSSσσZmQmfN@@σσ′′=if Q is on
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