1Over the Next Several Days What is Fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾ Uniaxial Fully Reversed¾ Uniaxial Fluctuating¾ Multiaxial¾ Crack GrowthSome 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 Approachesbest 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−=∆stress range2σσ∆=aalternating component2minmaxσσσ+=mmean componentmaxminσσ=Rstress ratiomaAσσ=amplitude ratioFully ReversedRepeated FluctuatingUpdate What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾ Uniaxial Fully Reversed¾ Uniaxial Fluctuating¾ Multiaxial¾ Crack GrowthTesting 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 Analysis¾ Uniaxial Fully Reversed¾ Uniaxial Fluctuating¾ Multiaxial¾ Crack GrowthTypes 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 324 in your book…ksi 40for ksi 19ksi 40for 4.0ksi 60for ksi 24ksi 60for 4.0ksi 200for 100ksi200for 5.085@85@≥≅≤≅≤≅≤≅≥≅≤≅′′′′′′utfututfuteututeuteututeSSSSSSSSSSSksiSSSSEEsteelsironsaluminumsBUT, these are all for highly polished, circular rotating beams of a certain sizeCorrection FactorsfreliabtempsurfsizeloadfereliabtempsurfsizeloadeSCCCCCSSCCCCCS′′==pages 326+ in your bookConstructing 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 + blogN4Fatigue 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 Analysis¾ Uniaxial Fully Reversed¾ Uniaxial Fluctuating¾ Multiaxial¾ Crack Growth0=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)KfσaUniaxial, 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 stress5Update What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾ Uniaxial Fully Reversed¾ Uniaxial Fluctuating¾ Multiaxial¾ Crack Growth0=mσ0≠mσUniaxialMultiaxialTypes of Fatigue Loadingminmaxσσσ−=∆2σσ∆=a2minmaxσσσ+=mmaAσσ=maxminσσ=Rstress rangealternating componentmean componentstress ratioamplitude ratioFully ReversedRepeated FluctuatingDoes Mean Stress Matter? The DataTransform S-N --> σa-σmFluctuating Stress Failure PlotσaσmSySeor SfSutSyFailureSafetyconstructed for a given number of cycles NGerberSoderbergYieldmodified-Goodman6Definitions Factors 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)Four Cases (Use Ruler!)“Augmented” Modified-Goodman Plotvon Mises calculated for σaand for σmseparatelyσaσmSeor SfSutSySySyc1=′+′yaymSSσσ1=′+′fautmSSσσ1=′+′−ycaycmSSσσfaS=′σUniaxial Fluctuating StrategyStress & LoadingN (umber of cycles) Fluctuating Load (Fa)Tentative DesignTentative MaterialKfKtKfmσ1a, σ2a, σ3a; σ1m, σ2m, σ3m(principal)σ´a, σ´m(von Mises)σaσm(nom)σa(nom)σmUniaxial Fluctuating Strategy Fatigue AspectsSe´or Sf´Seor SfCloadCsurfCsizeCtempCreliabModified-Goodman Diagram7Uniaxial Fluctuating StrategyN (umber of cycles) Fluctuating Load (Fa)Tentative DesignTentative Material Tentative DesignTentative Materialσ1a, σ2a, σ3a; σ1m, σ2m,
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