Update What is fatigue? Types of Fatigue Loading Empirical Data Estimating Endurance/Fatigue Strength Strategies for Analysis¾Uniaxial Fully Reversed¾Uniaxial Fluctuating¾Multiaxial0=mσ0≠mσUniaxialMultiaxialDoes Mean Stress Matter?Fluctuating 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 segment DE:′−′=yamyfSSNσσ1Factor of Safety- Case 21=′+′yaymSSσσ1=′+′fautmSSσσZaPafN@@σσ′′=if P is on segment CD:′−′=utmaffSSNσσ1σavaries, σmconstantFactor of Safety – Case 31=′+′yaymSSσσ1=′+′fautmSSσσfmutautfZmRmfSSSSNσσσσ′+′=′′=@@If R is on CD, then through a similar procedure:σa and σmincrease at constant ratioFactor of Safety – Case 4BIGequations for this… see your book!σa and σmincrease independentlyUniaxial 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 DiagramUniaxial Fluctuating StrategyN (umber of cycles) Fluctuating Load (Fa)Tentative DesignTentative Material Tentative DesignTentative Materialσ1a, σ2a, σ3a; σ1m, σ2m, σ3m(principal)σ´a, σ´m(von Mises)KfσaKtσm(nom)σa(nom)KfmσmSe´or Sf´Seor SfSeor SfCloadCsurfCsizeCtempCreliabCloadCsurfCsizeCtempCreliabModified-Goodman DiagramModified-Goodman DiagramNfUniaxial, Fluctuating Example3032 353875 100250 1251030Fm=1 kNFa= 2 kN10ABCDABCDMBMcMmax(mm)3mm filletsSut=690 MPaSy=580 Mpa*NOT a rotating shaft*Strategy Find σ´aand σ´mwith appropriate stress concentration factors Find Se Plot modified-Goodman diagram Find factor of safetyModified-GoodmanσmSe=197Sy=580Sy=580 Sut= 69051.4102.5ODEFCZPSRQCase ICase IICase IIICase
View Full Document