3IntroductionFluctuating stresses in machinery often take the form of sinusoidal pattern because of the nature of the nature of some rotating machinery.Other patterns some quite irregular do occur.The smooth parts of the fracture surface usually exhibit beach marks which occurs as a result of changes in the magnitude of the fluctuating fatigue load.Fatigue behavior of materials is usually described by means of the S-N diagram which gives the number of cycles to failure, N as a function of the max applied alternating stress.
4IntroductionFracture surface which usually exhibits smooth areas which correspond to the gradual crack growth stage, and rough areas, which correspond to the catastrophic fracture stage.
5Characterizing Fluctuating Stresses In periodic patterns exhibiting a single maximum and single minimum of force, the shape of the wave is not important.The peaks on both sides (maximum, minimum) are important.
6Characterizing Fluctuating Stresses Fmax and Fmin in a cycle can be used to characterize the force pattern.A steady component and an alternating component can be constructed as follows:
13Characterizing Fluctuating Stresses The steady, or static, stress is not the same as the midrange stress.The steady stress may have any value between σmin and σmin .The steady stress exists because of a fixed load or preload applied to a part.The steady load is independent of the varying portion of the load.
14Characterizing Fluctuating Stresses A helical compression spring is always loaded into a space shorter than the free length of the spring.The stress created by this initial compression is called the steady, or static, component of the stress.
15Characterizing Fluctuating Stresses The equations use symbols σa and σm as the stress components at the location of scrutiny.In the absence of a notch, σa and σm are equal to the nominal stresses σao and σmo induced by loads Fa and Fm, respectively.With a notch they areσa = Kf σao andσm = Kf σmo , respectively.
20Stress Concentration Neuber equation, 𝑎 = Neuber constant and is a material constant.
21Design Against Fatigue S-N curve is a graphical representation of the maximum applied stress versus the number of stress cycles N before the fatigue failure on a semi-log graph.For ferrous metals like steel the curve becomes asymptotic at 10^6 cycles. The completely reversed stress which a material can withstand 10^6 cycles without failure is called ENDURANCE LIMIT of the material.For non ferrous materials, the curve slopes gradually even after 10^6 cycles.These materials do not have a limiting value of endurance in true sense.
23Design Against Fatigue In the majority cases, the reported fatigue strength or endurance limits of the materials are based on the test of carefully prepared small samples under laboratory condition.Such values cannot be directly used for design purposes because the behavior of a component or structure under fatigue loading does depend not only on the fatigue or endurance limit of the material used in making it, but also an several other factors.
24Design Against Fatigue The Endurance Limit:The strength corresponding to the knee in the S-N diagram is called the endurance limit Se, or the fatigue limit. TheEstimating Se’ or Sf’The determination of endurance limits by fatigue testing is now routine, though a lengthy procedure. Generally, stress testing is preferred to strain testing for endurance limits.For preliminary and prototype design and for some failure analysis as well, a quick method of estimating endurance limits is needed.
26Design Against Fatigue For steelswhere Sut is the minimum tensile strength. The prime mark on S′e in this equation refers to the rotating-beam specimen itself.
27Endurance Limit Modifying Factors Size and shape of the component or structureType of loading and state of stressStress concentrationSurface finishOperating temperatureService environmentMethod of fabrication
28Endurance Limit Modifying Factors Se = kakbkckdkekgkhSe’WhereSe = endurance limit of componentSe’ = endurance limit experimentalka = surface finish factor (machined parts have different finish)kb = size factor (larger parts greater probability of finding defects)kc = reliability / statistical scatter factor (accounts for random variation)
29Endurance Limit Modifying Factors Se = kakbkckdkekgkhSe’Wherekd = operating T factor (accounts for diff. in working T & room T)ke = loading factor (differences in loading types)kg = service environment factor (action of hostile environment)kh = manufacturing processes factor (influence of fabrication parameters)
30Endurance Limit Modifying Factors ka = surface finish factor (machined parts have different finish)
31Endurance Limit Modifying Factors kb = size factor (larger parts greater probability of finding defects)Large engineering parts have lower fatigue strength than smaller test specimenGreater is the probability of finding metallurgical flaws that can cause crack initiationFollowing values can be taken as rough guidelines :kb = 1.0 for component diameters less than 10 mmkb = 0.9 for diameters in the range 10 to 50 mmkb = 1 – [( D – 0.03)/15], where D is diameter expressed in inches, for sizes 50 to 225 mm.
32Endurance Limit Modifying Factors kb = size factor (larger parts greater probability of finding defects)Large engineering parts have lower fatigue strength than smaller test specimenGreater is the probability of finding metallurgical flaws that can cause crack initiationFollowing values can be taken as rough guidelines :kb = 1.0 for component diameters less than 10 mmkb = 0.9 for diameters in the range 10 to 50 mmkb = 1 – [( D – 0.03)/15], where D is diameter expressed in inches, for sizes 50 to 225 mm.
33Endurance Limit Modifying Factors kc = reliability / statistical scatter factor (accounts for random variation)Accounts for random variation in fatigue strength.The following value can be taken as guidelineskc = for 90% reliabilitykc = for 99 % reliabilitykc = for 99.9 % reliability
34Endurance Limit Modifying Factors kd = operating T factor (accounts for diff. in working T & room T)Accounts for the difference between the test temperature and operating temperature of the componentFor carbon and alloy steels, fatigue strength not affected by operating temperature – 45 to 4500C kd = 1At higher operating temperaturekd = 1 – 5800( T – 450 ) for T between 450 and 550oC, orkd = 1 – 3200( T – 840 ) for T between 840 and 1020oF
35Endurance Limit Modifying Factors ke = loading factor (differences in loading types)Accounts for the difference in loading between lab. test and service.Different type of loading, give different stress distributionke = 1 for application involving bendingke = 0.9 for axial loadingke = 0.58 for torsional loading
36Endurance Limit Modifying Factors kg = service environment factor (action of hostile environment)Accounts for the reduced fatigue strength due to the action of a hostile environment.
37Endurance Limit Modifying Factors kh = manufacturing processes factor (influence of fabrication parameters)Accounts for the influence of fabrication parameterHeat treatment, cold working, residual stresses and protective coating on the fatigue material.It is difficult to quantify, but important to included
38Endurance Limit Modifying Factors Endurance limit/Fatigue strengthThe endurance limit, or fatigue strength, of a given material can usually be related to its tensile strength, as shown in table (next slide)The endurance ratio, defined as (endurance limit/ tensile strength), can be used to predict fatigue behavior in the absence of endurance limits results.From the table shows, endurance ratio of most ferrous alloys varies between 0.4 and 0.6