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Fatigue Experiment designOutlineFatigue Our Model Theoretical fatigue life graph (S-N graph)Our objective

FatigueFatigue is a form of failure that occurs in structures subjected to dynamic stresses over an extended period.

Under these conditions it is possible to fail at stress levels considerably lower than tensile or yield strength for a static load

Single largest cause of failure in metals; also affects polymers and ceramics

Fatigue failure is characterized by three stagesCrack InitiationCrack PropagationFinal Fracture51.0-in. diameter steel pins from agricultural equipment.Material; AISI/SAE 4140 low allow carbon steelFracture surface of a failed bolt. The fracture surface exhibited beach marks, which is characteristic of a fatigue failure.

Ken YoussefiMAE dept., SJSU6Fatigue Failure, S-N Curve

Finite lifeInfinite lifeN < 103N > 103Se = endurance limit of the specimenSe7Relationship Between Endurance Limit and Ultimate Strength

Aluminum alloysSe =0.4Sut130 MPaSut < 330 MPaSut 330 MPaAluminumFor N = 5x108 cycle

Copper alloysSe =0.4Sut100 MPaSut < 280 MPaSut 280 MPaCopper alloysFor N = 5x108 cycleOur Model

Fig.: Model with notchFig.: Model without notchEither one of theseInput Accelerations

accetimeInput acceleration can be two types 1. Continuous sinusoidal wave, 2. sudden type wave For this phase of experiment, continuous sinusoidal wave will be tested as our target is to reveal the relation between strain range and number of cycle Theoretical S-N curve (low cycle)For low cycle fatigue there are some empirical equations to predict the S-N curve from the material characteristics. Though these equations give conservative data but we can at least have a idea of fatigue life. There are two equations for non ferrous low cycle fatigue Mansons correlation Langers equation

Material properties Theoretical S-N curveGlobal ObjectiveTo make primary loading vs secondary loading graph for different top node weightsTo investigate the effect of acceleration frequency on fatigue Moment by accelerationPrimary loading vs secondary (pseudo) loading curve Moment by weightTentative graphsObjective of this phase of experimentIs to achieve fatigue by vibration test for this material

Thickness: 6 mmNo of cycle Acceleration needed (m/s^2)100030100002210000017Thickness: 8 mmNo of cycle Acceleration needed (m/s^2)100048100003610000027.5Thickness: 10No of cycle Acceleration needed (m/s^2)100068100005010000039At top node mass : 238 gmPb 99% - Sb 1%Fatigue strength from material propertiesPb 98% - Sb 2%Thickness: 6 mmNo of cycle Acceleration needed (m/s^2)100033100002510000020Thickness: 8 mmNo of cycle Acceleration needed (m/s^2)100053100004110000031Thickness: 10No of cycle Acceleration needed (m/s^2)100075100005710000044At top node mass : 238 gmFatigue strength from material properties

Experiment we didMaterial: Pb 99% -1% SbTop mass : 238 gmFailure occur due to excessive deformation (collapse) no crack was observed.Thickness: 6 mmNo of cycle Acceleration needed (m/s^2)100034100003410000034We didnt get expected fatigue failure. So the fatigue strength from material fatigue data is not working for this loading and/or material. Previous fatigue test in our laboratory

19MaterialPbSb=%%Top mass820 gmInput (frequency)Hz(maximum acceleration)Not measured but approx. 1200 gal(wave form)(continuous sine wave )Thickness

Top massNo. of cycleFrequencyAccelerationInput wave1st 6 mm

820 gmUntil failure occursAbout NaturalMaximum possibleContinuous sinusoidal2nd 8mm 820 gmUntil failure occursAbout NaturalMaximum possibleContinuous sinusoidal3rd10 mm 820 gmUntil failure occursAbout NaturalMaximum possibleContinuous sinusoidalNext experimental planObjective: Is to achieve low cycle fatigue by this materialMaterial: 99% Pb-1% Sb / 98%Pb-2%Sb ContinueIf this tests will not give us fatigue then we have only option to play with top mass. If this top mass weight makes collapse after few cycle then we need to put less top mass to avoid collapse condition. But if it works, then we will get the following graph, where the primary moment is zero

Then our next step is to get fatigue by putting some primary load, so that we can put these data in complete failure mode graph

Experimental resultsWe got fatigue in the following two cases-SpecimenTop mass (kg)Acceleration(gal)Frequency (Hz)

No of cycleNatural Input6mm 1.72538007.819.80(1.25fn)Specimen failed by fatigue at 362 cycle (though the specimen had 20,000 cycle of earlier low loading history).6mm0.535230013.6726.77 (0.5fn)Total 4684 cycle. First crake was observed at around 3344 cycle then after 1340 cycle the specimen failed.

FatigueRatchetingCollapseYXmmLLlFailure mode map Our specimens3 different thickness models6mm8mm10mm

We have idea of fatigue data (top mass and acceleration) for 6 mm thickness at 0.5Xnatural frequency. Our specimen models3 different thickness models6mm8mm10mm

We have idea of fatigue data (top mass and acceleration) for 6 mm thickness at 0.5Xnatural frequency. How much loading we need to have to occur fatigue at 1.5fn frequency.

How much loading we need to have for 8mm and 10mm thickness model when we know the loading for 6 mm model. Frequency effectWe have achieved fatigue at 0.5fn frequency. But we want to have fatigue at frequency equal to 1.5fn. So how to predict the loading for 1.5fn from the data of 0.5fn. Frequency equivalenceFrom this diagram we have seen that the elastic deflection value increases about 2 times when the frequency is decreasing from 1.5 to 0.5 times of fn. As we have data of fatigue at 0.5fn frequency. So if we increase that loading 2 times at 1.5fn then we can have similar strain/deflection as 0.5fn. So to achieve fatigue at 1.5fn frequency we need to increase the loading 2 times than 0.5fn. Deflection vs normalized frequency graph

Frequency equivalenceSpecimen Mass [kg] at 0.5fn Required Mass [kg]at 1.5fn6mm0.5351.07If we want to keep the same acceleration then we need to increase mass 2 times to have equivalent strain/deflection.But we can also change the acceleration. The maximum acceleration our machine can achieve is 38 m/s2. Specimen Mass [kg]*acceleration[m/s2] at 0.5fn Required Mass [kg]*acceleration [m/s2]at 1.5fn6mm0.535*23 = 12.31N0.648*38=24.62NOur specimen models3 different thickness models6mm8mm10mm

We have idea of fatigue data (top mass and acceleration) for 6 mm thickness at 0.5Xnatural frequency. How much loading we need to have fatigue at 1.5Xfn frequency.

How much loading we need to have fatigue for 8mm and 10mm specimen when we know the loading for 6 mm model. Natural frequencyThickness of the specimenTop mass6 mmm18 mmm2=0.03027+2.37037.m1 (about 2.5 times)10 mmm2=0.0864864+4.62963.m1 ( about 5 times)Our failed specimen has natural frequency 13.67 Hz at the top mass of 535 gm. So to make the same natural frequency we need to have the following mass for 8 am 10 mm specimen-

SpecimenTop mass (kg) 6 mm0.535 8 mm1.3010 mm2.56Putting these mass we gain surface strain- Putting these mass we gain surface strain- So higher thickness models are more probable to get fatigue or in other words, less number of cycle may needed to have fatigue for higher thickness models if we want to have the same response of all model. SpecimenAcceleration (m/s2)Top mass (kg) 6 mm230.535 8 mm231.3010 mm232.56For 0.5fn input frequencyFor 1.5fn input frequencySpecimenAcceleration (m/s2)Top mass (kg) 6 mm380.648 8 mm381.57310 mm383.098Calculation for same strain instead of same natural frequencySpecimenTop mass (kg)Top mass (kg) 6 mmm10.535 8 mm1.78*m10.952310 mm2.78*m11.4873SpecimenAcceleration (m/s2)Top mass (kg) 6 mm230.535 8 mm230.952310 mm231.4873For 0.5fn input frequencyFor 1.5fn input frequencySpecimenAcceleration (m/s2)Top mass (kg) 6 mm380.648 8 mm381.15210 mm381.80SpecimenTop mass (kg)Same responseTop mass (kg) Same strain 6 mm0.535 0.535 8 mm1.300.952310 mm2.561.4873Problems and plan We have problem on top mass, as top mass is quite heavy we need a lots of small mass which causes extra vibration in the structure. So we need concentrated load.The above calculation is only theoretical calculation. Numerical calculation can be done to see the strain needed to have fatigue by simulating the exact experimental conditions (failure case). Do experiment in April/ May.

mLNo primary loading No gravityOnly inertia force AccelerationLoadingNo Gravity force (g = 0)Inertia forceInertia force due to ground acceleration

Fixed end

Ground AccelerationTop massNumerical simulation

AppendixStrain vs number of cycleStress strain curveStrain range at a close lookThe strain at which the fatigue occur is in between 0.0271 to 0.0273Frequency equivalence

4646Reversed stress

ReferencesCzyryca E.J., Gross M. R. 1966. Low-cycle Fatigue of Nonferrous Alloys for heat exchanger and saltwater piping. Phase IV MEL R&D Report 26/66.Yamada Y. 2007. Materials for spring. JSSE Springer. P. 33-34.Sylwester K. 2005. Load sequence influence on low cycle fatigue life. Technical Sciences, No.8.

Fatigue strength, SNumber of cycleS-N curve for one specific top node weightHigh frequency Natural frequency Low frequency Questions they askedRealistic seismic wave is different than sinusoidal wave. How can I incorporate the realistic event in my numerical simulation.

The real seismic wave is 3 dimensional but my finas seismic wave is in x-y direction only. So putting z direction acceleration can be interesting.

51PbSb=%%Hzgal