8/9/2019 302.L9.fatigue.20Nov02 (1)

1/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

1

Microstructure-Properties: II

Fatigue

27-302

Lecture 9

Fall, 2002

Prof. A. D. Rollett

8/9/2019 302.L9.fatigue.20Nov02 (1)

2/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

2

Materials Tetrahedron

Microstructure Properties

Processing

Performance

8/9/2019 302.L9.fatigue.20Nov02 (1)

3/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

3

Objective

The objective ofthis lectureisto explainthephenomenon of fatigue and also to show howresistanceto fatigue failuredepends on

microstructure. For27-302, Fall 2002: thisslidesetcontains morematerial thancan becoveredinthetime available.Slidesthatcontain material overand abovethat

expected forthiscourse are marked *.

8/9/2019 302.L9.fatigue.20Nov02 (1)

4/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

4

References

Mechanical BehaviorofMaterials (2000), T. H. Courtney,McGraw-Hill, Boston.

Phasetransformationsin metals and alloys, D.A. Porter, &K.E. Easterling, Chapman & Hall.

Materials Principles & Practice, Butterworth Heinemann,Edited by C. Newey & G. Weaver.

Mechanical Metallurgy, McGrawHill, G.E. Dieter, 3rd Ed.

Light Alloys(1996), I.J. Polmear, Wiley, 3rd Ed.

Hull, D. and D. J. Bacon(1984). Introductionto Dislocations.Oxford, UK, Pergamon.

8/9/2019 302.L9.fatigue.20Nov02 (1)

5/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

5

NotationW

a:=Alternatingstress

Wm := MeanstressR := Stressratio

I := strainNf := numberofcyclesto failureA := AmplituderatioIpl := PlasticstrainamplitudeIel := ElasticstrainamplitudeK:= Proportionalityconstant, cyclicstress-strainn:= Exponentincyclicstress-strainc := Exponentin Coffin-Manson Eq.;

also, crack lengthE := Youngsmodulusb := exponentin Basquin Eq.

m:= exponentin ParisLawK:= Stressintensity

K:=Stressintensityamplitude

a := crack length

8/9/2019 302.L9.fatigue.20Nov02 (1)

6/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

6

Fatigue

Fatigueisthenamegivento failureinresponsetoalternating loads(as opposedto monotonicstraining).

Instead of measuringtheresistanceto fatigue failurethrough anupperlimitto strain(asinductility), thetypicalmeasure of fatigueresistanceisexpressedinterms ofnumbers ofcyclesto failure. Fora givennumberofcycles(requiredin an application), sometimesthestress(thatcan besafelyendured bythe material) isspecified.

8/9/2019 302.L9.fatigue.20Nov02 (1)

7/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

7

Fatigue: general characteristics

Primarydesigncriterioninrotatingparts.

Fatigue as a name forthephenomenon based onthenotionof a material becoming tired, i.e. failing at lessthanitsnominal strength.

Cyclical strain(stress) leadsto fatigue failure. Occursin metals andpolymers butrarelyinceramics.

Also anissue forstatic parts, e.g. bridges.

Cyclic loadingstress limit

8/9/2019 302.L9.fatigue.20Nov02 (1)

8/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

8

Fatigue:general characteristics

Most applications ofstructural materialsinvolvecyclicloading; anynettensilestress leadsto fatigue.

Fatigue failuresurfaceshavethreecharacteristic features:[seenextslide, also Courtney figs. 12.1, 12.2]

A (near-)surfacedefect asthe origin ofthecrack Striationscorrespondingto slow, intermittentcrackgrowth

Dull, fibrous brittle fracturesurface(rapidgrowth).

Life ofstructural componentsgenerally limited bycyclicloading, notstaticstrength.

Mostenvironmental factorsshorten life.

8/9/2019 302.L9.fatigue.20Nov02 (1)

9/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

9

S-NCurves

S-N [stress-numberofcyclesto failure] curvedefines locusofcycles-to-failure forgivencyclicstress.

Rotating-beam fatiguetestisstandard; also alternatingtension-compression.

Plotstressversusthelog(numberofcyclesto failure), log(Nf).[seenextslide,also Courtney figs. 12.8, 12.9]

Forfrequencies< 200Hz,metals areinsensitivetofrequency; fatigue lifeinpolymersis frequency

dependent.

[Hertzberg]

8/9/2019 302.L9.fatigue.20Nov02 (1)

10/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

10

Fatigue testing, S-Ncurve

[Dieter]

Note the presence of a

fatigue limit in manysteels and its absence

in aluminum alloys.

log Nf

Wa

Wmean 1Wmean 2Wmean 3

Wmean 3 > Wmean 2 > Wmean 1Thegreaterthenumberofcyclesinthe loadinghistory,thesmallerthestressthatthe material can withstand

without failure.

8/9/2019 302.L9.fatigue.20Nov02 (1)

11/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

11

Endurance Limits

Some materialsexhibitendurance limits, i.e. astress below whichthe lifeisinfinite: [fig. 12.8] Steelstypicallyshow anendurance limit, = 40% ofyield;

thisistypically associated withthepresence of a solute

(carbon, nitrogen) thatpines dislocations andpreventsdislocation motion atsmall displacements orstrains(whichis apparentin an upperyieldpoint).

Aluminum alloys do notshow endurance limits; thisisrelatedto the absence of dislocation-pinningsolutes.

At large Nf, the lifetimeis dominated by nucleation. Thereforestrengtheningthesurface(shotpeening) is beneficial to

delay crack nucleation andextend life.

8/9/2019 302.L9.fatigue.20Nov02 (1)

12/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

12

Fatigue fracture

surface

[Hertzberg]

8/9/2019 302.L9.fatigue.20Nov02 (1)

13/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

13

Fatigue crack stages

Stage 1

Stage 2[Dieter]

8/9/2019 302.L9.fatigue.20Nov02 (1)

14/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

14

Fatigue Crack Propagation

Crack Nucleationpstressintensification atcracktip.

Stressintensitypcrackpropagation(growth);- stage I growth onshearplanes(45),stronginfluence ofmicrostructure [Courtney: fig.12.3a]- stage II growthnormal to tensile load(90)weakinfluence ofmicrostructure [Courtney: fig.12.3b].

Crackpropagationpcatastrophic, orductile failure atcrack

lengthdependent on boundaryconditions, fracturetoughness.

8/9/2019 302.L9.fatigue.20Nov02 (1)

15/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

15

Fatigue CrackNucleation

Flaws, cracks, voidscan all act ascracknucleationsites,especially atthesurface.

Therefore, smoothsurfacesincreasethetimeto nucleation;notches, stressrisersdecrease fatigue life.

Dislocation activity(slip) can also nucleate fatiguecracks.

8/9/2019 302.L9.fatigue.20Nov02 (1)

16/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

16

Dislocation Slip CrackNucleation

Dislocationslip -> tendencyto localizeslipin bands. [seeslide10, also Courtney fig. 12.3]

Persistent Slip Bands(PSBs) characteristic ofcyclicstrains.

Slip Bands -> extrusion at freesurface. [seenextslide forfig.from Murakamiet al.] Extrusions -> intrusions andcracknucleation.

8/9/2019 302.L9.fatigue.20Nov02 (1)

17/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

17

Slip steps

and thestress-strain

loop

8/9/2019 302.L9.fatigue.20Nov02 (1)

18/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

18Design Philosophy:Damage Tolerant

Design

S-N (stress-cycles) curves = basiccharacterization.

Old Design Philosophy = InfiniteLifedesign: acceptempirical information about fatigue life(S-N curves); apply a(large!) safety factor; retirecomponents orassemblies atthe

pre-set life limit, e.g. Nf=107. *CrackGrowth Ratecharacterization ->

*Modern Design Philosophy(AirForce, not Navycarriers!) =DamageTolerantdesign: acceptpresence ofcracksin

components. Determine life based onprediction ofcrackgrowthrate.

8/9/2019 302.L9.fatigue.20Nov02 (1)

19/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

19

Definitions: StressRatios

Alternating Stress

Meanstress| Wm = (Wmax +Wmin)/2.

Puresine wave|Meanstress=0.

Stressratio | R= Wmax/Wmin.

ForWm = 0, R=-1

Amplituderatio|

A = (1-R)/(1+R). Statistical approachshowssignificantdistributioninNf forgivenstress.

See Courtney fig. 12.6; also followingslide.

| Wa

8/9/2019 302.L9.fatigue.20Nov02 (1)

20/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

20

AlternatingStressDiagrams

[Dieter]

8/9/2019 302.L9.fatigue.20Nov02 (1)

21/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

21

Mean Stress

Alternatingstress| Wa = (Wmax-Wmin)/2. Raisingthemeanstress (Wm) decreasesNf. [seeslide19, also

Courtneyfig. 12.9]

Variousrelations between R = 0 limit andtheultimate (or

yield) stress areknown as Soderberg (linearto yieldstress),Goodman (linearto ultimate) andGerber(parabolictoultimate). [Courtney, fig. 12.10, problem12.3]

Wa

Wmeantensile strength

endurance limit at zero mean stress

Wa ! Wfat 1 Wmean

tensile strength

8/9/2019 302.L9.fatigue.20Nov02 (1)

22/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

22

Cyclic strain vs. cyclic stress

Cyclicstraincontrol complementscyclicstresscharacterization: applicableto thermal fatigue, orfixeddisplacementconditions.

Cyclicstress-straintestingdefined by a controlledstrainrange, Ipl. [seenextslide, Courtney, figs. 12.24,12.25]

Soft, annealed metalstendto harden; strengthenedmetalstendto soften.

Thus, many materialstendtowards a fixedcycle, i.e.constantstress, strain amplitudes.

8/9/2019 302.L9.fatigue.20Nov02 (1)

23/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

23

Cyclic stress-strain curve

[Courtney]

Largenumberofcyclestypicallyneededto reachasymptotichysteresis loop(~100).

Softening orhardeningpossible. [fig. 12.26]

8/9/2019 302.L9.fatigue.20Nov02 (1)

24/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

24

Cyclic stress-strain

Wavy-slip materialsgenerallyreach asymptoteincyclicstress-strain: planarslipmaterials(e.g. brass) exhibithistorydependence.

Cyclicstress-straincurvedefined bytheextrema, i.e.the tips ofthehysteresisloops. [Courtney fig. 12.27]

Cyclicstress-straincurvestendto lie below those for

monotonictensiletests. Polymerstendto softenin

cyclicstraining.

[Courtney]

8/9/2019 302.L9.fatigue.20Nov02 (1)

25/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

25

Cyclic Strain Control

Strainis a more logical independentvariable forcharacterization of fatigue. [fig. 12.11]

Define anelasticstrainrange as Iel = W/E.

Define a plasticstrainrange, Ipl. Typically observe a changeinslope betweenthe

elastic andplasticregimes. [fig. 12.12]

Low cycle fatigue(small Nf) dominated byplasticstrain: highcycle fatigue(largeNf) dominated byelasticstrain.

8/9/2019 302.L9.fatigue.20Nov02 (1)

26/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

26

Strain control

of fatigue

[Courtney]

8/9/2019 302.L9.fatigue.20Nov02 (1)

27/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

27

Cyclic Strain control: low cycle

Constitutiverelationforcyclicstress-strain:

n 0.1-0.2

Fatigue life: CoffinMansonrelation:

If

~true fracturestrain; closeto tensileductility

c -0.5to -0.7 c = -1/(1+5n); largenp longerlife.

( ! dK (I dn

(I

2! dIf 2 f

c

8/9/2019 302.L9.fatigue.20Nov02 (1)

28/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

28

Cyclic Strain control: high cycle

Forelastic-dominatedstrainsathighcycles, adaptBasquinsequation:

Intercept onstrain axis ofextrapolatedelastic line = Wf/E. Highcycle = elasticstraincontrol:

slope(inelasticregime) = b = -n/(1+5n)[Courtney, fig. 12.13]

Thehighcycle fatiguestrength, Wf, scaleswiththeyieldstress highstrengthgoodinhigh-cycle

Wa ! E(Ie2

! dWf 2 b

8/9/2019 302.L9.fatigue.20Nov02 (1)

29/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

29

Strain amplitude - cycles

[Courtney]

8/9/2019 302.L9.fatigue.20Nov02 (1)

30/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

30

Total strain (plastic+elastic) life

Low cycle = plasticcontrol: slope = c

Addtheelastic andplasticstrains.

Cross-overbetweenelastic andplasticcontrol istypically atNf= 103 cycles.

Ductilityuseful forlow-cycle; strengthforhighcycle

Examples ofMaragingsteel forhighcycleendurance,annealed4340 forlow cyclefatiguestrength.

(

2

!(Iel

2

(Ipl

2

!f2 f

b dIf 2Nf

c

8/9/2019 302.L9.fatigue.20Nov02 (1)

31/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

31

Fatigue Crack Propagation

CrackLength := a.Numberofcycles := NCrackGrowth Rate := da/dNAmplitude of Stress Intensity := K= Wc.

Definethreestages ofcrackgrowth, I, II and III,

in a plot of da/dN versus K. Stage II crackgrowth: application of linearelastic fracture mechanics.

Canconsiderthecrackgrowthrateto berelatedto the appliedstressintensity.

Crackgrowthratesomewhatinsensitiveto R (if R

8/9/2019 302.L9.fatigue.20Nov02 (1)

32/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

32

Fatigue Crack Propagation

Threestages ofcrackgrowth, I, II and III.

Stage I: transitionto afinitecrackgrowthratefrom no propagationbelow a thresholdvalue ofK.

Stage II: powerlawdependence ofcrackgrowthrate on K.

Stage III: acceleration of

growthrate with K,approachingcatastrophicfracture.

da/dN

th

c

I

IIIII

8/9/2019 302.L9.fatigue.20Nov02 (1)

33/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

33

*Paris Law

ParisLaw:

m~ 3 (steel); m~4(aluminum).

Cracknucleationignored! Threshold~ Stage I Thethresholdrepresents anendurance limit.

Forceramics, thresholdiscloseto KIC. Crackgrowthrateincreases withR (forR>0).

[fig. 12.18a]

dc

d! A((K)m

8/9/2019 302.L9.fatigue.20Nov02 (1)

34/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

34

*Striations- mechanism

Striations occurbydevelopment ofslip bandsineachcycle, followed bytip blunting, followed byclosure.

Canintegratethegrowthrateto obtaincycles asrelatedto cyclicstress-strain behavior. [Eqs. 12.6-12.8]

NII !dc

AEm (W c mc0

cf

NII !dc

dc / dNc0

cf

8/9/2019 302.L9.fatigue.20Nov02 (1)

35/52

Objective

Crack

InitiationS-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

35

*Striations, contd.

Providedthat m>2 andEisconstant, canintegrate.

Iftheinitial crack lengthis much lessthanthe final length,c0

8/9/2019 302.L9.fatigue.20Nov02 (1)

36/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

36

*Damage TolerantDesign

Calculateexpectedgrowthrates from dc/dN data. Perform NDE on all flight-critical components.

Ifcrackis found, calculatetheexpected life ofthe

component. Replace, rebuildiftoo closeto life limit.

Endurance limits.

8/9/2019 302.L9.fatigue.20Nov02 (1)

37/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

37

Geometrical effects

Notchesdecrease fatigue lifethroughstressconcentration. Increasingspecimensize lowers fatigue life. Surfaceroughness lowers life, againthroughstress

concentration.

Moderatecompressivestress atthesurfaceincreases life(shotpeening); itisharderto nucleate a crack whenthelocal stressstate opposescrack opening.

Corrosiveenvironment lowers life; corrosioneitherincreasestherate at which material isremoved from the

cracktip and/oritproduces material onthecracksurfacesthat forcesthecrack open(e.g. oxidation). Failure mechanisms

8/9/2019 302.L9.fatigue.20Nov02 (1)

38/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

38

Microstructure-FatigueRelationships

What aretheimportantissuesin microstructure-fatiguerelationships?

Answer: three majorfactors.1: geometry ofthespecimen(previousslide); anything onthesurface

thatis a site ofstressconcentration will promotecrack formation(shortenthetimerequired fornucleation ofcracks).

2: defectsinthe material; anythinginsidethe material thatcanreducethestress and/orstrainrequiredto nucleate a crack(shortenthetimerequired fornucleation ofcracks).

3: dislocationslipcharacteristics; ifdislocationglideisconfinedtoparticularslipplanes(calledplanarslip) thendislocationscanpileup at anygrain boundary orphase boundary. Thehead ofthepile-upis a stressconcentration whichcaninitiate a crack.

8/9/2019 302.L9.fatigue.20Nov02 (1)

39/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

39

Microstructure affects CrackNucleation

The maineffect ofmicrostructure(defects,surfacetreatment, etc.) isalmost all inthe low stressintensityregime, i.e. StageI. Defects, forexample,

makeiteasierto nucleatea crack, whichtranslatesinto a lowerthreshold forcrackpropagation(Kth).

Micr ostructure also affectsfracturetoughness andtherefore Stage III.

da/dN

th

c

I

IIIII

8/9/2019 302.L9.fatigue.20Nov02 (1)

40/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

40

Defects in Materials

Descriptions ofdefectsin materials atthesophomore level focuses,appropriately onintrinsicdefects(vacancies, dislocations). Forthematerialsengineer, however, defectsincludeextrinsicdefectssuch asvoids, inclusions, grain boundary films, and othertypes ofundesirablesecondphases.

Voids areintroducedeitherbygasevolutioninsolidification orbyincompletesinteringinpowderconsolidation.

Inclusions aresecondphasesentrainedin a material duringsolidification. In metals, inclusions aregenerally oxides from thesurfaceofthe metal melt, ora slag.

Grain boundary films arecommoninceramics asglassy films from

impurities. In aluminum alloys, thereis a hierachy ofnames forsecondphaseparticles; inclusions areunwanted oxides(e.g. Al2O3); dispersoids areintermetallicparticlesthat, onceprecipitated, arethermodynamicallystable(e.g. AlFeSicompounds); precipitates areintermetallicparticlesthatcan bedissolved orprecipiateddepending ontemperature(e.g.

AlCucompounds).

8/9/2019 302.L9.fatigue.20Nov02 (1)

41/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

41

Metallurgical Control: fine particles

Tendencyto localization of flow isdeleteriousto theinitiation of fatiguecracks, e.g. Al-7050 withnon-shearablevs. shearableprecipitates(Stage I in a da/dNplot). Also Al-Cu-Mg withshearableprecipitates butnon-shearable

dispersoids, vs. onlyshearableppts.

graph courtesy of J.

Staley,Alcoa

8/9/2019 302.L9.fatigue.20Nov02 (1)

42/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

42

Coarse particle effect on fatigue

Inclusionsnucleatecrackspcleanliness(w.r.t. coarseparticles) improves fatigue life, e.g. 7475improved by lowerFe+Sicomparedto 7075:0.12Fein 7475, comparedto 0.5Fein 7075;

0.1Siin 7475, comparedto 0.4Siin 7075.

graph courtesy of J.

Staley,Alcoa

8/9/2019 302.L9.fatigue.20Nov02 (1)

43/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

43

Alloy steel heat treatment

Increasinghardnesstendsto raisetheendurance limit forhighcycle fatigue. Thisis largely a function oftheresistanceto fatiguecrack formation(Stage I in a plot ofda/dN).

[Dieter]

Mobilesolutesthatpindislocationspfatiguelimit, e.g. carbon in steel

8/9/2019 302.L9.fatigue.20Nov02 (1)

44/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

44

Casting porosity affects fatigue

Castingtendsto resultinporosity. Pores areeffectivesitesfornucleation offatigue cracks. Castingsthustendto have lowerfatigueresistance(asmeasured by S-N curves) than wrought materials.

Castingtechnologies, such assqueeze casting, thatreduceporositytendtoeliminatethisdifference.

[Polmear]

Gravity castversussqueeze castversus

wroughtAl-7010

8/9/2019 302.L9.fatigue.20Nov02 (1)

45/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

45

Titanium alloys

FormanyTi alloys, theproportion ofhcp(alpha) and bcc(beta) phasesdepends

strongly ontheheattreatment. Cooling from thetwo-phaseregionresultsin a two-phasestructure, as Polmearsexample, 6.7a. Rapidcooling from abovethetransusinthesinglephase(beta) regionresultsin a two-phase microstructure with Widmanstttenlaths of(martensitic) alpha in a beta matrix, 6.7b.

The fatigueproperties ofthetwo-phasestructure aresignificantly betterthantheWidmanstttenstructure(moreresistanceto fatiguecrack formation).

The alloyinthisexampleis IM834, Ti-5.5Al-4Sn-4Zr-0.3Mo-1Nb-0.35Si-0.6C.

[Polmear]

8/9/2019 302.L9.fatigue.20Nov02 (1)

46/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

46

*Design Considerations

Ifcrackgrowthrates arenormalized bytheelastic modulus,then material dependenceis mostlyremoved![Courtney fig.12.20]

Candistinguish betweenintrinsic fatigue [use Eq. 12.4 for

combinedelastic, plasticstrainrange] forsmall cracksizesandextrinsic fatigue [use Eq. 12.6 forcrackgrowthratecontrolled] at longercrack lengths. [fig. 12.21.]

Inspection ofdesigncharts, fig. 12.22, showsthatceramicssensitiveto crackpropagation(highendurance limitinrelationto fatiguethreshold).

8/9/2019 302.L9.fatigue.20Nov02 (1)

47/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

47

*Design Considerations: 2

Metalsshow a higherfatiguethresholdinrelationtotheirendurance limit. PMMA andMg are atthelowerend ofthetoughnessrangeintheirclass.[Courtney fig. 12.22]

Also interestingto compare fracturetoughness withfatiguethreshold. [Courtney fig. 12.23]

Notethatceramics are almost onratio=1 line,

whereas metalstendto lie well below, i.e. fatigueismoresignificantcriterion.

48

8/9/2019 302.L9.fatigue.20Nov02 (1)

48/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

48

*Fatigue

property map

[Courtney]

49

8/9/2019 302.L9.fatigue.20Nov02 (1)

49/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

49

*Fatigue

property map

[Courtney]

50

8/9/2019 302.L9.fatigue.20Nov02 (1)

50/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

50

*Variable Stress/Strain Histories

Whenthestress/strainhistoryisstochasticallyvarying, a rule forcombiningportions of fatigue lifeisneeded.

Palmgren-MinerRuleisuseful: ni isthenumberofcycles ateachstress level, and Nfi isthe failurepoint forthatstress.[Ex. Problem 12.2]

ni

Nfi! 1

i

* Courtneys Eq. 12.9isconfusing; hehas Nfinthenumeratoralso

51

8/9/2019 302.L9.fatigue.20Nov02 (1)

51/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

51

*Fatigue in Polymers

Manydifferences from metals

Cyclicstress-strain behavioroftenexhibitssoftening; also affected byvisco-elasticeffects;

crazinginthetensileportionproducesasymmetries, figs. 12.34, 12.25.

S-N curvesexhibitthreeregions, withsteeplydecreasingregion II, fig. 12.31.

Nearnessto Tg resultsinstrongtemperaturesensitivity, fig. 12.42

52

8/9/2019 302.L9.fatigue.20Nov02 (1)

52/52

Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

52

Fatigue: summary

Critical to practical use ofstructural materials. Fatigue affects moststructural components, even

apparentlystatically loaded ones.

Well characterizedempirically. Connection betweendislocation behaviorand

fatigue life offersexcitingresearch opportunities,i.e. physically based models are lacking!