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1

Microstructure-Properties: II

Fatigue27-302

Lecture 9

Fall, 2002

Prof. A. D. Rollett

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2

Materials Tetrahedron

Microstructure Properties

ProcessingPerformance

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3

Objective

The objective of this lecture is to explain thephenomenon of fatigue and also to show howresistance to fatigue failure depends onmicrostructure.

For 27-302, Fall 2002: this slide set containsmore material than can be covered in thetime available. Slides that contain material

over and above that expected for this courseare marked *.

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4

References

Mechanical Behavior of Materials (2000), T. H.Courtney, McGraw-Hill, Boston.

Phase transformations in metals and alloys, D.A.Porter, & K.E. Easterling, Chapman & Hall.

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

Mechanical Metallurgy, McGrawHill, G.E. Dieter, 3rdEd.

Light Alloys (1996), I.J. Polmear, Wiley, 3rd Ed. Hull, D. and D. J. Bacon (1984). Introduction to

Dislocations. Oxford, UK, Pergamon.

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5

Notationsa := Alternating stresssm := Mean stressR := Stress ratioe := strain

Nf := number of cycles to failureA := Amplitude ratioepl:= Plastic strain amplitudeeel:= Elastic strain amplitudeK:= Proportionality constant, cyclic stress-strain

n:= Exponent in cyclic stress-strainc:= Exponent in Coffin-Manson Eq.;

also, crack length

E:= Youngs modulusb:= exponent in Basquin Eq.

m:= exponent in Paris LawK:= Stress intensity

K:= Stress intensity amplitude

a:= crack length

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6

Fatigue

Fatigue is the name given to failure in response toalternating loads (as opposed to monotonicstraining).

Instead of measuring the resistance to fatigue

failure through an upper limit to strain (as inductility), the typical measure of fatigue resistanceis expressed in terms of numbers of cycles tofailure. For a given number of cycles (required in

an application), sometimes the stress (that can besafely endured by the material) is specified.

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7

Fatigue: general characteristics

Primary design criterion in rotating parts. Fatigue as a name for the phenomenon based on the

notion of a material becoming tired, i.e. failing at

less than its nominal strength.

Cyclical strain (stress) leads to fatigue failure. Occurs in metals and polymers but rarely in

ceramics.

Also an issue for static parts, e.g. bridges.

Cyclic loading stress limit

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8

Fatigue:general characteristics

Most applications of structural materials involve cyclicloading; any net tensile stress leads to fatigue.

Fatigue failure surfaces have three characteristicfeatures:[see next slide, also Courtney figs. 12.1, 12.2]

A (near-)surface defect as the origin of the crack Striations corresponding to slow, intermittent crack growth

Dull, fibrous brittle fracture surface (rapid growth).

Life of structural components generally limited by

cyclic loading, not static strength. Most environmental factors shorten life.

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9

S-N Curves

S-N [stress-number of cycles to failure] curve defineslocus of cycles-to-failure for given cyclic stress.

Rotating-beam fatigue test is standard; alsoalternating tension-compression.

Plot stress versus thelog(number of cyclesto failure), log(Nf).[see next slide,also Courtney figs. 12.8, 12.9]

For frequencies < 200Hz,metals are insensitive tofrequency; fatigue life inpolymers is frequency

dependent.

[Hertzberg]

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10

Fatigue testing, S-N curve

[Dieter]

Note the presence of a

fatigue limit in manysteels and its absence

in aluminum alloys.

log Nf

sa

smean 1

smean 2

smean 3

smean 3

> smean 2

> smean 1

The greater the number ofcycles in the loading history,the smaller the stress thatthe material can withstand

without failure.

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11

Endurance Limits

Some materials exhibit endurance limits, i.e.a stress below which the life is infinite:[fig. 12.8] Steels typically show an endurance limit, = 40% of

yield; this is typically associated with the presence

of a solute (carbon, nitrogen) that pinesdislocations and prevents dislocation motion atsmall displacements or strains (which is apparentin an upper yield point).

Aluminum alloys do not show endurance limits;

this is related to the absence of dislocation-pinningsolutes.

At large Nf, the lifetime is dominated by nucleation. Therefore strengthening the surface (shot peening) is

beneficial to delay crack nucleation and extend life.

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12

Fatigue fracture

surface

[Hertzberg]

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13

Fatigue crack stages

Stage 1

Stage 2[Dieter]

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14

Fatigue Crack Propagation

Crack Nucleation stress intensification at crack tip.

Stress intensity crack propagation (growth);- stage I growth on shear planes (45),

strong influence of microstructure[Courtney: fig.12.3a]- stage II growth normal to tensile load (90)

weak influence of microstructure[Courtney: fig.12.3b].

Crack propagation catastrophic, or ductile failure

at crack length dependent on boundary conditions,fracture toughness.

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15

Fatigue Crack Nucleation

Flaws, cracks, voids can all act as crack nucleationsites, especially at the surface.

Therefore, smooth surfaces increase the time tonucleation; notches, stress risers decrease fatigue

life. Dislocation activity (slip) can also nucleate fatigue

cracks.

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17

Slip steps

and thestress-strain

loop

D i Phil h D T l

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18Design Philosophy: Damage Tolerant

Design

S-N (stress-cycles) curves = basic characterization. Old Design Philosophy = Infinite Life design: accept

empirical information about fatigue life (S-N curves);apply a (large!) safety factor; retire components or

assemblies at the pre-set life limit, e.g. Nf=107

. *Crack Growth Rate characterization ->

*Modern Design Philosophy (Air Force, not Navycarriers!) = Damage Tolerant design: accept

presence of cracks in components. Determine lifebased on prediction of crack growth rate.

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19

Definitions: Stress Ratios

Alternating Stress Mean stress sm= (smax+smin)/2.

Pure sine wave Mean stress=0.

Stress ratio R = smax/smin.

For sm= 0, R=-1

Amplitude ratio A = (1-R)/(1+R).

Statistical approach shows significantdistribution in Nffor given stress.

See Courtney fig. 12.6; also following slide.

sa

20

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20

Alternating Stress Diagrams

[Dieter]

21

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21

Mean Stress

Alternating stress sa= (smax-smin)/2. Raising the mean stress (sm)decreases Nf. [see slide 19,

also Courtney fig. 12.9]

Various relations between R = 0 limit and the ultimate

(or yield) stress are known as Soderberg (linear toyield stress), Goodman (linear to ultimate) andGerber (parabolic to ultimate). [Courtney, fig. 12.10, problem12.3]

sa

smean

tensile strength

endurance limit at zero mean stress

sa sfat 1 smean

tensile strength

22

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22

Cyclic strain vs. cyclic stress

Cyclic strain control complements cyclicstress characterization: applicable to thermalfatigue, or fixed displacement conditions.

Cyclic stress-strain testing defined by acontrolled strain range, epl. [see next slide,Courtney, figs. 12.24,12.25]

Soft, annealed metals tend to harden;

strengthened metals tend to soften. Thus, many materials tend towards a fixed

cycle, i.e. constant stress, strain amplitudes.

23

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23

Cyclic stress-strain curve

[Courtney]

Large number of cycles typically needed to reach

asymptotic hysteresis loop (~100). Softening or hardening possible.[fig. 12.26]

24

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24

Cyclic stress-strain

Wavy-slip materials

generally reach asymptotein cyclic stress-strain:planar slip materials (e.g.brass) exhibit historydependence.

Cyclic stress-strain curvedefined by the extrema,i.e. the tips of the

hysteresis loops. [Courtneyfig. 12.27]

Cyclic stress-strain curvestend to lie below those formonotonic tensile tests.

Polymers tend to soften incyclic straining.

[Courtney]

25

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25

Cyclic Strain Control

Strain is a more logical independent variablefor characterization of fatigue.[fig. 12.11]

Define an elastic strain rangeas eel= s/E.

Define a plastic strain range, epl.

Typically observe a change in slope betweenthe elastic and plastic regimes. [fig. 12.12]

Low cycle fatigue (small Nf) dominated by

plastic strain: high cycle fatigue (large Nf)dominated by elastic strain.

26

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26

Strain control

of fatigue

[Courtney]

27

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27

Cyclic Strain control: low cycle

Constitutive relationfor cyclic stress-strain:

n 0.1-0.2

Fatigue life: Coffin Manson relation:

ef~ true fracture strain; close to tensileductility

c -0.5 to -0.7

c= -1/(1+5n); large nlonger life.

s K e n

ep2

e f 2Nfc

28

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28

Cyclic Strain control: high cycle

For elastic-dominated strainsat high cycles, adaptBasquins equation:

Intercept on strain axis of extrapolatedelastic line = sf/E.

High cycle = elastic strain control:slope (in elastic regime) = b = -

n/(1+5n) [Courtney, fig. 12.13] The high cycle fatigue strength, sf,

scales with the yield stress high

strength good in high-cycle

saEee2

sf 2N b

29

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29

Strain amplitude - cycles

[Courtney]

30

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30

Total strain (plastic+elastic)life

Low cycle = plastic control: slope = c Add the elastic and plastic strains.

Cross-over between elastic and plastic control istypically at Nf= 10

3cycles.

Ductility useful for low-cycle; strength for high cycle

Examples of Maraging steel for high cycleendurance, annealed 4340 for low cycle fatiguestrength.

2 eel

2 epl

2 s f

E2Nfb e f 2Nfc

31

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31

Fatigue Crack Propagation

Crack Length := a.Number of cycles :=NCrack Growth Rate := da/dNAmplitude of Stress Intensity := K = sc.

Define three stages of crack growth, I, II and III,in a plot of da/dNversus K.

Stage II crack growth: application of linear elastic fracturemechanics.

Can consider the crack growth rate to be related to the appliedstress intensity.

Crack growth rate somewhat insensitive to R (if R

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32

Fatigue Crack Propagation

Three stages of crackgrowth, I, II and III.

Stage I: transition to afinite crack growth ratefrom no propagationbelow a threshold value

of K. Stage II: power law

dependence of crackgrowth rate on K.

Stage III: acceleration

of growth rate with K,approachingcatastrophic fracture.

da/dN

KKth

Kc

I

IIIII

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33

*Paris Law

Paris Law:

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

Crack nucleation ignored! Threshold ~ Stage I

The threshold represents an endurancelimit.

For ceramics, threshold is close to KIC.

Crack growth rate increases with R(forR>0).[fig. 12.18a]

dc

dN A(K)m

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*Striations- mechanism

Striations occur by development of slip bandsin each cycle, followed by tip blunting,followed by closure.

Can integrate the growth rate to obtain cyclesas related to cyclic stress-strain behavior. [Eqs.12.6-12.8]

NII dcA

m s cmc0cfNII dc

dc / dNc0

cf

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*Striations, contd.

Provided that m>2 and is constant, can integrate.

If the initial crack length is much less than the finallength, c0

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Geometrical effects

Notches decrease fatigue life through stressconcentration.

Increasing specimen size lowers fatigue life.

Surface roughness lowers life, again through stressconcentration.

Moderate compressive stress at the surfaceincreases life (shot peening); it is harder to nucleate acrack when the local stress state opposes crackopening.

Corrosive environment lowers life; corrosion eitherincreases the rate at which material is removed fromthe crack tip and/or it produces material on the cracksurfaces that forces the crack open (e.g. oxidation).

Failure mechanisms

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Microstructure-Fatigue Relationships

What are the important issues in microstructure-fatigue relationships?

Answer: three major factors.

1: geometry of the specimen (previous slide); anything on thesurface that is a site of stress concentration will promotecrack formation (shorten the time required for nucleation ofcracks).

2: defects in the material; anything inside the material that canreduce the stress and/or strain required to nucleate a crack(shorten the time required for nucleation of cracks).

3: dislocation slip characteristics; if dislocation glide is confinedto particular slip planes (called planar slip) then dislocationscan pile up at any grain boundary or phase boundary. Thehead of the pile-up is a stress concentration which caninitiate a crack.

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Microstructure affects Crack Nucleation

The main effect ofmicrostructure (defects,surface treatment, etc.)is almost all in the lowstress intensity regime,i.e. Stage I. Defects,

for example, make iteasier to nucleate acrack, which translatesinto a lower thresholdfor crack propagation(Kth).

Microstructure alsoaffects fracturetoughness andtherefore Stage III.

da/dN

KKth

Kc

I

IIIII

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Defects in Materials

Descriptions of defects in materials at the sophomore levelfocuses, appropriately on intrinsic defects (vacancies,dislocations). For the materials engineer, however, defectsinclude extrinsic defects such as voids, inclusions, grainboundary films, and other types of undesirable second phases.

Voids are introduced either by gas evolution in solidification or

by incomplete sintering in powder consolidation. Inclusions are second phases entrained in a material during

solidification. In metals, inclusions are generally oxides from thesurface of the metal melt, or a slag.

Grain boundary films are common in ceramics as glassy filmsfrom impurities.

In aluminum alloys, there is a hierachy of names for secondphase particles; inclusions are unwanted oxides (e.g. Al2O3);dispersoids are intermetallic particles that, once precipitated, arethermodynamically stable (e.g. AlFeSi compounds);precipitatesare intermetallic particles that can be dissolved or precipiated

depending on temperature (e.g. AlCu compounds).

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Metallurgical Control: fine particles

Tendency to localization of flow is deleterious to theinitiation of fatigue cracks, e.g. Al-7050 with non-shearable vs. shearable precipitates (Stage I in ada/dN plot). Also Al-Cu-Mg with shearableprecipitates but non-shearable dispersoids, vs. onlyshearable ppts.

graph courtesy of J.

Staley, Alcoa

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Coarse particle effect on fatigue

Inclusions nucleate cracks cleanliness (w.r.t.coarse particles) improves fatigue life, e.g. 7475improved by lower Fe+Si compared to 7075:0.12Fe in 7475, compared to 0.5Fe in 7075;

0.1Si in 7475, compared to 0.4Si in 7075.

graph courtesy of J.

Staley, Alcoa

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Alloy steel heat treatment

Increasing hardness tends to raise the endurancelimit for high cycle fatigue. This is largely a functionof the resistance to fatigue crack formation (Stage I ina plot of da/dN).

[Dieter]

Mobile solutes that pin

dislocations fatigue

limit, e.g. carbon in steel

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Casting porosity affects fatigue

Casting tends to result in porosity. Pores are effective sites fornucleation of fatigue cracks. Castings thus tend to have lowerfatigue resistance (as measured by S-N curves) than wroughtmaterials.

Casting technologies, such as squeeze casting, that reduce porosity

tend to eliminate this difference.

[Polmear]

Gravity castversus

squeeze cast

versus

wroughtAl-7010

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*Design Considerations

If crack growth rates are normalized by the elasticmodulus, then material dependence is mostlyremoved! [Courtney fig. 12.20]

Can distinguish between intrinsic fatigue[use Eq.

12.4 for combined elastic, plastic strain range] forsmall crack sizes and extrinsic fatigue[use Eq. 12.6for crack growth rate controlled] at longer cracklengths. [fig. 12.21.]

Inspection of design charts, fig. 12.22, shows thatceramics sensitive to crack propagation (highendurance limit in relation to fatigue threshold).

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*Design Considerations: 2

Metals show a higher fatigue threshold inrelation to their endurance limit. PMMA andMg are at the lower end of the toughnessrange in their class. [Courtney fig. 12.22]

Also interesting to compare fracturetoughness with fatigue threshold. [Courtney fig.12.23]

Note that ceramics are almost on ratio=1 line,whereas metals tend to lie well below, i.e.fatigue is more significant criterion.

48

*F ti

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*Fatigue

property map

[Courtney]

49

*Fatigue

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*Fatigue

property map

[Courtney]

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*Variable Stress/Strain Histories

When the stress/strain history isstochastically varying, a rule for combiningportions of fatigue life is needed.

Palmgren-Miner Rule is useful: ni is the

number of cycles at each stress level, and Nfiis the failure point for that stress.[Ex. Problem 12.2]

ni

Nfi1

i* Courtneys Eq. 12.9 is confusing; he has Nfin the numerator also

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stress-strn

Crack

Propagate

Microstr.

effects

Design

*Fatigue in Polymers

Many differences from metals Cyclic stress-strain behavior often exhibits

softening; also affected by visco-elasticeffects; crazing in the tensile portion

produces asymmetries, figs. 12.34, 12.25.

S-N curves exhibit three regions, with steeplydecreasing region II, fig. 12.31.

Nearness to Tgresults in strong temperaturesensitivity, fig. 12.42

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Objective

Crack

Initiation

S-N

curves

Cyclic

stress-strn

Crack

Propagate

Microstr.

effects

Design

Fatigue: summary

Critical to practical use of structural materials. Fatigue affects most structural components,

even apparently statically loaded ones.

Well characterized empirically.

Connection between dislocation behavior andfatigue life offers exciting researchopportunities, i.e. physically based models

are lacking!