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WHENMATERIALSARE

GETTINGTIRED

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Sub-topics

Cyclic stresses

FatigueCrack propagation

Resistance to fatigue

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FATIGUE: FACTS

Fatigue is important as it is the largest cause of

failure in metals, estimated to comprise

approximately 90%of all metallic failures; polymers

and ceramics are also susceptible to this type of

failure.

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FATIGUEFAILURE

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Fatigue failures occur due to

cyclic loading at

stresses below a materialsyield strength https://www.youtube.com/watch?v=dGQfUWvP0II

https://www.youtube.com/watch?v=dGQfUWvP0IIhttps://www.youtube.com/watch?v=dGQfUWvP0IIhttps://www.youtube.com/watch?v=dGQfUWvP0IIhttps://www.youtube.com/watch?v=dGQfUWvP0II

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SCHEMATICOFTHESTRESSCYCLINGONTHE

UNDERSIDEOFAWING

4

Loading cycles can be

in the millions for an

aircraft;

fatigue testing must

employ millions of

fatigue cycles

to provide meaningful

design data.

https://www.youtube.com/watch?v=ywDsB3umK2Y

https://www.youtube.com/watch?v=ywDsB3umK2Yhttps://www.youtube.com/watch?v=ywDsB3umK2Y

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FATIGUE

Fatigueis a form of failure that occurs in structuressubjected to dynamic and fluctuating stresses

Under these circumstances it is possible for failure tooccur at a stress level considerably lower than thetensile or yield strength for a static load.

It is catastrophicand insidious, occurring very suddenlyand without warning.

Primary design criterion in rotating parts.

Fatigue as a name for the phenomenon based on thenotion of a material becoming tired, i.e. failing at less

than its nominal strength. Cyclic strain (stress) leads to fatigue failure.

Occurs in metals and polymers but rarely in ceramics.

Alsoan issue for static parts, e.g. bridges.5

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FATIGUE: GENERALCHARACTERISTICS

Most applications of structuralmaterials involve cyclic

loadinge.

Fatigue failure surfaces

have three characteristicfeatures:

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 shortenlife.6

the crack

length

exceeds a

critical value

at the

appliedstress.

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THREESTAGESOFFATIGUE

First, a tiny crack initiates or nucleates often at a time wellafter loading begins. Normally, nucleation sites are located ator near the surface, where the stress is at a maximum, andinclude surface defects such as scratches or pits, sharpcorners due to poor design or manufacture, inclusions, grain

boundaries, or dislocation concentrations. Next, the crack gradually propagates as the load continues to

cycle.

Finally, a sudden fracture of the material occurs when theremaining cross-section of the material is too small to supportthe applied load. Thus, components fail by fatigue becauseeven though the overall applied stress may remain below theyield stress, at a local length scale, the stress intensityexceeds the tensile strength.

For fatigue to occur, at least part of the stress in the materialhas to be tensile.

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FACTORSCAUSINGFATIGUEFAILURE

1) A maximum tensile stress of

sufficiently high value.

2) A large amount of variation or

fluctuation in the applied stress.3) A sufficiently large number of

cycles of the applied stress.

Stress concentration Corrosion Temperature Overload Metallurgical structure Residual stress

Combined stress

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CYCLICSTRESSES

Reversed stress cycle, in

which the

stress alternates from a

maximum tensile stress

to a maximum compressivestress of

equal magnitude

Repeated stress cycle, in

which maximum and

minimum stresses are

asymmetrical relative to

the zero stress level;

mean stress m, range of

stress r , and stress

amplitude a are indicated.

Random

stress cycle.

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PARAMETERS

mean stress

range of stress

stress amplitude

stress ratio R10

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S-N CURVES

S-N[stress-number of cycles to failure] curve defines

number of cycles-to-failure for given cyclic stress.

Rotating-beam fatigue test is standard; also alternating

tension-compression.

Plot stress versus the log(number of cycles to failure),

log(Nf).

For frequencies < 200Hz, metals are insensitive to

frequency; fatigue life in polymers isfrequency

dependent.

rotating-bending tests

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SN BEHAVIOR

Stress amplitude (S)

versus logarithm of the

number of cycles to

fatigue failure (N) for a

material that displays afatigue limit

The higher the magnitude of the stress, the smaller the number ofcycles the material is capable to sustain before failure

There is a limiting stress level, called the fatigue limit (also

sometimes theendurance limit), belowwhich fatigue failure will not

occur.12

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ENDURANCELIMITS

Some materials exhibit endurance limits, i.e.a stress below which the life is infinite: Steels typically show an endurance limit of about

40% - 60% of yield strength; this is typically

associated with the presence of a solutes (carbon,nitrogen) that pines dislocations and preventsdislocation motion at small displacements orstrains.

Aluminum alloys do not show endurance limits;this is related to the absence of dislocation-pinning solutes.

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

beneficial to delay crack nucleation and extend life. 13

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SN BEHAVIORStress amplitude (S) versus logarithm

of the number of cycles to

fatigue failure (N) for a material that

does not display a fatigue limit.

Most nonferrous alloys (e.g., aluminum, copper, magnesium) do not

have a fatigue limit, in that the SN curve continues its downward trend at

increasingly greater N values

Fatigue will ultimately occur

regardless of the magnitude of the

stress. For these materials, the

fatigue response is specified as

fatigue strength, which is definedas the stress level at which failure

will occur for some specified

number of cycles (e.g., 107cycles).

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FATIGUELIFEfatigue life Nf

characterizes a materials

fatigue behavior

It is the number of cycles to

cause failure at a specified

stress level, as taken from

the SN plot

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There always exists considerable scatter in fatigue data, that is, a variation in

the measured N value for a number of specimens tested at the same stress

level. This may lead to significant design uncertaintieswhen fatigue life and/orfatigue limit (or strength) are being considered.

The scatter in results is a consequence of the fatigue sensitivity to a number

of test and material parameters that are impossible to control precisely. These

parameters include specimen fabrication and surface preparation,

metallurgical variables, specimen alignmentin the apparatus, mean stress,

and test frequency.

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STATISTICALNATUREOFFATIGUE

Because the S-N fatigue data is normally scattered, it

should be therefore represented on a probability basis.

Considerable number of specimens is used to obtain

statistical parameters.

At 1, 1% of specimens would be expected to fail at N1cycles.

50% of specimens would be expected to fail at N2

cycles.

For engineering purposes, it is sufficiently accurate toassume a logarithmic normal distribution of fatigue life in

the region of the probability of failure of P = 0.10 to P =

0.90. 16

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FATIGUESN PROBABILITYOFFAILURE

CURVESFORA7075-T6ALUMINUMALLOY

The probabilityof failure

The data obtained is normally scattered at the same stress level by using

several specimens.

This requires statistic approach to define the fatigue limit.

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Constant

probability

curves

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HIGH- CYCLICFATIGUE

For low stress levels wherein deformations are

totally elastic, longer lives result. This is called

high-cycle fatigue inasmuch as relatively large

numbers of cycles are required to produce fatigue

failure.

High-cycle fatigue is associated with fatigue lives

greater than about 104to 107cycles.

The S-N curve in the high-cycle region is

sometimes described by the Basquinequation

p and C are empirical constants18

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LOW- CYCLEFATIGUE

is associated with relatively high loads that

produce not only elastic strain but also some

plastic strain during each cycle.

Consequently, fatigue lives are relatively short

occurs at less than about 104to 105cycles

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DESIGNOFAROTATINGSHAFT

A solid shaft for a cement oven produced from tool steel

must be 240 cm long and must survive continuousoperation for one year with an applied load of 55,600 N.

The shaft makes one revolution per minute during

operation.

Design a shaft that will satisfy these requirements.

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The maximum

stress acting

on this type

of specimen

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PROCESSOFFATIGUEFAILURE

Characterized by three distinct steps:

(1) crack initiation, wherein a small crack forms at

some point of high stress concentration;

(2) crack propagation, during which this crackadvances incrementally with each stress cycle;

(3) final failure, which occurs very rapidly once the

advancing crack has reached a critical size.

The fatigue life Nf , the total number of cycles to failure, therefore can

be taken as the sum of the number of cycles for crack initiation Ni and

crack propagation Np

The contribution of the final failure step to the total fatigue life is

insignificant since it occurs so rapidly

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CRACKINITIATION

Cracks associated with fatigue failure almost

always initiate (or nucleate) on the surface of a

component at some point of stress concentration.

Crack nucleation sites include surface scratches,

sharp fillets, keyways, threads, dents, and the like.

In addition, cyclic loading can produce

microscopic surface discontinuities resulting

from dislocation slip steps which may also act as

stress raisers, and therefore as crack initiationsites.

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INITIATIONOFFATIGUECRACKANDSLIP

BANDCRACKGROWTH(STAGEI)

Fatigue cracks are normally initiated at a free surface.Slip lines are formed during the first few thousand cyclesof stress.

Back and forth fine slip movements of

fatigue could build up notches or ridgesat the surface => act as stress raiser =>

initiate crack

In stage I, the fatigue crack tends to propagate initiallyalong slip planes (extrusion and intrusion of persistent

slip bands) and later take the direction normal to themaximum tensile stress (stage II).

The crack propagation rate in stage I is generally verylow on the order of nm/cycles giving featurelesssurface.

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CRACKPROPAGATION

Once a stable crack has nucleated, it

then initially propagates very slowlyand, in polycrystalline metals, along

crystallographic planes of high shear

stress; this is stage I propagation

This stage may constitute a large or

small fraction of the total fatigue life

depending on stress level and the

nature of the test specimen; high stresses

and the presence of notches favor a short

lived stage I. In polycrystalline metals, cracks normally extend

through only several grains during this propagationstage.

The fatigue surface that is formed during stage Ipropagation has a flat and featureless appearance

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FATIGUECRACKPROPAGATION

MECHANISM

repetitive crack tip plastic blunting and sharpening

zero or maximum

compressive load

small tensile

load

maximum

tensile load

small

compressive load

zero or maximum

compressive load

small tensile load25

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FATIGUECRACKPROPAGATIION

For design against

fatigue failure, fracture

mechanics is utilised to

monitor the fatiguecrack

growth ratein the stage

II

The fatigue crack growth

rate da/dNvaries with stress

intensity factor range K, which

is a function of stress range and crack length a. 27

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CRACKPROPAGATIONRATE

Life of a structural component may be related to therate of crack growth.

During stage II propagation, cracks may grow from a

barely perceivable size to some critical length.Crack length versus the number

of cycles at stress levels 1 and

2.

Crack growth rate da/dNis

indicated at crack length a1 for

both stress levels.

The parametersA andm are constants for

the particular material

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CRACKGROWTHRATEANDNUMBEROF

CYCLES

Knowledge of crack growth rate is of assistance in

designing components and in nondestructive evaluation

to determine if a crack poses imminent danger to the

structure.

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Integration betweenthe initial size of a

crack and the crack

size required

for fracture to occurai is the initial flaw size and ac is the

flaw size required for fracture.

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DESIGNOFAFATIGUERESISTANTPLATE

A high-strength steel plate, which has a plane strain

fracture toughness of 80 Mpa m1/2is alternately loadedin tension to 500 MPa and

in compression to 60 MPa.

The plate is to survive for 10 years with the stress being

applied at a frequency of once every 5 minutes.

Design a manufacturing and testing procedure that

ensures that the component will serve as intended.

Assume a geometry factor Y = 1.0.

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FORENSICFRACTURECASE

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K1cof the tank materialmeasured to be 45 MPam10 mm crack found inlongitudinal weld

Stress based onmaximum design

pressure

Stress at which a plate with the given

K1cwill fail with a 10 mm crack

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HOWLONGISALIFE?

How long would it have lasted beforefatigue grew the crack to an unstable size?

Residual life = 7 x 106cycles

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DESIGNFORFATIGUE

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100 resolutions

per second

At least 300

resolutions per

second

High-cycle fatigue3 x 106cycles

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Selection chart for

con-rod based onmaterial index

Further selectioncriteria includes the

use of S-N curves

For a design life of 2.5 x 106cycles, a stress of

620 MPa can be safely applied

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FEATURESOFFATIGUEFAILURE

two types of markings termed beachmarks and

striations

indicate the position of the crack tip at some point intime and appear as concentric ridges that expandaway from the crack initiation site(s), frequently in a

circular or semicircular pattern.

Fracture surface of a rotating

steel shaft that experienced

fatigue failure.

Beachmark ridges are

visible in the photograph

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FACTORS THAT AFFECT FATIGUE LIFE

Stress concentration Size effect Surface effects Combined stresses

Cumulative fatiguedamage and sequenceeffects

Metallurgical variables Corrosion Temperature

Demonstration of influence

of mean stress m on SN fatigue

behavior

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EFFECTOFMEANSTRESS, STRESSRANGEANDSTRESS

INTENSITY(NOTCH) ONS-N FATIGUECURVE

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EFFECTOFSTRESSCONCENTRATIONON

FATIGUE

Kt is theoretical stress-

concentration

factor, depending on

elasticity of crack tip

Kf is fatigue notch factor,

ratio of fatigue strength of

notched and unnotched

specimens

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PROBLEM

Demonstration of how design can reduce stress mplification.

(a) Poor design: sharp corner.

(b) Good design: fatigue lifetime improved by incorporating

rounded fillet into a rotating shaft at the point where there is

a change in diameter.

What design is better?

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SURFACEEFFECTSONFATIIGUE

Fatigue properties are very sensitive to surface

conditions,

Fatigue initiation normally starts at the surface

since the maximum stress is at the surface.

The factors which affect the surface of a fatigue

specimen can be roughly divided into three

categories

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SURFACEROUGHNESS

Different surface finishes produced

by different machining processes can

appreciably affect fatigue performance.

Polished surface (very fine scratches), normallyknown as par bar which is used in laboratory,gives the best fatigue strength

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SURFACERESIDUALSTRESS

Superposition of

applied and residual

stresses

(a) Shows the elastic stress distribution in a beam

with no residual stress.(b) Typical residual stress distribution produced by

shot peening where the high compressive stress

is balanced by the tensile stress underneath.

(c) The stress distribution due to the algebraic

summation of the external bending stress and the

residual stress

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Compressive forces on

the surface resistcrack growth

method of producing

these stresses is

Shot penning

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COMMERCIALMETHODSINTRODUCING

FAVOURABLECOMPRESSIVESTRESS

Surface rolling - Compressive stress is introduced in

between the rollers during sheet rolling

Shot peening - Projecting fine steel or cast-iron shot

against the surface at high velocity

Polishing- Reducing surface scratches

Thermal stress - Quenching or surface treatments

introduce volume change giving compressive stress.

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FATIGUESTRENGTHIMPROVEMENTBY

CONTROLLINGMETALLURGICALVARIABLES

Grain size has its greatest

effect on fatigue life in thelow-stress, high cycle regime

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FATIGUESTRENGTHIMPROVEMENTBY

CONTROLLINGMETALLURGICALVARIABLES

Promote homogeneous slip /plastic deformationthrough thermo-mechanical processing => reduces

residual stress/ stress concentration.

Heat treatments to give hardened surface butshould avoid stress concentration.

Avoid inclusions = >stress concentration =>fatigue strength

Interstitial atoms increase yield strength , if plusstrain aging => fatigue strength

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EFFECTOFCORROSIONONFATIGUE

Fatigue corrosion occurs when material is

subjected to cyclic stress in a corrosive condition.

Corrosive attack produces pitting on metal surface.

Pits act as notches => fatigue strength

Chemical attack greatly accelerates the rate of

fatigue crack propagation

Corrosion fatigue of brass

Role of a

corrosiveenvironment on

fatigue

crack propagation49

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THERMALEFFECT

induced at elevated temperatures by fluctuating thermal

stresses;

mechanical stresses from an external source need not be

present

The origin of these thermal stresses is the restraint to the

dimensional expansion and/or contraction that would

normally occur in a structural member with variations in

temperature

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THERMALFATIGUE

Thermal fatigue occurs when metal issubjected to high and low temperature, producing

fluctuating cyclic thermal stress

Normally occurs in hightemperature equipment.

Low thermal conductivityand high

thermal expansion

properties are

critical.The thermal stress developed by a

temperature change T is

is linear thermal coefficient of expansionE is elastic modulus

If failure occurs by one application of thermal stress,

the condition is called thermal shock.

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DESIGNFORFATIGUEThere are several distinct approaches concerning for

design for fatigue 1) Infinite-life design: Keeping the stress at some

fraction of the fatigue limit of the material.

2) Safe-life design: Based on the assumption that the

material has flaws and has finite life. Safety factor isused to compensate for environmental effects,varieties in material production/ manufacturing.

3) Fail-safe design: The fatigue cracks will bedetected and repaired before it actually causes failure.

For aircraft industry. 4) Damage tolerant design: Use fracture mechanics

to determine whether the existing crack will grow largeenough to cause failure. 52

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DESIGNEXAMPLE1

A relatively large sheet of steel is to be exposed to

cyclic tensile and compressive stresses of

magnitudes 100 MPa and 50 MPa, respectively.

Prior to testing, it has been determined that the

length of the largest surface crack is 2.0 mm. Estimate the fatigue life of this sheet if its plane

strain fracture toughness is 25 Mpa m1/2and the

values of m andA are 3.0 and 1.0 x 10-12,

respectively, for in MPa and a in m.Assume that the parameter Y is independent of

crack length and has a value of 1.0.53

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