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Low Cycle Fatigue (LCF)High Cycle Fatigue (HCF)

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What is Fatigue?

The ASTM definition.....

“The process of progressive localized permanent structural change

occurring in material subjected to conditions which produce fluctuating

stresses and strains at some point or points and which may culminate incrack or complete fracture after a sufficient number of fluctuations.”

Translation:

“Cyclic damage leading to local cracking or fracture.”

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TimeDesign

RequirementsMaterial

Properties

Historical Basic Engineering

Properties

Strength,

Creep

1960’s - 1970’s Add ... Fatigue HCF, LCF, TMF

Late 1970’s Add ... Damage

Tolerance

Crack Growth

Requirements have evolved for Gas Turbine Engines....

Emphasis today is on Cyclic Properties...

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High Cycle Fatigue 8 Allowable vibratory stresses

Low Cycle Fatigue 8 Crack initiation life

8 1/1000 to small crack

8 Component

retirement

Crack Growth 8 Remaining life from crack

8 Safety inspection

interval

8 Inspection size

requirement

Emphasis today is on Cyclic Properties...

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For Crack I ni tiation, High Cycle Fatigue

(HCF) and Low Cycle Fatigue (LCF) are

treated separately. Why?

General distinction for Gas Turbines:

CF - Usually high frequency, due to resonant

vibration. Failure criteria based on allowable

stresses. Millions of Cycles

CF - Usually low frequency, due to engine

start/stop or throttle cycles. Accurate life

prediction required. Thousands of Cycles

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Turbine Disk Design Requirements

• Environmentally friendly

• Fatigue cracking resistance

initiation

propagation

• Creep resistant

• Strong

• Lightweight

• Predictable/Inspectable

• Affordable

• Environmentally stable

Nickel Superalloy Balances All Requirements

Most Severe Structural Challenge: High structural loads, fatigue, & creep

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Combustor, Turbine ComponentsPresent a Severe Thermal Fatigue Cracking Challenge

• Mechanical fatigue, caused

by cyclic thermal strains

• High temperature

accelerates fatigue damage

• Exacerbated by crack tip

oxidation

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Fatigue is a Major Challenge for Many Engine Components,

Including Fan Blades

• Caused by Load Cycling

• Occurs at cyclic loads well belowthe Ultimate Strength

• High Cycle Fatigue (HCF)

Caused by vibration/flutter

• Low Cycle Fatigue (LCF)

Caused by engine cycling

fatigue crack in iti ation site

Compressor blade tested in

a vibratory fatigue test rig

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Cycl ic vs. Monotonic Curves: Behavior can be signif icantly dif ferent ...

From Metal Fatigue in Engineering, H.O. Fuchs and R.I. Stephens, John Wiley &

Sons, NY, 1980

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Crack Size: How big is big? ...

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HCF: S-N Curves ...

8 Initially used to address HCF for allowable

stress, but what about predicting actual cycles

of life? ...

8 HCF cycle prediction is more of a statistical

estimate with a large scatter allocation,

instead of an exact science

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P&WA Stress Control HCF Test Apparatus

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Specimen Fully Reversed Stress/Strain Cycle S/N Plot

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Alternating Stress Amplitude:

a max min

2

Mean Stress:

0

2 max min

Stress Ratio: R

min

max

Stress Range:

max min

Basic Cycle

Terms to Remember

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8 Soderberg (USA, 1930) a

e

m

yS S

1

8 Goodman (England, 1899) a

e

m

uS S 1

8 Gerber (Germany, 1874) a

e

m

uS S

2

1

(Where S e is the fully reversed endurance limit.)

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Cyclic Deformation Parameters: Fatigue loop i l lustration ...

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Fatigue: How do HCF and LCF fi t with

Stress vs. L ife? ...

* Exists in theor onl

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HCF: S-N Curves ...

8 Fatigue Strength is the Maximum Stress that can

be repeatedly applied for a specified number o

cycles (typically 107) without failure. Titanium

alloys are curve fit to 109

cycles.

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HCF: Notes on Approaches ...

8 Soderberg is highly conservative and seldom

used

8

Actual test data usually falls betweenGoodman & Gerber Curves

8 This is not a large difference in the theories

when the mean stress is small in relation to

the alternating stress.

8 P&W has found the most success with the

Goodman a roach

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HCF: A Chr istienson Diagram Contains all of

this information ...

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CF: An example of Pratt’s Goodman

diagram which combines Stress Amplitude and

Mean Stress Effects ...

8 The discontinuous slope on the x-axis modifies

for the yield value instead of the ultimate as

re uired b a traditional Goodman Dia ram.

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HCF: Cyclic l imits ...

8 10

7

cycles - Most other alloys8 109 cycles - Titanium, certain Nickel Blade

Alloys8 10

9 cycles - ????? (Proposed following the

HCF Initiative)

Why no actual 109 Testing?

8 Present frequency capability is 200 Hz,

which is 1.6 years!!

8 Assuming 25 tests on two machines, this is

20 years to characterize a single material !!!

Target now is 2000 Hz for coupon testing,

which is 2 months for a sin le test.

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HCF: Elastic Stress-Life Relationshi ...

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HCF Notches: Parameters of I nterest ...

Parameter Description

K t Elastic Stress

Concentration

K f Fatigue Notch

Factor (K f K t)

Material constant

(related to grain size)

r Notch radius

q Notch sensitivity

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HCF Notches: Neuber proposed the

following relationship ...

K K

r f

t

11

1 /

q

K

K r

f

t

1

1

1

1 /

Where:

Se(notched)

=Se(unnotched)

/ K f

8 In the previous equations, the notched value

would then be substituted.

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LCF Testing: Ver if ication ...

Three primary ways of verification testing:

8 Subcomponents

8 Spin Pit

8 Ferris Wheel

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P&WA Strain Control LCF/TMF Test Apparatus

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LCF Testing: Typical set-up involves

uniaxial loadin ...

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Strain Range - e

Stress Range - P/A = max - min

Max. Tensile Stress - T

Mean Stress - m = 0.5*(max + min)

Inelastic Strain - ei, e p

Temperature - T

Cyclic Fatigue: Testing Parameters of I nterest ...

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Elastic Modulus, (monotonic) or (cyclic) E e

e

e e

Stress Ratio, R

min

max

e e e tot elastic inelastic e e e

inelastic plastic creep where

Max. Stress, max mean

2

Min. Stress,

min

mean

2

Cyclic Loading: Key Relationships ...

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Total Strain = Elastic Strain Range + Plastic Strain Range

e e e tot e p

Where and

E

e

p

n

K

2

2

1

'

'

e

tot E K

n

2

2

1

'

'

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LCF: Pratt & Whitney Def inition ...

8 Nucleation to detectable crack.

8 Initiation is a 1/32” crack along the surface.

8 The acceptable probability of occurrence of

an LCF crack as 1 crack occurring in a

sample size of 1000 (1/1000 or B.1) havinga 1/32 inch long crack at the predicted

minimum life.

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LCF: Character istics ...

8 From stress/strain cycling in the plastic

range at significantly higher stresses than for HCF.

8 The stress/strain cycles that cause LCF

cracking are produced by significant engine

power level changes.

8 Microscopic changes in a material that has

been subjected to LCF cycling may be seen

after only a few cycles. Microscopic dislocations in the crystal

structure. The dislocations link up to form

cracks. Depends on the stresses and

orientation of the individual grain.

8 Hi hl statistical in nature.

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LCF: What are the arameters? ...

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LCF: Mean Stress Effects must be included ...

8Simple approach by J. Morrow:

e e t

u m f f f

S S

E N N

34 0 12 0 6 0 6. . . .

8Alternative approach by Smith, Watson &

Topper (1970):

e e max a f

b

f f

b c E N E N 2 2

2 2

where max=m+ a and ea is the alternating strain

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Notch LCF: Overall phil osophy ...

8K t < ~1.5

8Local stress-strain calculated

8Smooth LCF curves used

8K t > ~1.5

8Local stress-strain calculated

8 Notch LCF curves used usually mean

stress/strain range, temperature corrected

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Notch LCF: Strain Range-Mean Stress

Curves ...

Strain Range, e

K K

E

K K

E

t t max max

max

min min

min

Where:

K max & K min are temp. correction factors on strain at max and minstress points

K vs. T is derived from LCF tests at various temperatures

K t is the geometric stress concentration factor

max & min are the nominal max and min stresses

Emax & Emin are elastic moduli at the max and min stress points

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Notch LCF: Notch Factors ...

K t K and K e relate local behavior to nominal:

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Notch LCF : Sur face stresses and strains in

stress concentration areas are important

and need to be calculated ...

Three methods used most often:

8Linear Rule - elastic equivalent stress

method

8

Neuber Rule - ideally for plane stress cases

8Glinka Method - energy based method

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Notch LCF: Linear Rule ...

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Notch LCF: Neuber Rule ...

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Notch LCF: Neuber Rule for Cyclic

Loadin must be solved incrementall ...

Reversed loading cyclic e curves assumes

kinematic hardening and relates e using cyclice curve with a 2X stress-strain multiplier

from the new reference ori in.

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Notch LCF: Glinka Relationshi ...

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Cumulative Damage: How is it done? ...

Definition - The means by which the damage

associated with a complex stress history may be

calculated or estimated by allowing the combining

cycles of different stress magnitudes.

Why is this needed?

8Military combat missions have many in-flightthrottle excursions.

8Reduce mission into major and minor (or sub)

cycles8Major (Type I) cycle is the largest overall strain excursion

in the mission.

8

Full power excursions from intermediate, or above, to idleand back are called Type III cycles.

8These excursions generally impact the overall life.

8Excursions of smaller magnitude (Type IV) are generally

not damaging.*

* This may be untrue for some components

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Cumulative Damage: M ethodology ...

8Many different methods have been proposed

8Linear cumulative damage - Miner’s Rule - appears to do the

best job for the type of stress excursions encountered in jet

engine operation.

8Miner’s Rule states: n N

i

i

1

Where:

Ni is life capability for stress excursion I

ni is the actual number of occurrences of excursion I

8The basic assumption is that fatigue damage is cumulative

and the life capability of a part will be exhausted when the

sum of the life fractions reaches 1.0

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Cumulative Damage: Cycle counting using

the ASTM Rainf low technique determines

airs ...

The airs are A-D, B-C, E-F, and G-H.

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Cyclic Stress-Strain Behavior: Derived fr om loci of cyclic endpoints ...

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Constitutive Modeling Approach

ANSYS analysis of

constitutive specimen

Model parameter temperature

dependencies

Rate dependent test data

and model corr elation

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

3.0E+07

3.5E+07

0 500 1000 1500 2000

Temperature (F)

P a r a m e t e r

Constant 1

Constant 2

Constant 3

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Constitutive Modeling Approach

specimen corr elation specimen predicti on component analysis

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Metallurgical Aspects...

Relevant Topics:

8

Crystal Structure8 Deformation Mechanisms

8 Crack Initiation .. Sequence of Events

8 Visual Aspects - Fractography

Understanding Metallurgical Aspects of Fatigue

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Deformation for crystal structures can be visualized li ke a sliding row

of br icks...

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Cubic Arrangement

Hexagonal Close-Packed

Structure

Zn, Mg, Be, a-Ti, etc.

Metals have a highly ordered crystal structure...

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Dislocation: occurs at all temperatures,

but is predominant at lower temperatures.

Diffusion: important at higher temperatures,

especially above one half the melting temperature

Two predominant deformation mechanisms in metals...

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Can you find the I l lustrated Dislocation Defect?

Edge dislocation. (a) “Bubble-raft” model of an imperfection in a crystal structure.

Note the extra row of atoms. (b) Schematic illustration of a dislocation. [Bragg and

Nye, Proc. Roy. Soc. (London), A190, 474, 1947.]

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8 Solid solution strengthening

8 Precipitation hardening

8 Microstructure control (grain size and morphology, precipitate

control, etc.)

8

Dispersion strengthening

Pure metals are easily deformed. Several methods are used to inhibit

deformation...

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Solid Solution Strengthening: Perturbations to crystal lattice retard

dislocation motion...

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Precipitation Hardening: Local areas of compositional and/or

structural di fferences retard dislocation motion...

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Grain Boundary Strengthening: Crystallographic and/or

compositional boundary. Strengthens at low temperature; but weak

link at high temperature...

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Grain Boundary Resistance: Wil l resist dislocation motion at the

boundary...

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Grain Boundaries I l lustrated: Notice the vacancies and excess atoms at boundaries...

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Grain Boundary Mechanics:

Crystallographic and/or compositional boundary. Strengthens at low

temperature; weak link at high temperature...

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Persistent Slip Band Formation: A product of cyclic deformation important to fatigue initiation for ductile

metals ...

From Metal Fatigue in Engineering, H.O. Fuchs and R.I. Stephens, John Wiley

& Sons, NY, 1980

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Diffusion: A high temperature deformation mechanism ...

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Melting Point (F) 1/2 Melting Point (F)

Aluminum 1220 379

Titanium 3035 1288

Nickel 2647 1094

Iron 2798 1170

Cobalt 2723 1132

Ice 32 -213

Diffusion: Usual ly considered at temperatures above half the melting

point ( K) ...

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Grain Boundary Sliding: A dif fusion controlled deformation process ...

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Grain Boundary Sliding: Can provide large deformation at boundary with

relatively small intergranular deformation ...

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8 from dislocations - as in slip

8 from diffusion - as in grain boundary sliding

8 or from both

Fatigue Crack I ni tiation: Occurs when enough local deformation

damage accumulates to produce a crack ...

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Stage I Crystallographic Fracture, along a few planes, britt appearance, at angle to principal loading direction.

Stage II Usually transgranular, but numerous fracture planes

to principal loading direction. Striations often seen at highmagnification for more ductile alloys.

Stage III Final fracture; brittle, ductile or both.

Fracture Stages: Steps of an I dealized Fatigue Process ...

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Fracture Stages: F atigue origin often at a Mechanical or Metallurgical

Ar tif act ...

Schematic of stages I and II transcrystalline microscopic fatigue crack growth.

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Typical F atigue Fractures: Several Common Features ...

1. Distinct crack initiation site or sites.

2. Beach marks indicative of crack growth arrest.

3. Distinct final fracture region.

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Fatigue Features: I ni tiation sites . . .

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Fatigue Features: Beach marks ...

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Final Fracture

Fatigue Area

Fatigue Features: F inal F racture ...

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IN100, (Tests Conducted in Air at 650°C, Frequency, = 0.33 Hz)

Ramberg-Osgood Relationship: Describes cyclic inelastic behavior ...

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Failure Mode Some General Characteristics

Overstress Rapid fracture, may be ductile or brittle, large

deformation, often transgranular, often the final stage

of some other fracture mode.

Creep/Stress Rupture Usually long term event, large deformation,

intergranular, elevated temperature

High Cycle Fatigue Often short term event, small deformation,transgranular

Low Cycle Fatigue Moderate time event, moderate deformation, fracture

dependent on time/temp.

Thermomechanical Fatigue Moderate time event, subset of LCF with deformation

due largely to thermally induced stresses, fracture

usually shows heavy oxidation/alloy depletion

Typical Failure Modes: General Character istics ...

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I sotropic

- assumes symmetrical behavior in tension and compression.

Kinematic

- assumes yield stress, following inelastic deformation, is degraded ...

Cyclic Behavior Must be Modeled: After Tensile yield, there are two models

which describe compressive behavior ...

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Hardening Models: Def ines the Bauschinger effect ...

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Cyclic Effects on Stress-Strain Behavior: Progressive changes occur dur ing cyclic

loading ...

From Metal Fatigue in Engineering, H.O. Fuchs and R.I. Stephens, John Wiley &

Sons, NY, 1980

Material: Copper in 3 Conditions

S

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8 Cyclic properties are important to our product.

8 Principal deformation mechanisms are slip at low temperature and diffusio

at high temperature.

8 Cracking can be crystallographic, transgranular, or intergranular.

8 Simple deformation models can be used to consolidate data and predict loc

stresses and strains.

Summary:

lcf-hcf

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