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

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 in crack or complete fracture after a sufficient number of fluctuations.”   Translation:

“Cyclic damage leading to local cracking or fracture.”

 

 Time

 

DesignRequirements

MaterialProperties

Historical Basic EngineeringProperties

 

Strength,Creep

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

Late 1970’s Add ... DamageTolerance

Crack Growth

Requirements have evolved for Gas Turbine Engines....Emphasis today is on Cyclic Properties...

High Cycle Fatigue Allowable vibratory stresses Low Cycle Fatigue Crack initiation life

1/1000 to small crack Component

retirement Crack Growth Remaining life from crack

Safety inspection interval

Inspection size requirement

Emphasis today is on Cyclic Properties...

For Crack Initiation, High Cycle Fatigue (HCF) and Low Cycle Fatigue (LCF) are treated separately. Why? General distinction for Gas Turbines: HCF - Usually high frequency, due to resonant vibration. Failure criteria based on allowable stresses. Millions of Cycles LCF - Usually low frequency, due to engine start/stop or throttle cycles. Accurate life prediction required. Thousands of Cycles

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

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

Fatigue is a Major Challenge for Many Engine Components,Including Fan Blades

• Caused by Load Cycling

• Occurs at cyclic loads well below the Ultimate Strength

• High Cycle Fatigue (HCF)

Caused by vibration/flutter

• Low Cycle Fatigue (LCF)

Caused by engine cycling

fatigue crack initiation site

Compressor blade tested in a vibratory fatigue test rig

Cyclic vs. Monotonic Curves: Behavior can be significantly different ...

From Metal Fatigue in Engineering, H.O. Fuchs and R.I. Stephens, John Wiley & Sons, NY, 1980

Crack Size: How big is big? ...

HCF: S-N Curves ... Initially used to address HCF for allowable

stress, but what about predicting actual cycles of life? ...

HCF cycle prediction is more of a statistical estimate with a large scatter allocation, instead of an exact science

P&WA Stress Control HCF Test Apparatus

Specimen Fully Reversed Stress/Strain Cycle S/N Plot

A l t e r n a t i n g S t r e s s A m p l i t u d e :

a m a x m i n

2

M e a n S t r e s s :

0 2

m a x m i n

S t r e s s R a t i o : R

m i n

m a x

S t r e s s R a n g e : m a x m i n

Basic Cycle

Terms to Remember

S o d e r b e r g ( U S A , 1 9 3 0 ) a

e

m

yS S 1

G o o d m a n ( E n g l a n d , 1 8 9 9 ) a

e

m

uS S 1

G e r b e r ( G e r m a n y , 1 8 7 4 ) a

e

m

uS S

2

1

( W h e r e S e i s t h e f u l l y r e v e r s e d e n d u r a n c e l i m i t . )

Cyclic Deformation Parameters: Fatigue loop illustration ...

Fatigue: How do HCF and LCF fit withStress vs. Life? ...

* Exists in theory only

HCF: S-N Curves ...

Fatigue Strength is the Maximum Stress that canbe repeatedly applied for a specified number ofcycles (typically 107) without failure. Titaniumalloys are curve fit to 109 cycles.

HCF: Notes on Approaches ...

Soderberg is highly conservative and seldomused

Actual test data usually falls betweenGoodman & Gerber Curves

This is not a large difference in the theorieswhen the mean stress is small in relation tothe alternating stress.

P&W has found the most success with theGoodman approach

HCF: A Christienson Diagram Contains all ofthis information ...

HCF: An example of Pratt’s Goodmandiagram which combines Stress Amplitude andMean Stress Effects ...

The discontinuous slope on the x-axis modifiesfor the yield value instead of the ultimate asrequired by a traditional Goodman Diagram.

HCF: Cyclic limits ...

107 cycles - Most other alloys 109 cycles - Titanium, certain Nickel Blade

Alloys 109 cycles - ????? (Proposed following the

HCF Initiative)

Why no actual 109 Testing?

Present frequency capability is 200 Hz,which is 1.6 years!!

Assuming 25 tests on two machines, this is20 years to characterize a single material !!!

Target now is 2000 Hz for coupon testing,which is 2 months for a single test.

HCF: Elastic Stress-Life Relationship ...

HCF Notches: Parameters of Interest ... Parameter Description Kt Elastic Stress Concentration Kf Fatigue Notch Factor (Kf

Kt) Material constant (related to grain size) r Notch radius q Notch sensitivity

H C F N o t c h e s : N e u b e r p r o p o s e d t h ef o l l o w i n g r e l a t i o n s h i p . . .

KK

rft

11

1 /

qK

K rf

t

1

1

1

1 /

W h e r e :S e

( n o t c h e d ) = S e( u n n o t c h e d ) / K f

I n t h e p r e v i o u s e q u a t i o n s , t h e n o t c h e d v a l u ew o u l d t h e n b e s u b s t i t u t e d .

LCF Testing: Verification ...

Three primary ways of verification testing:

Subcomponents

Spin Pit

Ferris Wheel

P&WA Strain Control LCF/TMF Test Apparatus

LCF Testing: Typical set-up involvesuniaxial loading ...

Strain Range -  

Stress Range - P/A = max - min

 Max. Tensile Stress - T

 Mean Stress - m = 0.5*(max + min)

 Inelastic Strain - i, p

  Temperature - T

Cyclic Fatigue: Testing Parameters of Interest ...

Elastic Modulus, (monotonic) or (cyclic)Ee

e

Stress Ratio, R

min

max

tot elastic inelastic inelastic plastic creep where

Max. Stress, max mean

2

Min. Stress, min mean

2

Cyclic Loading: Key Relationships ...

Total Strain = Elastic Strain Range + Plastic Strain Range 

tot e p

Where and E

p

n

K

22

1

'

'

tot E K

n

2

2

1

'

'

LCF: Pratt & Whitney Definition ...

Nucleation to detectable crack.

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

The acceptable probability of occurrence ofan LCF crack as 1 crack occurring in asample size of 1000 (1/1000 or B.1) havinga 1/32 inch long crack at the predictedminimum life.

LCF: Characteristics ...

From stress/strain cycling in the plasticrange at significantly higher stresses than forHCF.

The stress/strain cycles that cause LCFcracking are produced by significant enginepower level changes.

Microscopic changes in a material that hasbeen subjected to LCF cycling may be seenafter only a few cycles.

Microscopic dislocations in the crystalstructure.

The dislocations link up to formcracks.

Depends on the stresses andorientation of the individual grain.

Highly statistical in nature.

LCF: What are the parameters? ...

L C F : M e a n S t r e s s E f f e c t s m u s t b e i n c l u d e d . . .

S i m p l e a p p r o a c h b y J . M o r r o w :

t

u mf f f

S S

EN N

3 4 0 1 2 0 6 0 6. . . .

A l t e r n a t i v e a p p r o a c h b y S m i t h , W a t s o n & T o p p e r ( 1 9 7 0 ) :

m a x a fb

f fb cE N E N 2 22 2

w h e r e

m a x = m +

a a n d a i s t h e a l t e r n a t i n g s t r a i n

Notch LCF: Overall philosophy ... Kt < ~1.5

Local stress-strain calculated

Smooth LCF curves used Kt > ~1.5

Local stress-strain calculated

Notch LCF curves used usually mean stress/strain range, temperature corrected

Notch LCF: Strain Range-Mean StressCurves ...

S t r a i n R a n g e ,

K K

E

K K

Et tm a x m a x

m a x

m i n m i n

m i n

W h e r e : K m a x & K m i n a r e t e m p . c o r r e c t i o n f a c t o r s o n s t r a i n a t m a x a n d m i ns t r e s s p o i n t sK v s . T i s d e r i v e d f r o m L C F t e s t s a t v a r i o u s t e m p e r a t u r e sK t i s t h e g e o m e t r i c s t r e s s c o n c e n t r a t i o n f a c t o r

m a x & m i n a r e t h e n o m i n a l m a x a n d m i n s t r e s s e s

E m a x & E m i n a r e e l a s t i c m o d u l i a t t h e m a x a n d m i n s t r e s s p o i n t s

Notch LCF: Notch Factors ...

Kt, K, and K relate local behavior to nominal:

Notch LCF: Surface stresses and strains in stress concentration areas are important and need to be calculated ... Three methods used most often:

Linear Rule - elastic equivalent stress method

Neuber Rule - ideally for plane stress cases

Glinka Method - energy based method

Notch LCF: Linear Rule ...

Notch LCF: Neuber Rule ...

Notch LCF: Neuber Rule for CyclicLoading must be solved incrementally...

Reversed loading cyclic curves assumeskinematic hardening and relates using cyclic curve with a 2X stress-strain multiplierfrom the new reference origin.

Notch LCF: Glinka Relationship ...

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? Military combat missions have many in-flight

throttle excursions. Reduce mission into major and minor (or sub)

cycles Major (Type I) cycle is the largest overall strain excursion

in the mission. Full power excursions from intermediate, or above, to idle

and back are called Type III cycles. These excursions generally impact the overall life. Excursions of smaller magnitude (Type IV) are generally

not damaging.* * This may be untrue for some components

Cum ulative Dam age: M ethodology ... Many different methods have been proposed Linear cumulative damage - Miner’s Rule - appears to do the

best job for the type of stress excursions encountered in jet engine operation.

Miner’s Rule states: n

Ni

i 1

Where: N i is life capability for stress excursion I n i is the actual number of occurrences of excursion I The 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

Cumulative Damage: Cycle counting usingthe ASTM Rainflow technique determinespairs ...

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

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

Constitutive Modeling Approach

ANSYS analysis of constitutive specimen

Model parameter temperature dependencies

Rate dependent test dataand model correlation

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 2000Temperature (F)

Para

met

er

Constant 1

Constant 2

Constant 3

Constitutive Modeling Approach

specimen correlation specimen prediction component analysis

Metallurgical Aspects...  Relevant Topics:      Crystal Structure      Deformation Mechanisms      Crack Initiation .. Sequence of Events      Visual Aspects - Fractography

Understanding Metallurgical Aspects of Fatigue

Deformation for crystal structures can be visualized like a sliding row of bricks...

  Cubic Arrangement     Hexagonal Close-Packed

Structure Zn, Mg, Be, -Ti, etc. 

Metals have a highly ordered crystal structure...

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...

Can you find the Illustrated 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.]

      Solid solution strengthening      Precipitation hardening      Microstructure control (grain size and morphology, precipitate control, etc.)

      Dispersion strengthening

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

Solid Solution Strengthening: Perturbations to crystal lattice retard dislocation motion...

Precipitation Hardening: Local areas of compositional and/or structural differences retard dislocation motion...

Grain Boundary Strengthening: Crystallographic and/or compositional boundary. Strengthens at low temperature; but weak link at high temperature...

Grain Boundary Resistance: Will resist dislocation motion at the boundary...

Grain Boundaries Illustrated: Notice the vacancies and excess atoms at boundaries...

Grain Boundary Mechanics: 

Crystallographic and/or compositional boundary. Strengthens at low temperature; weak link at high temperature...

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

Diffusion: A high temperature deformation mechanism ...

  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: Usually considered at temperatures above half the melting point (K) ...

Grain Boundary Sliding: A diffusion controlled deformation process ...

Grain Boundary Sliding: Can provide large deformation at boundary with relatively small intergranular deformation ...

      from dislocations - as in slip       from diffusion - as in grain boundary sliding       or from both

Fatigue Crack Initiation: Occurs when enough local deformation damage accumulates to produce a crack ... 

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

  Stage II Usually transgranular, but numerous fracture planes normal

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 Idealized Fatigue Process ... 

Fracture Stages: Fatigue origin often at a Mechanical or Metallurgical Artifact ...

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

Typical Fatigue Fractures: Several Common Features ...  

1. Distinct crack initiation site or sites. 

2. Beach marks indicative of crack growth arrest. 

3. Distinct final fracture region.

Fatigue Features: Initiation sites . . .

Fatigue Features: Beach marks ...

Final Fracture

Fatigue Area

Fatigue Features: Final Fracture ...

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

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

 Failure Mode Some General CharacteristicsOverstress 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 Characteristics ...

Isotropic- 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 ...

Hardening Models: Defines the Bauschinger effect ...

Cyclic Effects on Stress-Strain Behavior: Progressive changes occur during cyclic loading ...

From Metal Fatigue in Engineering, H.O. Fuchs and R.I. Stephens, John Wiley & Sons, NY, 1980

Material: Copper in 3 Conditions

      Cyclic properties are important to our product.       Principal deformation mechanisms are slip at low temperature and diffusion at high temperature.       Cracking can be crystallographic, transgranular, or intergranular.       Simple deformation models can be used to consolidate data and predict local stresses and strains.

Summary: