Lcf-hcf Tutorial 4bi5q

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.”

 

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

Historical

Basic Engineering Properties

Strength, Creep

 

1960’s - 1970’s

Add ... Fatigue

HCF, LCF, TMF  

Late 1970’s

Add ... Damage Tolerance

Crack Growth

Emphasis today is on Cyclic Properties... High Cycle Fatigue   Low Cycle Fatigue

Allowable vibratory stresses Crack initiation life 1/1000 to small crack 

                                                  retirement   Crack Growth

  Component

Remaining life from crack

                                                 

  Safety 

                                                 

  Inspection 

inspection interval size requirement

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 Most Severe Structural Challenge: High structural loads, fatigue, & creep • Environmentally friendly • Fatigue cracking resistance initiation propagation • Creep resistant • Strong • Lightweight • Predictable/Inspectable • Affordable • Environmentally stable Nickel Superalloy Balances All Requirements

Combustor, Turbine Components Present 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 fatigue crack initiation site

• High Cycle Fatigue (HCF) Caused by vibration/flutter • Low Cycle Fatigue (LCF) Caused by engine cycling

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

Basic Cycle

to Alternating Stress Amplitude:

a 

 max   min 2

0 

 max   min 2

Mean Stress:

Stress Ratio: Stress Range:

R

 min  max

   max   min

Soderberg (USA, 1930) Goodman (England, 1899)

a m  1 Se S y a m  1 Se Su

 a   m  Gerber (, 1874)          Se  Su 

2

(Where Se is the fully reversed endurance limit.)

1

Cyclic Deformation Parameters: Fatigue loop illustration ...  

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

* Exists in theory only

HCF: S-N Curves ...

 Fatigue  Strength is  the Maximum Stress that can

be  repeatedly  applied  for  a  specified  number  of cycles    (typically  107)  without  failure.    Titanium alloys are curve fit to 109  cycles.

HCF: Notes on Approaches ... Soderberg is highly conservative and seldom

used Actual test data usually falls between

Goodman & Gerber Curves This is not a large difference in the theories

when the mean stress is small in relation to the alternating stress. P&W has found the most success with the

Goodman approach

HCF: A Christienson Diagram Contains all of this information ...

HCF: An example of Pratt’s Goodman diagram which combines Stress Amplitude and Mean Stress Effects ...

The discontinuous slope on the x-axis modifies

for the yield value instead of the ultimate as required 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) 9

Why no actual 10 Testing? Present frequency capability is 200 Hz,

which is 1.6 years!! 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 single test.

HCF: Elastic Stress-Life Relationship ...

HCF Notches: Parameters of Interest ...   Parameter            Kt          Concentration      Kf          Factor (KfKt)                (related to grain size)      r              q         

       Description   

  Elastic Stress 

 

  Fatigue Notch 

        Material constant   

 Notch radius 

        Notch sensitivity 

HCF Notches: Neuber proposed the following relationship ...

Kf  1

q

Where:

Kf 1 Kt  1

Kt  1 1  / r 

1 1  / r

Se(notched)=Se(unnotched) / Kf

In the previous equations, the notched value

would then be substituted.

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 involves uniaxial loading ...

Cyclic Fatigue: Testing Parameters of Interest ...

                  Strain Range   Stress Range   Max. Tensile Stress   Mean Stress   Inelastic Strain   Temperature

-



-

P/A = max - min

-

T

-

m = 0.5*(max + min)

-

i, p

-

T

Cyclic Loading: Key Relationships ...

 e

  e

E        Elastic Modulus,                               (monotonic) or            (cyclic)             Stress Ratio, 

 tot   elastic   inelastic

 min R  max where

 inelastic   plastic   creep

Max. Stress, 

 max   mean 

 2

Min. Stress, 

 min   mean 

 2

Total Strain = Elastic Strain Range + Plastic Strain Range  

 tot   e   p     Where                             and  E

 tot

      2   E 2 K '

    p  2   2K '

1 n'

1 n'

LCF: Pratt & Whitney Definition ... Nucleation to detectable crack.

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

The acceptable probability of occurrence of

an LCF crack as 1 crack occurring in a sample size of 1000 (1/1000 or B.1) having a 1/32 inch long crack at the predicted minimum life.

LCF: Characteristics ... From stress/strain cycling in the plastic

range at significantly higher stresses than for HCF. The stress/strain cycles that cause LCF

cracking are produced by significant engine power level changes. 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. Highly statistical in nature.

LCF: What are the parameters? ...

LCF: Mean Stress Effects must be included ...   Simple approach by J. Morrow: 

   t  3.4

 Su  Sm  N 0.12   0.6 N 0.6 E

     

f

f

f

 

Alternative approach by Smith, Watson & 

Topper (1970):   

 max  a E    f



2

 2 N  2b   f  f E  2 N  b c     where max=m+a and a is the alternating strain 

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 Stress Curves ...

Strain

Range,   

Kt Kmax max Kt Kmin min  E max E min

Where:  Kmax & Kmin are temp. correction factors on strain at max and min stress points K vs. T is derived from LCF tests at various temperatures Kt 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

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 Cyclic Loading must be solved incrementally...

Reversed  loading  cyclic    curves  assumes kinematic hardening and relates  using cyclic   curve  with  a  2X  stress-strain  multiplier from 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 

Cumulative Damage: Methodology ...   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: 

ni   1  Ni

Where:      Ni is life capability for stress excursion I      ni 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 using the ASTM Rainflow technique determines pairs ...

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

Parameter

3.5E+07 3.0E+07

Constant 1 Constant 2

2.5E+07

Constant 3

2.0E+07 1.5E+07 1.0E+07 5.0E+06 0.0E+00 0

Rate dependent test data and model correlation

500

1000 Temperature (F)

1500

Model parameter temperature dependencies

2000

ANSYS analysis of constitutive specimen

Constitutive Modeling Approach

specimen correlation

specimen prediction

component analysis

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

      

      

      

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

Metals have a highly ordered crystal structure...     Cubic Arrangement           Hexagonal Close-Packed      Structure    Zn, Mg, Be, -Ti, etc.  

Two predominant deformation mechanisms in metals...

   Dislocation:  occurs at all temperatures,       but is predominant at lower temperatures.              Diffusion:  important at higher temperatures,                   especially above one half the melting temperature        

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.]

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



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

      

      

      

      

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 ... 

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

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

Aluminum

1220

379

Titanium

3035

1288

Nickel

2647

1094

Iron

2798

1170

Cobalt

2723

1132

32

-213

Ice

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

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

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



      

from dislocations - as in slip

  

      

from diffusion - as in grain boundary sliding

  

      

or from both

Fracture Stages: Steps of an Idealized Fatigue Process ...   Stage I     Stage II

Crystallographic Fracture, along a few planes, brittl appearance, at angle to principal loading direction.

Usually transgranular, but numerous fracture planes to principal loading direction.  Striations often seen at high magnification for more ductile alloys.

    Stage III Final fracture; brittle, ductile or both.

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 ...

Fatigue Features: Final Fracture ...

Final Fracture

Fatigue Area

Ramberg-Osgood Relationship: Describes cyclic inelastic behavior ... IN100, (Tests Conducted in Air at 650°C, Frequency, = 0.33 Hz)

Typical Failure Modes: General Characteristics ...   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

Cyclic Behavior Must be Modeled: After Tensile yield, there are two models which describe compressive behavior ...

Isotropic

- assumes symmetrical behavior in tension and compression.   Kinematic

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

Hardening Models: Defines the Bauschinger effect ...

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

                                                                                             Material:

Copper in 3 Conditions

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

Summary:



      

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 loca stresses and strains. 