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
8
Allowable vibratory stresses
Low Cycle Fatigue
8
8
Crack initiation life
1/1000 to small crack
8
Component
8
Safety inspection
8
Inspection size
retirement
Crack Growth
8
Remaining life from crack
interval
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 ...
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
P&WA Stress Control HCF Test Apparatus
Specimen
Fully Reversed Stress/Strain Cycle
S/N Plot
Basic Cycle
Terms to Remember
Alternating Stress Amplitude:
a 
Mean Stress:
0 
Stress Ratio:
Stress Range:
 max   min
2
 max   min
2
R
 min
 max
   max   min
8Soderberg
8Goodman
8Gerber
a
(USA, 1930)
Se
a
(England, 1899)
(Germany, 1874)
Se
a

m

m
Sy
Su
2
1
1
 
  m  1
Se  Su 
(Where Se is the fully reversed endurance limit.)
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 ...
8 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 ...
8Soderberg
is highly conservative and seldom
used
8Actual
test data usually falls between
Goodman & Gerber Curves
8This
is not a large difference in the theories
when the mean stress is small in relation to
the alternating stress.
8P&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 ...
8The 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 ...
8107
8109
cycles - Most other alloys
cycles - Titanium, certain Nickel Blade
Alloys
8109 cycles - ????? (Proposed following the
HCF Initiative)
Why no actual 109 Testing?
8Present
frequency capability is 200 Hz,
which is 1.6 years!!
8Assuming
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
Description
Kt
Concentration
Elastic Stress
Kf
Factor (KfKt)
Fatigue Notch

(related to grain size)
Material constant
r
Notch radius
q
Notch sensitivity
HCF Notches: Neuber proposed the
following relationship ...
Kf  1
q
Kf 1
Kt  1
Kt  1
1  / r

1
1  / r
Where:
Se(notched)=Se(unnotched) / Kf
8In
the previous equations, the notched value
would then be substituted.
LCF Testing: Verification ...
Three primary ways of verification testing:
8Subcomponents
8Spin
Pit
8Ferris
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
-
e
Stress Range
-
  P/A = max - min
Max. Tensile Stress
-
T
Mean Stress
-
m = 0.5*(max + min)
Inelastic Strain
-
ei , ep
Temperature
-
T
Cyclic Loading: Key Relationships ...
Elastic Modulus,
E
Stress Ratio,
e tot  e elastic  e inelastic
Max. Stress,
Min. Stress,

ee
(monotonic) or

(cyclic)
e e
 min
R
 max
where
e inelastic  e plastic  e creep
 max   mean 

2
 min   mean 

2
Total Strain = Elastic Strain Range + Plastic Strain Range
e tot  e e  e p
Where

E
e tot
1
   n '
e p  2

 2K '
and

  

 2


E
2 K '
1
n'
LCF: Pratt & Whitney Definition ...
8Nucleation
8Initiation
8The
to detectable crack.
is a 1/32” crack along the surface.
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 ...
8From
stress/strain cycling in the plastic
range at significantly higher stresses than for
HCF.
8The
stress/strain cycles that cause LCF
cracking are produced by significant engine
power level changes.
8Microscopic
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.
8Highly
statistical in nature.
LCF: What are the parameters? ...
LCF: Mean Stress Effects must be included ...
8Simple approach
e t  3.4
by J. Morrow:
 Su  Sm  N 0.12  e 0.6 N 0.6
E
8Alternative approach
f
f
f
by Smith, Watson &
Topper (1970):
 max e a E   f   2 N 
2
2b
  f e f E  2 N 
b c
where max=m+ a and ea is the alternating strain
Notch LCF: Overall philosophy ...
8Kt < ~1.5
8Local stress-strain
8Smooth
calculated
LCF curves used
8Kt > ~1.5
8Local stress-strain
8Notch
calculated
LCF curves used usually mean
stress/strain range, temperature corrected
Notch LCF: Strain Range-Mean Stress
Curves ...
Strain Range,
e 
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 Ke 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:
8Linear Rule
- elastic equivalent stress
method
8Neuber Rule
- ideally for plane stress cases
8Glinka 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 e curves assumes
kinematic hardening and relates e using cyclic
e 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?
8Military combat missions have many in-flight
throttle excursions.
8Reduce mission into major and minor (or sub)
cycles
8Major (Type I) cycle is the largest overall strain excursion
in the mission.
8Full power excursions from intermediate, or above, to idle
and 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
Cumulative Damage: Methodology ...
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:

ni

Ni
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
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
3.5E+07
Constant 1
3.0E+07
Constant 2
Parameter
2.5E+07
Constant 3
2.0E+07
1.5E+07
1.0E+07
5.0E+06
0.0E+00
0
500
1000
1500
2000
Temperature (F)
Rate dependent test data
and model correlation
Model parameter temperature
dependencies
ANSYS analysis of
constitutive specimen
Constitutive Modeling Approach
specimen correlation
specimen prediction
component analysis
Understanding Metallurgical Aspects of Fatigue
Metallurgical Aspects...
Relevant Topics:
8 Crystal Structure
8 Deformation Mechanisms
8 Crack Initiation .. Sequence of Events
8 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, a-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...
8
Dispersion strengthening
8 Solid solution strengthening
8 Precipitation hardening
8 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 ...
8
from dislocations - as in slip
8
from diffusion - as in grain boundary sliding
8
or from both
Fracture Stages: Steps of an Idealized Fatigue Process ...
Stage I
Crystallographic Fracture, along a few planes, brittl
appearance, at angle to principal loading direction.
Stage II
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
Overstress
Some General Characteristics
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
transgranular
Often short term event, small deformation,
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:
8
Cyclic properties are important to our product.
Principal deformation mechanisms are slip at low temperature and diffusion
at high temperature.
8
8
Cracking can be crystallographic, transgranular, or intergranular.
Simple deformation models can be used to consolidate data and predict loca
stresses and strains.
8