Three Stages of Fatigue Failure Identifying Fatigue · PDF fileFracture ¾sudden,...
Transcript of Three Stages of Fatigue Failure Identifying Fatigue · PDF fileFracture ¾sudden,...
1
Over the Next Several DaysWhat is Fatigue? Types of Fatigue LoadingEmpirical DataEstimating Endurance/Fatigue StrengthStrategies for Analysis
Uniaxial Fully ReversedUniaxial FluctuatingMultiaxialCrack Growth
Some HistoryRail car axles The all-important microcrackRole of stress concentrations
Comet airplanes
Three Stages of Fatigue FailureCrack InitiationCrack Propagation
oscillating stress… crack grows, stops growing, grows, stops growing… with crack growth due to tensile stresses
Fracturesudden, brittle-like failure
Identifying Fatigue Fractures
beachmarks
Three Approaches
best model of crack propagation, for low-cycle fatigue
LEFM (Fracture Mechanics)
useful when yielding begins (i.e., during crack initiation), for low-cycle fatigueStrain-Life
stress-based, for high-cycle fatigue, aims to prevent crack initiationStress-Life
Low vs. High Cycle>103 cycles, high cycle fatigue
<103 cycles, low cycle fatigue
car crank shaft –
manufacturing equipment @ 100 rpm –
ships, planes, vehicle chassis
~2.5 E8 Rev/105 miles
1.25 E8 Rev/year
2
Types of Fatigue Loading
minmax σσσ −=∆ stress range
2σσ ∆
=aalternating component
2minmax σσσ +
=mmean
component max
minσσ
=Rstress ratio
m
aAσσ
=amplitude ratio
Fully Reversed Repeated Fluctuating
UpdateWhat is fatigue? Types of Fatigue LoadingEmpirical DataEstimating Endurance/Fatigue StrengthStrategies for Analysis
Uniaxial Fully ReversedUniaxial FluctuatingMultiaxialCrack Growth
Testing Fatigue PropertiesRotating Beam – most data is from this type
Axiallower or higher? Why?
CantileverTorsion
Fully Reversed Empirical Data
Wrought Steel
An S-N Curve (Stress-Life)
Fully Reversed Empirical Data
Aluminum
Endurance Limit
A stress level below which a material can be cycled infinitely without failure
Many materials have an endurance limit:low-strength carbon and alloy steels, some stainless steels, irons, molybdenum alloys, titanium alloys, and some polymers
Many other materials DO NOT have an endurance limit:aluminum, magnesium, copper, nickel alloys, some stainless steels, high-strength carbon and alloy steels
eS ′
for these, we use a FATIGUE STRENGTH defined for a certain number of cycles (5E8 is typical)fS ′
3
UpdateWhat is fatigue? Types of Fatigue LoadingEmpirical DataEstimating Endurance/Fatigue StrengthStrategies for Analysis
Uniaxial Fully ReversedUniaxial FluctuatingMultiaxialCrack Growth
Types of Fatigue Loading
minmax σσσ −=∆
2σσ ∆
=a
2minmax σσσ +
=m
m
aAσσ
=
max
minσσ
=R
stress range
alternating component
mean component
stress ratio
amplitude ratio
Fully Reversed Repeated Fluctuating
Getting Fatigue Data1) Test a prototype2) Test the exact material used3) Published fatigue data4) Use static data to estimate
Estimating Se´ From Static Datasee page 324 in your book…
ksi 40for ksi 19ksi 40for 4.0ksi 60for ksi 24ksi 60for 4.0ksi 200for 100ksi200for 5.0
85@
85@
≥≅≤≅≤≅≤≅≥≅≤≅
′
′
′
′
′
′
utf
ututf
ute
utute
ute
utute
SSSSSSSSSSSksiSSSS
E
E
steels
irons
aluminums
BUT, these are all for highly polished, circular rotating beams of a certain size
Correction Factors
freliabtempsurfsizeloadf
ereliabtempsurfsizeloade
SCCCCCS
SCCCCCS
′
′
=
=
pages 326+ in your book
Constructing Estimated S-N Curves
Sm=0.9Sut for bendingSm=0.75Sut for axial loading
The material strength at 103 cycles, Sm:
The line from Sm to Se or Sf, Sn=aNb
or logSn=loga + blogN
4
Fatigue Stress Concentration
Kf = 1+q(Kt-1)
q = notch sensitivityfunction of material, Sut, Neuber constant, anotch radius, r
ra
q+
=1
1
UpdateWhat is fatigue? Types of Fatigue LoadingEmpirical DataEstimating Endurance/Fatigue StrengthStrategies for Analysis
Uniaxial Fully ReversedUniaxial FluctuatingMultiaxialCrack Growth
0=mσ 0≠mσ
Uniaxial
Multiaxial
Types of Fatigue Loading
minmax σσσ −=∆
2σσ ∆
=a
2minmax σσσ +
=m
m
aAσσ
=
max
minσσ
=R
stress range
alternating component
mean component
stress ratio
amplitude ratio
Fully Reversed Repeated Fluctuating
Uniaxial, Fully Reversed StrategyLoading & Stress Half
N (umber of cycles) Fluctuating Load (Fa)
Tentative DesignTentative Material
Kt σa (nominal)
σ1, σ2, σ3 (principal)
σ´ (von Mises)
Kf
σa
Uniaxial, Fully Reversed StrategyFatigue Half
Se´ or Sf´
Se or Sf
CloadCsurfCsizeCtempCreliab
Estimated S-N Curve
N (umber of cycles) Fluctuating Load (Fa)
Tentative DesignTentative Material Tentative DesignTentative Material
σ1, σ2, σ3 (principal)
σ´ (von Mises)
σ1, σ2, σ3 (principal)
σ´ (von Mises)
KfKf
σaσa
Kt σa (nominal)Kt σa (nominal)Kt σa (nominal)
Uniaxial Fully Reversed Strategy
Se´ or Sf´
Se or SfSe or Sf
CloadCsurfCsizeCtempCreliab
CloadCsurfCsizeCtempCreliab
Estimated S-N CurveEstimated S-N Curve
σ ′= n
fSN
Nf = fatigue safety factor; Sn = Fatigue strength at n cycles;σ ´= largest von Mises alternating stress
5
UpdateWhat is fatigue? Types of Fatigue LoadingEmpirical DataEstimating Endurance/Fatigue StrengthStrategies for Analysis
Uniaxial Fully ReversedUniaxial FluctuatingMultiaxialCrack Growth
0=mσ 0≠mσ
Uniaxial
Multiaxial
Types of Fatigue Loading
minmax σσσ −=∆
2σσ ∆
=a
2minmax σσσ +
=m
m
aAσσ
=
max
minσσ
=R
stress range
alternating component
mean component
stress ratio
amplitude ratio
Fully Reversed Repeated Fluctuating
Does Mean Stress Matter? The Data
Transform S-N --> σa-σm Fluctuating Stress Failure Plotσa
σm
Sy
Se or Sf
SutSy
Failure
Safety
constructed for a given number of cycles N
GerberSoderberg
Yield
modified-Goodman
6
Definitions Factors of Safety Four cases
1) σa constant, σm varies2) σa varies, σm constant3) σa and σm increase at constant ratio4) σa and σm increase independentlyIf you know how the stress can vary, only use one of four casesIf stress can vary in any manner, Case 4 should be used (the most conservative)
Four Cases (Use Ruler!)“Augmented” Modified-Goodman Plot
von Mises calculated for σa and for σm separately
σa
σm
Se or Sf
SutSy
Sy
Syc
1=′
+′
y
a
y
mSSσσ
1=′
+′
f
a
ut
mSSσσ1=
′+
′−
yc
a
yc
mSSσσ
fa S=′σ
Uniaxial Fluctuating StrategyStress & Loading
N (umber of cycles) Fluctuating Load (Fa)
Tentative DesignTentative Material
Kf
Kt
Kfm
σ1a, σ2a, σ3a; σ1m, σ2m, σ3m (principal)
σ´a, σ´m (von Mises)
σa
σm (nom) σa (nom)
σm
Uniaxial Fluctuating Strategy Fatigue Aspects
Se´ or Sf´
Se or Sf
CloadCsurfCsizeCtempCreliab
Modified-Goodman Diagram
7
Uniaxial Fluctuating StrategyN (umber of cycles) Fluctuating Load (Fa)
Tentative DesignTentative Material Tentative DesignTentative Material
σ1a, σ2a, σ3a; σ1m, σ2m, σ3m (principal)
σ´a, σ´m (von Mises)
Kf
σa
Kt σm (nom) σa (nom)
Kfm
σm
Se´ or Sf´
Se or SfSe or Sf
CloadCsurfCsizeCtempCreliab
CloadCsurfCsizeCtempCreliab
Modified-Goodman DiagramModified-Goodman Diagram
Nf
StrategyFind σ´a and σ´m with appropriate stress concentration factorsFind Se
Plot modified-Goodman diagramFind factor of safety
UpdateWhat is fatigue? Types of Fatigue LoadingEmpirical DataEstimating Endurance/Fatigue StrengthStrategies for Analysis
Uniaxial Fully ReversedUniaxial FluctuatingMultiaxialCrack Growth
0=mσ 0≠mσ
Uniaxial
Multiaxial
Types of Fatigue Loading
minmax σσσ −=∆
2σσ ∆
=a
2minmax σσσ +
=m
m
aAσσ
=
max
minσσ
=R
stress range
alternating component
mean component
stress ratio
amplitude ratio
Fully Reversed Repeated Fluctuating
Multiaxial Fatiguesimple multiaxial stress
periodic, synchronous, in-phasecomplex multiaxial stress
everything elseassuming synchronicity and being in-phase is usually conservative
Fully Reversed MultiaxialFind von Mises equivalent stress for alternating component
Cload implications
( ) ( ) ( )2
213
232
221 aaaaa a
aσσσσσσ
σ−+−+−
=′
a
yf
SN
σ ′=
8
Fluctuating MultiaxialSines MethodVon Mises Method
( ) ( ) ( )2
213
232
221 aaaaa a
aσσσσσσ
σ−+−+−
=′
( ) ( ) ( )2
213
232
221 mmmmm m
mσσσσσσ
σ−+−+−
=′
Modified-Goodman Diagram
UpdateWhat is fatigue? Types of Fatigue LoadingEmpirical DataEstimating Endurance/Fatigue StrengthStrategies for Analysis
Uniaxial Fully ReversedUniaxial FluctuatingMultiaxialCrack Growth
0=mσ 0≠mσ
Uniaxial
Multiaxial
Crack Growth Experiments
dNdaln
( )K∆ln
n
Time
Stre
ss Measure a vs. cycles
( ) aK πσβ ∆=∆Calculate:
Then plot
( )nKAdNda
∆=Which Follows
Crack Growth Analysis
aK πβσ=
Calculate:
cc aK πβσ=22
2
σπβc
cKa =∴
dNdaln
( )K∆ln
n
( )nKAdNda
∆=From
( )( )( )daK
AKAdadN n
n−∆=
∆=
1
( )( ) ( )( )
daaA
daKA
N cc a
a
nnna
af ∫∫⎟⎠⎞
⎜⎝⎛ −
−−
∆=∆=00
211 πσβ
( )( )
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛ +−∆
⎟⎠⎞
⎜⎝⎛ +−−
−=
=
=
12
)1(
12
1
0
nn
N anA
caa
aa
f πσβ
( )( )
⎥⎥⎦
⎤
⎢⎢⎣
⎡
⎟⎟⎠
⎞⎜⎜⎝
⎛−⎟
⎠⎞
⎜⎝⎛ −∆
−−−−
=)
21(
0)
21()1(
211 nn
cn
N aanA
f πσβ
Overall Strategy