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Explaining the differences from Stress-Life Fatigue
The Strain-Life Method (Local Strain, εε-N, or “Crack Initiation”)
* Relates local strain to fatigue damage at that point
* Useful when cycles have some plastic strain component * Suitable for predicting life in components which are
supposed to be defect free, i.e., not structural joints, sharp features, etc.
(Low Cycle Fatigue – LCF)
MSC Fatigue Features * Based on Local Strain Concepts * Mean Stress Correction * Elastic-Plastic Conversion * Statistical Confidence Parameters * Palmgren-Miner Linear Damage * User Defined Life * Cyclic Stress-Strain Modeling * Surface Conditions * Factor of Safety Analysis * Biaxiality Indicators * Multiple Loads
Strain-Life (ε-N)
σ1/2cycle
1cycle
1/2cycle
1cycle1cycle
1/2cycle
Strain
ε
Time
Cyclic Testing - Hysteresis Loops and End Point Definition
2Nf
Stabilized Hysteresis Loop
Stre
ss
Stra
in
Stress-Strain Relationships
Monotonic:
Cyclic:
ε = σE
+ 1/n
[ ] σK
εa = σa σa
E K’
1/n’ + [ ]
a = amplitude! Ramberg-Osgood Relationships
ε-N Fatigue Tests
* Specimens are subjected to constant amplitude strain using an extensometer in the servo loop
* εN test controls plastic strain, the parameter that governs fatigue
* The number of cycles to crack initiation is plotted against the total strain on a log-log plot and the best fit curve computed
( ) ( )cffb
ff
a NNE
22 `` ⋅+⋅= ε
σε
Elastic & Plastic Components (Due to Basquin, Coffin and Manson)
(2Nf)b + εf’(2Nf)c
σf’
E Δε2
=
Elastic (Basquin)
Plastic (Coffin-Manson)
Neuber’s Rule
The strain concentration factor, and the stress concentration factor,
after plastic yielding. Neither are known but Neuber suggested that the square root of the product of the stress and strain concentration factors was equal to Kt . Hence Neuber’s Rule is simply:
Re-arrangement of this Rule gives a useful equation:
eKe
ε=
SK σσ =
( )2. Te KKK =σ
( ) σε=SeKT2
Another re-arrangement gives:
in which the LHS is known. This can be solved with the cyclic stress strain curve equation simultaneously to derive σ and ε Topper simply replaced Kt by Kf to make Neuber’s Rule applicable in fatigue analysis for local stress strain tracking.
Use of Kf in Neuber’s Rule
( ) σε=EeKT2
1
2 3
Kf
σ
e
s
ε
Cyclic Stress Strain Curve
Neuber Equation
Solution point
Graphical Solution for Local σ and ε
1
KfKK
e
3 Cyclic Stress
NSolution
2
Morrow Life Plot
Stra
in A
mpl
itude
(M/M
)
Life (Reversals) nCode nSoft
STW Life Plot
STW
Par
amet
er (M
Pa)
Life (Reversals) nCode nSoft
Morrow Smith-Topper-Watson
( ) ( ) Δ Ε Ν Ν ε σ σ
ε 2 2 2 =
+ f m f
b f f
c ' ' ( ) ( ) c + b
f f f 2b f
2 f
max 2 ' ' 2 ' 2
Ν + Ν Ε
= Δ σ ε σ
σ ε
Correcting for Mean Stress