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