Static Analysis:
Fatigue
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Section II – Static Analysis
Objectives
Module 9 - Fatigue
Page 2
This module will present the methods for estimating fatigue life using
the Fatigue Wizard found in Autodesk® Simulation Multiphysics.

Two methods will be reviewed: Stress-Life and Strain-Life.

The Strain-Life method will be used for low-cycle fatigue situations having
less than 104 cycles to failure.

The Stress-Life method will be used for high-cycle fatigue situations having
more than 104 cycles to failure.
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Section II – Static Analysis
Fatigue
Module 9 - Fatigue
Page 3

Fatigue is the progressive damage
that occurs when a material is
subjected to cyclic loading.

The loading and unloading of a
mechanical component can lead
to the initiation of a small crack
that grows to a critical size and
results in fracture.

Fatigue failures can occur when
the stresses are significantly
below the yield strength of the
metal.
© 2011 Autodesk
The Fatigue Wizard in Autodesk®
Simulation Multiphysics leads you
through the steps needed to perform
a fatigue analysis.
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Section II – Static Analysis
Design Objectives
Module 9 - Fatigue
Page 4



A mechanical component can be designed to meet one or more
objectives.
It can be designed to carry a specific load (Figure 1) and/or it can be
designed to achieve a specific life (Figure 2).
Fatigue calculations are associated with obtaining a specific life.
Life
Strength
stress
stress
X failure
X failure
Figure 1
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time
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time
Figure2
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Section II – Static Analysis
High and Low Cycle Fatigue
Module 9 - Fatigue
Page 5

High cycle fatigue involves stress
levels significantly below the
yield strength.
Fatigue Life
Estimation Methods
High Cycle Fatigue


Low cycle fatigue involves stress
levels near or greater than the
yield strength of the material.
Stress Life
Fatigue life
determined
using S-N Curve.
High cycle fatigue generally has
cycles to failure of 104 or greater.
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Low Cycle Fatigue
Strain Life
Fatigue life is
determined
using the
Basquin-CoffinManson
Equations.
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Section II – Static Analysis
High Cycle Fatigue
Module 9 - Fatigue
Rotating Beam Fatigue Test





An alternating stress can be
developed using a rotating beam
test.
The stress is completely reversed,
meaning that the stress alternates
between tension and compression.
The test fixture uses a four point
bending setup that removes shear
from the test section.
Different stress levels are obtained
by changing the load.
The cycles to failure at a specific
load level are counted.
© 2011 Autodesk
Page 6
Mott, R.L., Machine Elements in Mechanical Design, 3rd
Ed., Prentice-Hall, 1999 (p.145).
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Section II – Static Analysis
High Cycle Fatigue
Module 9 - Fatigue
Fatigue Strength

The fatigue strength is the
stress level that a material
can endure for N cycles.

A plot of fatigue strength
versus the number of cycles
to failure gives an S-N curve.

An S-N curve is often
plotted on a Log-Log scale.
Page 7
S-N Curve for an Alloy Steel
Cycles to Failure, N
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Section II – Static Analysis
High Cycle Fatigue
Module 9 - Fatigue
Endurance Limit

The stress level at which the
material can withstand an
infinite number of cycles is
called the Endurance Limit.

Not all metals exhibit an
Endurance Limit.


Page 8
S-N Curve for 4120 Alloy Steel
Se , Endurance Limit
Ferrous metals typically exhibit
an Endurance Limit.
Non-ferrous metals may not
exhibit an Endurance Limit.
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Infinite Life Region
Cycles to Failure
Parts having stress levels below the
endurance limit will have infinite life.
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Section II – Static Analysis
High Cycle Fatigue
Module 9 - Fatigue
Endurance Limit Modification Factors

The Endurance Limit is
determined using specimens
having smooth polished surfaces.

A variety of factors, including
surface roughness, can reduce
the Endurance Limit.

Factors effecting the endurance
limit include: surface finish, size,
environment, and type of test.
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Page 9
Surface Finish Reduction Factors
available in Autodesk® Simulation
Multiphysics
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Section II – Static Analysis
High Cycle Fatigue
Module 9 - Fatigue
Alternating and Mean Stress Components

High cycle fatigue life
estimation methods are based
on the S-N curve.

The S-N curve is developed for
completely reversed loading
(zero mean stress).

A tension mean stress will
reduce the fatigue life.
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Page 10
Alternating Stress
Mean Stress
a
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a 
 max   min
2
   min
 m  max
2
 max
m
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High Cycle Fatigue
Mean Stress Interaction Equations



Several criteria are used to account
for the reduction in fatigue life
associated with a tensile mean
stress.
Two common interaction equations
are the Goodman equation and the
Gerber Equation.
If these equations are used for
infinite life design, the fatigue life,
S(N), used in the equation is the
endurance limit, Se.
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Section II – Static Analysis
Module 9 - Fatigue
Page 11
Goodman Equation
K fa
S N 

m
Sut
1
Gerber Equation
K fa
2
m 
  1
 
S N   Sut 
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High Cycle Fatigue
Mean Stress Interaction


The Fatigue Strength, S(N), can be
found from the mean stress
interaction equation, when there is
a mean stress component.
Once S(N) is obtained, the number
of cycles to failure is found using the
S-N curve.
Section II – Static Analysis
Module 9 - Fatigue
Page 12
Gerber Equation
K fa
m 
  1
 
S N   Sut 
Solving for S(N) yields
S N  
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2
K fa
m 

1  
 Sut 
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High Cycle Fatigue
Multicomponent Stress States
Section II – Static Analysis
Module 9 - Fatigue
Page 13

The S-N curve and associated mean and alternating stress
components are developed for a single stress component.

The von Mises stress is used to determine an equivalent stress
component when multi-axial stress components exist.

The equivalent mean and alternating stresses are then
computed from the mean and alternating stress components.
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Section II – Static Analysis
High Cycle Fatigue
Module 9 - Fatigue
Complex Load Histories

The S-N curve is created using a
sinusoidal stress.

Each cycle involves one stress
reversal.


Complex load histories must be
converted into a set of stress
reversals having different amplitudes.
A cumulative damage law is then
used to assess the combined effect of
the stress reversals.
© 2011 Autodesk
Page 14
The Rainflow Cycle Counting
Method is a commonly used
method for breaking a complex
load history into a set of simple
stress cycles.
ASTM E1049-85(reapproved 2005)
provides a standard practice for
applying this method.
The Fatigue Wizard in Autodesk®
Simulation Multiphysics uses the
Rainflow Counting Method.
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Section II – Static Analysis
High Cycle Fatigue
Module 9 - Fatigue
Cumulative Damage Laws

All of the cycles from the
Rainflow Counting Method use
up some of the life of the
component.
Page 15
Miner’s Rule is the most commonly
used Cumulative Damage Law and is
used by the Fatigue Wizard.
h

A cumulative damage law
accounts for the effects of all
of the cycles when assessing
the life of the component.
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ni
i N  1
i
Miner’s Rule
ni
Number of stress cycles due
to load cycle i
Ni
Cycles to failure due to
load cycle i (from S-N
Curve)
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Low Cycle Fatigue
Strain – Life Method

The Strain-Life Method is used to
determine the fatigue life in the
low cycle fatigue regime.

This method is based on straincontrolled cyclic load tests
carried out on axial fatigue test
load frames.

A cyclic-stress-strain curve for a
material loaded into the plastic
strain region is shown in the
figure.
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Section II – Static Analysis
Module 9 - Fatigue
Page 16
Stress
E

Strain
 p
 e
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Section II – Static Analysis
Low Cycle Fatigue
Module 9 - Fatigue
Strain-Life Equations


Page 17
The Basquin-Coffin-Manson
equation for the total strain is used
to determine the fatigue life.
The coefficients and exponents are
determined experimentally.
Basquin-Coffin-Manson Equation


Experimental or
approximate
coefficients can
be used with
the Fatigue
Wizard.
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'
f
 'f
E
2 N    2 N 
b
'
f
c
Fatigue strength coefficient
b
Fatigue strength exponent
 'f
Fatigue ductility coefficient
c
Fatigue ductility exponent
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Section II – Static Analysis
Low Cycle Fatigue
Module 9 - Fatigue
Total Strain Curve

The Basquin-Coffin-Manson
equation is the sum of two
effects.

The first curve is dominated by
elastic strains (red).

The second curve is dominated
by plastic strains (black).

Page 18
Plastic
Strain
Elastic
Strain
The transition between low and
high cycle fatigue is located at
the intersection of the two
curves.
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Section II – Static Analysis
Low Cycle Fatigue
Module 9 - Fatigue
Neuber Method




The Basquin-Coffin-Manson equation
requires a method for determining the
total strain (sum of elastic and plastic
components).
An elastic-plastic stress analysis could
be performed.
As an alternative, the Neuber Method
provides a method for estimating the
total strain based on an elastic analysis.
If the Finite Element mesh is
sufficiently fine to capture the stress
concentration, the stress concentration
factor, Kt, can be set to one.
© 2011 Autodesk
Page 19
Computed
Real
K  com com  
2
t
 com 
 com
E
K t com 
2
E

 
 
   ' 
E K 
K t com 
2
E
1
n'
Ramberg-Osgood Eq.
Cyclic Stress-Strain
1


'
n
   


 ' 
E  K  


Iteratively solve for stress then find strain.
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Section II – Static Analysis
Low Cycle Fatigue
Module 9 - Fatigue
Mean Stress Effects

Two mean stress correction
methods are used in the
Fatigue Wizard:
Page 20
Fatigue Life Estimates Determined
by the Fatigue Wizard.
1) Morrow and
 2) Smith-Watson-Topper.


The Morrow method is best
when the loading is
predominately compressive.

The Smith-Watson-Topper
method is best if the stress
is predominately tensile.
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Smith-Watson-Topper
Morrow
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Low Cycle Fatigue
Cumulative Damage

The Rainflow Counting Method
and Miner’s Cumulative
Damage Rule discussed with
respect to high-cycle fatigue
are also used with low-cyclefatigue.

The Rainflow Counting method
uses data entered in the
Fatigue Wizard’s Load Case
History table.
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Section II – Static Analysis
Module 9 - Fatigue
Page 21
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Section II – Static Analysis
Module Summary
Module 9 - Fatigue
Page 22

This module has presented a summary of the methods used to
estimate fatigue life using the Fatigue Wizard found in Autodesk®
Simulation Multiphysics.

Two methods are available: Stress-Life and Strain-Life.

The Strain-Life method should be used for low-cycle fatigue
situations having less than 104 cycles to failure.

The Stress-Life method can be used for high-cycle fatigue situations
having more than 104 cycles to failure.
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