Quick Fatigue
Analysis GuideThis guide is made for non-experienced FEA users. It provides basic knowledge needed to start your fatigue calculations quickly.
Experienced FEA analysts can also use this guide to get used to the NFX workflow.
TABLE OF CONTENTS:
What is Fatigue? …………………………....... 3
Fatigue Design Philosophy………………....... 4
Life Estimation Methods …………………....... 5
Fatigue Loading ………………………………. 6
Wőhler’s Curve, S-N Curve ………………….. 7
Stress Life approach …………………………. 8
Strain Life approach ………………..………… 9
Strain Life Curve ……………………………… 10
Fatigue Workflow in midas NFX …………….. 11
Fatigue Module ……………………. 12
Approach Selection, Stress Option …………. 13
Fatigue Property, Mean Stress Correction …. 14
Load/Stress History …………………………... 15
Fatigue Results ……………………………….. 16
Fatigue failure is defined as the tendency of a material to
fracture by means of progressive brittle cracking under
repeated alternating or cyclic stresses of an intensity
considerably below the normal strength.
Although the fracture is of a brittle type, it may take some
time to propagate, depending on both the intensity and
frequency of the stress cycles.
All structures and mechanical components that are cyclically
loaded can fail by fatigue.
Fundamental requirements during design and manufacturing
to avoid fatigue failure are different for each different case
and should be considered during the design phase.
What is Fatigue Failure?
Page 3
Examples of fatigue failure
1
Before attempting to carry out a fatigue calculation, or even
choosing a way of calculating, it is necessary in critical
situations to decide on a design philosophy.
The three main approaches are Safe-Life, Fail-Safe and
Damage-Tolerant.
Fatigue Design Philosophy
Page 4
2
Fail-Safe
Safe-Life
Damage-Tolerant
Products are designed to survive a specific design life. Full
scale tests are usually carried out with margins of safety
applied. Fairly optimized structures.
A “safe-life” stool.
Any less than three legs and it would fall over!
Products are designed to avoid any failure regardless of costs.
If the structure were to fail in some part, it would still function
correctly, until necessary repairs could be made.
A “Fail-Safe” stool.
Failure of one leg would not result in overall failure.
Products are designed to take into account inspection
criterion to investigate the structure periodically to see
whether or not cracks have started.
A “damage-tolerant” stool.
The stool has some built in redundancy and is inspected
regularly.
Fatigue analysis itself usually refers to one of two
methodologies.
The stress-life (or S-N method), is commonly referred to as
the total life method since it makes no distinction between
initiating or growing a crack. This was the first fatigue
analysis method to be developed over 100 years ago.
The local-strain or strain-life (E-N) method, commonly
referred to as the crack initiation method, was more
recently developed and is intended to describe only the
‘initiation’ of a crack.
Fracture specifically describes the growth or propagation of
a crack once it has been initiated and has given rise to
many so-called crack growth methodologies.
Life estimation methods
Page 5
3
An idealization of the fatigue design process
Total Life Crack Initiation Crack Growth
Some load histories may be simple and repetitive, while in
other cases they may be completely random. They can also
have constant or variable amplitudes.
For simple cases, constant amplitude loading is used to obtain
material fatigue behavior/properties for fatigue design.
Some real life load histories can occasionally be modelled with
constant amplitude as well.
Constant amplitude loading has been introduced below:
Fatigue Loading
Page 6
4S
tress
(-)
Com
pre
ssio
n
Tensio
n (
+)
time
Sa
Sr
time
Str
ess
(-)
Tensio
n (
+) Sr
Smin
SmaxSm
Sa
Examples of stress cycles, (a) fully reversed, and (b) offset.
Stresses can be replaced with load, moment, torque, strain, deflection or stress intensity factors.
Cycle – 2 reversals
𝑅 =𝑆𝑚𝑖𝑛
𝑆𝑚𝑎𝑥
Smin – minimum stress
Smax – maximum stress
Sa – alternating stress (stress amplitude)
Sm – mean stress
Sr – stress range
R – stress ratio
R = -1 fully reversed cycleR = 0 pulsating tension
a) b)
This curve has been developed by German August Wőhler for
his systematic fatigue tests done in the 1870’s.
S-N Curve plots the diagram of amplitude of nominal stress
as a function for the number of cycles to failure for un-
notched (smooth) specimens.
Mathematical description of the material S-N curve:
Wőhler’s Curve, S-N Curve
Page 7
5
σa – applied alternating stress
A – constant, value of σa at one cycle
B – Basquin’s exponent, slope of the log-log curve
Nf - the number of cycles of stress that a specimen
sustains before failure occurs
A
B
Sa= σa= A·Nf-B
Stress life method, more commonly known as the S-N or
Nominal Stress method is used for total life calculation.
It assumes the structure to be fully elastic (even in local fatigue
related details like notches). Initiation or growing phase of a
crack is not considered and is applicable to high cycle fatigue
problems (low load-long life). This approach should not be
used to estimate fatigue lives below 10,000 cycles.
Some basic features related to Stress-Life approach:
· Material and component S-N curves
· Stress concentration factors,
· Miner’s cumulative damage theory
· Goodman or Gerber mean stress correction
· Rainflow Cycles Counting
Stress-Life approach
Page 8
6
Gerber-Goodman diagram
Rainflow cycles counting example
This method is also called Critical Location (CLA) approach,
Local Stress-Strain, E-N or Crack Initiation.
It applies when the structural durability depends on the stress
amplitude of local strain at the crack initiation place. Strain-life
design method is based on relating the fatigue life of notched
parts to the life of small unnotched specimens cycled to the
same strains as the material at the notch root.
This approach is best suited for low cycle fatigue problems,
where the applied stresses have a significant plastic component.
Strain-Life approach7
Δε
Δε
ΔS
ΔS
The concept of similitude between a strain controlled
test specimen and a component being designed
Critical zone
Smooth specimen
Notch
Page 9
E-N curve shows the relationship between the strain and the
number of cycles causing fatigue failure as expressed in the
equation below.
By applying a number of individual strain amplitudes to the E-N
curve, which have been extracted through rainflow-counting,
each number of cycles and the corresponding individual
damage level are obtained.
Strain-Life Curve8
σf’ – fatigue strength coefficient
εf’ – fatigue ductility coefficient
C – fatigue ductility exponent
∆𝜺
𝟐=𝝈𝒇′
𝑬∙ 𝟐𝑵𝒇
𝒃+ 𝜺𝒇
′ ∙ (𝟐𝑵𝒇)𝑪
Δε/2 – total strain amplitude = εa
Nf - the number of cycles of stress that a
specimen sustains before failure occurs
E – modulus of elasticity
Page 10
A flowchart of the fatigue setup in midas NFX can be described
as shown in the image below:
Workflow in midas NFX9
Page 11
Linear Static Analysis Case
Fatigue Module
1. Approach Selection
2. Stress Option
3. Fatigue Property (Material Fatigue Data)
4. Mean Stress Correction
5. Output Request
6. Fatigue Load
7. Fatigue Post-Processing
To start your fatigue analysis setup, it is necessary to perform
linear static analysis to your model.
When the static results are loaded, you can enter the Fatigue
Analysis dialog box.
From Linear Analysis Case to the Fatigue Module10
Boundary Menu
(Designer Mode)
Basic Method
Page 12
The first step is always the selection of a proper fatigue
approach. Midas NFX supports Stress Life and Strain Life
methods to compute the durability of your designs. Data can
be provided through load history, stress history or stress/strain
history for EN method.
Approach Selection, Stress Option11
Page 13
Experimental test data is mostly uniaxial whereas FE results
are usually multiaxial. At some point, stress must be converted
from a multiaxial stress state to a uniaxial one. In midasNFX
the following options are supported:
- Equivalent (Von Mises)
- Signed Von Mises
- Absolute Maximum Principal
- Maximum Shear
Clicking the Define Property button provides access to fatigue
material definition. Depending on the selected method fatigue,
curves can be specified directly or by using experimental data.
Page 14
Fatigue Property, Mean Stress Correction
12
Mean Stress Correction is available for both SN and EN
methods. This can be done by using:
- Gerber and Goodman formulas for SN
- Morrow and Smith-Watson-Topper for EN
Fatigue load can be provided as Load or Stress history.
Users can define this input in many ways depending on
requirements and available data.
Load/Stress History13
Page 15
Analysis can be
performed with regard to
applied stress
concentration factor.
Fatigue Load as full histogram.
Fatigue Load as single cycle.
Fatigue results are calculated as Damage and Fatigue Life
Cycles. Under the Output Request, the required output
vector can be selected.
Fatigue results14
Page 16
Fatigue lifecycle according to Goodman
mean stress correction.
Fatigue damage output vector.
Fatigue lifecycle according to Gerber
mean stress correction.
Life x Damage = 1
Damage can be also specified in
percentages.
Now you are ready to go !”
Please contact us if you have any questions
during your trial:
Email: [email protected]
Telephone: +44 (0) 1908 776717
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