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: info@midasfea.com

Telephone: +44 (0) 1908 776717