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1Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
Image courtesy of National Optical Astronomy Observatory,
operated by the Association of Universities for Research in
Astronomy, under cooperative agreement with the National Science
Foundation.
The COSMOS CompanionFatigue Analysis in
COSMOSWorks
Volume 117
Sponsored by:
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2Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
2 2006 SolidWorks Corp. Confidential.
What is the COSMOS Companion?
The COSMOS Companion is a series of short subjects to help
design engineers build better products with SolidWorks Analysis
Video presentations and accompanying exercises A tool for
Continuous Learning on your schedule Pre-recorded videos are
accompanied by a more detailed
webcast with Q & A Download videos and review webcast
schedule at:
http://www.cosmosm.com/pages/news/COSMOS_Companion.html
It is not an alternative to instructor-led introductory training
We highly recommend you take a course with your local reseller
to
build a solid knowledge base
If you are new to the COSMOS Companion, a few comments on the
program are warranted. The COSMOS Companion series was developed in
response to the request from many of our users for more detailed
information on specific and/or new functionality within the COSMOS
products. Additionally, many users have been asking for
clarification of common design analysis questions to enable them to
make more representative analysis models and make better decisions
with the data. Whats more, users have asked for this material to be
made available in a variety of formats so they can review it how
and when they wish. To address this, each COSMOS Companion topic
has been pre-recorded and made available thru the COSMOS Companion
homepage as a downloadable or streaming video with audio, as static
PDF slides for printing, or as a live webcast enabling attendees to
ask questions and engage in additional discussion. We are trying to
provide continuous learning on your schedule so you can be as
effective and efficient as possible when using COSMOS for design
analysis and validation.It is important to note that this material
is not developed as an alternative to instructor led training. We
still believe that the best introduction to any of the COSMOS
products is in a class led by your resellers certified instructor.
In this program, we are hoping to build on the lessons learned in
your initial training. In fact, we will make the assumption that
you have basic knowledge of the interface and workflow from intro
training or equivalent experience. We will try not to repeat what
was taught in those classes or can be found in the on-line help but
to augment that information.
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3Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
3 2006 SolidWorks Corp. Confidential.
Topics to be Covered
Introduction to Fatigue Design Considerations S-N Curves Fatigue
Prediction in COSMOSWorks Summary
Remember that this is only an introduction to fatigue and the
tools for evaluating it within the COSMOSWorks environment. If
fatigue is an important part of your product performance, I highly
encourage you to research the topic more thoroughly, either thru
the references listed at the end of the session or by attending
workshops and seminars offered by a variety of providers.
Successful FE based fatigue analysis depends more on your knowledge
of fatigue and related subjects than your knowledge of the
software.
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4Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
4 2006 SolidWorks Corp. Confidential.
Why Consider Fatigue?
Traditionally designers consider the ultimate strength of their
components. Design for Strength
In-service load is rarely static in nature; there is usually
some variation.
A Design for Life approach rather than a Design for
Strengthapproach can account for these load variations
In simple terms, if you are using Yield Strength or Ultimate
Strength to make predictions about the acceptability of a design,
you are inherently making a static failure determination. However,
many systems undergo repetitive or cyclic loading where multiple
occurrences of stress well below the yield strength of a material
can lead to catastrophic failure. Designing a system to handle all
the repetitive loads it might see in its useful service is called a
Design for Life strategy.
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5Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
5 2006 SolidWorks Corp. Confidential.
Design Strategies for Fatigue
Ignore Fatigue - Hope for Best!!!! Over-Design How much is
enough? Predict Life Acknowledge Uncertainty
You have a couple of methods available to you in a Design for
Life approach. The easiest, yet riskiest, is to ignore fatigue
effects completely and hope for the bestessentially burying your
head in the sand until the potential problem passes. While, when
phrased like this, most of us would admit that approach is
dangerous, it is unfortunately very common. A common variant to
this is designing a system without even being aware fatigue effects
might come into play. A very dangerous proposition. Slightly less
risky is to admit fatigue is an issue but attempt to over design
your system so that this failure mechanism never occurs. Despite
the waste inherent in this approach, if you dont make some attempt
to quantify cyclic loading and allowable strengths, how do you know
enough is enough?Your safest route is to attempt to predict life
based on as much information as you can gather about your system.
An important thing to remember is that fatigue is an elusive
quantity to predict and there are many uncertainties in the
calculations that must be accounted for.
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6Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
6 2006 SolidWorks Corp. Confidential.
The Nature of Fatigue
Static Overload Design One or few loadings at peak stress
Readily comparable to published failure data
Cyclic Loading Design Typically a surface failure Typically a
tensile failure Compression in excess of yield may cause
tension
Microscopic Cracks Form and Grow to Failure Seed cracks
Allowables less clear than static failure Trends more
meaningful
Before exploring the uncertainties in a fatigue calculation, a
little bit on the nature of fatigue failure is warranted. Fatigue
failures, involving cyclic or repetitive loads, differ from static
failures in a couple of important ways. First of all, a static
failure is assumed to occur after one or a few load applications
where stress magnitudes exceed allowables. If you know what the
allowables are, the prediction is pretty straightforward with
COSMOSWorks results available. Finding appropriate allowables for
fatigue can require testing as they vary with load type and
magnitudes, or Stress Ratio (which will be defined shortly.) While
static failure can initiate in the middle of a volume, as with
tensile yielding in plasticity, fatigue failure occur on the
surface of a part where existing surface imperfections grow to
cracks that cause a part to fail. Fatigue requires tensile stress
on a surface. Interestingly enough, if a notched part is put into
compression such that only the notched area yields in compression
thus taking a new set or equilibrium, the elastic remainder of the
part will pull that into tension when the load is released causing
a possible fatigue location.Since the allowables are tied to many
variables that well discuss shortly, a safe route for fatigue
analysis is to perform a series of trend studies to examine how
much improvement can be gained over a known system or with as
little cost as possible. Making a Go No Go decision as you might in
a static overload scenario is not commonly recommended.
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7Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
7 2006 SolidWorks Corp. Confidential.
The Nature of Fatigue
Fatigue is a process where repeated variations in loading cause
failure even when the nominal stresses are below the material yield
strength Tensile macro-level stresses must
occur Fatigue failure begins on the
surface of a part due to surface imperfections Results from
cyclic, plastic
deformation The failure surface shows
characteristic beach marks
Stage I
Force
thickness length
time
Force Stress range, Sr
Stage II
As stated in the last slide, fatigue occurs in the presence of
tensile yielding. Even though the macro level stresses, those that
youll see on your perfectly smooth COSMOSWorks model, are well
below yield, stresses at the valleys of surface imperfections can
greatly exceed yield due to notch effects. Thus cracking starts on
a microscopic level and the cracks grow with each applied load.
When the cracks grow to a certain critical length, failure occurs.
The failure surface is typically marked with progressive lines,
sort of like the rings in a tree trunk. These are called beach
marksand indicate the start and stop points of the crack front as
it propagates across the part.
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8Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
8 2006 SolidWorks Corp. Confidential.
The Nature of Fatigue
Components of cyclic loading include:
Mean stress, m Stress amplitude , a Stress ratio, R
The stress ratio, R, the ratio of the minimum stress to the
maximum stress. Variations in the stress ratios can
significantly affect fatigue life Static Loading: R = 1
R=-1
R=0
R
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9Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
9 2006 SolidWorks Corp. Confidential.
Uncertainty in Fatigue Analysis
Test Data is Typically Represented by a Scatter or Probability
Descriptor Any Overload can Dramatically Reduce Fatigue Life
Reality - Multi-Axial ; Fatigue Data Uni-Axial Life Calculations
are Less Precise than Stress Calculations
Exact Correlation is a Fluke
Relative Life and Identifying Failure Locations More Valid
As mentioned previously, there are a number of uncertainties
that must be accounted for in a fatigue study. First of all, a
simple test to determine how many cycles a specimen can take at a
given load will often result in a variety of results so that you
are forced to look at a mean or conservative value in determining
an appropriate allowable. It is unreasonable to expect a
calculation to be more precise than the physical test data. Another
factor that comes into play is that any load in excess of the
expected cyclic maximum will likely invalidate any life predictions
because that damage is usually impossible to quantify. Finally,
fatigue testing is done in a uni-axial condition, which means that
the max and min stresses are always oriented in the same direction.
However, in reality, the stress distribution in most systems is
multi-axial or in all different directions. The most tensile stress
at a given location could be oriented 90 degrees from the most
compressive stress, making mean and alternating stress calculations
difficult.What this adds up to mean is that life calculations are
much less precise than static stress calculations. So much so that
when a prediction correlates closely to test, it is probably an
accident and not repeatable.Therefore, the techniques well be
reviewing for fatigue analysis in COSMOSWorks are best applied
towards identifying the likely areas of fatigue failure and
exploring trends. If you can determine using COSMOSWorks the
estimated life of a known acceptable system, you can use that
result to determine if a new system will last as long. If not, some
correction might be required. Remember that the life calculation of
the known system is valid as calculated and shouldnt be expected to
correlate exactly to the known life. Think trends, not
absolutes.
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10
Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
10 2006 SolidWorks Corp. Confidential.
Uncertainty in Fatigue Analysis
These factors comprise some of the sources of uncertainty in
fatigue predictions: Geometry Stress Risers Surface Finish
Load History Physical Measurements Knowledge of System Behavior
Unexpected (or noted) load peaks
Material Properties SN Curve Availability of Data Uncertainty or
Scatter of Data Fatigue Strength - Allowables
The factors that influence this uncertainty are many but here is
a list of some of the more common one. Obviously, highly stressed
areas are more likely to see a crack grow than less stressed ones.
Any stress sensitivity to dimensional tolerances in a hot spot can
cause observed life to fluctuate. The more coarse a surface is, the
more & deeper seed cracks exist. Variations in surface finish
have a great impact on fatigue variability.Your ability, or
inability, or measure applied loads are directly related to your
ability to calculate lifeas with static overload predictions. A
lack of complete understanding of how parts are loaded or interact
with each other represents a similar barrier to making life
predictions.The material properties, for fatigue, are difficult to
characterize since even tightly controlled test specimens are
subject to the same variability your parts are. Even knowing this,
finding fatigue curves, or SN curves that are applicable to your
material is very difficult. Once found, youll need to interpret the
data scatter from the testing and decide what stress level makes
sense to provide enough factor of safety for your design.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
11 2006 SolidWorks Corp. Confidential.
Fatigue Prediction Methods
Three major methods for determining component fatigue life:
Stress Life (SN) Strain Life (EN) Linear Elastic Fracture Mechanics
(LEFM)
== ++
Total LifeTotal Life
SN Analysis SN Analysis
Crack InitiationCrack Initiation
EN AnalysisEN Analysis
Crack GrowthCrack Growth
LEFMLEFM
COSMOSWorks uses a Stress Life (SN) Method
COSMOSWorks employs a Stress-Life method for predicting fatigue
which utilizes the more popular and available Stress-Life (SN) data
curve, (not surprisingly!) Other methods include Crack Initiation
analysis and Crack Growth analysis. These are simply two distinct
phases of the fatigue process, the sum of which is the total
fatigue life of a specimen. Thus, the SN method is the shortest
path to predicting ultimate failure which is the primary concern of
most design engineers.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
12 2006 SolidWorks Corp. Confidential.
High vs. Low Cycle Fatigue
High Cycle Low Cycle
Low Stress High Stress
> 100,000 Cycles 10-100,000 Cycles
Stress-Life (S-N) Curves Valid Strain-Life (E-N) Methods more
Appropriate
Total Life Predictions Possible Crack Initiation Dominant
Mode
May show no plastic deformation
Microscopic cracks begin immediately; predictions typically
estimate occurrence of 1-2 mm
crack size
The SN method is most applicable to High Cycle fatigue events
which represent failures that occur after many cycles vs. low cycle
fatigue which can happen after only a few cycles. The threshold for
determining if a fatigue failure is truly high cycle varies with
published references but 100,000 cycles is a widely accepted value.
It might be somewhat less than this for some materials but if your
part makes it 100,000 cycles before failure, high cycle fatigue
methods, as in COSMOSWorks, are appropriate.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
13 2006 SolidWorks Corp. Confidential.
Fatigue Strength & S-N Curves
The time for a crack to initiate and grow to cause component
failure is a function of the component material and applied
stress
The data is plotted in the form of a stress-to-number of cycles
to failure (SN) curve
The fatigue strength of a material, Sf(N) is the stress level
that a material can endure for N cycles
The fatigue life of a component is a function of the material
properties and the magnitude of the applied cyclic stress. Thats
why an SN curve is so appropriate for representing a materials
resistance to fatigue. The X axis represents number of cycles,or
life, and is usually expressed in log format. The Y axis is
alternating stress. When fatigue strength is reported, it is
typically stated as the stress a part can sustain in a cyclic
environment while lasting a desired number of cycles. As mentioned
previously, the frequency or the speed of cycling is not typically
a factor in determining failure, it is cycle count. Therefore, a
less frequently cycled part may seem to have more fatigue
resistance than a more quickly cycled part because it last longer.
However, the number of cycles at failure should be comparable.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
14 2006 SolidWorks Corp. Confidential.
Fatigue Strength & S-N Curves
Fatigue strength is typically measured by a rotating beam
fatigue test.
Data Scatter at Constant R Data Variation with Changing R
An SN curve is generated typically using a polished cylindrical
specimen that is spun while being loaded normal to its axis. As the
part rotates, the half that was in tension at the front of the
specimen goes into equal and opposite compression at the back of
the specimen. Thus cycles are clocked pretty quickly. The amount of
normal load determines the applied stress. As can be seen from
these charts, the cycles to failure at a constant R can vary
greatly as can the shape of the mean curve when the same material
is tested at multiple R values. Knowing what R value your data is
derived from is important. Additionally, knowing the magnitude of
scatter in the test results, (vs. simply looking at a Mean curve)
can help you gauge what safety factor to use in results
interpretation.
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15
Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
15 2006 SolidWorks Corp. Confidential.
S-N Curves in COSMOSWorks
Interpolation MethodMaterials with existing SN (or SS) curves
are identified in the
Library list
Stress Ratio of test
Enter or Import Tabular Data (Set Units First)
In COSMOSWorks, the SN curve is input thru the Fatigue SN Curves
tab on the standard material form.The Stress Ratio (R) requested in
this form is the ratio of the test, not your application. This is
important to note.You can type curve data directly into the form
but make sure you set your units first. Changing the units
midstream will convert all existing numbers.You may have notices
that in the COSMOS Materials library, some material names have an
SS or an SN suffix. This indicates that a Stress-Strain (SS) or a
SN curve exists for the material. Dont jump to the conclusion that
this is applicable to your material without a little research. I
typically try to double-source my SN data, at a minimum. The curve
in the database can be one source and if you find an independent
source that matches it, youre good to go. Otherwise, you have more
digging to do.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
16 2006 SolidWorks Corp. Confidential.
S-N Curves in COSMOSWorks
Multiplies Reference Sa Values by Ratio, Ecurrent/Eref
ReferenceSN Curve
ASME Reference Curves
COSMOSWorks does provide another utility for estimating an SN
curve based on the elastic modulii of various steels. This is based
on an ASME specification and can yield representative curves
although not necessarily correct ones. If you are focusing solely
on trends, as recommended several times in this unit, this might be
all you need. Keep using a consistent curve here and your trends
should be valid.
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17
Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
17 2006 SolidWorks Corp. Confidential.
Mean Stress Correction
Variations in the mean stress can significantly affect fatigue
life.
An important concept that was alluded to previously is that
stress measurements at different R values may yield different
fatigue strengths. R is directly related to the mean stress in a
cyclic load application. Consequently, some techniques have been
developed over the years to adjust the prediction of fatigue in a
physical event having one Mean Stress by using test data derived
from another mean stress.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
18 2006 SolidWorks Corp. Confidential.
Mean Stress Correction
To avoid measuring SN curves for all mean stresses, use a Mean
Stress Correction Method
This allows adjustment to the fatigue strength for different
mean stresses
COSMOSWorks provides Goodman, Gerber, and Soderbergcorrection
options
The most common techniques of compensating for different mean
stress, called Mean Stress Correction Methods, are the Goodman,
Soderberg, and Gerber methods. The references listed at the end of
this session do a better job of explaining these then I can so Ill
simply state that the COSMOSWorks fatigue UI can apply any of these
based on what you deem most appropriate.
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19
Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
19 2006 SolidWorks Corp. Confidential.
Variable Amplitude Loading
Many loads arent nice clean constant amplitude sinusoids To
account for variable
amplitude loading, COSMOS uses a Cumulative Damage Theory Miners
Rule It assumes no cracks/damage
present at the beginning of study Estimates how much damage
(based on total life) has been done by the applied load
cycles
Id like to make a brief mention of variable amplitude loading.
Since this is positioned as an introductory session on fatigue,
getting too deep into variable amplitude fatigue would be
counter-productive and will be saved for a separate session.
Suffice it to say that many structures arent loaded with a
well-behaved sinusoid. They are loaded as several magnitudes for
various numbers of cycles. To account for that, a simple method for
summing the effects of each stress peak, or group of stress peaks,
has been derived based on the amount of damage each is responsible
for.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
20 2006 SolidWorks Corp. Confidential.
Variable Amplitude Loading
Miners Rule Failure can be considered 100% Damaged If N1 Cycles
at S1 Stress causes Fatigue Failure
1 Cycle (n1) @ S1 causes 1/N1 * 100% Damage
If N2 Cycles at S2 Stress causes Fatigue Failure 1 Cycle (n2) @
S2 causes 1/N2 * 100% Damage
Failure occurs when: (n1/N1)+(n2/N2)++(nn/Nn)= 100%
Comparing %Damage from one design to next is excellent way to
evaluate design changes
COSMOSWorks uses Miners Rule for accumulating damage in a
variable loading event. Basically, the assumption is that a damage
level of 100% correlates to a failed part. Thus, it is assumed that
cycles at a given stress can be counted and the amount of damage
assigned to these cycles is estimated based on how much damage a
single cycle would have caused. Since it has been shown that higher
stress cycles at the beginning of a parts life cause failure to
happen more quickly than when the higherstressed cycles are at the
end of the life, this is still an approximate method. As with
constant amplitude loading, trend studies are still the best
approach.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
21 2006 SolidWorks Corp. Confidential.
Fatigue Prediction In COSMOSWorks
Basic Process Define one or more Static Structural studies
Specify or define a SN curve for each material you wish to
evaluate durability for Multiple materials can have their own SN
curve
Solve for displacement and stress
Define a Fatigue Study Specify as either a variable or constant
amplitude study Define Events based on previously solved
studies
Events can run simultaneously or sequential Set Study Properties
for:
Mean Stress Correction Alternating Stress Calculation Method
Fatigue Strength Reduction Factor
Determine if you need results on just surfaces or through entire
volume
Solve and review results
Once you understand the mechanisms and the nature of fatigue,
making the calculations in COSMOSWorks is pretty straightforward
and the COSMOSWorks Professional training guide does a good job of
guiding you through the interface. The workflow is as shown on the
slide. The actual fatigue calculations typically take seconds once
the static solutions have completed so if fatigue is a concern and
you are setting up static studies anyway, there really is little
excuse for not attempting to learn something from the fatigue
studyeven if it is just to see how sensitive the fatigue life in a
critical part is to minor dimensional changes. You may be
surprised.
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
22 2006 SolidWorks Corp. Confidential.
Presentation Summary
In this COSMOS Companion unit, we reviewed: The basic nature and
concepts related to fatigue failure
The differences between failure prediction for cyclic loading
and static loading
How fatigue, or life, prediction is NOT an exact science
2 : 1 Safety Factor minimum Scatter in test data and variations
in real parts limit resolution of prediction
Some thoughts on designing for fatigue
The fatigue analysis tools available in COSMOSWorks
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
23 2006 SolidWorks Corp. Confidential.
Additional References
COSMOSWorks Fatigue White Paper by Steve Endersby
www.solidworks.com/pages/services/WhitePaper.html
ASM International www.asminternational.org
Fatigue Calculator www.fatiguecalculator.com
DOT/FAA/AR-MMPDS-01
www2.tech.purdue.edu/at/courses/at308/Tech
nical_Links/MMPDS/OptionsMenu.pdf
Mechanical Engineering Design; Shigley & Mischke;
McGraw-Hill
Failure of Materials in Mechanical Design; Jack Collins; Wiley
Interscience
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Volume 117 The COSMOS CompanionFatigue Analysis in
COSMOSWorks
24 2006 SolidWorks Corp. Confidential.
Conclusion
For more information
Contact your local reseller for more in-depth training or
support on using COSMOSWorks Fatigue Studies in your design
process
Review the on-line help for a more detailed description of the
features discussed
Attend, or better yet, present at a local COSMOS or SolidWorks
user group. See http://www.swugn.org/ for a user group near you