Cosmos Works Fatigue

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Volume 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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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 AnalysisVideo presentations and accompanying exercisesA tool for Continuous Learning on your schedulePre-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. What’s 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 reseller’s 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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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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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 Strength’approach 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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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 best…essentially 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 don’t 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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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 we’ll 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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Fatigue is a process where repeated variations in loading cause failure even when the nominal stresses are below the material yield strengthTensile macro-level stresses must occurFatigue failure begins on the surface of a part due to surface imperfectionsResults from cyclic, plastic deformationThe 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 you’ll 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 marks”and indicate the start and stop points of the crack front as it propagates across the part.

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Components of cyclic loading include:

Mean stress, σmStress amplitude , σaStress 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<1

σm = 0

Cyclic or repetitive loading is often characterized by a sinusoid where the most tensile stress represents the top of the wave and the most compressive stress represents the bottom. The period, or frequency, of the curve does not come into play when studying fatigue, just the stress amplitudes. The Mean Stress and Stress Amplitude, often represented by the term, Peak Alternating Stress, can be derived from the extremes of the wave. Another important term is the stress ratio which indicates the magnitude of the alternating stress. The critical values to note are when R=0, called ‘zero based loading’ as a part is loaded and unloaded, R=-1 which indicates fully reversing stress about a zero mean stress, and R=1 which is simply static loading. The fatigue strength of a material can vary with the magnitude of R.

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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 we’ll 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 shouldn’t be expected to correlate exactly to the known life. Think trends, not absolutes.

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Uncertainty in Fatigue Analysis…

These factors comprise some of the sources of uncertainty in fatigue predictions:– Geometry

Stress RisersSurface Finish

– Load HistoryPhysical MeasurementsKnowledge of System BehaviorUnexpected (or noted) load peaks

– Material PropertiesSN CurveAvailability of DataUncertainty or Scatter of DataFatigue 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 life…as 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, you’ll 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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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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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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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. That’s why an SN curve is so appropriate for representing a material’s 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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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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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. Don’t 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, you’re good to go. Otherwise, you have more digging to do.

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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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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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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 I’ll simply state that the COSMOSWorks fatigue UI can apply any of these based on what you deem most appropriate.

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Variable Amplitude Loading

Many loads aren’t nice clean constant amplitude sinusoids…To account for variable amplitude loading, COSMOS uses a Cumulative Damage Theory – Miners RuleIt assumes no cracks/damage present at the beginning of studyEstimates how much damage (based on total life) has been done by the applied load cycles

I’d 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 aren’t 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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Variable Amplitude Loading

Miner’s RuleFailure can be considered 100% DamagedIf 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 Miner’s 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 part’s 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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Fatigue Prediction In COSMOSWorks

Basic ProcessDefine one or more Static Structural studies

– Specify or define a SN curve for each material you wish to evaluate durability forMultiple 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 CorrectionAlternating Stress Calculation MethodFatigue 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 study…even 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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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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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-HillFailure of Materials in Mechanical Design; Jack Collins; Wiley Interscience

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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

Cosmos Works Fatigue

Documents

Transcript of Cosmos Works Fatigue