I will try to answer with whatever limited knowledge I have about fatigue.

1 and 2 -Fatigue is phenomenon based on fluctuations of loading. Here loading may change within short span of time or may take some days to change. But the "change" that is fluctuations in loading is required to happen fatigue. Since fatigue calculations are based on the endurance strength and does not take into account how load is fluctuating. It does take in to account fluctuation time. Component with less time for one fluctuating load cycle will complete its fatigue life cycles quickly than components having higher time of one fluctuation load cycle if the stress range of both components is same. So basically vibrating components will complete its fatigue life quickly than components having no vibration but with fluctuating load by other means which take more time to complete one cycle.

So this answers your question 1 and 2.

3-I guess when you have excitation with different frequencies you have random signals/vibrations. It is better to segregate the strong signals from the weak. For this you need to do PSD analysis of interested range of frequencies. For more information read the response in following question. 

https://www.researchgate.net/post/What_is_power_spectral_density2/1

4-Consider a component having natural frequency of 10 Hz.. If the components working frequency is 10 Hz or close to 10 Hz,  it will fail quickly due to large amplitudes that is deformations/amplified loads associated with resonance. If the working frequency is much less(or higher, obviously) than the natural frequency, amplitudes are very less and component can sustain for more time than components having working frequencies closer to natural frequency.  Hence components are designed to work either at very low frequencies or higher frequencies compared to their natural frequency. Modal analysis will give you the value of natural frequencies for particular mode of vibration. You can then decide on which frequency range the component will work so that resonant proof design is ensured.

Thank you Nikhil,

Does that mean that design against fatigue and design against resonance should be done independently ?

I guess, if the component is in dynamic loading then both are related and can be done independently or together based on requirement or application.

For example, for rotor shaft it is necessary to have its natural frequency well above or below its working speed frequency. And also the design life cycles for fatigue loading should be higher than the required life cycles of the shaft.

Very good example, what I understood from your answer is that modal analysis should be performed to find out the natural frequency of the shaft, so than we can avoid resonance. Then we need to estimate Fatigue life using either PSD or Rainflow method. Correct ?

I guess you are correct. Only thing I don't know is Which is better PSD vs Rainflow and for which applications.

I am "static" guy. So it is better to have consultation with "dynamic" guy for more Information :)

Hi Omar,

Although this may not completely answer your question, I have a few insights that may make things clearer for you.

First, 'static fatigue' , 'fatigue' and 'acoustic fatigue' refer to slightly different concepts. Probably, what unifies these concepts is that they all imply failure of a structure or part at a load level inferior to that which is expected to cause short-term failure.

In the case of 'static fatigue', the load is not usually varying over time. However, the material response does, leading to failure over time. This means that a creep failure for example would be considered a 'static fatigue failure'.

In general, the term 'fatigue' implies a load that is time varying. It could be 'cyclic' or 'spectrum' type. In cyclic, loading, the amplitude is usually constant or in steps, so cycles at a given load are just counted. Under spectrum loading however, the cycles may not be clearly identified. In order to obtain an equivalent cyclic loading, the rainflow counting method is often used. It permits to identify peaks and valleys making a cycle (or half-cycle) and redefines a new equivalent cyclic loading.

'Acoustic fatigue' would be a particular case of fatigue, where the loading comes from acoustic waves and the materials response is vibration. I am not all that familiar whit the specific methods of acoustic fatigue, but it seems evident that modal response and natural frequency are going to play a major role in determining the actual loads or most likely strains.

That being said, there are multiple important things to know about S-N curves and Miner's rule. First, S-N curves are empirical and usually come from constant amplitude cyclic loading at one given load ratio R=σmin/σmax. Usually, the S-N curve is not used under 1000 cycles, where fracture mechanics may be better suited. At very high cycle counts, generating S-N curves becomes impractical and because the curves become very horizontal and the scatter in results increases, it also becomes quite hard to have a good knowledge about the probability of failure. Also, although it is often assumed that metal fatigue is independent of frequency, if the material is viscoelstic (e.g. metals at higher temperatures or polymers and composites at room temperature), frequency effects may become important.

So is load ordering. In metals, if the load is well under the yield limit, the order in which the load cycles are applied is usually considered irrelevant (this is the assumption under Miner's rule, linear accumulation of damage). In practice, this may not be acceptable, in part because of local plastic strains or because of viscoelasticity.

For points 3 and 4, as I said before, I'm not as familiar with acoustic fatigue, but my  guess would be that for 3, possibly the fatigue can be associated with the energy of the acoustic signal. For 4, it appears evident to me that in the case of acoustic or vibration response, the strain amplitude will depend strongly on the vibration response of the structure so the analysis becomes essential.

I hope this helps,.

Regards,

Laurent

Thank you Laurent,

That was very helpful.

@Laurent Cormier

I differ with your statement-"a creep failure for example would be considered a 'static fatigue failure." Creep failure mode and fatigue failure mode are two different phenomenon. What you will do for high temperature fatigue where creep will also play important role along with fatigue due to cyclic loads? Creep strains will decrease the life cycles of the component. We need to take into account the creep as well as fatigue for such environment which is called creep-fatigue interaction.

Fatigue is based on time varying loads whereas creep is based on constant/varying loading at high temperatures where creep is prominent. I guess Static fatigue or dynamic fatigue is different in the sense of loading only and not fatigue as failure phenomenon. So this differentiation is in my view is rather not required.

For the cyclic loads which are crossing yield limits, we required to do strain based life assessment. For cyclic loads which are elastic one stress based life cycle calculation is done.

Hello,

There are basically two types of fatigue , Low Cycle Fatigue (LCF) and High Cycle Fatigue (HCF). The fatigue due due vibrations fall in the HCF category where the number of cycles are typically greater than 10000. What is mentioned above communications as "Static Fatigue" in fact belongs to the LCF category.  The HCF fatigue curves are usually the Woher's Curves or the S-N curves and the failure is evaluated based on the Miners's Rule. Strain based approach is better suited for LCF. In the HCF regime both time domain and frequency domain approaches are possible. For random signals (e,g fluid excitation etc) frequency domain method is more efficient. The theory of random vibrations is used for determination of the RMS (Root Mean Square) of the  Stress  from the Stress Power Spectral Density (PSD) which is  Stress Amplitude squared/ Frequency. Finally the expected damage is calculated based on the S-N curves and Miner's rules. If the expected  Damage is >1 then fatigue failure is predicted. Probability based models are used for the stress distribution.

@Nikhil Patil

I would argue that your statements are more misleading than mines. I took the time to define parameters in my previous post to avoid confusion, but I'll try to restat things more clearly.

First, static fatigue does not require cyclic stress, but it does requires the action of time.

Second, creep does not need high temperatures. for example, natural rubber or ice creep at quite low temperatures, as do many polymers.

I agree that creep failure and cyclic fatigue failure modes differ. However, high temperature fatigue is creep-fatigue interaction, not static fatigue. Static fatigue is the failure of a component under a static load lower than that which would cause 'instantaneous' failure. In this context, fatigue does not relate to time-varying load, but to time-varying material behaviour.

In high temperature fatigue, it is the mean stress component that can lead to creep, which is interacting with the basic cyclic fatigue process. The overall strain increases due to creep and this is superimposed to the fatigue strain, which eventually exceeds the material's allowable. If one wants to be nitpicking, it could be argued that in many high temperature environments, stress-induced corrosion and thermo-oxydation are failure modes that differ from creep and fatigue...

I think one key point in both my previous post and this one is that fatigue does not have to be from time-varying loading. It has to relate to time dependent phenomenons leading to failure.

Finally, I agree with you that post yield fatigue needs to be viewed from a strain perspective in order to account for plastic strains.

Best regards,

Laurent

@Fatih Aruk

If you are at a temperature which is not expected to promote creep in your material, the effective loading is a stress fluctuation from 45 to 55 MPa, or constant amplitude fatigue at R=0.8. Thus, either you make/use an S-N curve at that ratio or you just use a R=-1 fatigue curve and Goodman's diagram to approximate at R=0.8.

If creep is expected to play a role, there are rules similar to Miner's rule that account for time at load that can be used to estimate the creep fatigue interactions. Otherwise, there are fatigue-creep interaction diagrams that can be used (somewhat analogous to Goodman diagrams.).

Best regards,

Laurent

@Laurent Cormier

Yes. You can argue about my statements but they are not misleading that is for sure. I have given scope for arguing because I have not set context for it. My explanation was based on metals which are mostly used in engineering and limited to steel and its alloys as my engineering experience is limited to steels.

But at the same time you also have not set context for the statements in first as well as second post  which is why there is still difference of opinion. On the basis of this I differ with you the statements made in your both posts.

Static fatigue is the term mainly used for the glass and ceramics where it is similar to creep and is limited to these materials. This clears your statement "a creep failure for example would be considered a Static fatigue failure" for the above materials. Hydrogen induced cracking may referred as static fatigue of metals. But actually it is called as hydrogen induced cracking or form of hydrogen embrittlement.This term was associated with environmental cracking but is now becoming obsolete. -ASM Materials Engineering Dictionary.

Then also for Static fatigue to happen in metals there should be corrosive environment  and not the cyclic stress along with action of time. This is  generally termed as environmental cracking/corrosion/hydrogen based cracking and not static fatigue for metals. So time varying behavior requirement to happen static fatigue is limited to glass and ceramics and not the general engineering metals where you still require time varying load for fatigue to happen.

For creep I agree that temperature is varying for each materials and not required that it should be high as you pointed out. My context was steels and its alloys to mention creep at high temperature.

Fatigue in general relate to time varying loads and differentiation of static and dynamic fatigue is not required in the context of engineering metals such as steel. This is my view

Disagreement is to show no offense to any person or his perspective but to have healthy discussion and getting new insights. :))

Regards,

Nikhil

Combination of Low Cycle Fatigue (LCF) and High Cycle Fatigue(HCF) is still a subject of active research. The final result has not yet entered into the text books, but there are technical papers on the same. Now coming back to your question above, the stress range is 50 MPa. This should be used along with S-N Curve for the material along with mean stress correction to arrive at the allowable number of cycles. The self weight is a constant quantity and the stress is taken as the mean stress. This mean stress is also known as a static offset in the literature.  Hope this helps. 

@Nikhil Patil

Dear Nikhil,

I think that we might have mostly reached an agreement.

First, I must agree with you about the iimportance of a healty discussion without  aggression in case of disagreement.  If you found any of my statements to be offensive, please accept my apologies as they were not meant to be. Assertive, yes, offensive certainly not.

I must also agree on the importance of context, which is often found lacking in forum posts, mine not excluded. Because the original question did not state any specific material, I tried to make my statements as general as possible and this is why I did not restrict my answer to the behaviour of metals.

When I mention environmental stress cracking and thermo-oxydation, it was meant to illustrate the fact (may be not very effectively) that there are multiple synergistic phenomenons occuring that can lead to failure, be it fatigue or static.

As for the need to differentiate between static and cyclic fatigue in metals, the term static fatigue indeed appear to be used a lot less.

Best regards,

Laurent

@Fatih,

Pardon me, the statement 'Let's say you apply a dead weight to a beam in axial direction' led me to think that this was a constant stress.

In the case of a low-cycle fatigue cyclic stress of 0-50 MPa (unknown frequency) superimposed to a high cycle fatigue reversed stress of +/-5 MPa at 100 Hz, I guess I would be tempted to just analyses in terms of strain and use a cumulative damage model such as Miner's sum, although a non-linear criterion might be preferable.

There would be many caveats with such an approach though. One problem is that in the low-cycle regime, the life might not be independent of the order in which cycles are superimposed if there are plastic strains. Another problem is that for such low stresses, the material is likely not metallic and might not show a fatigue limit. Moreover, at high frequency, there may be heat generation leading to changes in material behaviour.

Honestly, that is just a guess solution to a problem that is not trivial. I am not aware of a textbook solution for combining high-cycle and low-cycle fatigue. Googling for 'combined high and low cycle fatigue' gives a couple returns that seem relevant.

Best regards,

Laurent

You are asking good questions. Actually the relationship between dynamics and fatigue has been studied a lot recently, and packages from nCode https://www.ncode.com and fe-safe https://www.3ds.com/products-services/simulia/products/fe-safe/ have methods of fatigue life prediction from PSDs. In fact, nCode even includes a simple modal package to estimate vibration at a given point on a component given PSDs measured elsewhere. What they do internally is generate a shaped random time series from the PSDs, and then pass the time histories into the normal Rainflow>Miners>etc path to predict life.

See also: https://re-test.com/fatigue-analysis-techniques

I kindly share brief info about your questions:

Miner's rule does use the cycles N from the S-N curve. And the S-N curves info is acquired from Lab fatigue testing using static loads. If the product or element of interest is submitted to vibration stress, the load that causes the fatigue is Dynamic. For practical purposes, the dynamic load may be considered the static load multiplied by a dynamic load factor. That factor can be obtained from the response acceleration (g) of the PSD applied to the product.

The PSD is the best way to represent the energy (grms) induced to a product or system (it induces fatigue). Then a good question is how to convert the energy (grms) induced by the PSD into stress (mpa).

Finally, the modal analysis is a study that does use the material's properties and product's design to know the resonance frequency (which most induces fatigue to the product's structure).

Regards,