Yield/start for S-S curve FEA? 4

[cbrf23]

When defining an S-S curve for FEA, do you use traditional .2% offset for yield, or do you go by the first point at which the curve begins to deviate from linearity?

Not sure if all FEA software is the same, but the software I'm using (Solidworks Simulation Premium) tells me the first point in my data-set (coordinate points to define the curve) must be the yield point.

I'm new to FEA (this is my first project) and I'm hoping to get some guidance on best practices here

My understanding is that SW Simulation treats anything below the yield point as elastic, so basically creates a straight line from the origin to the fist point.
So because of this, using a .2% offset yield results in a simulation curve that deviates quite a bit from the "real" curve, as it's missing quite a bit of information on the elasto-plastic transition.
I can get a much more "true-to-life" curve using a smaller offset. e.g. For the example below, I plugged in a 0.0000000000000001% offset, which I'll call the first point of non-linearity in the curve. (this is as small as I could go before excel refused to solve for the offset)

I'm going to be doing low-cycle fatigue studies, so I think especially for this application I'd want to have the most accurate elasto-plastic definition possible; no?

Now my only concern is I don't know if having a lower initial yield point would skew the results.
I wouldn't think so, as it's my understanding SW Simulation calculates a new yield point for each cycle based on the provided curve - so it should just be more accurate; no?
I do believe the lower yield could skew any FOS rating(s); but I'm not at all concerned with FOS in this study, just fatigue performance, so error in FOS is allowable.

I’ve simplified the curve quite a bit; I’m down to 7 points using 0.2% offset or 14 using a 0.0000000000000001% offset – so I think either curve will be acceptable from a performance standpoint.
Not sure if there is anything else to consider here; like I said I'm new to this, so looking for some expert advice


Check out the attached image to see a comparison between a .2% and a 0.0000000000000001% offset on the same material.
The blue line is the engineering stress-strain curve for the material.
The green line is a 0.2% offset.
The purple line is a 0.0000000000000001% offset.
The red line is a linear interpolation between the origin and the .2% offset yield point (how Solidworks would complete the curve).
The pink box is all of the elasto-plasticity data that is lost using a .2% offset yield.

 

[TGS4]

You definitely don't want the red line - that is incorrect. Furthermore, I don't think that this is how your software is going to interpret it.

I generally use 1e-6 plastic strain as the point to define the proportional limit (that is the term that you were looking for, BTW).

 

[rb1957]

you want the line that best reflects your data ! If you're going to hang your hat on a material curve, you better make sure it's as good as you can get ... how much scatter between batches ? Since it's "only" modelling you can use several different material curves to see the difference ... what's more important (slope or yield stress) ?

another day in paradise, or is paradise one day closer ?

 

[aerostress82]

Looks like you are dealing with an Aluminum alloy or smt similar.

By definition some aerospace Al-alloys (maybe automotive too - just not familiar) don't have a definite yield point and this is where things are getting confusing in your model.

I will try to make sense why you should use which, so you have the whole picture.
I did this in 2 ways previously as I was dealing with a non-linear static analysis - but as your case is fatigue, your "every strain from any event" will count to add up to the total life of your part.
[ol 1]
[li]You may model the Stress-Strain curve such that the slope up to the yield point is equal to the Elastic Modulus (E) of your part. This is a very common simplification for a simple linear analysis - but always question what result you need from a model if you follow this method.[/li]
[li]You may model everything in your Stress-Strain curve (blue line) as is and count on that output for your fatigue analysis. This would give you the best result for fatigue. Just as a simplification, after yield point you can just define a horizontal line for the material curve (which will be perfectly plastic). This will be a good conservative approximation but still it won't be too conservative.[/li]
[/ol]

I've added the below explanation as you mentioned you are new with FEA:
Your fatigue results will be calculated from the summation of all your "damages per each event" (if you have a transient analysis going on for fatigue).
Or, your fatigue results will be calculated from 1 force application. The total life (1.0) will be divided by this damage from your force application load case on your model, and this will give you what your life is.

As explained in both cases, the damage is calculated from your strain from the model, so the strain you are getting is significantly relevant with what's being calculated as fatigue life.

I've dealt with fatigue for 1 year through FEA software (not hand calculation fatigue), so just wanted to summarize why your material curve data is very relevant with what you get. I think you can make a better judgement of your current and future cases after these details.

Spaceship!!

 

[realtime2]

In addition to the items that the previous contributors mentioned; a few other features
to be aware of:

For fatigue studies that rely on calculating the stress-strain behavior at a
notch or hot finite element one should use the cyclic stress-strain curve for the
material, not the monotonic tensile test. Aluminums in particular cyclically harden (a lot)
when one applies even small plastic strains in repetition. Other materials like
steels can have unique yielding behavior on the first load application- like in a
tensile test. The upper yield point in a carbon steel is such an example. After
the dislocations are released from their carbon pins the upper yield point is
gone during the fatigue cycling. Same goes for the "flat" Lueder's yield region
that follows the upper yield point in a tensile test. Repeated slightly plastic
stress-strain cycles kill all these features, and one gets a smooth curve, as in
your blue representation curve, during fatigue.

Also many of the higher strength steels may cyclically soften substantially. The worst
case might by 30 or 40 percent in terms of cyclic yield vs tensile yield.

Low carbon steels soften at small strain amplitudes and harden at larger
strain amplitudes. The SAE Fatigue Design Handbook AE-10 introduces some of
these behaviors, as do many books on fatigue. The cyclic stress-strain curve is the
shake-down result of repeated plastic straining. The cyclic stress-strain points
are measured at half-fatigue life where the shake-down or initial transient behavior has ended.

As long as your model follows the cyclic stress-strain curve the life predictions
should be reasonable. A lot of the medium and long life fatigue events in most
vehicles have stress-strain levels in the region around the end of the elastic
behavior zone so it is important that one gets the stress-strain as representative
as possible.

 

[rb1957]

sorry, but there's little value in copying and pasteing the previous post ... we can read it just fine.

another day in paradise, or is paradise one day closer ?

 

[cbrf23]

Gentleman,
Thank you all for the excellent advice, you have confirmed my thoughts and validated the position I took on this matter.

@aerostress82, I believe the image I posted was from a 17-4PH cond H900 curve or a 4130 curve - I can't recall at this point, but since the question was on general practice I'm okay with that

 

[mmar2087]

You are correct about the behaviour in SW Simulation regarding linear behaviour below the first point in the s-s curve.
It ignors input for E-modulus and instead calculates this based on the first point in the s-s table.

Your start point should, as TGS4 mention, be the proportional limit, where the curve deviates from the linear portion.

Using Rp0,2 as the first point, following the red curve, will leave you with a lower E-modulus and incorrect behaviour below this point.
It would also not lead to a residual plastic strain of 0,2% when the load is removed which is what the Rp0,2 limit concerns.

 

[aerostress82]

I had been studying fatigue the last couple of days. So, I can comment better on this problem I hope:
[ul]
[li]For every material, you will have separate cyclic and monotonic stress-strain curves.[/li]
[li]If you are looking at a cyclic fatigue analysis, you are supposed to use the cyclic stress-strain curve. (I think this is your case)[/li]
[li]Monotonic stress-strain curves seem to be only used for a "single loading" on a structure. Your material will be going under cyclic-hardening / cyclic-softening under this kind of loading. Meaning, you will get a higher/lower yield with every monotonic load application on your material.[/li]
[li]One thing to be "very very" careful about is that: There is no such thing like "monotonic yield stress should always be higher than cyclic yield stress" or vice versa. These 2 curves vary depending on the type of the metal (soft metal / hard metal). So, you should be very exact with your cyclic and monotonic stress-strain curves and use them according to your type of loading on the structure.[/li]
[/ul]

Hope these add up to all above comments from me and other fellows.

I would advise you to read a 40-50 page of any "basic" fatigue book for at least metal fatigue. Plastic fatigue is easier than metal fatigue, so you could probably study that one as a next step too. I don't think everyone is perfectly knowledgeable with fatigue even if that's their main expertise. I've seen this before in a main automotive manufacturer company, and it looks scary now when I compare "what I've been guided through at the time by seniors" and "what I have found out about fatigue after reading it on my own at my available time". This would be my final humble advice to you from 1 years' experience in automotive. Good luck!

Spaceship!!


Aerospace Engineer, M.Sc. / Aircraft Stress Engineer with 7 years of experience
(United States)

 

[cbrf23]

With regards to the cyclic loading, this is something I struggled with on this study, but ultimately decided the tensile (monotonic) test was more representative of behavior for this study.
My reasoning is as follows:
Our application involves very low-cycle fatigue (e.g. 2,500-5,000 cycles) at very high stress levels - e.g. straight tensile loading around 65-70% of yield, with localized stresses at contact points, with additional loading from bending, etc. which exceed yield.
Most cyclic fatigue S-S curves are based on high-cycle fatigue (e.g. hundreds of thousands to millions of cycles) at relatively low load.
I was concerned about the lack of information in the plastic region of the fatigue curves I found for the materials I have.
Also, the behavioral difference between low-cycle (generally considered less than 10k cycles) and high-cycle fatigue is fairly well documented for many metallic materials.
From what I can make of the data on the materials I'm working with, these strain hardening/softening effects are not appreciable in low-cycle fatigue cases, and do not have a pronounced effect on fatigue life until you get into higher-cycle applications.
So, given the number of cycles for this particular study, I decided to go with tensile load data, which has the side benefit of being more readily available from more sources, so I can get a more averaged idea of typical behavior.

In a perfect world, I would have S-S data from multiple studies on the cyclic behavior of my materials at exactly the load and number of cycles we need.
But, in the real-world we do our best with the data we have available and try to do our best to make reasonable approximations through FEA.

Also, I have discussed with my VAR the fatigue model used by SW Simulation for fatigue studies and it is based on high-cycle theory, so we don't expect a very accurate prediction of fatigue-life. However, we do think it will give a reasonable approximation for determining relativistic performance between design choices and optimization of design, which is the goal for these studies.

We do laboratory testing to determine actual performance, however I'm looking to use FEA to reduce the cost and lead-times of making multiple prototypes and fixtures, and get to an optimized design quicker using a combination of FEA and real world testing.

Thanks again to all for the participation and insights in this discussion.

 

[realtime2]

Hi cbrf23,
Probably its a bit late to ask, but what is your material?

 

[realtime2]

An example of severe effects on stress-strain behavior due to cyclic
softening:

http://fde.uwaterloo.ca/Fde/Materials/Steel/Sae1045/allsae1045Loops.gif

(Warning 7.8 Mbytes)
The animation is found on this web page:

http://fde.uwaterloo.ca/Fde/Materials/Steel/Sae1045/sae1045.html

It shows the stress-strain loops of a fatigue test that is initially
solely in the elastic region; below the Syield of 1360 mpa (~200 ksi).

It appears that for the first 30 cycles the stress-strain path is all
elastic, but at cycle 40 the loop opens up slightly. Due to cyclic
plasticity the loops keep getting bigger after that.

Such a sequence is an extreme example but would be a real concern for
a hanger rod or a component with no possible load re-distribution paths.
In most structures the fatigue critical point is at a stress concentration where
the plastic strain region is constrained by the surrounding elastic field.
-or perhaps a beam where the outer elements go plastic but the inner elastic
core keeps the surface strains from running away.

It does however show that one needs to be aware of the cyclic stress-strain
curve in a fatigue critical analysis, and to check if one's material will
soften or harden when cycles are imposed.