discussion - stress strain curve

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Stress-strain curve ANNEX 3.D

Vlad Lappo, P.Eng., M.Sc.

Mechanical Engineer, Teng Inc

Dear members,

I would like a few clarifications about creating a stress-strain curve in accordance

with Sec VIII Div II ANNEX 3.D for elastic-plastic analysis.

1. Is it applicable for kinematic or isotropic hardening (or both).

2. How do you built up the curve to put in a typical FEA software? Do you just enter

SIGMA_t vs.EPSILON_t as a multilinear curve? What is the applicability range (i.e.

zero to true ultimate tensile stress (UTS_t), YS to UTS_t. ASME PTB-3 Example

E5.2.3 Elastic-Plastic Analysis starts with YS and zero strain!?

3. Is it important which yield criteria a given FEA uses to apply the entered stress-

strain curve? (I.e. ANSYS uses von-Mises yield criterium).

4. While I use ANSYS it seems that Abaqus Knowledge Base Answer 3099

describes the details of implementing the cyclic stress-strain curve with kinematic

hardening. Is it possible for some one to share it just to familiarize with the

application?

Also, performing some initial testing with sample plasticity I find that AFTER adding

plasticity achieving convergence becomes more difficult. Can anyone having some

hands-on experience with modeling elastic-plastic behavior in FEA comment on what

causes the lack of convergence and provide any remedies (mesh refinement, higher

order elements, any other solver settings, etc).

Kind regards,

Vlad

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After reviewing and comparing, it appears that Sec VIII Div II ANNEX 3.D provides the complete

true stress/true strain curve including the elastic part. However, a typical FEA software such as

ANSYS (and possibly ABAQUS) require a different data input for plasticity. The following

paragraph was taken from the ANSYS manual describing the multilinear isotropic hardening:

"You must supply the data in the form of plastic strain vs. stress. The first point of the curve must

be the yield point, that is, zero plastic strain and yield stress. The slope of the stress-strain curve

is assumed to be zero beyond the last user-defined stress-strain data point. No segment of the

curve can have a slope of less than zero."

I tried reproducing the data from ASME PTB-3 Example E5.2.3 Elastic-Plastic Analysis using the

equations of ANNEX 3.D; however, I don't arrive to the same values of strain.

I did notice that in Example E5.2.3 for higher stress values the strain becomes close to GAMMA_1

+ GAMMA_2 - EPSILON_ys but it appears to be some other parameter(s) that I am missing in

order to convert the stress/strain data into the format required by the FEA programs...

Also, any idea on how Tangent modulus comes in all this? Is it for the purpose of defining bi-linear

elastic-plastic curve only?

Thanks!

Trevor Seipp, P.Eng.

Division Manager and Consulting Engineer at Becht Engineering

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the plastic strain is greater than 1e-6. (You certainly don't want to use the engineering yield,

because that already assumes 0.2% plastic strain, which is far too far beyond the proportional

limit.) THAT is the point of "first yield" that I input into my multi-linear curve. I generally

recommend using increments of true stress of no more than 500 psi in order to capture non-linear

behaviour in the curve. You have to understand whether or not your software requires total strain

or plastic strain, because the equations in Annex 3.D give total strain. If your software requires

only plastic strain, then you will need to subtract the elastic strain.

Don't worry about the tangent modulus - it's merely the instantaneous derivative of the curve itself.

It's not used (yet) in Part 5.

For an analysis per 5.2.4, I generally use isotropic hardening, because I am expecting large

deformations/strain due to the factoring of the loads. Note that kinematic hardening is more

appropriate when the deformations/strains of small. Kinematic hardening is explicitly called out

when doing an elastic-plastic ratcheting assessment.

As far as which yield criterion to use - the Code is very explicit calling out the von Mises yield

function and associated flow rule (5.2.4.4, Step 3).

Are you actually doing elastic-plastic fatigue? If not (and frankly most people don't really need to)

then I wouldn't worry about implementing the cyclic stress-strain curve. Get the monotonic curve

working right first.

Unless you have an absolutely good reason to do otherwise, I would use 2nd order (quadratic)

elements. You mesh needs to be sufficiently refined so as the results are effectively independent

of the mesh (that really goes without saying for any FEA...). As far as convergence is concerned -

the failure point is determined by the lack of convergence, so it's difficult to say whether or not

your issue is a setup issue or a a real issue.


Patrick Marcotte

Sr. Engineer, Piping & Pressure Vessels at PVP Engineering Ltd

Top Contributor

Unless there is some quirk in your software, it does not matter whether you use isotropic or

kinematic hardening for evaluating monotonic collapse. Isotropic hardening increases the yield

stress in both tension and compression if the yield point was exceeded in the previous cycle. So

for cyclic analysis with significant stress reversal, isotropic hardening can be considered un-

conservative. Kinematic hardening is a conservative simplification of the bauschinger effect.

If you use the cyclic stress strain curve, then you are assuming that you have accumulated

enough cycles and plastic strain that your material is now stable. This is not appropriate if you are

running a cycle by cycle analysis. On the other hand, the cyclically stable curve is useful for

material behavior at the tip of a crack, owing to the large but localized plastic strains (which is why

it is used in the welded fatigue curve).

Unless there is some geometric weakening (e.g. something akin to a p-delta effect), then I would

suggest running a lower bound collapse analysis (small displacement/small strain/elastic-perfectly

plastic analysis... also referred to as material nonlinearity only). This is far easier to apply than

elastic-plastic. You may even choose to perform both limit and elastic-plastic.




Thank you Trevor,

I am curious about your approach of defining the plastic strain at somehow arbitrary value (1e-6 in

your case). What are the repercussions? Material becomes plastic at lower stress. Hence, there is

more plastic strain developed for a given load. Also, it follows closer the curvature of the stress-

strain curve at the knee region. This results in the smaller area under the curve (i.e. less energy).

The effects will be diminishing for large plastic strains. Also, the fact that ANNEX 3.D uses

EPSILON_ys=0.002 explicitly does it imply that the Code whats users to use this point as a

starting point for plastic strain while I can see that this would miss a part of the knee of the stress-

strain curve?

The elastic strain at any point seems to be just the unloading from the given stress to zero along

the initial Young modulus (i.e. SIGMA_t / E) which is the first term of the EPSILON_t equation.

With regards to von-Mises failure criterium, I understand that it is required by the Code; however, I

am a bit confused by the definition of SIGMA_t in ANNEX 3.D where it can be any of the

membrane, membrane plus bending, or membrane plus bending plus peak. I was more puzzled

by which of these a specific software would use and I suppose it would be better to clarify this with

the software documentation.



Thank you gentlemen,

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I suppose I will clarify that I am not doing the analysis of a pressure vessel. I am using the

edge settlement where plastic deformation has taken place. Therefore, I feel that isotropic

hardening model is applicable. I don't perform any fatigue or cyclic loading evaluation in this case.

My main objective is to model the as found conditions as close as possible, evaluate the existing

stresses/strains and come up with safe margins. I am not looking at any crack propagation either.


Patrick Marcotte

Sr. Engineer, Piping & Pressure Vessels at PVP Engineering Ltd

Top Contributor

Well an additional concern you may have with using the annex 3d curves is whether there is also

some work hardening present due to the fabrication. You may need to offset the yield point.

Also if the edge has in fact settled very locally, I would also give consideration to the local failure

criteria. There is both a gross structural discontinuity and a plastic strain concentration, elevating

your chance for local failure. The net effect of which is to reduce your available ductility.


Trevor Seipp, P.Eng.

Division Manager and Consulting Engineer at Becht Engineering

Vlad - compare the curves yourself in an Excel spreadsheet. Plot the full curve from the equations

in Annex 3.D. Then, plot the curve as if you had zero plastic strain at the engineering yield, and

your plasticity only kicked in at that point. When I do that, the latter curve plots above the full curve

(which would be unconservative). I chose 1e-6 as an arbitrary value - at that value I can't visually

distinguish the full curve from my truncated curve. 1e-5 doesn't make that much of a difference

either. At 1e-4 I start to visually see a difference in the curves. The important part is to use the

proportional limit and not the engineering yield.

From my experience, there is not advantage whatsoever to using the Limit Load analysis method.

You can't check Local Failure (triaxiality-based strain limits), and you can't use it to check for

buckling. Furthermore, the magnitude of displacements and strains have no physical meaning,

and therefore cannot be used to evaluate limits on those variables.

Patrick, the methodology in FFS-1 does not recommend adjusting the engineering yield due to

work hardening. In fact, in PTB-1 it says that the curves in Annex 3.D (or the identical

methodology in FFS-1) for carbon steels don't show the typical yield plateau due to the assumed

work hardening - i.e. no further modification is required. Besides, the point in not to determine the

as-fabricated stress state and superimpose the design loads on top - the process is to evaluate

the factored design loads alone.

Patrick, you also said previously "If you use the cyclic stress strain curve, then you are assuming

that you have accumulated enough cycles and plastic strain that your material is now stable. This

is not appropriate if you are running a cycle by cycle analysis." However, 5.5.4.2, Step 4 clearly

states "For cycle-by-cycle analysis, constant-amplitude loading is cycled using cyclic stress

amplitude-strain amplitude curve." Do you believe that there is something wrong with the Code

approach?

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