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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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Like Reply privatelyFlag as inappropriate 14 days ago
Vlad Lappo, P.Eng., M.Sc.
Mechanical Engineer, Teng Inc
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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Like Reply privatelyFlag as inappropriate 14 days ago
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.
Like Reply privatelyFlag as inappropriate 13 days ago
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.
Like Reply privatelyFlag as inappropriate 13 days ago
Vlad Lappo, P.Eng., M.Sc.
Mechanical Engineer, Teng Inc
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.
Vlad Lappo, P.Eng., M.Sc.
Mechanical Engineer, Teng Inc
Thank you gentlemen,
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Like Reply privatelyFlag as inappropriate 13 days ago
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.
Like Reply privatelyFlag as inappropriate 12 days ago
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.
Like Reply privatelyFlag as inappropriate 12 days ago
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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