Excluding Peak Stresses From FEA Results 5

[Paulettea]

Dear All

As per ASME BPVC Sec. VIII-2 Par. 5.5.6 in order to perform ratcheting analysis using an elastic method, it is necessary to calculate primary plus secondary stress range and peak stresses must be excluded in the process. When the FEA results of a linear elastic model are available, the software does not exclude any type of stress. In fact, the software does not have any idea about peak stresses or stress categories at all. Is there any trick to understand what portion of stresses belong to stress concentrations?

Furthermore, for protection against plastic collapse there is a need for separation of primary and secondary stresses. The code clearly mentions that this process of stress categorization needs significant knowledge and judgement. Here again obtaining FEA results seems to be an easy part of the story and the troublesome stress categorization is a main issue. However, I need to know if there are guidelines in order to do stress categorization after obtaining FEA results. What are the tricks if there is any?

Warm Regards

 

[Paulettea]

But elastic shakedown is ensured by ratchet analysis. do you mean something other than that?

 

[TGS4]

Passing a ratcheting assessment does not necessarily mean elastic shakedown. You could still have stable cyclic plasticity (and hence no ratcheting), which requires a modification of the fatigue analysis.

 

[MrPDes]

TGS4, for such a hole I wouldn't expect "Plastic Collapse" to be the mode of failure as you suggest. Plastic collapse is typically the principle mode of failure in regions of dominant Pm or Pb.

If an analysis revealed an SIF at the edge of the hole greater than 4 (i.e. PL/Pm > 4) then the equipments design would fail the "local failure" rules. However I don't predict this will be the principle mode of failure either.

As the region immediately adjacent to the hole is primarily PL, I would expect the principle mode of failure to be "Excessive Plastic Deformation" which occurs local to the hole. If an analysis revealed an SIF at the edge of the hole greater than 1.5 (i.e. PL/Pm > 1.5) then the equipments design would fail due to "Excessive Plastic Deformation".

Although not the definition of the code, it could be argued that "Excessive Plastic Deformation" is a local (or maybe regional) failure as it does not cause unbound "plastic collapse" on a single cycle, (however it doesn't shake down under repeated cycles).

My understanding is that:

Pm < S protects against Plastic Collapse.
PL < 1.5S protects against regional "Excessive Plastic Deformation".
PB < 1.5S protects against Plastic Collapse. (Not applicable to the hole as there isn't any PB)
PL + PB < 1.5S protects against Local "Excessive Plastic Deformation" and Plastic Collapse depending on if PL or PB is dominant.

 

[TGS4]

MrPDes, your understanding is quite flawed. Hopefully this will help you and Paulettea (who would likely benefit greatly from a training course, as well).

Local failure, as defined by the ASME Code, relates to two phenomenon: one mathematical and one physical. However, both occur in situations of high triaxiality - that is where the principal stresses are close to the same. Mathematically, the invariant (von Mises or Tresca doesn't matter) depends on the differences between the principal stresses. So, when S1=S2=S3, what is the invariant? It's zero, regardless of the magnitude of S1=S2=S3. That's a problem, because our detection of the onset of plasticity in our multi-axial world depends on the invariant exceeded yield. Physically, the phenomenon is that as the trixiality ratio increases (and the triaxiality ratio is defined as the algebraic average of the principle stresses divided by the invariant), the limiting plastic strain decreases. So, at a triaxiality ratio of 1.0 (essentially uniaxial), the strain limit is equal to the uniaxial strain limit. However, as the triaxiality increases, the plastic strain limit decreases exponentially. For example, a SA516-70 at room temperature, with a yield of 38ksi and an ultimate of 70ksi, the allowable plastic strain at a triaxiality ratio of 1.0 would be 2.294e-01, at 10.0 would be 3.313e-03, and at 30.0 would be 2.694e-07. Essentially, a ductile material, in a state of high triaxiality, behaves in a brittle manner.

As an aside, please note this quotation regarding the elastic analysis method for Protection Against Local Failure from ASME PTB-1 (2014)

Two issues that are apparent are: the use of an elastic stress basis for a local criterion, and the stress category that is used with this criterion. It is not apparent how pseudo elastic stresses, i.e. elastically calculated stresses that exceed the yield strength, can be used to evaluate a local fracture strain of a ductile material with strain hardening. In addition, the type of stress used in the criterion (i.e. linearized or average values verse stress at a point) and stress category (i.e. primary, secondary and peak) needs to be resolved. ... For ductile materials, a local criterion based on elastic analysis may not meaningful and the elastic-plastic method that follows is recommended for all applications.

Plastic collapse, on the other hand, is related to all things local (pay special attention to 5.2.2.2(b)(1) and (2)) and global as far as plastic deformation and excessive plastic deformation goes. The "elastic analysis method" of linearizing, classifying and categorizing pseudo-elastic stresses (that exceed the proportional limit) for comparison with factors on an allowable stress basis is approximate, at best, and the Code assures us that the limits to these pseudo-elastic stresses are conservatively set so as to make this approximate method conservative. ALL of the limits that you listed are with respect to plastic collapse. If you understand that primary bending typically occurs only in flat plates, then you will better see the historical rationale behind the limits. But they are all related to plastic collapse.

In this specific case, whether or not one could classify the stresses at such a hole in a cylinder under axial tension as primary or not (I would argue not, as described in one of my previous posts) would determine whether or not the stresses in the immediate vicinity of such a hole would lead to plastic collapse.

Unfortunately, other than experience, there is no good guidance on how to perform such categorization. Hence 5.2.1.2.

For components with a complex geometry and/or complex loading, the categorization of stresses requires significant knowledge and judgment. This is especially true for three-dimensional stress fields. Application of the limit load or elastic–plastic analysis methods in 5.2.3 and 5.2.4, respectively, is recommended for cases where the categorization process may produce ambiguous results.

 

[victorpbr]

Excellent explanation TGS4. I'd like to thank you for that. I did some searching and saw a lot a posts where you mention that elastic-plastic analysis is more suitable than the elastic method, this post helped me visualize why and made me more interested on learning it.

Like you suggested for Paulletea, I reckon I also need some training on this matter, however could not find any near where I live, so I have to go with self-studying for now. Apart from the code, do you have any references you can recommend on elastic-plastic analysis for pressure vessels?

 

[TGS4]

You're welcome.

Regarding training, I see that you are in Brasil. Unfortunately, I am not aware of training locally, either, and there is not any self-study courses that are specific to this material.

That leaves you with three options: bringing the trainer (such as me) to you/your company, organizing a "public" course by bringing in a trainer (such as me) to your locale, or attending virtual training. This year, my training course had one virtual attendee - it consists of viewing the course in real time over the internet. The feedback was excellent, and would be a good option if the other two are not viable.

 

[MrPDes]

TGS4,
I am fully aware of the concept of local failure, however I visualise it geometrically rather than mathematically. Local failure is prevented because the stress extends through the wall of the yield surface or the sum of the Principal stresses is limited to 4S. This 4S limit has the effect of placing a dome on top of the Mon mises yield cylinder with a radius of 4S and centred at the origin. In the case of the hole in cylinder, the stress (even if there is a SIF of greater than 4) extends through the wall of the yield cylinder resulting in a yield type of failure.

In terms of your interpretation of the limits of "plastic collapse" and "Excessive Plastic Deformation", there is some confusion.

Unbounded collapse is the principal failure mode for locations of pure general membrane stress (Pm < S) and for pure Primary Bending (Pb < 1.5S) such as your suggested example of the bending at the centre of a flat head.
However, locations of local membrane stress fail exclusively due to "Excessive Plastic Deformation". Unbounded collapse does not occur local to this hole or a nozzle. Even if this hole was in a pressure vessel and had a sealing plate and O-Ring pushing outwards to seal the hole, "Excessive Plastic Deformation" would be the failure mode.

victorpbr,
Unless you can't tell, I am largely self taught. As demonstrated in TGS4's explanation, sometimes the two terms collapse and excessive plastic deformation are used interchangeably, without clear relation to a failure criterion. ASME VIII seems to wrap up both failure modes under the umbrella term "Plastic Collapse", however as explained they are different and are applicable to specific stress categories. Hence why S is the minimum of Su/3.4 (protection against collapse) and Sy/1.5 (protection against excessive plastic deformation).

I attended an ASME VIII Div 2 refresher course recently where I had about 90% of the knowledge of the teacher and the teacher had about 70% of the knowledge that I have. There was a second student who also knew more than both of us. They are good opportunities to exchange knowledge. A great aspect of the course was that the teacher taught allot of it using ANSYS software. Otherwise in terms of resources I would suggest the following:
WRC 429 1998 - 3D Stress Criteria - Guidelines for application, is a good resource that provides allot of detail on collapse and excessive plastic deformation and the how the different stress categories (Pm, Pb, PL) effect them. WRC 429 doesn't address local failure.
The ASME PTB manuals also provide allot of nuggets of info, however they do tend to use umbrella terms and say a bunch of factors are combined into a single factor. ASME PTB-1 2014 Section VIII Div 2 - Criteria and Commentary provides allot of references to other WRC bulletins to learn more.
Pressure Vessel Design : Concepts and Principles by Spence, J.; Tooth, A. S. is the best text book I have come across.

 

[TGS4]

Unfortunately, your "understanding" of local failure is incorrect. A refresher in PTB-1 should be a good start. Elastic stresses and local failure just don't mix.

 

[victorpbr]

TGS4, Did not knew the possibility of taking the course over the internet, I'll seriously put some thought on doing it next year. First I'll get more familiar with this Division of the code in order to have a better understanding.

MrPDes, Thank you for the references, exactly what I was after, I will start next week studying them.

Regarding learning methods, in my opinion the best scenario is a combination of both, first some self-study, then a training to improve the first understandings and then more self study continously, there is always something new being published.

Thank you guys, You'll probably see some posts of mine regarding this subject soon.

 

[Paulettea]

TGS4, that was a great post there.

fortunately, (maybe unfortunately) this thread brought up other issues. I wanted to ask this question in a separate thread but now I ask it.
By my understanding the local failure is a point phenomenon. I mean when you compare local failure with plastic collapse there is a clear physical difference. If a point in a component reaches yield stress it does not necessarily indicate the collapse of the whole section since the very adjacent points still can carry loads and may be far from yielding. Therefore, we consider a line through thickness of the section and argue that if the average value of stress over this line exceeds yield then there will be a plastic collapse.

Local failure on the other hand is a very different story. If the limit on the sum of principle stresses is exceeded in any point (as opposed to a line or a section) a crack will develop at that point. This is totally independent of the state of the stress in adjacent points. It is even independent of the source of the stress. I mean it does not matter if the stress is primary or secondary stress. However, the code statement on the limit on the sum of principal stresses does not make sense to me:

Elastic Analysis – Triaxial Stress Limit. The algebraic sum of the three linearized primary principal stresses from Design Load Combination (1) of Table 5.3 shall be used for checking this criterion.
σ1+σ2+σ3<4S

Why shall we exclude secondary stresses in this check. If it was about plastic collapse I could agree with that since secondary stresses are not load control and by some straining their magnitude can be reduced. But here when we talk about local failure there is nothing special about load control or displacement control and a crack will develop at the point of failure

 

[TGS4]

Pauletta - please see my quote above from PTB-1. The consensus is that the rustic analysis method for local failure is mostly bunk. Unfortunately, we haven't found a better way to treat it, so the 50 year old version persists, in the face of contrary evidence. But, that's how the Code goes.

 

[Paulettea]

TGS4, I read some paragraphs in PTB-1 regarding what you said. I saw something in the text that was very strange to me.

σ1+σ2+σ3<4S[/sub]-----------(5.23)
In Old VIII-2, Equation (5.23) is used as a limit on the sum of the linearized primary stress. In VIII-2, the same criterion is used and is categorized as a means to prevent a local failure; high hydrostatic stress reduces the fracture strain of a material.
It should be noted that in VIII-2 and Old VIII-2, the criterion of Equation (5.23) is based on linearized primary stress whereas in VIII-3, the criterion is based on the primary, secondary, and peak stress at a point. In addition, the criterion in VIII-3 is slightly different as shown in Equation (5.24).
σ1+σ2+σ3<2.5σ[sub]YS[/sub]-----------(5.24)

I am not familiar with VIII-3, actually I have never used it at all, but I know that there may be some difference in the design margin for the allowable stresses. It is also possible that different approaches can be used in different divisions of the code that is understandable. What I cannot understand is that in VIII-2 the same criterion is used as that of VIII-3 but with a method which seems to be wrong.

The material of construction in a vessel does not understand that I am using VIII-3 or VIII-2, it simply follows laws of nature which seems to be represented in a better mathematical form in VIII-3.

Are the people who are working on VIII-3 different from those working on VIII-2? At least they can share ideas.

 

[TGS4]

It should be noted that VIII-3 has retired ALL of their elastic methods to an appendix and removed them from the text proper. That is because they are essentially inappropriate. And that includes the limit of the sum of the principal stresses.

I should note that in the original (old) Div 2, this limit was implemented "for completeness". It was too address the numerical issue only and was not intended specifically for this failure mode. The Code Committee responsible for Part 5 debated this topic heatedly and for a long time without any suitable resolution appearing. We still have it on our agenda, but we have all agreed not to discuss it until we have adequately handled every other issue, including world peace.