Elastic-plastic (EP) analysis 3

[salmon2]

All,
I understand and am quite familiar with stress linearization and categorization with linear-elastic analysis. Only did couple nonlinear/EP analysises before. I like stress linearization as it allows me to interpret linear FEA results in a reasonable way.

I am wondering what is the principal rationale which excludes EP analysis from stress linearization? What if I still use stress linearization to process EP streses?

Thanks.

 

[TGS4]

The biggest issues that I have with stress linearization is:
- where to put valid stress classification lines?
- how to properly classify the stresses (primary, secondary, membrane, bending, etc)?
- what if the linearized stress results are ambiguous?

The absolutely fantastic thing about elastic-plastic analysis using a factored load approach is that you don' have to do any of that. In fact, the post-processing is so minimal, he only question that you'll ask yourself is "why didn't I do this sooner?"

The whole thing about stress linearization is that it assumes a linear-elastic stress-strain curve. When you use a LRFD (Load and Resistance Factored Design) approach, you are using the actual stress-strain curve to see exactly what load margin you have on plastic collapse. You factor the loads (that's your margin), and see whether or not the structure collapses. The post-processing consists of:
a) Did it collapse (and by collapse, I mean did the finite element analysis solution converge to a statically-permissible solution) prior to the required factored load? If yes, then the loads/structure is unacceptable, if no, then everything is fine.
b) Check for any serviceability-criteria displacements
c) There isn't even a c)... ;-)

So, why would you even want to bother with the hassle of linearizing factored EP results?

 

[salmon2]

Thank you - TGS4.

1) can you please elaborate more on this "Did it collapse (and by collapse, I mean did the finite element analysis solution converge to a statically-permissible solution) prior to the required factored load"? I guess I am still confused with definition of "collapse". Maybe you can point me to the artical # in ASME VIII, div 2, part 5 about EP analysis criteria.

In API upstream where I am working, collapse for pipes means under external pressure and there are elastic collapse, plastic collapse and transition collapse. Load with internal pressure is called "burst". And I assume you term any failures with "collapse"?

2) Do you happen to know the thin walled theory and thick walled theory? I read somewhere that Div 2 is only appropriate for thin walled pipes, and thick wall should use Div 3. Do you agree with this?

I understand manual calculations usually base on thin wall assumption. But wether wall is thin or thick should NOT matter for FEA in my opinion, esp EP FEA.

3) So you have to have true strain/stress data for EP FEA. How do you get that usually?

Typical tensile tests only give you several points by ASTM E8. I tried to get the full load/displacement curve from labs at an extra cost, but one could only convert engineering strain/stress to the true ones up to the necking point, not the fracture point. This is because when the necking begin to happend, it becomes a 3-dimensional stress field. Do you have experience with this?

 

[TGS4]

1) 5.2.4.4, Step 5, as well as 5.2.4.3(a). The failure mode in 5.2 is called plastic collapse. It is different than buckling (although I highly recommend using the EP method for analyzing buckling). Burst, in this terminology, is a form of plastic collapse.

2) Yes, I am very familiar with both thick-walled and thin-walled theory. Note the caveats for the elastic stress analysis method in 5.2.1.3. EP is fine for the whole range - in fact Div. 3 prefers EP.

3) Per 5.2.4.4 Step 3, you obtain the true stress-true strain curves(s) from Appendix 3-D.

Your last point is the reason that we have the local failure criteria - in states of high-triaxiality, the ductility will decrease, such as post-necking.

I will also note that the EP analysis methodology is the exact same between Divisions 2 and 3 - on purpose.

Feel free to come back and ask more questions.

 

[salmon2]

TGS4 - I took me a while to check the references and understand. Thank you so much and obviously you are the man for ASME. A huge star for you.

Several followingup questions:

1) about true stress and strain curve, I read annex 3.d as that after necking, perfect-plastic shall be assumed, right? Which is conservative and fine to me.

2) Can you construct a true strain/stress curve from a standard tensile test (no temperature considered)? If not, what is the procedure and is it normal for outside mechnical labs?

2) What values or code do you use to factor your load? I don't see any in ASME Div 2.

3) Do you usually do ratcheting analysis? Which route do you go?

4) So the only difference between div 2 and 3 is that div 3 requires fracture mechanic if both use EP FEA?

5) Time wise, which one is more efficient between elastic and EP analysises to you? Honestly I can run many elastic cases, many iterations, in one day (correct or not, I don't know), while a EP or non-linear analysis will take good couple days for me. But I am far more familiar with elastic than EP.

 

[TGS4]

1) This is not entirely correct. The divergence between the engineering stress-engineering strain curve and the true stress-true strain curve is that after the initiation of necking, the engineering curve has a negative slope, whereas the true curve maintains a positive slope (the stress is updated based on the reduced area). However, after the true ultimate stress is reached, then the stress-strain curve becomes perfectly plastic.

2) I suppose that you could, but for ASME Code purposes, you are required to use Annex 3-D. For converting from engineering to true, I wold consult a Strength of Materials textbook.

2) As described in 5.3.3.1, Step 1, you are to use the load case combinations (and subsequent load factors) from Table 5.5.

3) Absolutely I always perform a ratcheting assessment (as it is required by Code for all components and cannot be exempted. I prefer the E-P method in 5.5.7.

4) Division 3 has different load factors.

5) Time wise, I find the E-P method vastly superior. The minimal post-processing time compensates for the added computational time. And, I can run the computer overnight... The added pre-processing time consists of adding the full stress-strain curves. When you apply the loads, it's the same effort, only you apply a load factor.