Local failure assessment of nozzle junctions - weld sharp edges 1

[fem.fan]

Hi, i need to analyze the nozzle junction of a pressure vessel (designed by ASME XIII div. 1) according to appendix 46 (following the steps of div. 2 part 5).
i am using an elastic plastic model.

i´ve searched a lot of threads of this subject but none of them answers my particular inquiry:

when modeling the welds with sharp edges, there is a stress singularity and of course the stress and strains do not converge to a value when refining the mesh. even though for plastic collapse failure mode it is possible to ignore this effect, when analyzing local failure it is problematic, as there will always be large and unrelistic plastic strains that surpass the allowable by the code.
it is not possible to model a fillet radius since it is not known, besides of producing a huge computational cost.

the following image ilustrates the situation.

how can i verify this failure mode in this contion?

thanks in advance

 

[TGS4]

The elastic-plastic method is surprisingly forgiving for poor geometries, including singularities such as what you have modeled.

Have you done a comparison of the averaged and un-averaged plots of SLDR? Is you mesh converged for SLDR? Remember that apparent convergence for stress and stress does not equate to convergence for SLDR.

I wil admit that I have not run into this problem in my 15+ years doing these types of analyses. Don't forget that your load factor for checking local failure is not β, but only 1.7.

 

[fem.fan]

Thanks for keeping the discussion, it´s very enriching.

The mesh is converged only "certain distance away" from the singularity. In this particular example let´s say 0.2 mm, but you will never get convergence on the singularity and it´s near vicinity by definition, the stress and strains grow indefinitely there. This is a numerical problem, no matter what load factor you use.

Remember that i made this simulation only as an example, my concern is general.

 

[rb1957]

How does the 3rd pic relate to the other two ?



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

 

[fem.fan]

SLDR = plastic strains / strain limit

 

[TGS4]

Notch geometries are very real when it comes to Local Failure. The geometry that you used as an example is real when it comes to the inside of a air cooler header box wrapper plate (for example). These locations can actually experience local failure. We can just do our best, and try to follow the guidance in Seipp 2013 with respect to convergence for SLDR.

One additional note - I do not believe that a bi-linear curve is appropriate here. You will need to upgrade your software. But good for you for trying out the elastic-plastic analysis method.

Happy to help in any way.

 

[TGS4]

rb1957 - some things that you might find interesting about this failure mode...

If you go to metal forming (deep drawing, wire extrusion, etc) formulae, you will find very similar equations for strain limits. In conditions of high compressive triaxiality, the strain limit can be many multiples of the uniaxial strain limit. (Think of successively drawing a wire from a rough billet). However, in conditions of high tensile triaxiality, the opposite happens - the strain limit decreases until the material is effectively brittle.

This condition is relevant because in the limit of pure triaxiality, the stress invariant (which is based on the difference between the principal stresses - could be von Mises, could even be Tresca) collapses to zero, even though there are non-zero principal stresses. At the limit of pure triaxiality, when the material is ideally brittle, the stress of interest is no longer the invariant (usually von Mises in a ductile material), but the maximum principal stress. However, you need to be able to figure out when that switch-over happens. The ASME Code has a prescribed limit, defined in Equation 5.6. There have been real failures that can be attributed to this failure mode - hence its inclusion in the ASME Code starting in the 2007 Edition. However, the numerical issue (invariant going to zero) was recognized waaaay back when the ASME Code first introduced Design By Analysis in the inaugural (1968) Edition of ASME Section VIII, Division 2 and ASME Section III.

 

[rb1957]

I haven't thought much about this detail, but I would have thought that the differences between parent metal, weld filler, and heat affected zone would be (in reality) more significant than the precise geometry of the toe of the weld.

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

 

[fem.fan]

TGS4 - i´ve been thinking and the problem was "solved" because it was a 2D plain stress simulation and consequently the triaxality too low. so i gave a third dimension to the problem and a pressure of 100 MPa (i chose this value trying not to produce generalised plastic strain) and as i expected, in the singularity the SLDR is greater than 1. you can see tha this happens only there because the plastic strains and stresses are unreallistically large.

SLDR

Plastic strain

limit strain

the same with 3mm radius

SLDR

plastic strain

limit strain

 

[mskds545]

fem.fan,

I'm late to this discussion, but I've run into this as well. I once ran a model of a lightly loaded sharp inside corner down to an absurdly fine mesh size and found that the stress and plastic strain increased slowly and steadily at an increasing rate with diminishing element edge length, but the plastic strain is extremely localized. I generally ignore this unless there are more generalized triaxial stresses in the area.

Of course, sharp inside corners in ugly welds do cause failures. Typically undercut, overlap, convex fillets, moreso than sharp toes on 45 degree fillets. My advice is that you focus on getting good welds, and don't worry too much about the numerical singularity. If there is a larger volume that is near the strain limit, I might grind the weld toe to make sure I get a smooth transition. If it's a critical service, I might also do a fracture mechanics calculation to understand how likely a crack is to run from the weld toe. Fracture mechanics is better suited to dealing with the singularity.

-mskds545