ASME VIII, division 2 -> Local failure 2

[Pierrelouis]

Good afternoon all,

Some questions about the Part 5, Design By Analysis :

1. For protection against Local Failure, do we need to considered load case combinations for test conditions when using Elastic and Elastic-Plastic method ? Or only the ones for Design conditions or required to evaluate protection against Local Failure ?

2. Our pressure vessels does not buckle because of internal pressure. Is there a paragraph in ASME which allows to avoid/justify that protection against Buckling is not applicable ?

Many thanks

 

[TGS4]

1) 5.3.2 is very clear about which load combination to use for the elastic analysis method. 5.3.3.1, Step 1 is also very clear about which load combination to use for the elastic-plastic method. It is not required to demonstrate protection against local failure for the pressure test condition.

2) Even under internal pressure, compressive stresses can exist (for example in the knuckle of a formed head). If you can confirm that there are no compressive stresses (remember the admonition in Table 5.3 or Table 5.5 that the load combinations include consideration for some loads not being active), then you satisfy 5.4.1.1.

 

[fraccionadora]

TGS4 hi,i want to ask something related to local failure criteria.
I understand that Von mises theory measures the shape distortion and does not limit the sum of principal stresses, a hydrostatic stress state does not produce shape distortion and von mises stress regardless of how high the magnitude of the principal stresses, but displacement occurs. If my interpretation is not mistaken until that point, elastic local failure criteria limiting the sum of principals which von mises do not account for. Is the purpose of elastic local failure criteria to limit the displacements caused by a stress state similar to the hydrostatic stress state? That does not make sense to me name this failure mode as local failure and i feel like i am missing something or maybe looking from wrong point of view. Could you please share your comments? Thanks.

 

[NRP99]

fraccionadora

This link might help you understand more about local failure.

The sum of principals stress limit is nothing but limiting high tri-axiality=(s1+s2+s3)/3 or hydrostatic tension due to tensile plus hydrostatic state of stress encountered at and around notches/geometry changes.

It is preferred to take elastic-plastic analysis route rather than elastic analysis to check local failure mode due to presence of plastic strains.

 

[DriveMeNuts]

My understanding is that if you have a component that experiences little Triaxial stress when apply loads to it, then the conventional Plastic Collapse Von Mises stress/Stain limits are adequate to predict failure.

If the same component experiences substantial Hydrostatic tension when loads are applied, then the conventional limits Plastic Collapse Von Mises stress/Stain limits do not predict failure accurately.

Where a local region on a component has large triaxial Tension stress, the Plastic Collapse method doesn't work. A separate failure predicting method that considers the relationship between Von Mises and Triaxial is required.

From the Local Failure equation for Elastic-Plastic analysis, there is a material factor that makes 304 and 316 Grade Stainless Steel far superior to any other material. Would this be due to the cold stretch properties of these materials? Where when they are cold-formed, the material work hardens and thins uniformly. With Carbon Steel, the material quickly forms localised work-hardened regions and isolated patches of run away thinning which results in a faster failure. Correct me if I'm wrong?

It seems like Local Failure is an extension of the Plastic Collapse method because the PC method doesn't cover all bases. As a result, could the Elastic-Plastic Local Failure Method be applied without the need for the Plastic Collapse analysis? Perhaps the Local failure method is too approximate for now, and a future more advanced variation may work?

 

[BJI]

It seems like Local Failure is an extension of the Plastic Collapse method because the PC method doesn't cover all bases. As a result, could the Elastic-Plastic Local Failure Method be applied without the need for the Plastic Collapse analysis? Perhaps the Local failure method is too approximate for now, and a future more advanced variation may work?

Not really, although the initiation of rupture would be due to the state of triaxial stress. It is a fracture failure mode, whereby the loss in ductility leads to failure at lower stress levels than would be indicated by the PC method. It requires some form of stress concentration to initiate the localised triaxial stress state. So it isn't that the EP method is approximate, rather there are only very specific applications where it will actually be limiting. It is actually quite a rare failure mode, so most codes don't include such methods. However, it is always included (or should be) in strain based acceptance criteria and is also included in the form of localised stress/strain limits in some other codes (usually more approximate). I like that for completeness ASME opted to include a method, rather than leave it up to the designer, however, it is highly sensitive to mesh refinement. In most cases where I have suspected local failure to be a possible failure mode, I have found that I needed to refine the mesh significantly (unrealistically) to get it close to failing the criteria. Same goes when using a damage material model in FEA.

For related reading I would look into fracture mechanics, specifically the triaxial stress state ahead of the crack tip and plane strain conditions; damage initiation failure material models (prior to damage evolution not covered by VIII-2) and notched bar local failure testing.

Perhaps using a facture mechanics approach would be more suitable to handling the singularity stresses at notch locations, provided a suitable fracture toughness could be correlated to the sub-surface triaxial stress state. Interested to hear what others think?

 

[NRP99]

It is actually quite a rare failure mode, so most codes don't include such methods. However, it is always included (or should be) in strain based acceptance criteria and is also included in the form of localized stress/strain limits in some other codes (usually more approximate). I like that for completeness ASME opted to include a method, rather than leave it up to the designer, however, it is highly sensitive to mesh refinement. In most cases where I have suspected local failure to be a possible failure mode, I have found that I needed to refine the mesh significantly (unrealistically) to get it close to failing the criteria. Same goes when using a damage material model in FEA.

You are right. The local failure mode is rare type (brittle) failure which is possible in scenario where there is hydrostatic tension causing plastic deformations to the extent of local rupture in region of notches/geometric changes. But outside this local zone there are no plastic strains (due to low level of tri-axiality) or stress levels are even elastic.

The logical thinking behind not including this failure mode in structural components is that this failure mode requires complex stress distribution like pressurized components and the historical successful experience of classical analytical calculations driven design which was prevalent before the FEA came to existence. It is strange that quantification of local failure requires only FEA. That is why most of the codes(structural codes like AISC, Eurocode etc) excluded it (Because either design is by formula or by limit analysis).

Honestly, I do not know much about fracture mechanics but lot of tests conducted on notched bar specimens showed global failure mode (yielding) which makes it even more difficult for ductile materials to fail by local failure. And I think the "notch strengthening" of region may be the reason for it. I guess but not sure though, materials that are prone to brittle fracture due to outside factors such as complex stress state, temperature and high rate of loading which may cause the strains inside tri-axiality zones going beyond critical fracture strains are probably fail by local failure mode. And hence this is rarely case for structural components when loads are producing only yield strains, temperature is not at alarming level and presence of dynamic loads is minimal.

 

[TGS4]

(Sorry for the long delay in responding - I have been on vacation)

BJI and NPR99 have it mostly right. The local failure mode is a rare but real failure mode related to loss of ductility.

There are two phenomenon going on:
1) Our method of relating multi-axial stress states to the uniaxial stress state for ductile materials is through the von Mises yield criteria (the pre-2007 VIII-2 and the current III use(d) Tresca). In that formulation, the invariant used relies on the differences between the principal stresses - in a square root sum of the squares of the differences for von Mises and the max difference for Tresca. Either way, in a state of pure triaxial stresses, the difference are zero and the invariant becomes zero - regardless of the magnitude of the individual principal stresses. This leads to a numerical breakdown of sorts.

2) In a state of high triaxiality, the material will behave in a more brittle fashion. Of course, this switches failure criteria from von Mises to Max Principal Stress - although the switch-point is difficult to pin-point. So, the elastic-plastic rules in 5.3.3 capture this aspect by limiting the actual calculated plastic strain to the so-called limiting plastic strain that captures the transition from ductile-to-brittle behaviour.

2a) One interesting aspect of this behaviour is that if you reverse the sign of the triaxiality (and make it compressive instead of tensile), the maximum multi-axial strain can exceed (and in some cases vastly exceed) the uniaxial strain limit. Of course, this is phenomenon that occurs curing most metal-forming activities such as deep-drawing and wire-drawing. Metal forming textbooks will have an identical strain limit equation to what is in 5.3.3 - but with the expectation that the triaxiality will be compressive, leading to greater forming capability.

So, this phenomenon is part of continuum. In a manner of speaking, it is an extension of Protection Against Plastic Collapse, but it is more than that.

This failure mode needs tensile triaxiality to occur. In general pressure vessels and structures, with thin walls, the stress state is at best biaxial, with the third direction principal stress being between zero and negative the internal pressure.

If you wish to bring fracture mechanics into the picture, remember that in fracture mechanics, the stress direction of interest is normal to the crack face. Why? Because at the crack tip, the material is behaving in a brittle manner - mostly due to the triaxial stress state immediately ahead of the crack tip. So, the failure criteria is related to a more brittle material than a ductile material.

One final though - you know when you perform a uniaxial tensile test of a ductile material? You get some amount of necking with a cup-cone failure, but the center of the specimen has a brittle failure surface? Local Failure. With the necking, subsurface you get a triaxial stress state, which switches the failure mode to brittle. Think about that the next time you witness a tensile test...

Happy to discuss further.

 

[NRP99]

There are clearly limitations of using FEA in predicting the strains in high triaxial zones accurately. But I think, may be currently no other methods are available to quantify strains at high tri-axiality zones. If that is the case how we are going to get further?

Can Neuber's strain concentration approximation (Eq 7-29 in Mechanical Metallurgy by Dieter) results in highly conservative/unconservative results? Or any other approach to be used?

Of course, lot have been considered by ASME and based on various outcomes, decided to include FEA method which may have better merits.

 

[DriveMeNuts]

I notice that both Div 1 and 2 apply a design margin on local failure of 1.7 and Div 3 has 1.28.
The Div 3 equation local failure equation also has an error (i.e. e^1 + m2). I'll send an e-mail to the committee.

 

[TGS4]

DriveMeNuts - the VIII-3 equation has some "challenges" with parentheses, but the equation itself is correct.

Remember that that design margin is with respect to the specific load case. There is no stated margin against load cases that include thermal loads.