Pipe Stress Relaxation 4

[frd03]

Hello everyone, In spite of to use the rules presented in ASME code to flexibility analysis, recently I solved to study the origins and concepts about allowable stress SA and I found the paper wrote by A.R.C. Markl (1956 )which was applied by ASME to piping-flexibility analysis.
The stress relaxation effect was the base to definte the SA-stress but I understand that stress relaxation is dependent mainly of Creep effect and yelding of material pipe so when I am working with piping around 250oC/300oC the creep effect is not present and sometimes the level of total stress not reach the yelding point, How the stress could to get relaxation with pass of cycles or time ??
Thanks for your help
Francisco Dominguez

 

[JohnBreen]

Hello Francisco Dominguez,

First of all you must understand that the methods in the ASME B31 Piping Codes that we use to calculate stresses do not calculate true elastic stresses. Consider for example the fact that the B31.3 SIF's are about one half of the stress indices used in the ASME Section III rules for Nuclear Class 1 piping systems (where the intention is to calculate elastic stresses). The “effective” stresses that we calculate are to be compared to the B31 Code “allowable stresses” (and “stress ranges) and these “allowable stresses” are to be used with (compared to) the associated B31 stress equations chosen to be used with this methodology. The B31 stress equations are “beam theory” equations that do not address local membrane stresses in more complex piping components (e.g., elbows and branch connections).

Piping engineers (including Markl) have long known that stresses in such components as elbows exceed the yield strength of the material in small areas even when our B31 methods of calculation predict stresses that are below the B31 Code ALLOWABLE stress range. After a few cycles, these yielded areas have "shaken down" (the yielded areas are strain hardened and the strains are transferred to adjacent more ductile material). Upon "cool-down" a residual stress in the opposite direction is left in the piping system and it has become "self sprung" (similar to the condition created when a system is intentionally "cold sprung" during its construction). Note that it is important that the cold residual stress does not exceed the yield strength of the material. If the yielding does not continue to be transferred to adjacent ductile material on successive heat-up and cool-down cycles (this would cause elongation and ratcheting with eventual failure) the system will "shake down" (i.e., "relax") This is a beneficial effect.

The design conditions for many piping systems do not ever result in any plastic deformation and these systems continue to operate entirely in the elastic regime for their entire design life. Designing these systems to the B31 Code rules will assure a level of conservatism that will result in good fatigue life.

Regards, John.

 

[frd03]

Dear JohnBreen, Thanks for your answer.

But I would like to continue this subject. Considering intermediate temperatures ( below the "creep" ) for. ex. 250 / 300 oC, iniatilly I would not have a "viscoplasticity" condition on pipe material so How can I consider a local stress redistribuition ? The load and features material not has a time-depedence only a local hardening.
Imagine a pipe with hydrocarbon. under pressure and 250 oC, suppose a point on the pipe near a anchor where the circunferencial stress Sp = 10 kgf/mm2, the longitudinal stress Sl= 8 kgf/mm2 and due to the route configuration the Se ( displacement stress )= 20 kgf/mm2 and all values are in agree with the code ( bellow Sh and Sa ) but theorically I would have an amount of longitudinal stress of 28 kgf/mm2
in this point, above the yeld stress !! How long or how many cycles I would need to relax these stress ?? How will be the final stress values ?? While this I have a pipe with a gas under overstress !
I ask your opinion about this it will be very important to me

Regards
Francisco Dominguez

 

[unclesyd]

JohnBreen may want to correct me as I think what you are talking about is known as the "Shakedown Concept".

 

[frd03]

Hi,unclesyd

I got some references and really the "Shakedown Concept" is in agree with the behavior related in may question but the problem would be to get functions or a way to simulate this to predict time, cycles or mainly final values to the stress after this re-distribuition . The shakedown can develop only with plastic stresses or would need a kind of "cold creep", too ??

 

[JohnBreen]

Hello,

Interesting discussion.

We are indeed discussing "shakedown". The "shakedown" of a piping system to purely elastic response (no further “shakedown” with its associated plastic response – i.e., “fully relaxed”) may take place with or without creep. Clearly it requires some amount of TEMPORARY elastic-plastic response in small area of the piping system for the first few thermal cycles, but NOT necessarily creep. "Shakedown" can and will take place at temperatures below those required for the material to creep. On the other hand, continuous material creep may take place after the system has “shake down” – consider that the circumferential stresses in high energy piping will make the pipe diameter continue to “grow” due to creep.

Frd03 introduces the term "cold creep" but alas I think this may confuse the issue. Creep is not necessary for "shakedown" (albeit, the term “cold creep” speaks to the similar result of temporary elastic-plastic deformation). Regarding the magnitudes and locations of the residual stresses present in the piping system after it has completely "shaken down" to purely elastic response, I do not think it is something that can be predicted or calculated. In the real world, piping materials are not homogeneous (piping is not perfectly round nor is it uniform in wall thickness - unlike our FEA models would have us believe). The piping and components come out of the pipe mill with a wide variety of physical characteristics (just like people). The process of making elbows and bends complicates the issue as it introduces many strain hardened areas, distributed around these components in an unpredictable pattern. Once the piping system is placed into service, the more highly stressed areas of elbows and bends are once again subjected to material yielding in their more ductile zones - but exactly where can only be guessed at. Also, consider that the "heat-up" process is not instantaneous - the elbows closest to the "source" of the heat will be subjected to some yielding first and then as the temperature in the piping approaches a uniform temperature (if in fact that ever happens) the yielding in the "more distant" components will lessen. The entire process is unpredictable and the final distribution of stresses around the piping system is equally unpredictable.

But the benefits of lower stresses in the piping system are manifested in longer fatigue life and the negative side of that is only apparent when we have to replace a pump in a hot system and the permanent deformation of the piping makes the chore “more interesting”. But that is another topic for another thread.

Regards, John.