2007 B&PV Division 2 Part 5 Secondary & Peak Stress Clarification 1

[Transient1]

Questions below.

I understand peak stresses (F) as arising basically from geometric discontinuities/nonlinear stress distributions. Secondary stresses (Q) seem more elusive. In the examples of stress categorization, Q can at times be thermal stresses, membrane stresses, gradient through plate thickness, etc.

(1) So what is a secondary stress really?

(2) Each stress categorization excludes secondary and peak stresses for plastic collapse. I can understand ignoring peak stresses but why secondary stresses?

(3) How far away from the discontinuity (peak stress) do you have to be before it is considered part of Local Primary Membrane Equivalent Stress (P_L)?

Thanks in advance.

 

[trottiey]

As I understand it, the basic distinction between primary and secondary load is whether they are caused by an applied deflection or an applied load. For example, thermal stress or installation loads will impose a deflection rather than a load. If that deflection pushes the material beyond yield, then the strain remains linearly related to the imposed deflection, but the stress will be less than what would be predicted by a linear model. As you get to flat portion of the stress-strain curve, secondary stresses become self-limiting and ductile rupture is basically impossible.

Compare this to a pressure load. If pressure pushes a material beyond yield, the stress remains linearly related to the imposed pressure, but the strain will be higher than what would be predicted by a linear model. If significant necking starts to occur, that would lead to rupture.

Thinking about it this way, it makes sense that peak and secondary stresses would be excluded from plastic collapse. Once the material starts to go plastic, the peak and secondary stresses will drop until some stable equilibrium is achieved. (Usually. It's still possible to crush a pop can by stepping on it, which is why you still need limits on secondary stress. )

Beware that this doesn't work with brittle materials. If the stress-strain curve doesn't go flat, then the secondary stresses will never be fully self-limiting. And then you've got stress corrosion cracking to think about. But Section II basically doesn't permit brittle materials for shells and heads, so that's usually not a concern for pressure vessels.

I can't help with your third question, unfortunately.

 

[TGS4]

trottiey - your soda can example is a different failure mechanism - buckling.

Re questions (3), you're mixing your issues. Pl is the linearized membrane stress. It will include the effects of the peak stress at your stress classification line. So, at your SCL, you will calculate a linearized through-thickness stress distribution, the "average" being the membrane, or Pl, the linearized at the inner/outer surfaces being the P+Q, and the stresses from the actual stress distribution that exceeds the P+Q being the peak.

 

[Transient1]

That TGS4, I really was confusing my issues. I understand now that peak stress is averaged into the linearized stress. Also, that the difference between local and global is whether the load area applied is local (i.e., a flange connected to a heavy pipe) or global (pressure).

 

[prex]

(1) A secondary stress is a self limiting stress. The only way to machine detect whether a stress is primary or secondary is to perform an elastoplastic analysis: if, by increasing the load, the strains (or part of them) do not increase after a full plastic condition is reached, then those stresses (or part of them) are secondary.
(2) Secondary stresses are self limiting after the plastic condition is reached, so failure may only occur because of incremental strain over more than one load cycle (low cycle fatigue, just like peak stresses are associated with high cycle fatigue)
(3) The distance that makes a secondary stress a local primary one is generally specified by codes, but insight by the designer is also important. One must remember that a local primary stress remains a secondary stress (self limiting) and that the classification as primary is only meant at avoiding excessive distortion; if excessive distortion is not anticipated, there is no reason to do so.

prex

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[napoleonm]

Prex:
The term:
“gradient through plate thickness” mean bending across the thickness?...

So for a thick wall vessel (Rm/t = 1.34) the bending stress across the wall away from discontinuities (so we are in the shell), the bending due to internal pressure only is classified as secondary stress Q? Or is considerate as primary bending Pb

See: forum: Stress classification for a Thick pressure vessel at central section