2007 B&PV Division 2 Part 5 Secondary & Peak Stress Clarification
2007 B&PV Division 2 Part 5 Secondary & Peak Stress Clarification
(OP)
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.
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.





RE: 2007 B&PV Division 2 Part 5 Secondary & Peak Stress Clarification
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.
RE: 2007 B&PV Division 2 Part 5 Secondary & Peak Stress Clarification
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.
RE: 2007 B&PV Division 2 Part 5 Secondary & Peak Stress Clarification
RE: 2007 B&PV Division 2 Part 5 Secondary & Peak Stress Clarification
(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.
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RE: 2007 B&PV Division 2 Part 5 Secondary & Peak Stress Clarification
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