Trying to understanding primary plus secondary stress difference range and why we evaluate it. 1

[engineer121394]

Here is my understanding so far:
-Design stress, or allowable stress (Sm) is “typically” (ultimately depending on the application, and assuming Su is not limiting) 2*Sy/3
-primary stress (P) is result of external loading (weight, pressure, shock etc.) The limit is Sm
-secondary stress (Q) is stress from compatibility condition loads like preload or thermal loads.
-Primary (P) plus secondary (Q) stress difference range (later denoted as S_diff) considers the sum of the primary and secondary stresses (excluding peak stress) between two different states (i.e. comparing P+Q for pressurized vs unpressurized operating states). The limit for this is 3*Sm (or 2*Sy). We evaluate this to determine if ratcheting will occur (low cycle fatigue failure mode where progressive plastic deformation occurs for each loading cycle). If this limit is exceeded, fatigue penalty factors are applied to fatigue limits to account for plastic deformation (because typical fatigue analysis assumes the material is within elastic limits).

My question:

Why do we evaluate primary plus secondary stress difference range when we also evaluate fatigue stress? Wouldn’t high cycle fatigue always be limiting?

Wouldn’t fatigue strength limits be bounded by a materials yield strength? If the following is true:
- S_alt = S_diff/2 (neglecting S_alt peak stresses)
- Limit for S_alt is less than Sy
- Limit for S_diff is 2*Sy

…Then wouldn’t high cycle fatigue be limiting. Why evaluate primary plus secondary stress difference range?

What am I missing?

 

[TGS4]

I'm going to assist you a little to clean up your terminology to match the current version of ASME Section VIII, Division 2, Part 5 - will help with your understanding a little. The allowable (equivalent - or von Mises, if you will) stress is S, not Sm. The primary stress is divided into two categories, primary general - P_m, and primary local - P_L. The primary general membrane stress, P_m, is limited to S. The primary local membrane stress is limited to S_PL (which is defined as the greater of 1.5S or Sy). The primary-plus-secondary membrane-plus-bending stress range - Δ(P_L + P_b + Q) - is limited to S_PS. The upcoming 2025 Edition will define S_PS = (S_y-cold,k + S_y-hot,k) - so please stop using 3S for this limit.

Additionally, you need to change your focus from trying to figure out which failure mode might be limiting, to evaluating all applicable failure modes.

First, you need to demonstrate Protection Against Plastic Collapse. The elastic limits are P_m ≤ S, P_L ≤ S_PL, and P_L + P_b ≤ S_PL. Or perhaps you perform an Limit Load Analysis or Elastic-Plastic Analysis.

Second, you need to demonstrate Protection Against Local Failure.

Third, you need to demonstrate Protection Against Collapse From Buckling.

Fourth, you need to demonstrate Protection Against Failure From Cyclic Loading: Ratcheting. Even if you don't ratchet, but have stable cyclic plasticity, that invalidates the fatigue screening approaches and you are mandated to perform a fatigue analysis. That fatigue analysis will come with a cyclic plasticity correction factor (the Code calls this the fatigue penalty factor).

Fifth, you need to demonstrate Protection Against Failure From Cyclic Loading: Fatigue. Maybe you can pass one of the fatigue screening methods (caveat - see the note above regarding no cyclic plasticity), or maybe you need to perform a fatigue analysis.

Each one of these failure modes has its own design margin - some of which are related to yield (I prefer to refer to this value as the minimum-specified engineering yield, which is based on the 0.2% offset method - noted to be different from the proportional limit), some are based on the engineering ultimate strength, some some are based on a S-N curve that is obtained from experiments - and depends on the number of duty cycles that a component will see over its lifetime.