Borzki,

Failure theory used to evaluate the "equivalent" stress (e.g. Von Mises/Distortion Energy or Tresca/Max. Shear Stress)is less relevant we we talk about Stress Concentration Factors (SCFs) vs Stress Intensification Factors (SIFs) employment.

The essence is that:

SIF = (Local_SCF) x (Secondary_SCF) / 2, or

i = K x C / 2,

as per ASME BPVC III-1/NB and NC.

Local SCF (K) is relevant for welding joints, indeed, meaning butt welds or and/or fillet welds (see the Weldolet classical case).

For seamless fittings (welding tees, elbows, reducers), it is a common approach to separate butt welds' stress concentrations from fitting body's stress concentrations.

Therefore, for these seamless fittings, Local_SCF = K is less relevant and Secondary_SCF = C quantifies the most significant concentration effect.

I suggest to you to have a look in ASME BPVC III-1/Subsection NB, Section 3600 (Piping Design), where there are given in detail the relevant C and K values for all typical fittings and welds.

In general, for seamless elbows, K = 1 (for bending and torsion), so that SIF = C/2.
Therefore, B31 SIF for elbows represent 50% from the actual overall SCF = KxC corresponding to Pl+Pb+Q+F total peak stress range. This is obvious when you'll compare B31 SIF with ASME III-1/NB or IGE TD12 SCF.

When we discuss about bending and torsion SIFs and SCFs, "intrados" and "extrados" sections are irrelevant. Commonly, the maximum stresses found from "beam theory" are superposed in absolute values, applying the SCFs to the nominal stresses calculated by straight pipe spool formulas.

Please also note that ASME Nuclear Code (III-1), or ASME BPVC VIII-3 High Pressure Code use Tresca Theory to evaluate the Stress Intensity Range for fatigue assessment, while ASME BPVC VIII-2 post-2007 uses Von Mises Theory to evaluate the Equivalent Stress Range.

PD5500 uses also Tresca theory for Design by Analysis, but PD5500 fatigue curves are based on Maximum Principal Secondary Stress (S1>S2>S3). The local stress concentrations are accounted by the "de-rated" fatigue curves associated to the typical welding joints and loading schemes.

Therefore, B31 Codes-based stresses (e.g.maximum principal, stress intensity, or Von Mises Equivalent Stress) cannot be used directly with ASME VIII-2 or PD 5500 fatigue curves. The B31 Code-based calculated stresses must be corrected/adjusted in order to make the conversion to overall maximum peak stress range (ASME VIII-2) or to maximum secondary stress range (PD 5500), in the later case being necessary to assume/chose the applicable fatigue curve class.

Please note that so far, I did not have time to review the newly-introduced fatigue analysis method provided by ASME B31.3 / Appendix W (2018, 2020 editions). It looks it is somehow similar to DNV Simplified Fatigue Mathod (based on Weibull probabilistic distribution).
It might be a real progress to use this method for B31.3 Code-based piping systems subjected to high-cycle fatigue loadings (e.g. offshore systems), because such endless discussions about SCFs, SIFs, fatigue curves applicability would bot be required any more.

Best regards,