Michael,

I'm afraid you still persist in confusion.

The Stress Concentration Factor (SCF) or Stress Intensification Factor (SIF) concept as used in "classical" pressure vessel (ASME VIII-2) and piping (B31) engineering IS NOT USED in Fracture Mechanics.

Fracture Mechanics operate with the STRESS INTENSITY FACTOR (K) concept, which is fundamentally different than SCF/SIF.

SCF/SIF is a dimensionless quantity and is associated with a structural discontinuity. It may be a gross structural discontinuity (such as tubular junction, shell-nozzle junction etc.) and we deal with Secondary SCF/SIF in this case, or it may be a local structural discontinuity (weld toe, local thickness decrease, or quite a crack), and in such case we deal with Peak SCF/SIF.

However, if the local discontinuity is a crack, the corresponding peak SCF/SIF DOES NOT GIVE ANY PREDICTION REGARDING THE POTENTIAL MANNER OF CRACK EXTENSION.
The Peak SCF/SIF indicates ONLY the secondary stress (Pm+Pl+Q) increase up to the maximum Peak level (Pm+Pl+Q+F), but the crack may extend by ductile/stable mechanism (e.g. crack size increases if load/stress increases) or by unstable/brittle mechanism (e.g. crack increases with high speed even if load/stress decreases), REGARDLESS the value of Peak SCF/SIF.

Stress Intensity Factor (K) used in Fracture Mechanics gives a clear information about the crack extension/growth mechanism.
In the simplest definition form, for a filiform crack of "2xa" (mm) length in an "infinite" thin plane plate subjected to uniform tensile load perpendicular to crack plane/direction, with a normal nominal tensile stress S (MPa), the Stress Intensity Factor corresponding to Mode I of crack growth is:

KI = sqrt(PI*a) * S,

so that Stress Intensity Factor (KI) is expressed in N/sqrt(mm3).

The given crack will grow by unstable/brittle mechanism if Stress Intensity Factor (KI) is equal to or higher than the CRITICAL VALUE OF STRESS INTENSITY FACTOR (KIC), this latest quantity being a MATERIAL Characteristic (e.g. Material Toughness Characteristic) which depends mainly of Temperature - when temperature decreases KIC decreases and the risk of crack unstable growth is higher.

Conclusion: SCF/SIF as used by us, piping stress / preessure vessel engineers, when we perform "classical" design in accordance with ASME B31 and ASME VIII-2 codes, DOES NOT HAVE ANY CONNECTION with Fracture Mechanics prediction assessments.

Regards,