Hi Aaron,
The B31.3 Code paragraph referenced simply says that there is expected to be a beneficial "relaxation" of the piping system that takes place through the first few start-up cycles. The allowable stress range is set with the understanding that there may be (if the actual stresses are up around the limit of the allowable stress range) some initial and very local plastic deformation (typically at bends and elbows). At a typical elbow, a small "patch" of material somewhere on the extrados of one or more elbows will yield and will experience strain hardening. Upon cool-down, there may be some yielding in the opposite direction (due to the strain hardening it will be outside the "patch" that was initially yielded). BUT, after these "few start-up cycles", the "relaxed" (i.e., permanently deformed) areas will no longer yield on heat-up or cool-down. The piping will assume a slightly different shape and all further operating cycles will experience purely elastic behavior.
The operative phrase in Kellogg is "with EACH cycle". The basic assumption of the "new" (circa 1955) piping flexibility (i.e., fatigue) rules is that the piping system will "shake down" to purely elastic response after "a few start-up cycles" (please see John Brock's write-up in the fifth edition of the Piping Handbook by Crocker and King - the report of the original B31.1 "Flexibility Committee" that proposed these rules is reproduced there). What Kellogg is really saying is that after these LIMITED "few start-up cycles" there will be no further plastic flow - there will be no continuous ratcheting.
I hope this will be of some help.
Regards, John.
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John Breen