I downloaded and read the article cited as Ref. 10 in the Wikipedia entry on Fatigue Limit, "There is no infinite fatigue life in metallic materials" by C. Bathias.
Bathias used a piezoelectric fatigue machine capable of accelerating fatigue testing by producing 10 to the tenth power stress cycles in less than a week. Bathias states that the concept of a fatigue limit is bound to the hypothesis of the existence of a horizontal asymptote (a line that continually approaches a given curve but does not meet it at any finite distance) on the S-N curve between 10 to the sixth power and 10 to the seventh power, so a sample that reaches 10 to the seventh power cycles and isn't broken is considered to have an infinite life. Bathias says this is a convenient and economical approximation, but is not a rigorous approach.
Here is the S/N curve of steel and aluminum from the Wikipedia article on fatigue limit showing the near horizontal asymptote of steel (blue line):
Here is the S/N curve for medium strength steel from the Bathias article taken from ASM Atlas of Fatigue Curves, which Bathias says is an approximation.
Bathias goes on in the article to show that using a piezoelectric fatigue machine generating stress cycles at 20kHz to accelerate fatigue life testing out to 10 to the tenth power number of cycles, he produces fatigue failures below the fatigue limit (near horizontal asymptote).
While I think this article probably does advance the knowledge of fatigue failures, I'm not convinced that it has any practical value when applied to fatigue of steel tube bicycle frames over decades of normal use.
I could be wrong.
