Normal type of loading using Response Spectra is Seismic, sometimes PSV system which uses Force Spectrum loading, also sometimes Slug and surge, by converting the time history of slug and surge load to the frequency domain.

Depending on the source of loading, the number of cycles can be defined.

It's either high cycle fatigue or low cycle fatigue.

If you have the steady-state dynamic type of loading, then you can define using the endurance limit of material (e.g., recip pumps/compressor pulsations). If I'm not mistaken for carbon steel, it is 1E11 or 1E12 cycles for endurance.

If it's a transient type of dynamic loading (low cycle fatigue) which may lead to excessive deformation, then the yield of the material will govern depending on the number of cycles (e.g., less than 7000 to 5000 cycles). Typical transient dynamic loads can be surge/water hammer, slug, PSV pop up, Transient Thermal (mixing tees).

Knowing the type of loading, can give you a hint which failure mode to consider.

Warm Regards,