What does this equation mean?

The parameters C and m are fitted, not derived, and depend on environment, frequency, temperature and stress ratio. A mechanics review that proposes a generalised form of the law opens by conceding that “fatigue life prediction is still very much an empirical art rather than a science”, and notes that the power law holds only in an intermediate regime, deviating near the threshold below which cracks do not propagate and again in the fast-growth stage approaching final fracture [ 6 ] . The same review sets out the live disagreement in the field: short cracks, comparable in size to the microstructure or to the local plastic zone, grow at rates that the long-crack law does not describe, and there is no consensus on whether a single stress-intensity-based similitude parameter can be repaired to cover them or whether short-crack behaviour requires a separate model with its own length scale [ 6 ] . Practitioners who need a number today generally handle this by treating the threshold conservatively rather than by resolving the physics.