  The fractional power-law material behavior has been investigated within the
framework of a modified mean field theory, in which high-temperature structure
precursors in a crystalline or polycrystalline material are treated as a
partially ordered liquid over a wide range of temperature. By doing so, the
relaxation behavior of the material can be studied via a modified
Landau-Khalatnikov equation. It then becomes clear that, as the special cases
of the fractional power-law behavior, seemingly quite different fatigue
phenomena and physical deterioration are governed by a fundamental physical
phenomenon, i.e., the competition between ordered structures and partially
ordered high-temperature structure precursors during a series of atomic
relaxation processes.
