Extension of the Derby relation to metals severely deformed to their steady-state ultrafine-grain size

It was documented by Derby in 1992 that the flow stress is in power-law relationship with the steady-state grain size obtained in dynamic recrystallization. This relation has been found valid in this paper also for ultrafine-grained metals that can be obtained by severe plastic deformation. For these materials, the exponent is −0.5, which is the Hall-Petch relation. In copper, a uniform dislocation density without geometrically necessary dislocations is valid for this state.