The Hall–Petch relationship for the sizes of deformation jumps in metals

The paper presents an attempt to use the Hall–Petch relationship to relate the yield strength of copper and titanium in three different states (initial, annealed, and after equal-channel angular pressing) to the sizes of nano- and micrometer deformation jumps measured using a precision interferometric technique. It is shown that, upon a compression strain near the yield point, one can observe six levels of deformation with three nano- and three micrometer sizes of deformation jumps from 1–2 nm to 20–35 $\mu$m. Each of the six structural states of metals is characterized by its own set of deformation jump sizes. Dependences of the yield strengths of copper and titanium on the jump sizes $L^{-1/2}$ are constructed, and the general regularities and features of deformation jumps for each of the metals in different structural states are discussed.