Review on the Hall-Petch relation in ferritic steel

Yielding of polycrystalline low carbon steel is characterized by a clear yield point followed by unstable Lüders deformation and such a yielding behavior is taken over to fine grained steel with the grain size of 1μm or less. Yield strength of ferritic steel is increased with grain refinement standing on the Hall-Petch relation. The following equation is realized up to 0.2μm grain size in the relation between yield strength σ_y and grain size d: σ_y [MPa]= 100+600×d[μm] ^-1/2. In low carbon steel, it might be concluded that the Hall-Petch coefficient (k_y) is around 600MPa·μm^1/2. However, the k_y value of interstitial free steels is substantially small as 130-180MPa·μm^1/2 and it can be greatly increased by a small amount of solute carbon less than 20ppm. It was also cleared that the disappearance of yield point by purifying is due to the decrease in the k _y value. On the other hand, the k_y value is changeable depending on heat treatment conditions such as cooling condition from an elevated temperature and aging treatment at 90°C. These results suggest the contribution of carbon segregation at grain boundary in terms of the change in the k_y value. On the contrary, substitutional elements such as Cr and Si do not give large influence to the k_y value in comparison with the effect by carbon.