Theoretical discussion of dislocation strengthening in cold rolled iron

In work hardened metals, it is known that the strength of metals is heightened with increasing dislocation density. In the case of cold worked iron, dislocation is introduced heterogeneously and forms dislocation cell structure. Yield stress increases with an increase of volume fraction of cell wall where dislocation density ρ is much higher than the matrix. Applying the composite model to cold worked iron with dislocation cell structure, it was theoretically explained that linear relationship is realized between √ ρ and the increment of strength δs, so called Bailey-Hirsch relation. On the other hand, the Bailey-Hirsch equation; δs[GPa]=18√ρ/10⁹ was constructed from the experimental data which were already reported for cold worked iron. In previous papers, dislocation density was measured directly by transmission electron microscopy. As a result, it was confirmed that experimental data agree well with the result which was theoretically introduced based on the composite model and that the above Bailey-Hirsch equation can be applied for cold worked iron in which dislocation density is below 4×10¹⁴/m² at least.