Evaluation of dislocation density in cold-worked iron as measured via X-ray diffractometry

The yield stress of metals increases in proportion to the square root of dislocation density; this relationship is known as the Bailey-Hirsch relation. The increase in yield stress Δσ is expressed as a function of the shear modulus G, the Burgers vector of dislocation b, and dislocation density ρ using the equation: Δσ=αGb√ρ. Here, α denotes the dislocation strengthening coefficient. Research using transmission electron micrographs has revealed a linear relationship between √ρ and Δσ. Various values from 0.77 to 1.4 were reported for α in cold-worked iron, but the equation Δσ≒1.8×10-8 √ρ (α=0.9) has been established as applying to a variety of situations. On the other hand, the micro-strain ϵ has been measured via the Williamson-Hall method for two kinds of cold-worked iron: 0.001%C steel and 0.0056%C steel, with grain sizes of 120 μm and 50 μm, respectively. Plastic strain was induced by cold rolling up to a thickness reduction of 90%. The work hardening behavior is significantly different between these two steels but it was found that Δσ can be calculated for both using the equation Δσ[GPa] = 220×ϵ. From these results, the conversion equation; ρ[m ^-2 ] ≒ 1.5×10 ²⁰ ϵ2 was introduced to relate ϵ and ρ. As a result, it was confirmed that the Bailey-Hirsch relation can be treated as a common standard for understanding of dislocation density, regardless of the measurement methods employed.