Analysis of dislocation density by direct-fitting/modified Williamson-Hall (DF/mWH) method in tempered low-carbon martensitic steel

To calculate the dislocation density of tempered low-carbon martensitic steels (Fe-0.15%C alloy) by the direct-fitting/modified Williamson-Hall (DF/mWH) method, the unknown parameter A in tempered martensite was investigated. In the DF/mWH method, the dislocation density ρ is defined as ρ=2φ²/(πA²b²). Here, φ and b correspond to the slope of the DF/mWH plot and the magnitude of the Burgers vector, respectively. In low-carbon martensitic steels tempered at 573 - 873 K, φ and ρ were estimated by the DF/mWH method and the modified Williamson-Hall/Warren-Averbach method, respectively. As a result, these parameters decreased with increasing tempering temperature. By substituting φ and ρ in the above equation, the parameter A can be obtained as a function of the tempering parameter λ as follows: A = –1.53 × 10⁻⁵ × λ + 0.982 The parameter A in low-carbon martensitic steels tempered at 573 - 873 K for 18 ks was calculated to be 0.7 - 0.8. Using the parameters A and φ obtained by the DF/mWH method, dislocation density ρ can be easily estimated.