ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Mechanical Properties
Proposal of Simplified Modified Williamson-Hall Equation
Setsuo TakakiTakuro MasumuraToshihiro Tsuchiyama
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2018 Volume 58 Issue 12 Pages 2354-2356


Williamson-Hall (WH) plots are characterized by irregular arrangement of data due to the elastic anisotropy in each {hkl} plane. In order to correct the effect of elastic anisotropy, Ungár developed a unique methodology using the contrast factor C, so called the modified Williamson-Hall (mWH) method. When X-ray with the wave length λ was used for diffraction analysis and diffraction angle θ and integral breadth β was obtained in each diffraction peak, the following mWH equation is constructed as functions of the parameter K (=2sinθ/λ) and ΔK (=βcosθ/λ).

Here, the parameter α is dependent on the crystallite size. The parameter φ and O are constants but the O-value is much smaller than the φ-value. In the mWH plots in 60% cold rolled ferrite (Fe-0.0056%C), ultra low carbon martensite (Fe-18%Ni) and 20% cold rolled austenite (SUS316L), it was confirmed that the value of OK2C is negligibly small. As a result, the following simplified equation is applicable for the analysis by mWH method.

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© 2018 by The Iron and Steel Institute of Japan
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