Extended Caking Method for Strain Analysis of Polycrystalline Diffraction Debye–Scherrer Rings

Abstract

Polycrystalline diffraction is a robust methodology employed to assess elastic strain within crystalline components. The Extended Caking (exCaking) method represents a progression of this methodology beyond the conventional azimuthal segmentation (Caking) method for the quantification of elastic strains using Debye–Scherrer 2D X-ray diffraction rings. The proposed method is based on the premise that each complete diffraction ring contains comprehensive information about the complete elastic strain variation in the plane normal to the incident beam, which allows for the introduction of a novel algorithm that analyses Debye–Scherrer rings with complete angular variation using ellipse geometry, ensuring accuracy even for small eccentricity values and offering greater accuracy overall. The console application of the exCaking method allows for the accurate analysis of polycrystalline X-ray diffraction data according to the up-to-date rules presented in the project repository. This study presents both numerical and empirical examinations and error analysis to substantiate the method’s reliability and accuracy. A specific validation case study is also presented to analyze the distribution of residual elastic strains in terms of force balance in a Ti-6Al-4V titanium alloy bar plastically deformed by four-point bending.

Keywords

• polycrystalline diffraction
• synchrotron X-ray
• Debye–Scherrer rings
• trigonometric averaging
• residual stress