Evaluation of elastic constants of M23C6 and M7C3 embedded in Fe-Cr-C alloys using in-situ XRD tensile test and self-consistent model

This paper investigates the elastic properties of the model Fe-Cr-C alloys, specifically focusing on M₂₃C₆ and M₇C₃. The study uses in-situ synchrotron X-ray data during tensile deformation to determine the individual elastic characteristics of the matrix and iron/chromium carbides. The experimental results obtained from in-situ X-ray diffraction (XRD) are compared to the elastic constants of carbides that were reported in previous studies and derived using density function theory (DFT). The appropriate elastic constants for M₂₃C₆ and M₇C₃ were selected based on the self-consistent code executing with reported elastic constants. The directional elastic modulus and Poisson's ratio of iron/chromium carbides are calculated, and the anisotropy of the elastic constants is evaluated using the XRD lattice deformations under loading. The elastic modulus of carbide varies with the volume fraction of carbide in the effective medium. The study finds that the hexagonal structure is more probable than orthorhombic structure for M₇C₃ due to well-matched estimations of the directional elastic modulus and Poisson's ratio obtained from in-situ XRD data and the self-consistent calculations. In-situ XRD analysis of elastic behavior of each diffraction can be used to demonstrate the elastic constants of carbides and shows potential for obtaining precise elastic constants by integrating with self-consistent modeling and DFT.