On the Oscillating Course of d^hkl−sin²ψ Plots for Plastically Deformed, Cold-Rolled Ferritic and Duplex Stainless Steel Sheets

This work deals with non-linear $d^{hkl}$−${sin}^2\psi$ distributions, often observed in X-ray residual stress analysis of plastically deformed metals. Two different alloys were examined: duplex stainless steel EN 1.4362 with an austenite:ferrite volume ratio of 50:50 and ferritic stainless steel EN 1.4016. By means of an in situ experiment with high-energy synchrotron X-ray diffraction, the phase-specific lattice strain response under increasing tensile deformation was analysed continuously with a sampling rate of $0.5$ Hz. From Debye–Scherrer rings of nine different lattice planes {hkl}, the $d^{hkl}$−${sin}^2\psi$ distributions were evaluated and the phase-specific stresses were calculated. For almost all lattice planes investigated, oscillating courses in the $d^{hkl}$−${sin}^2\psi$ distributions were observed, already occurring below the macro yield point and increasing in amplitude within the elasto-plastic region. By comparing the loaded and the unloaded state after deformation, the contribution of crystallographic texture and plastically induced intergranular strains to these oscillations could be separated. For the given material states, only a minor influence of crystallographic texture was observed. However, a strong dependence of the non-linearities on the respective lattice plane was found. In such cases, a stress evaluation according to the ${sin}^2\psi$ method leads to errors, which increase significantly if only a limited $\psi$ range is considered.