Separating macro- (Type I) and micro- (Type II+III) residual stresses by ring-core FIB-DIC milling and eigenstrain modelling of a plastically bent titanium alloy bar

A novel approach to separating macroscopic (Type I) from microscopic (Type II + III) residual stress is presented, based on Focused Ion Beam – Digital Image Correlation (FIB-DIC) ring-core stress evaluation and eigenstrain modelling. This approach was applied to study the residual stresses for a titanium alloy bar following plastic four-point bending. It was found that electrochemical polishing is a surface preparation technique that is very well suited for FIB-DIC ring-core measurements, in the sense that it removes the influence of prior sample grinding and polishing, leads to a stress profile that satisfies force and moment equilibrium, and thus enables the evaluation of absolute values of total residual stress. The obtained relief strain profile across the bar width is asymmetric, highlighting the difference in the alloy's response to tension and compression. Total experimental residual stress values were calculated using (i) the assumption of material elastic isotropy, with an average Young's modulus, and (ii) under the assumption of elastic anisotropy, taking into account the crystallographic orientation of each investigated grain. Based on the measured relief strain values, the eigenstrain distribution in the bar was reconstructed and used to obtain the macroscopic (Type I) residual stress profile. The differences in the residual stress between the eigenstrain reconstruction values and the individual experimental results were ascribed to the local microscopic (Type II + III) residual stresses. This conclusion was substantiated by revealing the correlation between the residual stress values in individual grains in the elastic zone and their respective Young's moduli in the loading direction, as well as the correlation between the residual stress values in grains located in the plastic zone and their respective Schmid factors for basal slip.