A statistical study of the relationship between plastic strain and lattice misorientation on the surface of a deformed Ni-based superalloy

Misorientation data from Electron Backscatter Diffraction (EBSD) is often used to identify strain localisation and quantify plastic strain at the microstructural scale. However, the exact relationship between local plastic strain and misorientation and how it changes at the grain and sub-grain level has not been studied in detail. We have used high resolution digital image correlation (HRDIC) to measure plastic strain at the sub-micron scale on the surface of a nickel superalloy strained to 2%. The strain values have been correlated to different misorientation measures at the grain and subgrain scale, over several hundreds of grains. We show that although the grain mean plastic strain is positively correlated to the lattice misorientation, there is a large scatter in the correlation, which depends on the misorientation measure used. There is also essentially no correlation between the magnitude of grain strain and grain orientation derived parameters like the Schmid factor and the Taylor factor, largely due to deformation bands at the mesoscale that are not crystallographic. At these strain levels, the relationship between misorientation and plastic strain is affected by the differences in how slip (discontinuous) and lattice rotation (continuous) develop, by local grain interactions and the development of transgranular strain localisation. It is therefore effectively not possible to quantify plastic strain within individual grains using EBSD derived misorientation values alone, although some measures of misorientation are more appropriate than others if there is an understanding of the underlying local plastic phenomena. Whereas slip is localised in slip bands, the misorientation varies smoothly in a manner that is only weakly spatially correlated to the slip. These findings have implications for the modelling of the deformed state of polycrystalline metals at the microstructural scale using continuum mechanics.