Recovering Grain-Boundary Inclination Parameters through Oblique Double Sectioning

A method for the retrieval of grain-boundary inclination parameters of the grain-boundary character distribution (GBCD) by oblique double sectioning (ODS) is proposed. In this hybrid approach, grain-boundary inclination parameters are directly measured by double sectioning, while a statistically reliable sampling of the microstructure is achieved by oblique sectioning. The solution to the fundamental equations is posed in a manner similar to the recovery of the orientation distributions from sets of incomplete pole figures, using classical Fourier representations of the distribution functions. The ODS is validated by and compared to the L _A /S _V stereology through simulations and experimental implementation in a sample of 439 stainless steel. Simulations show that the grain-boundary normal distributions recovered by ODS and stereology are comparable, giving errors on the order of 10⁻². Experimental implementation of ODS and the L _A /S _V stereology in alloy 439 stainless steel demonstrate additional practical limitations of the ODS methodology when applied to materials of large or uneven grain size.