Strain and the quantitative characterization of anisotropic microstructures

Abstract

Microstructures exhibit both crystallographic and morphological anisotropy. The orientation distribution function (ODF) for PL(t), the number of intersections per unit length of boundaries with test lines parallel to a unit vector. t. describes morphological anisotropy, the spatial distribution of internal interfaces that separate grains or phases. Weak anisotropy refers to a microstructure such that PL(t) vst is an ellipsoid. Coefficients of the direction cosines in the equation of the ellipsoid form a Cartesian tensor called the microstructural anisotropy tensor (MAT). This work develops a measure of internal total strain, the Eulerian finite grain strain tensor (EFGST), based on the MAT. The reference state for the EFGST is an isotropic network having the same surface area per unit volume, SV, as the deformed specimen. Analysis of the deformation of the network of ferrite-ferrite boundaries in a specimen of 1020 steel deformed in uniaxial tension illustrates that the EFGST measured at the centroid of the gage section changes congruently with a similar measure of bulk deformation, both having principal axes aligned with those of the bulk deformation. However, the values of strain are not identical due to nonuniform deformation in the gage section after necking.