Determination of boundary area and spacing in prismatic structures with applications to dislocation boundaries

An analysis is presented for the determination of boundary area per unit volume (SV) for structures that can be idealized as two-dimensional prismatic foams. An important application for this analysis is in the determination of SV for one class of dislocation boundary observed following deformation to high strains. Assuming a complete uniformly random distribution of inclination angles for these dislocation walls SV=πNL/2, where NL is the number of intercepts per unit length along a line perpendicular to the wall traces, in any plane perpendicular to the prism basal plane. Analyses of the inclination angle distribution from both measurements of projected boundary widths and from spacing measurements in two perpendicular sections show that while the assumption of a complete uniformly random distribution is an approximation, the error introduced by making this assumption is small.