Transformation of observed crack traces on a section to true crack density for fracture calculations

Abstract

A statistical procedure has been derived for transforming apparent crack orientations, lengths, and numbers that are observed on a polished section to true orientations, lengths, and numbers. The cracks are assumed to have circular cross sections, and the orientation distribution is assumed to have axial symmetry, but no form is imposed on the observed or computed orientation and length distributions. The transformation has been incorporated into a computer code which has been tested for an analytical case and has been used to transform observed crack data for Armco iron. Comparisons are made with transformations by two approximate methods to guide in detemining whether to use the complete transformation in specific applications. The transformation should also be applicable to other observed metallographic surface features, such as ellipsoidal grains, twins, inclusions, and platelets of a new material phase.