Characterization of non-planar crack tip displacement fields using a differential geometry approach in combination with 3D digital image correlation

Abstract

This paper describes a novel differential geometry method that is used in combination with 3D digital image correlation (3D-DIC) for crack tip field characterization on non-planar (curved) surfaces. The proposed approach allows any of the two-dimensional crack tip field models currently available in the literature to be extended to the analysis of a 3D developable surface with zero Gaussian curvature. The method was validated by analyzing the crack tip displacement fields on hollow thin-walled cylindrical specimens, manufactured from either 304L or 2024-T3 alloy that contained a central circumferential crack. The proposed approach was checked via a comparison between experimentally measured displacement fields (3D-DIC) and those reconstructed from a modified 2D crack tip model (utilizing either 2, 3, or 4 terms of the William's expansion series) and implementing a 3D geometrical correction. Further validation was provided by comparing model-derived stress intensity factors with values provided by empirical correlations.