About measuring the stress intensity factor of cracks in curved, brittle shells

Abstract

Most techniques of measuring the stress intensity factor (SIF) in the cracking process assume a crack in a planar medium. Currently, there is no effective approach for curved brittle shells, particularly for non-developable cases, i.e., shapes with non-vanishing Gaussian curvature. This paper introduces a novel approach to obtaining material properties related to fracture by experimentally observing weakly curved surfaces. Based on the DIC record of the displacement field around the crack tip, the truncated Williams expansion is fitted to the data adjusted according to the shallow shell equations. The convergence properties of the method are investigated by comparing experimental data of PMMA cylinders to theoretical and numerical predictions. The applicability of the technique to non-developable surfaces is verified. It is demonstrated that robust convergence requires the number of terms in the Williams expansion exceeding 6. For different geometries, the ratio of the data selection radius and the length of the crack should exceed 0.3.

Keywords

• curved shell
• stress intensity factor
• digital image correlation method
• williams expansion
• non-developable surface