The fracture mechanics of cantilever beams with an embedded sharp crack under end force loading

Abstract

Motivated by the need to develop model and non-model based methods for damage and crack detection in components and structures, this paper aims at establishing the near-tip mechanics of cantilever beams containing a fully embedded, through thickness sharp crack and subjected to an end force. Finite element (FE) models of the cracked beams were established with the aid of a specialized 2-D adaptive meshing algorithm. Beam geometries with a crack placed at various depths and locations along the beam axis and at various orientations have been modeled. Linear elastic and isotropic conditions were assumed throughout the homogeneous beam domain. Broad parametric studies were conducted to study the effects of crack length, crack orientation and crack location on the fracture characteristics dominating both the left and right crack tips. As such extensive results are reported for the near tip energy release rates and the associated Mode I and Mode II stress intensity factors and mode mixity.The study suggests that the near-tip conditions for both the left and right crack tips in systems with non-horizontal cracks are dominated by mixed mode conditions. Physically inadmissible crack surface interpenetrations are predicted associated with negative Mode I stress intensity factor component for at least one of the two crack tip regions for all incline cracks. The extent of crack surface interpenetration is shown to depend on the crack plane orientation relative to the beam axis.For beams containing a horizontal crack, i.e., cracks aligned with the beam axis, the simulation results suggests that such cracks are dominated by Mode II conditions at both crack tips regardless of its length and crack location in the beam. The findings of this study along with other related results regarding the deformation of a beam with an embedded horizontal crack form the foundation for the development of analytical models capable of capturing the overall deformation as well as the near-tip fracture characteristics of such cracked structures. In addition, the findings can assist in furthering our understanding of delamination processes in laminate systems and in developing model and non-model methods for damage and crack detection.