Constitutive model for a fiber tow bridging a delamination crack

A simple model is introduced for a fibrous tow, stitch, or rod that bridges a delamination crack in a laminate. The model is introduced for mode II delamination cracks but is intended for general mixed-mode cracks. Modeling is guided by prior observations and measurements on laminates reinforced through the thickness by stitches or short rods. Salient phenomena include shear deformation of the bridging tow, its debonding from and sliding relative to the surrounding laminate, and its sideways displacement through the laminate. The tow is represented as a beam that can shear and extend axially. Its axial displacement relative to the laminate is resisted over its debonded periphery by friction. The forces associated with its sideways displacement are estimated by regarding it as a punch being driven through a plastic medium (the laminate). Thus the mechanics of the whole problem are reduced to a set of one-dimensional equations. The distinction between continuous stitches and discontinuous rod reinforcement consists of a boundary condition. With realistic values assigned to undetermined parameters, experimental data for stitches are reproduced over the whole range of displacements up to ultimate failure of the stitch. The model generates a bridging traction law that can be used for optimal design of through-thickness reinforcement for damage tolerance in a wide variety of structures.