Analysis of a Stitched Double Cantilever Beam

Abstract

A simple analytical model is presented to describe crack propagation in stitched laminated Double Cantilever Beam (DCB) specimens. The stitches are smeared and modeled as continuous cohesive springs, which are assumed to be linear-elastic until final failure. Timoshenko beam theory is used to model the DCB specimen. As the specimen is loaded, the stitches are assumed to break when the strain in the stitches reaches the ultimate strain. The crack tip is assumed to advance as the energy release rate at the crack tip reaches the Mode I fracture toughness of the parent laminate. A closed form solution is obtained for the problem of beam on elastic foundation and it is used to simulate the DCB test and crack propagation. Results presented include, load-deflection diagrams, crack bridging length and apparent fracture toughness for various stitch parameters. A semi-empirical formula is derived for the bridging length as a function of the stitch ultimate strain and fracture toughness of the parent laminate. The results are compared with experimental results. It is found that, for the case with Kevlar stitches, the linear elastic model of the stitch yarn is not adequate. It is shown that inelastic behavior of the stitches plays a significant role in increasing the fracture toughness due to stitching.