Analytical estimation of cohesive parameters for a bilinear traction-separation law in dcb mode i loading

In this study, analytical solutions for estimating two cohesive parameters, stiffness and strength in a bilinear traction law, were developed in conjunction with the ASTM double-cantilever beam (DCB) mode I testing. A zero-thickness elastic foundation zone containing two layers in series was assumed in the analytical derivation: a cohesive zone located underneath a beam elastic zone that is adjacent to the beam bottom surface, for accurately identifying the DCB opening displacements at both loading point and crack tip. The total deflection was comprised of three contributions: bending, lateral shearing, and beam thickness deformation. The analytical analysis eliminates drawbacks caused by rigid thickness in the classical beam theory. Consequently, good agreement in the beam deflections at both the loading point and the crack tip was obtained between the proposed analytical solution and an evaluation of numerical study results. This good agreement ensured that accurate cohesive parameters were derived analytically. Results showed that the proposed method explains why different cohesive parameters can lead to similar load-displacement results. Discussion on the application of the proposed analytical methodology and the associated cohesive values is presented.