Linking bilinear traction law parameters to cohesive zone length for laminated composites and bonded joints

Abstract

A theoretical exploration for determining the characteristic length of the cohesive zone for a double cantilever beam (DCB) specimen under mode I loading was conducted. Two traction-separation laws were studied: (i) a law with only a linear elastic stage from zero to full traction strength; and (ii) a bilinear traction law illustrating a progressive softening stage. Two analytical solutions were derived for the first law, which fit well into two existing solution groups. A transcendental equation was derived for the bilinear traction law, and a graphical method was presented to identify the resultant cohesive zone length. The study using the bilinear traction law enabled the theoretical investigation of the individual effects of cohesive law parameters (i.e., strength, stiffness, and fracture energy) on the cohesive zone length. Correlations between the theoretical and finite element (FE) results were assessed. Effects of traction law parameters on the cohesive zone length were discussed.