Closed-form Solutions for Cohesive Zone Modeling

Abstract

Closed-form solutions for cohesive zone modeling within the framework of classical lamination theory (CLT), for the popular mode I double cantilever beam (DCB) test and the mode II end notched flexure (ENF) test are provided in this paper. Zerothickness virtual multi-linear traction-separation laws are introduced to simulate the cohesive interactions between potential crack surfaces. The problem is formulated by solution forms corresponding to each segment of the cohesive laws and using appropriate boundary and continuity conditions. Detailed algorithms for each case is provided to clearly show the influence of the cohesive zone law on the ensuing crack growth. Comprehensive parametric studies are performed on the crack growth response and the process zone length, revealing their relations to the delamination length, cohesive parameters and the shape of the traction-separation laws. With applicability to general multilayered structures, and the capability to incorporate arbitrary, piecewise linear cohesive constitutive laws, the closed-form solutions can serve as a tool to determine the accuracy of numerical solutions used in conjunction with the finite element simulations.