Computational fracture mechanics using cohesive element formulations

A computational framework for modeling fracture in materials using cohesive elements incorporating cohesive zone models within a nonlinear implicit finite element solution scheme is developed. The cohesive element method is used to study the problem of growth in fracture energy with peel velocity in peel testing of polymeric adhesives. Cohesive elements are used to model the intrinsic cohesive zone and crack propagation between two viscoelastic polymer sheets in a peel test. The growth of the fracture energy as a function of the peel velocity is studied for peel sheets characterized as standard linear viscoelastic solid material. Experimental data from peel tests of Butadiene rubber elastomers are modeled using the cohesive element framework. Interfacial failures in compressive shear strength (CSS) test of a 3-ply glass/polymer/glass composite specimen are modeled using cohesive elements. Various quasi-static and dynamic crack growth behaviors, obtained for different sizes of the initial pre-flaw along the interface, were studied. A 3D simulation of the square plan form of the CSS test reveals the mixed-mode behavior in crack growth along the free edge of the CSS test specimen. Formation of cone cracks under a rigid spherical indenter from surface pre-flaws in brittle elastic materials is studied using cohesive elements. Cohesive element discretizations result in considerable degradation of stiffness of the discretized elastic continuum. Stability of cohesive cracks is investigated. An extended form of Hamilton's variational principle is used to develop the equations of motion of cohesive cracks. A perturbation procedure for studying free vibrations of stable cohesive cracks is presented. Analytical solutions for natural frequencies of stable cracks in one-dimensional bar crack geometry are derived. Specialized forms of variable domain finite elements are developed for computing the natural frequencies for free vibrations of stable Griffith cracks. The natural frequencies and eigenmode shapes for free vibrations of stable cracks in common crack geometries are developed.