Numerical analysis of dynamic crack propagation in biaxially strained rubber sheets

Abstract

This paper proposes a computational framework for dynamic crack propagation in rubber in which a nonlinear finite element analysis using cohesive zone modeling approach is used. A suddenly initiated crack at the center of biaxially stretched sheet problem is studied under plane stress conditions. A transient dynamic analysis using implicit time integration scheme is performed. In the constitutive modeling, the continuum is characterized by finite-viscoelasticity theory and coupled with the fracture processes using a cohesive zone model. This computational framework was introduced previously by the present authors (Elmukashfi and Kroon, 2012). In the current work, the use of a rate-dependent cohesive model is examined in addition to investigation of generalized biaxial loading cases. A Kelvin–Voigt element is used to describe the rate-dependent cohesive model wherein the spring is described by a bilinear law and dashpot with a constant viscosity is adopted. An explicit integration is used to incorporate the rate-dependent cohesive model in the finite element environment. A parametric study over the cohesive viscosity is performed and the steady crack propagation velocity is evaluated and compared with experimental data. It appears that the viscosity varies with the crack speed. Further, the total work of fracture is estimated using rate-independent cohesive law such that the strength of the cohesive zone is assumed to be constant and the separation work per unit area is determined form the experimental data. The results show that fracture-related processes, i.e. creation of new surfaces, cavitation and crystallization; contribute to the total work of fracture in a contradictory manner.