Numerical implementation of a cohesive zone model for time and history dependent materials

Abstract

A cohesive zone model approach is used in order to study the behaviour of cracks in elasto-plastic materials. The cohesive zone model being studied is time-dependent, unlike standard cohesive zone models in elasto-plasticity. The stress distribution over the cohesive zone is related to the normalised equivalent stress functional, and is expressed in the form of an Abel-type integral equation. During the stationary crack stage as well as the propagating crack stage, the aim is to study the behaviour of the cohesive zone length with respect to time as well as the crack tip opening. To aid accomplishing this aim, the stress intensity factor was set to zero at the cohesive zone tip. As well as other material parameters, the external applied load participates in the model equations. We will consider two cases for the external load, namely the case when this load is constant in time, and the case when this load behaves linearly with time. We will implement numerical schemes to obtain the crack growth as well as the cohesive zone growth with respect to time for both the elastic case and the visco-elastic case while considering different sets of parameters. The numerical convergence rates are obtained for each of the problems solved. This justifies the suitability of the numerical schemes used.