A history-dependent cohesive zone model in elastic and visco-elastic materials under constant and variable loading

Abstract

A history-dependent cohesive zone model approach is used to study the crack behaviour in elastic and visco-elasto materials. The cohesive (yield) stress at the cohesive zone points is related to the nonlinear normalised equivalent stress functional over the stress history at these points, and is expressed in the form of an Abel-type (fractional) integral. We analyse the cohesive zone length evolution in time and the crack tip opening during the stationary crack stage as well as during the propagating crack stage. We consider the external load increasing linearly with time and compare the solution with the case of the constant load. We obtain the solution numerically and analyse the influence of the viscoelasticity by comparing with the case of purely elastic behaviour of the bulk of the material.