A Damage Mechanics Based Cohesive Zone Model with Damage Gradient Extension for Creep-Fatigue-Interaction

Abstract

In this paper a novel Cohesive Zone Model (CZM) is derived within the framework of continuum thermodynamics to describe cracking and delamination behaviour of coatings at high-temperatures. The separation variable in the Traction-Separation-Law (TSL) is decomposed into elastic and inelastic part. For evolution of inelastic separation, a power-law in combination with a damage evolution law is used to consider the tertiary stage of inelastic separation of the interface, additionally. Thereby, damage evolution is related to the corresponding thermodynamic driving force and the inelastic opening rate. For reasons of simplicity the resulting thermo-mechanical problem only considers heat conduction through the interface. Due to the fact that standard Newton-Raphson procedure gets unstable (e.g. snap-back) when softening occurs which is the case by using a CZM, this model is enhanced with the damage gradient, similar to approaches in phase field modelling. Further on, this extension is done to investigate if it is possible to overcome the size dependence of CZMs. Finally, the model is reduced to pure Mode I opening and an example for a Double Cantilever Beam (DCB) is analysed by the finite difference method.