Simulation of fatigue crack growth with a cyclic cohesive zone model

Abstract

Fatigue crack growth is simulated for an elastic solid with a cyclic cohesive zone model (CZM). Material degradation and thus separation follows from the current damage state, which represents the amount of maximum transferable traction across the cohesive zone. The traction–separation relation proposed in the cyclic CZM includes non-linear paths for both un- and reloading. This allows a smooth transition from reversible to damaged state. The exponential traction–separation envelope is controlled by two shape parameters. Moreover, a lower bound for damage evolution is introduced by a local damage dependent endurance limit, which enters the damage evolution equation. The cyclic CZM is applied to mode I fatigue crack growth under $K_{\mathrm{I}}$-controlled external loading conditions. The influences of the model parameters with respect to static failure load $K_{\mathrm{0}}$, threshold load $\varDelta K_{\mathrm{th}}$ and Paris parameters $m, C$ are investigated. The study reveals that the proposed endurance limit formulation is well suited to control the ratio $\varDelta K_{\mathrm{th}}/K_{\mathrm{0}}$ independent of $m$ and $C$. An identification procedure is suggested to identify the cohesive parameters with the help of Wöhler diagrams and fatigue crack growth rate curves.