Modelling fatigue damage in unidirectional fibre composites using a hybrid analytical–numerical approach

A hybrid analytical–numerical model at the microscale is developed to describe the formation and growth of fatigue damage zones in unidirectional fibre composites. Conceptually, the model builds upon the phenomenon of fatigue being mainly driven by the mutual influence of fibre breaks and respective fibre–matrix debond cracks occurring under cyclic tension-tension loading. The model consists of three steps. First, analytical relations are used to calculate the cycle-dependent material parameters and the debond crack length for a given broken fibre. Next, a numerical finite element simulation of a two-fibre model composite is utilised to determine the stress at the surface of a neighbouring fibre for varying load cycles. Last, a method called Procedural Domain Extension is introduced, utilising a Weibull distribution of fibre strengths to adaptively and computationally efficiently generate a growing fatigue damage zone. The model can qualitatively and quantitatively predict the formation and growth of the fatigue damage zone. Stresses in the broken and the neighbouring fibre are in good agreement with values reported in the literature. Fatigue characteristics like the fatigue damage zone growth rate or the positional distribution of the fibre breaks are in good agreement with experimental data.