An analytical approach to model transverse inter-fibre fracture evolution in cross-ply carbon fibre reinforced polymers laminates under a three-point bending test

The prerequisite to equip structures with in situ electrical health monitoring systems in a meaningful manner is to estimate potential damage locations. In this context, an analytical approach to model the spatial and temporal evolution of transverse inter-fibre fractures (IFF) is exemplified for [ 90 3 / 0 2 ] s cross-ply laminates under three-point bending. The model is based on the tensile load in the bottom 90°-layer. The effective stress is computed directly from the specimen displacement, whereas the strength is considered to be periodically distributed due to material inhomogeneities along the specimen. The continuous comparison between the sinusoidal strength function and the effective stress allows modelling progressive damage in form of IFF. A modified Hann window is used to consider their effect to the bottom 90°-layer. Experiments with the same configuration are performed and the observed IFF evolution is used to tune the model parameters in an optimisation procedure, e.g., the peak separation of the sinusoid and the length of the Hann window. The comparison between model and experiment shows a high level of agreement. The model is thus capable to reproduce experiments with minimal computational effort. This makes it highly suitable as input for electrical monitoring models that rely on the continuous damage evolution of the investigated structure. In its current form, the model is limited to the specified configuration. However, the simple analytical approach allows it to be easily adapted. It is furthermore shown that progressive composite damage in terms of spatial and temporal evolution can be accurately described using an analytical approach.