Multiscale modelling for fatigue crack propagation of notched laminates using the UMAP clustering algorithm

In this study, a novel multiscale fatigue-damage model was developed based on the parametric finite-volume direct-averaging micromechanics theory (FVDAM), the uniform manifold approximation and projection (UMAP) algorithm, and the extended finite element method (XFEM) to accurately portray the progressive propagation of fatigue cracks in notched laminates. The UMAP clustering technique was integrated with fatigue damage evolution for the first time, enabling the construction of a reduced-order unit cell with fatigue information. Compared with the conventional FVDAM unit cell, the data was reduced to 0.4% of its original size, significantly accelerating fatigue damage calculations. The reduced-order unit cell was then incorporated into XFEM, functions as the fatigue damage criterion, transmitting fatigue damage information to meso- and macro-scales, and enables fatigue crack simulation in notched laminates. To further accelerate the calculation, a cycle-jump scheme was integrated, resulting in computational time being 10 times shorter compared to cycle-by-cycle simulation while maintaining accuracy. To validate the effectiveness of the proposed model, experiments of notched [±60]_7s glass-fibre/epoxy laminates under three different fatigue loads were conducted. The simulation results of all three loads were within a scatter band of factor two, which was a good accuracy in fatigue, showing the effectiveness of the proposed model.