The Athena X-ray Integral Field Unit (X-IFU) will operate at 90 mK a hexagonal matrix of 3840 Transition Edge Sensor pixels providing spatially resolved high-resolution spectroscopy (2.5 eV FWHM up to 7 keV) between 0.2 and 12 keV. During the observation of very bright X-ray sources, the X-IFU detectors will receive high photon rates going up to several tens of counts per second per pixel and hundreds per readout channel, well above the normal operating mode of the instrument. In this paper, we investigate through detailed end-to-end simulations the performance achieved by the X-IFU at the highest count rates. Special care is notably taken to model and characterize pulse processing limitations, readout-chain saturation effects, as well as the non-Gaussian degradation of the energy redistribution from crosstalk at the focal plane level (both thermal and electrical). Overall, we show that the instrument performance should safely exceed the scientific requirements, and in particular that more than 50 % throughput at 1 Crab in the 5-8 keV band can be achieved with better than 10 eV average resolution with the use of a Beryllium filter, enabling breakthrough science in the field of bright sources.
