Resonance-induced fatigue characteristics of monolayer black phosphorus with different notch shapes

Predicting the fatigue life of two-dimensional materials is crucial for improving the reliability of flexible electronic devices. However, it remains unclear how excitation frequency regulates energy dissipation during the fatigue process. This study examines the fatigue behavior of black phosphorus with triangular, rectangular and circular notches under sinusoidal cyclic loading, investigating the influence of temperature, excitation amplitude, and frequency on fatigue life. Interestingly, the fatigue life of the three types of notches does not decrease monotonically with increasing excitation frequency. Instead, distinct troughs, which indicate a pronounced reduction in fatigue life, occur at a specific frequency and at its second harmonic. We propose a method to determine the natural frequency of the model, confirming that resonance conditions markedly accelerate fatigue failure. By analyzing the evolution of stress, potential energy, and kinetic energy under various working conditions, we explore phonon energy dissipation during dynamic fatigue and establish a new criterion for fatigue damage failure. Furthermore, by tracking the evolution of mechanical properties over successive cycles, the irreversible progression of fatigue damage to its maximum allowable limit and eventual fracture is visually captured. This work provides critical theoretical guidance for the design of black phosphorus-based nanoelectromechanical systems.