Phononic origin of resonance in atomic scale fatigue of MoS₂

Previous researchers have conducted extensive investigations on the impact of various working conditions on fatigue damage. However, further research is still needed to understand the underlying mechanism of how the excitation frequency of cyclic loading affects the fatigue life. This article systematically discloses the phononic origin of atomic scale fatigue resonance, focusing on single-layer molybdenum disulfide (SL MoS₂) as a prototypical material. We first devise a method to initiate free vibration in the SL MoS₂ system by applying an initial condition, enabling the measurement of its natural vibration period and calculation of natural frequency. When excitation frequency matches natural frequency and its harmonics, primary and sub-harmonic resonances occur, leading to a notable decrease in fatigue life. Moreover, when the excitation frequency approaches but has not yet reached the natural frequency, the beat vibration phenomenon occurs, characterized by periodic changes of amplitude. The excitation amplitude and frequency exert pivotal influences on determining the vibration amplitude and the onset of vibration instability. Finally, the phonon behaviors across varying excitation frequencies and different fatigue stages are investigated. During resonances, excited phonons are not only distributed at the excitation frequency, but also at the harmonics of the natural frequency. This resonance effect causes a significant amplification of lattice vibrations, accompanied by more phonons being excited, resulting in a faster entry into the vibrational instability stage. Our study offers valuable insights into regulating the fatigue performance of nanomaterials, thus playing a significant guiding role in the application of nanomaterials.