Harmonic balance framework for ultrasonic fatigue vibration
Résumé
Ultrasonic fatigue tests (UFT) operate at a longitudinal vibration eigenfrequency (20 kHz) for material characterization in the very high cycle fatigue regime. Recently, the acoustic nonlinearity beta has been used for in-situ characterization, which come from second harmonic generation studies of the vibration signal. This study offers an alternative methodology which exploits the dynamic properties of the UFT machine and specimen. Namely, the undamaged UFT specimen is represented as a single degree-of-freedom mass-spring-damper system whose free-end motion is of consideration. The frequency-domain nonlinearities, specifically the higher harmonics within the fatigue vibration signal, are introduced via a closing-crack model and a micro-plasticity model. The resulting nonlinear equation of motion is derived in a Harmonic balance-type framework. This constitutive model-based approach is compared to experimentally observed spectra, where the model’s nonlinear parameters are investigated for the assessment of microstructural damage. Traditional beta values are also juxtaposed with the model’s predicted nonlinear parameters.