A Spectral Correlation Based Nonlinear Ultrasonic Resonance Technique for Fatigue Crack Detection

Fatigue cracks are prone to develop in structural components under cyclic loadings. They exist as a major cause of failures in metallic structures. Numerous structural health monitoring (SHM) and nondestructive evaluation (NDE) techniques have been developed to detect fatigue cracks in their early stage for ensuring the safety and integrity of engineering infrastructures, among which, the nonlinear ultrasonic methods have been reported to be more sensitive to the incipient damage such as fatigue cracks, compared with the linear counterpart. This study focuses on exploiting a spectral correlation based nonlinear ultrasonic resonance technique for fatigue crack detection.

The current paper initiates with a reduced-order nonlinear oscillator model to illuminate the contact acoustic nonlinearity (CAN) and nonlinear resonance phenomenon. The analytical model is developed considering the rough surface condition of the fatigue cracks, with a crack open-close transition range for the effective modeling of the variable-stiffness CAN. In the crack open-close transition range, the structural stiffness is assumed to take the form of a polynomial expression. The frequency sweeping excitations are utilized to obtain the structural dynamic features. The nonlinear resonance procedure is numerically solved using the central difference method. Short time Fourier transform (STFT) is performed to extract the resonance spectroscopy. In this study, pristine, linear wave damage interaction case (an open notch case), and nonlinear wave damage interaction case (a fatigue crack case) with various damage severities are considered. Compared with the pristine and open notch cases, higher harmonic components appear induced from CAN during the nonlinear resonance procedure. Multiple damage indices (DIs) associated with the degree of nonlinearity of the interrogated materials are then proposed by correlating the ultrasonic resonance spectra. Subsequently, three case studies taking advantage of different nonlinear oscillation phenomena are conducted based on the spectral correlation algorithm to detect and monitor the fatigue crack growth: (1) time-history dependence, which evolves different resonance states depending on the loading history; (2) amplitude dependence, which renders significantly different nonlinear responses under various levels of excitation amplitudes; (3) breakage of superposition, which effectively distinguishes nonlinear resonance responses from the linear counterparts. Apparent resonance frequency mismatch and different DC response can be identified by comparing two resonance spectra serving as an instantaneous baseline for each other. Each of these three nonlinear behaviors can either work individually or collaborate synthetically to detect the nucleation and growth of the fatigue cracks. The proposed nonlinear ultrasonic resonance technique possesses great application potential for fatigue crack detection and quantification. The paper finishes with summary, discussion, concluding remarks, and suggestions for future work.