Fatigue crack localization using noncontact laser ultrasonics and state space attractors

A fatigue crack and its precursor often serves as a source of nonlinear mechanism for ultrasonic waves, and the resulting nonlinear features are often much more sensitive to the fatigue crack than their linear counterparts. Among various nonlinear ultrasonic techniques, the proposed laser nonlinear wave modulation spectroscopy (LNWMS) is unique in that (1) it utilizes a pulse laser to exert a single broadband input instead of conventional two distinctive sinusoidal waves, and (2) a complete noncontact measurement can be realized based on LNWMS. Under a broadband excitation, a nonlinear source exhibits modulations due to interactions among various input frequency components. These modulations are often weak and can be hardly directly detected. In this paper, a damage feature called Bhattacharyya distance is extracted from the ultrasonic time signal corresponding to a pulse laser input and used to quantify the degree of damage-induced nonlinearity and localize the crack. This feature is a measure of a statistical distance used to detect the geometrical changes between state space attractors reconstructed before and after damage formation. It has been successfully used for localizing fatigue cracks in metallic plates.