Closed crack imaging using time reversal method based on fundamental and second harmonic scattering

A recent variant of time reversal imaging is employed for reconstructing images of a closed crack, based on both the fundamental and the second harmonic components of the longitudinal scattered field due to an incident longitudinal wave. The scattered field data are generated by a finite element model that includes unilateral contact with Coulomb friction between the crack faces to account for the Contact Acoustic Nonlinearity. The closure state of the crack is controlled by specifying a pre-stress between the crack faces. The knowledge of the scattered field at the fundamental (incident) frequency and the second harmonic frequency for multiple incident angles provides the required inputs for the imaging algorithm. It is shown that the image reconstructed from the fundamental harmonic closely matches the image that is obtained from scattering data in the absence of contact, although contact between the crack faces reduces the amplitude of the scattered field in the former case. The fundamental harmonic image is shown to provide very accurate estimates of crack length for low to moderate levels of pre-stress. The second harmonic image is also shown to provide acceptable estimates of crack length and the image is shown to correlate with the source location of second harmonic along the crack, which becomes increasingly localized near the crack tips for decreasing levels of pre-stress. The influence of the number of sensors on the image quality is also discussed in order to identify the minimum sensors number requirement. Finally, multiple frequency imaging is performed over a fixed bandwidth to assess the potential improvement of the imaging algorithm when considering broadband information.