Time reversal invariance and contact acoustic nonlinearity: application for closed crack characterization

The time reversibility of a plane wave packet interacting with a closed crack subject to non-dissipative contact nonlinearity is investigated numerically through a finite element model. It is shown that time reversibility holds for this type contact acoustic nonlinearity, provided that the additional frequency information generated during the forward propagation, such as higher harmonics, subharmonics and zero-frequency component, is fully included during the retro-propagation. Alternatively, a loss of information due to a frequency filtering leads to a breakdown of the time reversal invariance. Therefore, a damage index based on the degradation of the time reversal invariance using filtered back-propagation is proposed to evaluate the nonlinear response generated by a closed crack as an alternative to higher or sub-harmonics measurement.