Purpose <p>To address the impact of intrinsic material nonlinearity on closed crack detection in thin plates, a phase-velocity mismatching Lamb wave mixing technique is introduced.</p> Methods <p>By coaxially mixing two phase-velocity mismatching S₀ modes in opposite directions, both sum- and difference-frequency Lamb waves are produced. When there are no closed cracks, the sum- and difference-frequency components remain weak due to their nonlinear accumulation over propagation distance. When there is a closed crack, the modulation of the primary waves causes the crack to open and close, resulting in the “clapping” effect. The waveforms of the primary waves become distorted in the time domain after passing through the crack, significantly enhancing the sum- and difference-frequency components. Consequently, closed cracks can be accurately detected based on the variations in harmonic properties within the plate. The two newly generated sum- or difference-frequency Lamb waves propagate symmetrically around the closed crack, exhibiting equal group velocities, periods, and amplitudes. This symmetry enables the accurate localization of closed cracks by measuring the time difference of their arrival at the two ends of the plate. Finite element simulations are employed for closed crack detection and localization.</p> Results <p>Results indicate that the sum- and difference-frequency components caused from closed-crack contact acoustic nonlinearity (CAN) are much stronger than those produced by the intrinsic material nonlinearity. Furthermore, the acoustic nonlinear parameter associated with the sideband at the sum frequency increases with the length of the closed crack and decreases with the width of the closed crack. The proposed technique achieves an impressive closed crack localization accuracy of 1.2 mm.</p> Conclusion <p>The findings of this study provide a feasible method for detection and localization of closed cracks.</p>