Nonlinear Frequency-Mixing Photoacoustic Characterisation of a Crack

Abstract

A one and two dimensional imaging of a crack by a novel nonlinear frequency-mixing photoacoustic method is presented. Acoustic waves are initiated by a pair of laser beams intensity-modulated at two different frequencies. The first laser beam, intensity modulated at a low frequency \(f_L\), generates a thermoelastic wave which modulates the local crack rigidity up to complete closing/opening of the crack, corresponding to crack breathing. The second laser beam, intensity modulated at much higher frequency \(f_H\), generates an acoustic wave incident on the breathing crack. The detection of acoustic waves at mixed frequencies \(f_H\pm nf_L\) (\(n=1,2,\dots \)), absent in the excitation frequency spectrum, provides detection of the crack, which can be achieved all-optically. The theory attributes the generation of the frequency-mixed spectral components to the modulation of the acoustic waves reflected/transmitted by the time-varying nonlinear rigidity of the crack. The crack rigidity is modified due to stationary and oscillating components from the laser-induced thermoelastic stresses. The amplitudes of the spectral sidelobes are non-monotonous functions of the increasing thermoelastic loading. Fitting such experimental evolutions with theoretical ones leads to estimating various local parameters of the crack, including its width and rigidity.