Asymptotic Description of the Acoustic Microscopy of a Surface-breaking Crack

An asymptotic description of the acoustic signature of a crack, breaking the surface of an otherwise homogeneous, isotropic elastic material, determined using either a line focus or a point focus scanning acoustic microscope is constructed. The incident focused beam is constructed as a Fourier integral that produces a specified profile in the focal plane. The wavefields scattered from the specimen are also represented as Fourier integrals. Because the lenses of the acoustic microscopes are characterized by a large Fresnel number and a F-number of order one, the Fourier integrals can be asymptotically approximated to obtain explicit expressions for the incident wavefield and the wavefield scattered from a defect-free surface. The latter wavefield contains the leaky Rayleigh wave that is incident to the surface-breaking crack. The surface-breaking crack is characterized by assigning it reflection and transmission coefficients. The wavefield scattered from the crack is estimated by tracing the leaky Rayleigh waves reflected and transmitted by the crack. Lastly, the acoustic signature is calculated by using the approximate incident and scattered wavefields in an electromechanical reciprocity identity that links the voltage measured at the microscope's transducer to the scattered acoustic wavefields at the surface of the specimen. Expressions for the acoustic signatures made using the line focus and point focus microscopes are compared. Moreover, from the expression for the acoustic signature, the leaky Rayleigh wave reflection and transmission coefficients can be extracted.