Numerical analysis of the acoustic signature of a surface-breaking crack

The boundary element method is used to calculate the acoustic signature, produced by a line focus scanning acoustic microscope, of an elastic object containing a surface-breaking crack. The acoustic signature has a vertical (z) and horizontal (x) dependence. A model of the microscope developed earlier is used and extended to take account of the crack. The mathematical formulation of the scattering problem for the cracked object leads to hypersingular integral equations. A suitable technique is employed to solve such equations by the boundary element method. An electromechanical reciprocity identity is used to relate the received voltage to the acoustic wavefields collected by the lens. The acoustic wavefield scattered from the cracked object is investigated, and curves are presented that display the acoustic signature, as functions of (x ,z), for cracks of various depths and orientations. A method to measure the depth of a surface-breaking crack using the acoustic signature is suggested.