Acoustic emission spectra associated with the formation of brittle cracks

In the present paper, the acoustic emission accompanying the formation of brittle cracks is investigated theoretically, using the approach earlier developed by the present author and his co-workers. This approach is based on the application of Huygens' principle for elastic solids and on the use of suitable elastic Green's functions. In the framework of this approach, the main input information required for calculations of acoustic emission spectra is the normal displacements of the crack edges as a function of frequency and wavenumber. A precise description of this function for different situations of crack formation requires the solution of a complex problem of fracture mechanics, which is not always practical. For that reason, different approximations of this function can be used for practical calculations. A simple approximation of this kind is used in this paper for calculations of the acoustic emission spectra and directivity functions of a crack of finite length. A more refined approximation based on the model of a crack of finite size as a resonator for Rayleigh waves propagating along the crack edges and partly reflecting from the crack tips is briefly discussed. The obtained theoretical results are compared with the existing experimental measurements, where available.