  In this paper, the acoustic emission accompanying the formation of brittle
cracks of finite length is investigated theoretically using the approach based
on the application of Huygens' principle for elastic solids. 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. Two simple approximate models defining
this function are used in this paper for calculations of the acoustic emission
spectra and directivity functions of a crack of finite length. The simplest
model considers a crack that opens monotonously to its static value. The more
refined model accounts for oscillations during crack opening and considers a
crack of finite size as a resonator for symmetric modes of Rayleigh waves
propagating along the crack edges and partly reflecting from the crack tips.
Analytical solutions for generated acoustic emission spectra are obtained for
both models and compared with each other. It is shown that resonant properties
of a crack are responsible for the appearance of noticeable peaks in the
frequency spectra of generated acoustic emission signals that can be used for
evaluation of crack sizes. The obtained analytical results are illustrated by
numerical calculations.
