Acoustic emission from finite two-dimensional cracks: Directivity functions and frequency spectra

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.