Wave radiation in lattice fracture

The square and triangular lattices are considered, where the uniform crack growth is accompanied by the wave radiation. The radiation energy and structure are studied. The energy radiated to the bulk of the lattice is found in a direct way. The radiation structure is described based on the crack problem solution and by means of the analysis of two-dimensional dispersion relations for the intact lattice. The mode III problem for square lattice is discussed in detail, whereas, in the case of the plane problem for the triangular lattice, the only those results are derived which follow from the two-dimensional dispersion relations. It is shown that there exists a finite crack-speed-dependent region of wavenumbers corresponding to the waves radiated to the bulk of the lattice. In the case of the triangular-cell lattice, in addition, one or several lattice Rayleigh waves are radiated. For the square lattice a complete solution for the wave field is presented with the crack-speed-dependent far-field asymptote. The latter is characterized by the wave amplitude asymptotically decreasing as the distance from the crack front in power -1/3. The asymptotically significant crack-speed-dependent direction of the radiation is determined. Such asymptotic results are also valid for the triangular lattice.