Feeding and dissipative waves in fracture and phase transition. III. Triangular-cell lattice

Wave configurations for modes I and II of crack propagation in an elastic triangular-cell lattice are studied. [Mode III was considered in Part I of the paper: Slepyan, L.I. Feeding and dissipative waves in fracture and phase transition. I. Some 1D structures and a square-cell lattice. J. Mech. Phys. Solids 49 (2001) 469.] A general solution incorporates a complete set of the feeding and dissipative waves. The solution is based on the wave dispersion dependences obtained in an explicit form. Also some general properties and the long-wave asymptotes of the corresponding Green function are found. This results in the determination of the wavenumbers and modes. The macrolevel-associated solutions exist as the sub-Rayleigh crack speed regime for both modes and as a shear-longitudinal wave-speed intersonic regime for mode II only. In particular, it is shown that any intersonic crack speed is possible, whereas only the speed (shear wave speed multiplied by √2) corresponds to a positive energy release in the cohesive-zone-free homogeneous-material model. This is a manifestation of the fact that the local energy release in the lattice is not connected with the singularity of the macrolevel field. Microlevel solutions, corresponding to a nonzero feeding wavenumber, exist for both modes, at least from the energy point of view, for any, sub- and super-Rayleigh, intersonic and supersonic crack speed regimes. In particular, in the super-Rayleigh regime, a high-frequency wave delivers energy to the crack, while the macrolevel wave carries energy away from the crack.