Microscopic fracture studies in the two-dimensional triangular lattice

Abstract

In order to understand the static and dynamic bases of macroscopic fracture mechanics, we study flawed microscopic crystals obeying Newton's equations of motion. The particles in these crystals interact with truncated Hooke's-law forces. The static results for energy, entropy, stress concentration, and crack structure are all consistent with expectations from macroscopic elasticity theory. Dynamic theory is less well developed. Our dynamic results illustrate the importance of surface energy and nonlinear terms in the interparticle forces in influencing crack morphology and propagation velocity. The propagating cracks, except in crystals preloaded nearly to the theoretical tensile strength, travel at speeds somewhat less than the long-wavelength Rayleigh surface-wave speed.