Jacqueline Jensen Final Defense

Abstract: We present the most general solution to date for the analytical model of a steady-state tensile crack in motion in a brittle triangular lattice. We have expanded the model to correctly include generality in the Poisson ratio, internal dissipation, and system size. Since the inception of fracture mechanics, it's been known that the boundary conditions for the free surfaces formed by a crack require the shear and tensile stresses to vanish. These boundary conditions lead to the expression for the Rayleigh wave speed, which is considered to be the limiting speed for cracks in tension. We claim that for our two-dimensional crystal, these boundary conditions are incorrect and therefore the surface wave speeds that influence crack motion are completely different from those of linear elastic fracture dynamics. We find cracks continue to exist at speeds beyond the surface wave speed, but controlled by a new scaling parameter. This scaling has been seen in experimental observations. With these findings, we compiled 160,000 analytical solutions together to show how internal dissipation and Poisson's ratio affect crack stability in the macroscopic limit. We compare our theoretical results with crack behavior seen in experiments.