Crevice Formation in Thin Plates by Stress Driven Mass Rearrangement

摘要

The mechanism of stress driven rearrangement has been proposed to explain many observations of surface irregularity. The rearrangement of material by stress driven mass transport is an inherently unstable process, leading to crevicing and the formation of crack-like features. The early stages of fracture and corrosion can be explained by this phenomenon, particularly when the surface is in equilibrium with either its own melt or in electrochemical equilibrium with its solute. Linear and nonlinear analyses of this phenomenon to date have been for semi-infinite configurations, or states of two dimensional stress or strain. In this paper we describe a new model for nonlinear non-equilibrium mechanics of plate thinning. The governing equations involve elastic strain energy and surface energy tending to destabilize and stabilize the system, respectively. The thinning process is driven by surface diffusion, which governs the evolution of the surface profile, and the kinetic equations are consistent with the thermodynamic requirement that the free energy must decrease. The4 evolution of a plate which is perturbed from a flat profile is described using numerical and analytical methods. A fully 3+1 D coupled finite element and finite diference formulation is used to solve for the elastic strain energy and the evolution of the surface profile. It is shown that the plate thins to zero thickness in finite time, with increasingly rapid thinning at later stages. The critical wavenumber for surface instability is discussed and the morphology of the initial linear instbility is described. At late stages of the crevice growth becomes increasingly faster, and a simple model is described which accounts for its rapid acceleration.