Thresholds and reversibility in brittle cracks: An atomistic surface force model

Abstract

A new picture of environmentally-enhanced fracture in highly brittle solids is presented. It is asserted that the fundamental relations for crack growth are uniquely expressible in terms of the surface force functions that govern the interactions between separating walls in an intrusive medium. These functions are the same, in principle, as those measured directly in the newest submolecular-precision microbalance devices. A fracture mechanics model, based on a modification of the Barenblatt cohesive zone concept, provides the necessary framework for formalizing this link between crack relations and surface force functions. The essence of the modification is the incorporation of an element of discreteness into the surface force function, to allow for geometrical constraints associated with the accommodation of intruding molecules at the crack walls. The model accounts naturally for the existence of zero-velocity thresholds; further, it explains observed shifts in these thresholds in cyclic load-unload-reload experiments, specifically the reduction in applied loading needed to propagate cracks through healed as compared to virgin interfaces. The threshold configurations emerge as thermodynamic equilibrium states, definable in terms of interfacial surface energies. Crack velocity data for cyclic loading in mica, fused silica and sapphire are presented in support of the model. Detailed considerations of the theoretical crack profiles in these three materials, with particular attention to the atomic structure of the “lattice” (elastic sphere approximation) at the interfaces, shows that intruding molecules must encounter significant diffusion barriers as they penetrate toward the tip region. It is concluded that such diffusion barriers control the fracture kinetics at low driving forces. At threshold the barriers become so large that the molecules can no longer penetrate to the tip region. This leads to a crucial prediction of our thesis, that the cohesive zone consists of two distinct parts: a “protected” primary zone adjacent to the tip, where intrinsic binding forces operate without influence from environmental influences; and a “reactive” secondary zone more remote from the tip, where extrinsic interactions with intruding chemical species are confined. The prevailing view of chemically enhanced brittle fracture, that crack velocity relations are determined by a concerted reaction with reactive species at a single line of crack-tip bonds, is seen as a limiting case of our model, operative at driving forces well above the threshold level. The new description offers the potential for using brittle fracture as a tool for investigating surface forces themselves.