The Role of First Order Surface Effects in Linear Elastic Fracture Mechanics

Abstract

Structures at relatively small scales (e.g. nano/micro scale) behave differently in comparison to those examined at the macro scale. This is mainly because a high surface area to volume ratio is present at this scale making physical factors such as surface stress/energy and electromagnetic forces much more significant. In particular, ‘surface effects’ induced by a local environmental change of the region near the surface of solids, greatly influence the general behavior of the corresponding bulk material especially when the scale of materials become compatible with the nano/micro scale. This in turn, suggest that a more accurate and comprehensive description of the general behavior of an elastic solid with one or more surfaces can be achieved by incorporating a description of the separate surface mechanics near each surface of the solid. In the dissertation, we examine the effects of first-order surface elasticity in linear elastic fracture mechanics. A complete analysis has been performed for both plane and anti-plane deformations and for cases in which cracks are present in a homogeneous material and subsequently in the interface between two dissimilar elastic materials. It is shown that the introduction of the effects of first-order surface elasticity results in, in most cases, the reduction of the stress singularity at the crack tip from the classical strong square root singularity to a weaker logarithmic singularity. In particular, the refined model (with first-order surface effects integrated) predicts a more realistic description of size-dependent stress distributions commonly existing at the small scale structures. In the case of an interface crack arising in the interfacial region between two dissimilar materials, the refined model removes the classical oscillatory behaviors of the corresponding stress distributions leading again to size-dependent and stable stresses in the vicinity of the crack.