Modeling fracture in nanomaterials via a virtual internal bond method
H. J. Gao and B. H. Ji
Engineering Fracture Mechanics, 70, 1777–1791 (2003).


The recent surging interest in nanotechnology is providing a strong impetus to understanding fracture processes in nanoscale materials. There are open challenges because many classical concepts of fracture mechanics are no longer applicable as the characteristic dimension of a structure becomes comparable to or smaller than the size of the cohesive zone near a crack tip. In materials with a characteristic size on the nanometer scale, the fracture process is often strongly dominated by the surface energy and nonlinear material properties. In this paper, we apply a recently developed virtual-internal-bond (VIB) method to investigating fracture of such nanomaterials. In the VIB method, a cohesive interactive law is directly incorporated into the constitutive model so that separate fracture criteria are no longer necessary. We demonstrate that, at a critical length scale typically on the order of nanometer scale, the fracture mechanism changes from the classical Griffith fracture to one of homogeneous failure near the theoretical strength of solids; when this transition occurs, the classical singular deformation field near a crack tip disappears and is replaced by a uniform stress distribution with no stress concentration near the crack tip.