Nanoscale planar field projections of atomic decohesion and slip in crystalline solids. Part I. A crack-tip cohesive zone

Abstract

The field projection method of Hong and Kim (2003) to identify the crack-tip cohesive zone constitutive relations in an isotropic elastic solid is extended to a nanoscale planar field projection of a cohesive crack tip on an interface between two anisotropic solids. This formulation is applicable to the elastic field of a cohesive crack tip on an interface or in a homogeneous material for any combination of anisotropies. This method is based on a new orthogonal eigenfunction expansion of the elastic field around an interfacial cohesive crack, as well as on the effective use of interaction J integrals. The nanoscale planar field projection is applied to characterizing a crack-tip cohesive zone naturally arising in the fields of atomistics. The atomistic fields analyzed are obtained from molecular statics simulations of decohesion in a gold single crystal along a direction in a (111) plane, for which the interatomic interactions are described by an embedded atom method potential. The field projection provides cohesive traction, interface separation, and the surface-stress gradient caused by the gradual variation of surface formation within the cohesive zone. Therefore, the cohesive traction and surface energy gradient can be measured as functions of the cohesive zone displacements. The introduction of an atomistic hybrid reference configuration for the deformation analysis has made it possible to complete the field projection and to evaluate the energy release rate of decohesion with high precision. The results of the hybrid analyses of the atomistics and continuum show that there is a nanoscale mechanism of decohesion lattice trapping or hardening caused by the characteristics of non-local atomistic deformations near the crack tip. These characteristics are represented by surface relaxation and the development of surface stresses in the cohesive zone.