A study of nanovoid, Griffith–Inglis crack, cohesive crack, and some associated interaction problems in fcc materials via the many body atomic scale FEM

Due to inadequacy of the classical continuum theories at the nano-scale when dealing with defects, stress concentrators, and relevant deformation phenomena in solids, a refined approach that can capture the discrete atomic features of solids is essential. The inability to detect the size effect, giving unrealistically high values for some components of the stress field right on the edge of the stress concentrators, and infirmity to address the complex interaction between small inhomogeneities, cracks and as such when they are only a few nanometers apart, are among some of the drawbacks of the classical approach. An atomistic study which employs atomic finite element method in conjunction with the effective SC potential (AFEM-SC) is proposed as a remedy for treating the above-mentioned type of dilemmas. The stress distributions in presence of single and interacting stress concentrators are addressed, and for some cases the elastic modulus of the solid is calculated. Furthermore, for the first time a quantitative analysis accounting for a realistic atomic force law, rather than the simplistic uniform cohesive force law considered by Dugdale from the continuum viewpoint, is provided. By examination of the interacting cracks and the influence of the region of atomic forces interesting results are inferred. In the numerical examples Ag is considered merely to demonstrate the applicability of the present theory.