ANALYSIS OF 3D PLANAR CRACKS WITH CONSIDERATION OF SURFACE STRESS EFFECTS

Abstract

An efficient numerical procedure for modeling planar cracks in three-dimensional, linear elastic, infinite media accounting for the surface stress effect is presented in this paper. The concept of surface stresses, which has been widely employed in the modeling of nano-scale problems, is considered in the present study to derive a suitable mathematical model capable of simulating nano-sized cracks. An infinitesimally thin layer of material on the crack surface is modeled by a surface with zero-thickness and perfectly adhered to the bulk material, with its behavior governed by the Gurtin-Murdoch constitutive law. In the formulation, the classical theory of isotropic linear elasticity is utilized to establish the governing equation of the bulk material in terms of completely regularized boundary integral equations for the displacements and tractions on the crack surface. For the zero-thickness layer, the final governing equation incorporating the surface stress effect is obtained in a weak form following the standard weighted residual technique. Solutions of the fully coupled system of equations are then obtained by the FEM-SGBEM coupling numerical procedure. Owing to the weakly singular feature of all involved boundary integral equations, standard C0 interpolation functions are used everywhere in the approximation of crack-face data and only special quadrature for evaluating nearly singular and weakly singular integrals is required. Once the implemented numerical scheme is validated with available benchmark solutions, it is applied to investigate the nano-scale influence of nano-sized cracks. Results from an extensive parametric study reveal that, the presence of surface stresses not only increases the near-surface material stiffness but also introduces size-dependent behavior of predicted solutions and the reduction of stresses in the region ahead of the crack front