Influence of surface roughness on the stress field around a nanosized hole with surface elasticity

摘要

Based on the complex variable techniques, the stress concentration around a nanosized hole with rough surface in an elastic plane under uniform remote in-plane loadings is studied in this paper. The hole is nearly circular with its surface asperities defined by a conformal mapping. The nanoscale effects on the stress field around the hole are described by the Gurtin-Murdoch model. Several numerical examples are presented to study the influence of the amplitude and period of the surface asperities on the stress field around the hole for a uniform remote uniaxial tensile loading. It is shown that for a given period of the surface asperities, the maximum normal, tangential and hoop stresses around the hole all increase significantly with increasing amplitude of the surface asperities. On the other hand, it is found that for a given amplitude of the surface asperities, when the period of the surface asperities decreases, the maximum normal and tangential stresses increase rapidly although the maximum hoop stress hardly changes.