Unified solution of a borehole problem with size effect

Abstract

Based on the strain gradient theory and the unified yield criterion, the borehole problem of an elasto-plastic plane strain body containing a traction-free hole subjected to uniform far-field stress is studied. The unified expressions for the plastic region radius and the stress concentration factor considering the size effect are derived on the basis of the unified yield criterion, respectively, which can be reduced to those based on the Tresca, von Mises and twin-shear criteria. The dependences of the plastic region radius and the stress concentration on the yield criteria, the material strain hardening level and the size effect are discussed. As a result, it is concluded that the influences of yield criteria and strain hardening level on the plastic region radius and the stress concentration are significant, and the size effect cannot be ignored when the hole size is in the order of tens of microns.