Plane-stress mixed-mode near-tip fields in elastic perfectly plastic solids

Abstract

Within the context of the small-strain approach, the plane-stress mixed-mode near-tip fields of a stationary crack in an elastic perfectly plastic solid under small-scale yielding conditions are examined by finite element methods. The finite element results show that asymptotically at the crack tip two elastic sectors exist under near mode I mixed-mode loading conditions, and one elastic sector exists under near mode II mixed-mode loading conditions. The fully yielded near-tip field, plastically deformed at all angles, is obtained only under pure mode II loading conditions. The corresponding asymptotic crack-tip solutions (consisting of constant stress sectors, curved fan sectors, and elastic sectors) are also constructed. The asymptotic crack-tip stress solutions agree well with the finite element results for the complete range of mixed-mode loadings. Some similarities and differences between the near-tip fields under plane-stress and plane-strain conditions are also discussed.