Plastic zones for 3D planar cracks embedded in an elastic-plastic layer sandwiched between two elastic adherents

This paper presents an extension of the well-known Varias-Suo-Shih and later Rogowski-Molski models for calculating the length of the plastic zone in a thin elastic-plastic layer with a crack in the plane strain condition with planar 3D crack geometry. Taking into account the usefulness of the first singular K and second nonsingular in-plane and anti-plane T-stress terms of the Williams expansion, an analytical and approximate expression is obtained which can be used to calculate the plastic zone length for any shape of planar crack embedded in a thin ductile layer sandwiched between two ideally elastic adherents and loaded in a mode I condition. The influence of the arbitrarily chosen material properties and load configurations on the plastic zone size are discussed. The proposed model was verified using the finite element method for internal and external circular crack problems.