Planar elastoplastic behavior in a body containing cracks with plastic strain localized in thin layers

Abstract

A general approach is given for planar treatments (planar state of stress and planar strain) in the elastoplastic equilibrium of a body containing cracks when the plastic strain is localized in thin layers. The plasticity region is represented as rectilinear cracks arising from the vertex of the main crack, on which the plasticity conditions are satisfied. The elastoplastic treatment is thus reduced to a treatment in the linear theory of elasticity for a body weakened by a kinked or branched crack with unknown lengths and orientations for the side branches. The latter are derived during the solution obtained by means of singular integral equations. Numerical results have been obtained for the stretching of an infinite plate containing an arbitrarily oriented rectilinear crack. Values are given for the crack opening at the vertex and for the length and orientation angle of the plasticity band.