The criterion of elastoplastic fracture of a structured plate with a sharp V-notch

Abstract

Computer simulation of the destruction of a plate of finite dimensions with a sharp V-shaped notch under normal disruption was carried out. The process of destruction of such a sample is described with the help of a modified Leonov-Panasyuk-Dugdale model using an additional parameter - the width of the zone of plasticity (the width of the pre-destruction zone). A model of an ideal elastoplastic material having a limiting elongation is chosen as the model of a deformable solid. The investigated class of materials includes, for example, low-alloy steels used in the structures operating at temperatures below the cold-brittle threshold. Under small-scale yielding conditions, in the presence of a singularity of the stress field in the vicinity of the vertex of the V-shaped notch, it is proposed to use a two-parameter discrete/integral strength criterion. The deformation criterion of destruction is formulated at the apex of the real cut-out, and the force criterion for normal stresses with allowance for averaging is formulated at the apex of the model crack. Numerical simulation of the propagation of plasticity zones in rectangular plates under quasistatic loading is performed. An estimate of the dimensions of the plastic zone in the vicinity of the vertex of the V-shaped notch is obtained, which in the limiting case can be an edge crack. The finite element method yields an expression for the generalized stress intensity factor for a crack in a sharp V-shaped notch. It is found that the results of numerical experiments on the prediction of the destructive load are in good agreement with the results of calculations based on the analytical model for the destruction of materials with a structure under normal disruption in the small-scale yielding regime. The diagrams of quasi-brittle fracture of the sample of a structured material are constructed.