Development of a model of a homogeneous continuous medium based on the material with defects in the form of hollows

¹ Aerospace Dept., Polytechnic Institute, South Ural State University (National Research University), Chelyabinsk, Russian Federation
² Aerospace Dept., South Ural State University (National Research University), Chelyabinsk, Russian Federation
³ Social-humanitarian Institute, South Ural State University (National Research University), Chelyabinsk, Russian Federation

^* Corresponding author: poroshin2816@mail.ru

Abstract

In a body of the billet received by casting, inevitably there are defects accompanying this process: blisters, hollows and other discontinuities affecting the deformation and strength properties of the metal. The experience showed that direct calculation of the stress-strain state by the FEM of the body with a defective structure requires the use of supercomputer-level computing power. A medium with multiple randomly distributed discontinuities was schematized by a regular structure formed by a set of elements in the form of a regular tetrahedron with spherical hollows at its vertices. The proposed technique makes it possible to create the model of a continuous homogeneous medium, which is equivalent in its deformation properties to the original discontinuous material. Using this approach was got a power-law approximation of the stress-strain curve of the model medium. The last one represents the basic characteristic of the material, both under single-shot loading and (if we take into account the cyclic hardening) in analyzing the kinetics of the stress and strain fields’ under repeatedly-variable loading. The discontinuity of the material was fixed using the Kolmogorov’s deformation criterion of ductile fracture. This criterion was applied in evaluating the limit state of the valve chamber under operating conditions.