Stress State of Unbounded Space Near a Cylindrical Cavity with a Non-Circular Cross-Section for Aging Elastic-Viscoplastic Materials.

The article deals with the determination of the stress state for an unbounded space in the vicinity of a cylindrical cavity (thick-walled slab with a hole), which has a cross-section of a shape close to a regular polygonal (Galin – Ivlev problem). As a model of the space material, we have used a model of the medium that takes into account the aging elastic-viscoplastic properties. The solution has been obtained within the framework of the method of a small parameter that characterizes the deviation of the hole shape from the circle, as well as the perturbation of static boundary conditions. In this case, the unperturbed state corresponds to an axisymmetric elastoplastic stress-strain state of a thick slab with a circular hole that is made of an aging elasto-viscoplastic material. As a result, analytical expressions for the stress components are obtained, as well as an equation for determining the shape and size of the interface between the domains of elastic and plastic deformation of the slab. [ABSTRACT FROM AUTHOR]