The Parameters of the Stress State in the Operations of Plastic Deformation

Abstract

The invariant characteristics of stress state arising on the sheet metal forming operations are considered. Using the trigonometric presentation of stresses, the stress state is constructed. In this case the trajectories of principal stresses are presented by the help of the arcs of circles, that confirms the nonmonotonicity of the processes of deformation.

Some exact solutions of the nonlinear evolutionary equation for the spreading of a plastic layer on a plane

“…Under these assumptions, the problem of determining the contour of a freely spreading plastic layer on a plane can be posed and solved separately from the boundary value problem of free spreading of a plastic layer in a region with a moving boundary. It is called the problem of free spreading of a plastic layer and is formulated as follows: it is required to find a curve 𝑦 = 𝜑(𝑥, 𝑡 1 ), symmetric with respect to the Ox axis that satisfies the nonlinear evolutionary differential equation [3]:…”

“…It should be recognized that the boundary evolution equation written in the form (2) looks the simplest, moreover, the divergent form of this form is convenient for the numerical study of the Cauchy problem of this equation. The set of known exact solutions of equation (3) (see [5]) includes the set of known solutions of equation ( 3) [3,6]. Let us consider some ways of reducing equation ( 3) to an ordinary differential equation and finding particular exact solutions.…”

“…Let us consider some ways of reducing equation ( 3) to an ordinary differential equation and finding particular exact solutions. Let us preliminarily single out two simple transformations of independent variables, which make it possible to obtain new exact solutions of equation (3). Let 𝑤(𝑥, 𝜏) ˗ be a solution of equation (3).…”

“…Let us preliminarily single out two simple transformations of independent variables, which make it possible to obtain new exact solutions of equation (3). Let 𝑤(𝑥, 𝜏) ˗ be a solution of equation (3). Then a function of the form…”

Mathematical Modeling of Technological Modes of Operation of Liquid Stamping of Aluminum Alloy AK7

“…The metal utilization rate increases to 0.95 due to reduced allowances for further machining and the absence of Gating systems [5] and the deformation forces are reduced by 3-5 times when the technology is implemented. The metal of forgings acquires a finegrained structure, and the physical and mechanical properties of products that are produced by stamping of crystallized metal increase by 15-20% [6][7][8]. All these trends are determined by the technological parameters of the liquid stamping process, which include, in particular, the deformation force, temperature intervals for pouring molten metal into the die cavity, the temperature of the die elements themselves, as well as the time of filling the die cavity and crystallization, the value of which is of particular importance when stamping thin-walled forgings.…”