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# Abstracts

## Mathematical models of stress-strain state at the metal forming

Sosenushkin E.N., Yanovskaya E.A., Sosenushkin A.E.

VPO "Moscow State Technical University" STANKIN "

1 pp. (accepted)

The paper discusses the invariant characteristics of the stress-strain state arising in the processing of metals pressure (OMD), for example, different operations, sheet metal forming: crimping, hand, drawing and flanging. In accordance with the provisions of mechanics of plastic solids [1], for an incompressible material the deformation of a material point is represented as the trajectory of the radius vector in five-dimensional space of independent components of the strain tensor. The deformation of the physical particle is called simple if the corresponding trajectory is a line, emerging from the origin, so all four of its curvature is. Otherwise (when at least one of the curvatures of the trajectory deformation different from zero at any small but finite segment of a trajectory, or the trajectory of deformation has a breaking point), the deformation is difficult. For classification and mathematical synthesis of the results of the simulation uses the trigonometric form of representation of stress and strain [2]. On the deviatoric plane was presents projections of the principal axes, in which the corresponding stress and strain States of the trajectory of the stress and strain are represented by arcs of circles [3-5]. Curved trajectory indicate nemonotonnost processes of deformation. Each of the areas specified by the angle change of the type of stress or strain States, corresponds to a single scheme of stresses and strains, the analysis of which allows to determine which process step describes the known mechanical schemes. This greatly facilitates the power of the analysis of these operations. Modeling takes into account the axial symmetry in all the studied formoizmeneniya operations OMD. If we consider the volumetric deformation, the schema of the stress state defined by the shear will accompany, for example, processes of angular pressing [6], each of which corresponds to the position of the workpiece in the channels of the matrix relative to the selected coordinate system.

The list of references.

1. Ilyushin, A. A. Works (1946-1966).t.2.Plasticity / M.:Fizmatlit,2004. 480с.

2. Malinin, N. N. Applied theory of plasticity and creep / M.: Mashinostroenie,1968. 400C.

3. Sosenushkin, E. N. The Parameters of the Stress State in the Operations of Plastic Deformation / E. N. Sosenushkin, V. A. Kadymov, E. A. Yanovskaya, A. A. Tatarintsev, Sosenushkin A. E. // Key Engineering Materials Submitted: 2015-09-16. ISSN: 1662-9795, Vol. 684, pp 57-66, doi:10.4028/www.scientific.net/KEM.684.57/Revised: 2015-11-13. Accepted: 2015-11-13. © 2016 Trans Tech Publications, Switzerland Online: 2016-02-18.

4. Sosenushkin, E. N. Mechanics of non-monotonic processes of plastic deformation / E. N. Sosenushkin, E. A. Yankovskaya, A. E. Sosenushkin, V. V. Emelyanov // Vestnik mashinostroeniya. 2015. No. 9. P. 29-33.

5. Sosenushkin, E. N. Progressive metal forming processes / E. N. Sosenushkin. M.: Mashinostroenie, 2011. 480 p.

6. Sosenushkin, E. N. Improvement of processes of severe plastic deformation / E. N. Sosenushkin, L. M., Ovechkin, A. E. Sosenushkin // Vestnik MSTU "Stankin". 2012. Vol. 1. No. 1. P. 21-29.

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