Computer Modeling of Elastic-Plastic Deformation in the Problems of Contact Interaction of Canonical Dies with a Half-Plane

• Date: 2018
• Main Authors: Сачук, Юрій Володимирович, Максимук, Олександр Васильович
• Format: Article
• Language: Ukrainian
• Published: Кам'янець-Подільський національний університет імені Івана Огієнка 2018
• Online Access: http://mcm-math.kpnu.edu.ua/article/view/159391
• Journal Title: Mathematical and computer modelling. Series: Physical and mathematical sciences

For a flat contact problem on the interaction of hard dies of a canonical form (cylindrical, hyperbolic, parabolic, elliptic) with a half-plane, the stress-strain state in the body was investigated. To calculate stress components and optimize computations, a method of grids with mirror reflection of results is used. The software tools for realization of advanced methods of calculation of the stressed state are analyzed and selected. 3D graphs of stresses and their corresponding level lines are constructed to facilitate analysis of the results. The construction of the 3D image of each of the stress components was carried out by means of the approximate computation of the integral by means of medium rectangles at each point of the partition, which contained the value of the elliptic integral of the third kind, constructed a series of integral sums and the numerical value of the integral. To determine the zones of elastic-plastic deformation various theories of plasticity have been analyzed and for the purpose of this goal the theory of maximum tangential stresses for the study of the conditions of the appearance of elastic-plastic zones in the body has been chosen for different areas of contact and geometric and physical-mechanical parameters. In the framework of this theory, a search for new structural materials with all necessary physical and mechanical parameters was made. New titanium alloys with improved mechanical properties have been selected to study the process of the emergence of regions of elastic-plastic deformation. New mechanical effects that arise in the process of interaction for different stamps are established and the conditions leading up to their appearance are investigated. The obtained results can be used in constructing an experimental numerical technique for determining the conditions for the appearance of plastic zones in the body for materials with different mechanical properties. The developed technique allows to determine the magnitude of the yield regions, their boundaries and the character of the distribution using the level lines and to determine the places of the greatest concentration of stresses and to determine the maximum values for different dies.