Моделирование совместного течения разнородных металлов и их деформации на основе вариационных принципов

Abstract

В статье на основе вариационных принципов механики сплошных сред разработаны математические зависимости для распределения истинного поля скоростей в очаге деформации при осадке двухслойных полос. Рассмотрены случаи, когда отсутствует скольжение между слоями двухслойной полосы и когда имеется скольжение, то есть при наличии схватывания между слоями двухслойной полосы и при его отсутствии. На основе полученных зависимостей определяются зависимости распределения деформаций по слоям двухслойной полосы при ее обжатии. Полученные зависимости позволяют определять поле скоростей в очаге деформации в двухслойных полосах, изготовленных из любых металлов.

Layered metal compositions have become part of the practice in a variety of industries, and the proportion of these materials in the total production volume is increasing every year. At the core technologies of their production often are empirical approaches based on diverse experimental material. In the paper, based on variation principles of mechanics of continua, the mathematical relations of distribution of true field of velocities at deformation zone in a case of upsetting of two-layered plates are developed. Cases when there is no friction between layers of two-layered plate and when there is the friction, i. e. when there is a gripping and there is no gripping are considered. Based on developed relations, the relations of distribution of deformations of layer of two-layered plate at its upsetting are determined. The resulting variation depending describing the true velocity field in the deformation in cases of sliding between layers of a two-layer strip, and in his absence, after integration and solutions for the parameter and are according to the distribution of strains in the layers. From the values of yield strength metal layers in a two-layer band, the original thickness of the layers and the absolute compression band can calculate the absolute (and relative) deformation layers. The dependences allow determining field of velocities at the deformation zone in two-layered plates made from any metals.