On the Non-Uniform Deformation of Material in Axially Symmetric Compression Caused by Friction : Part 2, Theoretical Analysis of Compression of Circular Cylinder by the Finite Element Method

Abstract

Non-uniform deformation of an elastic, strain-hardening circular cylinder in axial compression is analyzed by the finite element method. Deformation is pursued from elastic through partially plastic to totally plastic stages, allowing for the finite deformation or geometrical change of the material coordinates. As the boundary conditions, the experimentally determined values of the slip-ratio which was proposed by the authors are used instead of the conventional friction coefficient. Calculations of 23 cases are performed for various combinations of lubrication and height to diameter ratio. As the result, the followings have become clear: shape of bulge of the free side surface, relation between the load and the compressive strain, distribution of normal pressure and tangential stress together with the friction coefficient on the boundary surface, mean friction coefficient, patterns of appearance, growth of plastic zones, etc. These results are qualitatively in agreement with the theoretical results which were presented in Part 1 of this series of investigation; i.e. the results obtained by applying variational principle. Agreement with the experimental observations is also satisfactory.