On the Non-Uniform Deformation of Material in Axially Symmetric Compression Caused by Friction : Part 3, Theoretical Analysis of Compression of Hollow Cylinder by Finite Element Method

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When a hollow cylinder is compressed axially with rough plane tools, elastic-plastic deformation is disturbed by friction forces acting on the tool surfaces. This non-uniform deformation is analysed by the finite element method from elastic through partially plastic to fully plastic stages. Experimentally measured values of relative slip ratio introduced by the authors before are used as boundary conditions (namely in sticking, with no lubricant and with lubricants) instead of friction coefficient. Then, shape of bulge of inside and outside surfaces, load, distribution of pressure and of tangential stress on the contact surface between the tool and the cylinder, distribution of stress and strain, growth of plastic zones, etc. are calculated under various conditions. As the result, many new matters concerning them are made clear, for example, double bulge yields on the outside surface when h_0 (the ratio of height to outside diameter) is large, and the pressure on the contact surface decreases toward the outside when h_0 or a_r (the ratio of internal to external radius) is small but increases when h_0 or a_r is large.
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