On the Non-Uniform Deformation of a Block in Plane-Strain Compression Caused by Friction : Part 4, Analysis by Finite Element Method in General Conditions

Abstract

Finite element method is applied to the theoretical analysis of plane-strain compression of an elastic, plastic strain-hardening block under general conditions of lubrication, and deformations are pursued from elastic through partially plastic to fully plastic stages. The relative slip-ratio proposed and evaluated in Part 2 of our series of papers is used as the boundary condition instead of the friction coefficient which is often used in conventional treatments. As the result, it becomes clear (i) that the bulge of the free surface is single when the height to width ratio of the block h₀<2 and is double when h₀>2 in all conditions of lubrication, (ii) that relationship between the compression ratio and load is affected largely by h₀ and the condition of lubrication, (iii) that the initiation of the first yield is delayed but the attainment of a fully plastic state is accelerated by improvement of the condition of lubrication, and (iv) that plastic zones grow differently according to the value of h₀.