Abstract

The plane-strain compression of a plastic-rigid material is analysed on the assumption that the frictional conditions between the platens and the material aie such that the shear stress is the same fraction of the normal stress everywhere on the platen surface,unless this value attains the yield shear stress of the metal, which it can never exceed. This is the condition known as Coulomb friction, the ratio being defined as the coefficient of friction μ. The solution has been determined by a geometrical method recently proposed by Prager (1958) for integral ratios of platen breadth/material thickness of 7 and 3, and for values of the coefficient of friction of 0.05, 0.1, 0.15, 0.225, 0.8 and the limiting value of 1 1+ 1 2 π , above which value the yield shear stress is always attained along the complete zone of contact. Comparison is made with an approximate theory in which the state of stress is assumed constant across any section. A simple test is described by means of which the coefficient of friction for material being deformed under plane strain conditions may be determined.

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