Plane Strain Theories of Drawing

Abstract

A review is given of existing theories of drawing under conditions of plane strain†, and these theories are extended in certain respects. Comparison between accurate and approximate theories in which work hardening is neglected, shows that one of the approximate theories is reasonably accurate in predicting the distribution of pressure on the die, and the effect of friction on the drawing load. A new approximate method is proposed to allow simultaneously for work hardening, friction, and redundant work, in calculating die pressures and drawing loads. Redundant work is allowed for by suitably modifying the stress-strain curve of the metal. Formulae are derived for drawing through a wedge-shape die, using analytical approximations for the stress-strain curve. Similar formulae have not yet been found for dies with a cylindrical profile. The possible errors involved in calculating a mean coefficient of friction from the measurement of forces acting on each half of a wedge-shape die are analysed.