By John Noel Harris
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Extra resources for Mechanical Working of Metals. Theory and Practice
Plastic deformation commences when the stress on the workpiece attains the yield stress of the metal. As the height of the sample decreases it spreads outwards with an increase of cross-sectional area. This movement takes place against a frictional force between the ends of the workpiece and the platens. The deforming metal is subject to the complex stress system illustrated in Fig. 2. The stress system has altered from single, uniaxial to three-dimensional or triaxial. There is one applied stress from the platens and two are induced by the friction reaction.
According to this theory, yielding depends only on one of the applied stresses and is entirely independent of the other two. As might well be expected, this theory has been found to apply with reasonable accuracy to materials which fail by brittle fracture. Such materials include cast iron, concrete, hardened tool steel and glass. It does not accurately predict yield strengths where ductile failure occurs, which includes the majority of metals. 2. Maximum shear stress theory This is probably the oldest of the yield criterion theories and is credited to Coulomb (1736-1806).
It is named after the German 37 DEFORMATION OF METALS UNDER COMPLEX STRESS SYSTEMS engineer Otto Mohr (1835-1918) who devised it in 1882. The Mohr Circle represents these equations in a manner that makes it more easily understood and remembered, and brings out more lucidly their physical significance. It is a simple matter to show that these are the equations of a circle in a /x plane. 6) sin 20 — T cos 20. Squaring both sides of each equation. 26) and a is The centre of the circle lies at a point 38 MECHANICAL WORKING OF METALS Note that the centre always lies on the axis.