A Quantized Theory of Strain Hardening as Applied to the Cutting of Metals

Abstract

A theory of strain hardening is presented which utilizes the fact that metals deform blockwise rather than continuously. A metal is assumed to possess an orderly array of weak spots through which slip planes pass. The slip displacement which occurs upon a single plane is related to the spacing of weak points and the slip plane inclination. Use of a linear relation between shear plane displacement and resisting shear stress, enables the mean shear stress to be computed. In the two examples considered it is seen that the influence of normal stress on the shear plane is less important in cutting than has been generally believed. Strain hardening and the short range inhomogeneity of metals is seen to account for most of the dynamic increase in shear strength during cutting, including the increase in shear energy per unit volume with decreased depth of cut. This size effect is akin to the increase in tensile strength with decreased specimen diameter, both phenomena involving strain hardening as influenced by inhomogeneity. The quantity Aa 2 which represents in a single number the strain hardening and short range inhomogeneity characteristics of a metal should prove particularly valuable in analyzing the cutting characteristics of metals which strain harden extensively.