INTRODUCTION The process of metal cutting is a subject of great importance to the makers and users of machine tools. Extensive research has gone into the subject but has still left most of the phenomena unexplained. Tool life is the main interest and before any real improvement in this factor can be made, the basic metallurgical factors governing the interaction between tool and workpiece must be better understood. Such improvement can be effected through control of the wear process since both tool and workpiece are metallic and machining is a process of metal flow which is associated with a serious wear problem. The absence of exact knowledge has however hampered empirical and mathematical approaches to the problem. Basically all machining operations are considered as either oblique or orthogonal cutting, the former requiring three dimensions to specify the geometry of the cutting part of the tool and the latter two. The basic metal cutting process to be considered is that which is common, in one form or another, to all metal cutting operations using a tool, that of the wedge-shaped tool in fig. 1 (a-j) (1). Analyses of cutting have been mainly concentrated on the relatively simple case of orthogonal or two-dimensional cutting. Here the tool is so set that its cutting edge is perpendicular to the direction of relative motion between tool and workpiece and generates a plane parallel to the original work surface. In doing this the tool removes a layer of material termed the chip. One of the major objectives of metal cutting theory is the determination of machining forces, chip geometry, tool life, energy consumption and surface finish from a knowledge of the physical properties of the workpiece and tool material and the cutting conditions alone. If this could be achieved, lengthy chip measurements, delicate dynamometry, tedious and costly tool life tests and surface finish measurements might be dispensed with.