Surface energy, cutting edge radius and material flow stress size effects in continuous chip formation of metals

Finite element simulations of continuous chip formation have been carried out over a range of uncut chip thicknesses from 0.002 to 0.25 mm and for tools with cutting edge radii from 5 to 160 μm, using material models for annealed or normalised medium carbon steels. Expressions are derived for the dependence of ploughing forces on edge radius, uncut chip thickness and chip shear plane angle and flow stress. Non-linearity of force variation with uncut chip thickness is demonstrated, in addition to what might result from ploughing, caused by variations of temperature and strain-rate and hence of work material shear flow stress. These ploughing and non-linearity effects quantitatively account for the well-known size effects associated with machining, certainly for the machining of steels. There is no need to include ductile fracture energy from forming fresh surfaces in models of continuous chip formation in order to account for the size effect.